research opportunities arising from control and ... · research opportunities arising from control...

Research opportunities arising from control

and optimization of smart buildings

Qianchuan Zhao

CFINS Dept Automation and TNList

Tsinghua University

zhaoqctsinghuaeducn

20170825

ISA Workshop on Frontiers in Systems and Control

CFINS

2

Yu-Chi Ho chair professor group and ldquoCenter for Intelligent and Networked Systemsrdquo (CFINS) were established in October 2001 to provide a physical and intellectual environment for the intelligent analysis design and operation of complex and networked systems such as computer and communication networks buildings power systems and supply chains by making innovative use of analytical methods and information technology

httpcfinsautsinghuaeducn

What we mean by smart for buildings

3

Potential of ICT technology

4

bull MOORErsquos Law

bull AI


5

bull Utilize information relevant to the whole building system thanks to IoT as a result of the fast drop in the cost of hardware for computing storage and communication

bull Care about individual occupant thanks to the rapid development of machine learning techniques

Energy consumption

Type faction

Building40

（68Electr ）

Transportation 40

Others 20

Energy saving for buildings has been

omitted for long it has great potential 6

Energy consumption in buildings

It was estimated that 20 ~ 30

energy saving can be achieved by

optimizing the operation and

control of buildings

Office

BuildingHVAC37

28

Office Equipments

22

Elevator

3Other10

Lights

Hotel

44

254

9

18

Lights

HVAC

Office Equipments

Elevator

Other

7

System Architecture

Information fusion

Data driven modeling + prediction

Integrated building control

for energy saving

8

Control and optimization of building energy system

Energy supply in building

Distribution Battery

CHP

Wind

E-car

Fuel cellSolar

Lighting HVAC

Shading Window

Controllable devices

Elect

Heat

ComfortTemp HumidIllum CO2

Occupant demand

Minimization of energy cost

Micro-grid

9

List of possible challenges

10

bull Integrated control under full information may suffer the curse of dimensionality problem and time consuming evaluation of performance or constraints

bull Mache learning in general is a hard problem design of a good ML algorithm also include many decision variables (model structure parameters implementation input data hellip)

Ways to address the challenges

11

According to NFLT problem specific knowledge is needed to develop efficient solutions

bull Soft optimization for integrated control OO OCBA COO NP ADP EBO IPA hellip

bull Apply problem specific knowledge to reduce the search space for a good ML algorithm

Illustration of COO

G

S N

12

13

Below we will use individual thermal comfort model as an example of ML in smart building applications

Motivations

bull HVAC system

ndash First invented to serve the machine manufacturing process etc --Set point oriented control

bull When HVAC serves peoplehellip

ndash Set point oriented control like what they did on the machine

20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW

)S et pointE nergy consum ption

Tokyo Univ 2008 survey data

17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5

FIT Tsinghua Univ 2011 survey data

14

Motivations(contrsquod)

ndash Intelligent thermostat (Perry D et al 2011)

bull User-oriented control system

ndash User only inputs sensations

ndash Personalized and self-learning

12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)

Completed TasksIncomplete Tasks

Human perception

Indoor environment

Control

Perceive

15

Existing modelsbull The chamber study model

ndash Predicted Mean Vote-Predicted Percent Dissatisfied (PMV-PPD) model

bull quantifies the thermal comfort concept as a mapping from the environmental factors and personal factors to a 7-level comfort value scale based on an average over a large data set

air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level

Environmental factors Personal factors

PMV-PPD Model

Thermal sensation

cold cool slightly cool

neutral slightly warm

warm hot

PMV value -3 -2 -1 0 1 2 3

A 7-level thermal sensation scale

16

Existing modelsbull The models based on the human body physiology

ndash The two-node (core and skin) model

ndash The multi-segment mathematical model of human body

ndash The sensation and comfort model for human segments and the whole-body

bull Field study comfort modelndash The original models were presented by Humphreys and Nicol which

described a strong relationship of the comfortable temperatures inside a building to the mean temperatures prevailing inside the building

ndash Classified by de Dear and Brager as physiological behavioral and psychological

ndash The ASHRAE adaptive model ASHRAE standard 55-2004

ndash SCATS European adaptive comfort standard EN15251

17

Challengesbull The main challenges

ndash All these works focus on average thermal comfort models instead of personalized comfort models

ndash There exist less related literature and research on personalized comfort models

ndash The cases for the group are more complicated and challenging

18

Terminal Control Strategies for Energy and Comfort

Adaptive HMIOccupants

Sensors

TempHumidityAir speedCO2

Acoustic levelIlluminance

Controller

T

R

H

CO2

Dynamic

Comfort

Region

InterpreterEstimated

comfort zone

1e

oe T

RH

Optimization

CO2

HotColdDryHumidNoisyhelliphellip

00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered

simulatedEnergy metering

EnergyTemphelliphellip

bullPsychology

bullEngineering

bull industrial design

Human factors

Building manager

energy requirement

Lights Blind Window AC

Tsinghua-UTC Building Energy Energy Safety and Control System Research Center(CFINS DBS IE CPSR)

19

Sensation votes based model

Voting software Sensors

Setup 1 Every one hour the software will pop up to let the user vote2 The sensor box will record the environment measurements store them in local

computer through COM and further upload to the server database

20

PDTC -- PMV framework

bull Heat balance equation of human

ndash Mapping from the environment to the human thermal vote

ndash Heat balance of human body

0M W C R E S

NeuralCoolCold Warm Hot

21

PDTC -- the proposed model

bull Personalized Dynamic Thermal Comfort(PDTC)

ndash Perception thermal vote

ndash Considering the dynamics of human thermal perception

0 1 2 3( ) ( ) ( ) ( ) ( )( )a aPDTC k m k m k P m k t m k R C

0 1 2 3( )a aPTV m m P m t m R C

22

Parameter estimation

bull Parameter estimation ndash Least squares

bull Recursive least squares estimation with forgetting factorsndash Time-variant forgetting factors

0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k

m m m m k PDTC m m m m r

k k

eal vote

( ) ( )( )PDTC kk X k

( ) ( ) ( )k PDTC k truevote k

( ) [1 ( )]a ak P t R C

1 if the k and k-1 are in the same day( )

otherwisek

23

Results and validations

Office layout

Time From Nov 2009 ndash Jan 2010

12151217 1224 15 112 115-2

0

2

4

6

Subject A Recursive Results

m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es

Subject B Recursive Results

24


bull Model validation ndash accuracy

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4

Bias and MSE Correlation coefficient of residuals and inputs

SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25

A study case of applications

bull Personalized energy saving potentials

East Outside

External Wall

6m

6m

ow oWQ Q

Heat transfer of the

external wall and

window

iWQ


interior walls

Sensible and latent heating

load for warming and

humidifying outside air

fa S fa LQ Q

Lamps heat emission

ltQ

Appliances heat emission

eqpQ

occQHuman body heat emission

0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q

s t m k m k P m k t m threshod

h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8

Increase of heating load relative to PMV based results ()

Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity

Higher energy cost higher sentivity in comfor

and energy saving tradeoff

( ( ) ( )) ( ) 100PDTC a a PMV a a PMV a aR Q t h Q t h Q t h

| | 100PDTC threshold PDTC threshold PDTC thresholPDTC dS Q Q Q

26

bull Limitations of the previous work in real application

ndash Require the user to vote every one hour

ndash Nonlinear comfort constraint when online implemented

bull Can we be more user-friendly

27

Complaint driven more user-friendly

bull Settingsndash Users only complain whenever they felt necessary

bull Advantagesndash Less demanding for users

ndash No interruption for users

ndash Close-loop control

Human Machine Interface

YJiang et al ldquoA Human Machine Interface for Building Indoor Environment Controlrdquo Chinese Patent ZL 2010 2 02929811

28


bull Challenges

ndash No intensity information in complaints binary variables

ndash No comfort samplesbull No-complaint periods have many possible explanations

ndash Few information of inner complaint region bull Environmental parameters are set around the comfort region boundary(Closed-

loop test-bed effects)

29

Problem formulation

bull Problem formulation

ndash Only given the samples of target class ie a set of samples of a type of complaint 120594 = 1199091 1199092 hellip 119909119899 119909119894 isin1198772 ie in the temperature and relative humidity plane how to obtain a boundary description of the complaint region 119891(119908 119909) only based on the complaint samples 120594

Target class the cold or hot complaints which are from single subject

30

Important properties

Properties of the complaint regionThe complaint region in the environment parameter space (in normal environment parameter range) for a given complaint is connected Additionally some of the parameters are unidirectional

1 Existing researches conclude both the human comfort zone and discomfort zone are connected areas

2 Unidirectional parameter in human perception generally exists Some of the parameters are not clear

eg temperature in hot and cold complaints is unidirectional relative humidity is not clear

31

bull Pareto-frontier set of the complaint samplesndash A sample 119909119894 isin 1198772is in the pareto-frontier set with respect to the

generalized inequality le119878 iff there is no sample 119909119895 119895 ne 119894 such that

119909119895 le119878 119909119894

ndash where 119878 is a proper cone and 119909119895 le119878 119909119894 means 119909119895 minus 119909119894 isin 119878

Temperature

Relative humidityComplaint samples

2 2 | (1 0) 0(2) Rx x xS

The cone (direction) of

Pareto frontier set in the

direction 2S

No samples in this region

Stephen Boyd Lieven Vandenberghe Convex Optimization Cambridge University Press 2004

Multi-linear one-class classifier model

32


bull Multi-linear one-class classifier learning

ndash Least square linear estimation is performed for each of the pareto-frontier set 119881119896 and obtain a set of linear equations (classifiers)

bull Pareto-frontier set plays the role of support vector in support vector description method

bull Multi-linear approximation of the nonlinear boundary

bull The complain region can be described by

2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33


bull Performance metricsndash False Negative Rate (Missing detection rate) the rate of

complaints that were missed

ndash False Positive Rate (False detection rate) the rate of complaints that were mistaken as comfort

Empirical RuleIf the subject has not complained for 20 minutes and heshe will not complain for next 20minutes the current environment conditions are regarded as ldquocomfort samplesrdquo

1

1 comfort

iC y C

comf

N

o irt

FPR IN

1 The empirical rule is based on the results of transient thermal comfort research2 The higher FPR the more conservative of the classifier is

34

Experiment settings

Experiment test-bed Touch screen Human Machine Interface

Dedicated HVAC and other terminals

Integrated sensors and computers

Closed-loop operation mode in test-bed

Sensors Radiant ceilingHuman Machine Interface

Zhuo Mao Fulin Wang Teng Gao Yunchuang Dai Qianchuan Zhao Yin Zhao Biao Sun Jing Guo and Fan Zhang Research of the room occupant complaining behavior pattern for the indoor environmental control Advanced Materials Research Vols 374-377 (2012) pp 1064-1067

35

Results of the experiment data

24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065

Green polygon presents the parameter region of the experimentFPR is estimated as FPRC

36


1 Cold complaints usually occur in the lower temperature part and while hot complaints in the higher part

2 Data are collected in 3-4 continuous days during their experiments3 Ambiguous region which both hot and cold complaint had occurred exists

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37

Results of the experiment databull Comparison with the PMV model

1 Complaint-based comfort model may have a larger complaint area than the PMV model which indicates that indoor environment control based on PMV may cause complaints

2 Different regions in the learning results represent different perceptions

PMV numerical results in temperature and relative humidity plane The clothing index was chosen as 06 and air velocity was 0 which is accordance with our experiment conditions

-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38

Performance analysis

bull Comparison with other models

1 Leave-one-out methods were utilized to evaluate the FNR for each methods2 Comfort samples were extracted from the experiment record according to the

empirical rule in previous slide3 SVM model using the linear kernel function

Subjects Fisher Linear

discriminant model

SVM model Proposed model

Hot Cold Hot Cold Hot Cold

A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001

False Negative Rate Comparison

Richard ODuda Peter EHart and David GStork Pattern Classification2nd edition John Wiley amp Sons Inc 2001

The proposed model has low false negative rate

39

Experimental validation

40

Experimental valuation

41

Group thermal comfort modelbull The group comfort zone model

ndash We introduce here is a quite natural one take the convex hull of the individual comfort zones of the group

ndash Defining group comfort region as the intersection of all group memberrsquos individual comfort regions or the intersection of those of the majority when there are conflicts

42

Experiment resultsbull The comparison with PMV

ndash Large group in Lanzhou Testbed

bull It is obvious that the individualdifferences in thermalpreference often incurdissatisfactions in the groupThis indicates that the averagemodel such as PMV may havebias in predicting the thermalcomfort for large group

Pareto frontier set(cold) Pareto frontier set (hot)

43

Summary

44

bull Challenges

ndash Accurate occupant counting or localization problem

See T Labeodan W Zeiler G Boxem et al Occupancy measurement in

commercial office buildings for demand-driven control applications A survey and detection system evaluation Energy and Buildings 2015 93 303-314

ndash Data Mining for integrated building control and optimization

See F Xiao C Fan Data mining in building automation systems for improving

building operational performance Energy and Buildings 2014 75 109-118

F Cheng X Fu C Yan A framework for knowledge discovery in massive building automation data and its application in building diagnostics Automation in Construction 2015 50 81-90

Links

45

bull IEEE RAS TC on Smart Buildingshttpwwwieee-rasorgsmart-building

Q Jia Q Zhao H Darabi et al Smart building technology IEEE Robotics amp Automation Magazine 2014 21(2) 18-20

bull IFAC TC on Smart Citieshttptcifac-controlorg93

bull Q Zhao Research opportunities arising from control and optimization of smart buildings Control Theory and Technology Vol 15 No 1 pp 78ndash80 February 2017

References

46

bull Jiang Y Wang FL Jiang ZY Hou Y Zhao QC Liu Y Zhang F Jiang Y Human-Computer Interface of Two-Way Interactive Architectural Environment Control System International Patent WO2012019328 Application No PCTCN2010001582

bull Zhao QC Zhao Y Wang FL Wang JL Jiang Y Zhang F ldquoA data-driven method to describe the personalized dynamic thermal comfort in ordinary office environment from model to applicationrdquo Building and Environment 72(309-318) 2014

bull Zhao QC Zhao Y Wang FL Jiang Y Jiang Y Zhang F ldquoPreliminary study of learning individual thermal complaint behavior using one-class classifier for indoor environment controlrdquo Building and Environment 72(201-211) 2014

bull Zhao QC Chen ZJ Wang FL Jiang Y Ding JL ldquoExperimental study of group thermal comfort modelrdquo 2014 IEEE International Conference on Automation Science and Engineering (CASE) pp1075-1078

bull Z Cheng Q Zhao F Wang Y Jiang L Xia and J Ding ldquoSatisfaction based Q-learning for integrated lighting and blind controlrdquo Energy and Buildings vol 127 pp 43ndash55 2016

bull F Wang Z Chen Q Feng Q Zhao Z Cheng Z Guo Z Zhong ldquoExperimental comparison between set-point based and satisfaction based indoor thermal environment controlrdquo Energy and Buildings vol 128 pp 686ndash696 2016

Thanks Prof Ho for your inspiring guidance over the years

47


bull Determine pareto-frontier sets of samples

2 2

(1) (2)| 0 0S x R x x Example

By incorporating the prior knowledge the pareto-frontier set of a certain class of samples represent boundary profiles in specified direction which we interested most

Stephen Boyd Lieven Vandenberghe Convex Optimization Cambridge University Press2004

A sample is in the pareto-frontier set with respect to generalized inequality iff there does not exist any other sample such that

where S is a proper cone in Rm

m

ix R

S jx i j

Sj ix x

j ix Sx Generalized inequality means Sj ix x

4843

Unbiased theoretically

bull Expression noise when survey or vote

Jaffe-katz and Budescu 1989

1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3

IMPROBABLE 5 60 33 25

UNLIKELY 25 30 65 25

POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85

Percentage of Rankings Received by Any Term Across Subjects

WW Ranks

WN Ranks

4943

An intuitive illustration

0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043

Problems in the identification framework

bull Output-dependent observation noise

bull Observation noise is dependent on the system output

Unknown SystemsInputs

Identification

yyu

ˆ

Observation Noise

5143

Problem in the identification framework

bull Unbiased estimation of the system parameters

ndash Inconsistency of the noise at different outputs

ndash Output-dependent mean value (cannot remove the noise by average)


Identification

yyu

ˆ

Observation Noise

ˆE 5243

Proposed identification methods

bull Key ideas

ndash First identify the noiseless output 119910(119906119894) using the noise model

bull Decouple the relationship between the parameters and the noise

ndash Then identify the system parameters 120579 bull Return to the normal system identification


Identification

yyu

ˆ

Observation Noise

( )iy u

Estimate the noiseless outputˆE

119910(119906119894) estimation of 119910 119906119894 120579 estimation of 120579

5343

Noise model

bull Output-dependent bounded noise modelndash The noise is bounded and its bound is related to the noiseless output

ndash The probability density function has peak value at 0

bull Truncated distributions -- examples for different outputs in a bounded range

Truncated Normal Distribution (TN) Truncated Double Exponential Distribution (TDE)

-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)

With noise parameter 120582

-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443


bull When the noise parameter (120575) is known

ndash Choose the input as

ndash Construct the following identification equation

bull This is the function of when the noise parameter is known

bull An explicit for of the equation for example TN model is

1 2 012k I i i I d k Ku

0 1 I i I i k I i iu u u u

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k

i k I iu u yy E w y i IK

u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u

y u y u i Ib y u a y u K

Where 120593Φ are the pdf and cdf of standard normal distribution

5543


bull When the noise parameter (120575) is known (contrsquod)

ndash If the identification equation has unique solution

ndash The identification can be done by solving the following noiseless identification

bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T

K K K I KY y u y u y u

Note

1 The solution of identification is related to the number of repeated input

2 The inputs should satisfy the Persistent Exciting Condition

3 We name the identification method as Basic Identification Algorithm (BIA)

K 1 2iu i I

5643


bull When the noise parameter (120575) is unknownndash Underdetermined problem 119868 identification equations with 119868 + 1

unknown variables

bull Introduce an additional criterionndash Maximum likelihood under the constraint of identification equations

( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i

y u E w y u y u i IK

y u u i I

Note

1 When the system is identifiable then given 120575 there is unique 120579 and 119910 119906119894 2 The unknown parameter is usually a scalar and the optimization is converted to the

one-dimension search problem where each search step involves a procedure of

identification when the noise parameter is known3 We name the algorithm as Joint Identification Algorithm (JIA)

st

5743

Algorithms

Theorem 1Under the condition that the identification equation has unique solution then the proposed algorithm can obtain the unbiased estimate of the unknown system parameter when K

5843

Algorithms(contrsquod)

Theorem 2When the identification equations have unique solution for different the

results of Joint Identification converge to the true system parameter 120579 and noise parameter 120575 with in probability when K

5943

Numerical test and application

6043


bull Application in PDTC model

Y Zhao and Q Zhao ldquoSystem Identification for Output-dependent Bounded Noises and its Application in Learning Personalized Thermal Comfort Modelrdquo To appear in IEEE Proceedings of International Conference on Robotics and Automation Karlsruhe Germany 2013

6143

CFINS

2

Yu-Chi Ho chair professor group and ldquoCenter for Intelligent and Networked Systemsrdquo (CFINS) were established in October 2001 to provide a physical and intellectual environment for the intelligent analysis design and operation of complex and networked systems such as computer and communication networks buildings power systems and supply chains by making innovative use of analytical methods and information technology

httpcfinsautsinghuaeducn


3


4


bull AI


5



Energy consumption

Type faction

Building40

（68Electr ）

Transportation 40

Others 20








Office

BuildingHVAC37

28

Office Equipments

22

Elevator

3Other10

Lights

Hotel

44

254

9

18

Lights

HVAC

Office Equipments

Elevator

Other

7

System Architecture

Information fusion



for energy saving

8




CHP

Wind

E-car

Fuel cellSolar

Lighting HVAC

Shading Window


Elect

Heat


Occupant demand


Micro-grid

9


10




11




Illustration of COO

G

S N

12

13


Motivations

bull HVAC system




20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW



17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5


14






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143


3


4


bull AI


5



Energy consumption

Type faction

Building40

（68Electr ）

Transportation 40

Others 20








Office

BuildingHVAC37

28

Office Equipments

22

Elevator

3Other10

Lights

Hotel

44

254

9

18

Lights

HVAC

Office Equipments

Elevator

Other

7

System Architecture

Information fusion



for energy saving

8




CHP

Wind

E-car

Fuel cellSolar

Lighting HVAC

Shading Window


Elect

Heat


Occupant demand


Micro-grid

9


10




11




Illustration of COO

G

S N

12

13


Motivations

bull HVAC system




20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW



17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5


14






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143


4


bull AI


5



Energy consumption

Type faction

Building40

（68Electr ）

Transportation 40

Others 20








Office

BuildingHVAC37

28

Office Equipments

22

Elevator

3Other10

Lights

Hotel

44

254

9

18

Lights

HVAC

Office Equipments

Elevator

Other

7

System Architecture

Information fusion



for energy saving

8




CHP

Wind

E-car

Fuel cellSolar

Lighting HVAC

Shading Window


Elect

Heat


Occupant demand


Micro-grid

9


10




11




Illustration of COO

G

S N

12

13


Motivations

bull HVAC system




20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW



17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5


14






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143


5



Energy consumption

Type faction

Building40

（68Electr ）

Transportation 40

Others 20








Office

BuildingHVAC37

28

Office Equipments

22

Elevator

3Other10

Lights

Hotel

44

254

9

18

Lights

HVAC

Office Equipments

Elevator

Other

7

System Architecture

Information fusion



for energy saving

8




CHP

Wind

E-car

Fuel cellSolar

Lighting HVAC

Shading Window


Elect

Heat


Occupant demand


Micro-grid

9


10




11




Illustration of COO

G

S N

12

13


Motivations

bull HVAC system




20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW



17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5


14






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143

Energy consumption

Type faction

Building40

（68Electr ）

Transportation 40

Others 20








Office

BuildingHVAC37

28

Office Equipments

22

Elevator

3Other10

Lights

Hotel

44

254

9

18

Lights

HVAC

Office Equipments

Elevator

Other

7

System Architecture

Information fusion



for energy saving

8




CHP

Wind

E-car

Fuel cellSolar

Lighting HVAC

Shading Window


Elect

Heat


Occupant demand


Micro-grid

9


10




11




Illustration of COO

G

S N

12

13


Motivations

bull HVAC system




20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW



17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5


14






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143






Office

BuildingHVAC37

28

Office Equipments

22

Elevator

3Other10

Lights

Hotel

44

254

9

18

Lights

HVAC

Office Equipments

Elevator

Other

7

System Architecture

Information fusion



for energy saving

8




CHP

Wind

E-car

Fuel cellSolar

Lighting HVAC

Shading Window


Elect

Heat


Occupant demand


Micro-grid

9


10




11




Illustration of COO

G

S N

12

13


Motivations

bull HVAC system




20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW



17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5


14






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143

System Architecture

Information fusion



for energy saving

8




CHP

Wind

E-car

Fuel cellSolar

Lighting HVAC

Shading Window


Elect

Heat


Occupant demand


Micro-grid

9


10




11




Illustration of COO

G

S N

12

13


Motivations

bull HVAC system




20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW



17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5


14






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143




CHP

Wind

E-car

Fuel cellSolar

Lighting HVAC

Shading Window


Elect

Heat


Occupant demand


Micro-grid

9


10




11




Illustration of COO

G

S N

12

13


Motivations

bull HVAC system




20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW



17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5


14






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143


10




11




Illustration of COO

G

S N

12

13


Motivations

bull HVAC system




20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW



17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5


14






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143


11




Illustration of COO

G

S N

12

13


Motivations

bull HVAC system




20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW



17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5


14






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143

Illustration of COO

G

S N

12

13


Motivations

bull HVAC system




20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW



17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5


14






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143

13


Motivations

bull HVAC system




20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW



17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5


14






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143

Motivations

bull HVAC system




20

22

24

26

28

30

32

2008

119

2008

124

2008

129

2008

23

2008

28

2008

213

2008

218

2008

223

2008

228

2008

34

2008

39

2008

314

2008

319

2008

324

2008

329

2008

43

Set p

oint (oC)

0

2

4

6

8

10

12

14

Energy co

nsu

mptio

n (kW



17

19

21

23

25

27Set point

Day 1

Day 2

Day 3

Day 4

Day 5


14






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143






12

51

020

50

10

020

05

00

Task 1 Set to Heat

Thermostats

Tim

e (

s)

WEB TCH SMT BTN HYB

05

12

34

(min

ute

s)


Human perception

Indoor environment

Control

Perceive

15




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143




air temperature

radiant temperature

relative humidity

air velocity

clothing level

metabolic rate

activity level


PMV-PPD Model

Thermal sensation



warm hot

PMV value -3 -2 -1 0 1 2 3


16










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143










17





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143





18



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143



Sensors



Controller

T

R

H

CO2

Dynamic

Comfort

Region


comfort zone

1e

oe T

RH

Optimization

CO2


00

100

200

300

400

500

600

700

800

900

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161

Ro

om

lo

ad W

m2

metered



bullPsychology

bullEngineering


Human factors

Building manager

energy requirement



19





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143





20





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143





0M W C R E S


21







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143







22




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143




0 1 2 3

0 1 2 3

1 20 1 2 3 0 1 2 3

1

1

1

ˆ ˆ ˆ ˆ arg min ( ) ( ( ) )

arg min ( ) ( )

NN k

km m m m k

N

m m

N

m m k

k


k k

eal vote

( ) ( )( )PDTC kk X k


( ) [1 ( )]a ak P t R C


otherwisek

23


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143


Office layout


12151217 1224 15 112 115-2

0

2

4

6


m0

m1

m2

m3

12151217 1224 15 112 115-2

0

2

4

6

Month and Date

Para

mete

r V

alu

es


24



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143



-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject A

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject B

-20 -10 0 10 20-04

-02

0

02

04

Time offset

R

i

Subject C

-20 -10 0 10 20-04

-02

0

02

04

R

i

Subject D

1

2

3

4


SubjectPDTC

R-MSE

PDTC

R-Bias

PDTC

P-MSE

PDTC

P-BiasPMV

P-MSE

PMV

P-Bias

A 07230 0009 09703 007 24916 006

B 05319 -0015 05980 -0034 12999 0575

C 01442 -0058 01363 0026 05885 0058

D 05182 0064 05356 -005 04327 0272

E 07860 0064 09019 025 34994 -014

F 02860 0036 02684 00214 0713 -0047

G 03607 -0061 03634 01370 04633 -026

H 07167 -0087 08088 -0139 06777 0249

I 02371 -0025 02209 0023 0264 0932

25



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143



East Outside

External Wall

6m

6m

ow oWQ Q


external wall and

window

iWQ


interior walls




fa S fa LQ Q

Lamps heat emission

ltQ


eqpQ


0 1 2 3

( ) ( ) ( ) ( )

( ) (

(

)

)

a k a k

a k

t h all

k

a down up a down

a k

up

Min Q


h h h t t

k R C

t

-10 -8 -6 -4 -2 0 2 40

1

2

3

4

5

6

7

8


Se

ns

itiv

ity

re

lati

ve

he

ati

ng

lo

ad

d

ec

rea

se

(

)

A

B

C

D

E

F

G

H

I

PMV sensitivity





26





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143





27








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143








28


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143


bull Challenges





29

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143

Problem formulation




30






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143






31



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143



119909119895 le119878 119909119894


Temperature


2 2 | (1 0) 0(2) Rx x xS



direction 2S




32







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143







2min ( ) 12

k

j

w

x

T

k

V

w x c k

1kc

0 0 if ( ) 12

0 otherwise

T

T k i k i k

k k k

k

xw x c Vf x w x c k

33






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143






1

1 comfort

iC y C

comf

N

o irt

FPR IN


34

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143

Experiment settings







35


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143


24 26 28 30 3220

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject A

23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 26 28 3010

20

30

40

50

60

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject C

23 24 25 26 27 28 2940

45

50

55

60

65

Temperature 0C

Rela

tive h

um

idity

Subject D

FPR =031FPR =08

FPR =077 FPR =065


36




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143




23 24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject B

24 25 26 27 2840

45

50

55

60

65

Temperature 0C

Re

lati

ve

hu

mid

ity

Subject D

FPR =024FPR =038

37





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143





-02

-02

0

0

002

02

02

04

04

04

06

06

06

08

08

08

1

1

1

12

12

Temperature 0C

Rela

tive h

um

idit

y

23 24 25 26 27 2840

45

50

55

60

65

70

75

80

22 23 24 25 26 27 28 29 3035

40

45

50

55

60

65

Temperature (oC)

Re

lati

ve

hu

mid

ity

(

)

Cold

Complaint

Region

1 Possible

Comfort

Region

3 Unexplored

Region

Hot Complaint

Region

2 Possible

Uncomfortable

region

Hot Complaints

Cold Complaints

38






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143






discriminant model



A 04 -- 04 -- 008 --

B 017 0235 011 03 009 005

C 0253 -- 03 -- 008 --

D 054 038 045 041 007 006

E 047 0194 039 023 008 01

F 0307 058 029 038 007 001




39


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143


40


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143


41




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143




42





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143





43

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143

Summary

44

bull Challenges








Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143

Links

45





References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143

References

46








47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143


47



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143



2 2






m

ix R

S jx i j

Sj ix x


4843




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143




1 2 3 4 5 6 7 8 9 10 11 12 13 14

IMPOSSIBLE 93 5 3



POSSIBLE 5 68 18 10

LIKELY 18 50 33

PROBABLE 10 33 58

CERTAIN 100

IMPOSSIBLE 85 13 25

5 13 43 40 5

IMPROBABLE 25 28 20 40 8 25

20 15 10 65 10

UNLIKELY 15 23 38 15 75 25

35 3 5 70 18 5

POSSIBLE 3 3 25 8 75 25 25 10 5 10 25

50 25 45 35 10 5 25

PROBABLE 13 15 23 28 15

LIKELY 25 20 28 25 25

65 8 33 40 18 25

80 18 775 5

95 85 15

CERTAIN 25 25 10 85


WW Ranks

WN Ranks

4943


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143


0-3 3

-05 550

True vote


Noise distribution

Noise distribution

5043





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143





Identification

yyu

ˆ

Observation Noise

5143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143






Identification

yyu

ˆ

Observation Noise

ˆE 5243


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143


bull Key ideas





Identification

yyu

ˆ

Observation Noise

( )iy u



5343

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143

Noise model





-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

08

w

No

ise

dis

rib

uti

on

de

ns

itit

y

TDE(a=-3b=3 = 1y = -25)

TDE(a=-3b=3 = 1y = -15)

TDE(a=-3b=3 = 1y = 0)


-3 -2 -1 0 1 2 3 4 5 60

01

02

03

04

05

06

07

w

No

ise p

rob

ab

ilit

y d

en

sit

ity

TN(a=-3b=3 = 1 y = -25)

TN(a=-3b=3 = 1 y = -15)

TN(a=-3b=3 = 1 y = 0)


5443







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143







1 2 012k I i i I d k Ku


0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )iy u

0

( ) ( )( ) ( )

1ˆ( ) ( ) 1

( ) ( ) 1( ) ( )

i iK

i k I ii i k

a y u b y u



5543





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143





bull Where and

0

1( ) ( ( ( ) )) 1ˆ 2( )

1

K

i

k


u

( )i Ky u

T

KY

2[ ( ) ( ) ( )]T

i Iu u u 1 2[ ( ) ( ) ( ) ]T


Note




K 1 2iu i I

5643



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143



unknown variables


( ) 12 iy u i I

max log ( | )L D

0

1ˆ( ) ( ( ( ))) ( ) 1

1

( ) ( ) 1

K

i i k I i

k

T

i i


y u u i I

Note




st

5743

Algorithms


5843




5943


6043




6143

Algorithms


5843




5943


6043




6143




5943


6043




6143


6043




6143




6143

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