systems, domains and causal networks andrea castelletti politecnico di milano nrml06
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Systems, domains and causal networks
Andrea CastellettiPolitecnico di Milano
NRMNRML06L06
2
2. Conceptualisation
Sta
keh
old
ers
1. Reconnaissance
Defining Actions
(measures)
Identifying the Model
Defining Criteria and
Indicators
3Adriatic Sea
Fucino
VILLA VOMANO
PIAGANINI
PROVVIDENZA
CAMPOTOSTO
MONTORIO (M)
Gronda 1100 m.
PROVVIDENZA (P)
SAN GIACOMO (SG)Right interceptor 400 m.
Interceptors 1350 m.
Left interceptor 400 m.
Water works
Irrigation district(CBN)
S. LUCIA (SL)
Chiarino
Vomano
Physical scheme of the system
ComponentComponent: modelling elementary unit.
Every component has a specific function.
The model of the component must describe such a fuction.
Logical components are also allowed.
ComponentComponent: modelling elementary unit.
Every component has a specific function.
The model of the component must describe such a fuction.
Logical components are also allowed.
Choosing the components depends on:
• relevance of the component to the objective of the modelling exercise
• data availability
Choosing the components depends on:
• relevance of the component to the objective of the modelling exercise
• data availability
4
Identifying the Model
Definining the components and the system scheme
Identifying the models of the components Aggregated model
5Adriatic Sea
Fucino
VILLA VOMANO
PIAGANINI
PROVVIDENZA
CAMPOTOSTO
MONTORIO (M)
Interceptor 1100 m.
PROVVIDENZA (P)
SAN GIACOMO (SG)Right interceptor 400 m.
Interceptors 1350 m.
Left interceptor 400 m.
Water works
Irrigation District(CBN)
S. LUCIA (SL)
Chiarino
Vomano
6
Data analysis: time series provided by Enel
Campotosto: • level• aggregated daily flow rate the two intereceptors
Piaganini and Provvidenza: • level• daily flow rate from mass balance
Fucino
VILLA VOMANO
PIAGANINI
PROVVIDENZA
CAMPOTOSTO
MONTORIO (M)
Interceptor 1100 m.
PROVVIDENZA (P)
SAN GIACOMO (SG)
Right interceptor 400 m.
Interceptors 1350 m.
Left interceptors 400 m.
Waterworks
Irrigation district(CBN)
S. LUCIA (SL)
Chiarino
Vomano
During night-time without pumping
e.g. Provvidenza:
only aggregated flow dataonly aggregated flow data
7Adriatic Sea
Fucino
VILLA VOMANO
PIAGANINI
PROVVIDENZA
CAMPOTOSTO
MONTORIO (M)
Interceptor 1100 m.
PROVVIDENZA (P)
SAN GIACOMO (SG)Right interceptor 400 m.
Interceptors 1350 m.
Left interceptor 400 m.
Water works
Irrigation District(CBN)
S. LUCIA (SL)
Chiarino
Vomano
8Adriatic Sea
Fucino
VILLA VOMANO
PIAGANINI
PROVVIDENZA
CAMPOTOSTO
MONTORIO (M)
SAN GIACOMO (SG)
Irrigation district (CBN)
S. LUCIA (SL)
PROVVIDENZA (P)
Water works ???
Water works ???
9
Some difficulties in the scheme
1. PiaganiniPiaganini: there is no way to compute the indicator for the water works
?
Average water supply from hydropower reservoirsWW
10
How to solve them…
We need to fix a criterion for disaggregating the total inflow in the two single contributions of the interceptors. How?
Based on the surface and the morphological characteristics of the two catchments (regional analysis) we can assume a similar contribution from the two interceptors.
The hypothesis is validated using some flow rate measures locally available on the interceptors.
11
Some difficulties in the scheme
1. Piaganini: there is no way to compute the indicator for the water works
2. Campotosto: the contribution from the natural catchment is not accounted for.
12
Affluenti Campotosto
100 km2
Campotosto
13
Some difficulties in the scheme
1. Piaganini: there is no way to compute the indicator for the water works
2. Campotosto: the contribution from the natural catchment is not accounted for.
3. Provvidenza e Piaganini: understimation of snow-melting in spring and evaporation in summer.
14
Possible solutions
1. Piaganini: there is no way to compute the indicator for the water works
2. Campotosto: the contribution from the natural catchment is not accounted for.
3. Provvidenza e Piaganini: understimation of snow-melting in spring and evaporation in summer.
The daily inflow can be computed via mass balance using release and pumping data:
Provvidenza
Piaganini
Campotosto
15
Piaganini
P1i
ta
Snow melt is negligible
evaporation is NOT negligible
The estimate is reliable: we can use the new data obtained via mass balance (red) instead of those provided by Enel (blue).
The estimate is reliable: we can use the new data obtained via mass balance (red) instead of those provided by Enel (blue).
16
Provvidenza
Pr1ta
The estimate is not reliable.
Pumping is adding noise to data.
An understimation of evaporation is anyway evident in the data by Enel.
These data can be corrected by removing from them the evaporation that can be obtained from Piaganini, based on the many similarities between the two reservoirs.
The estimate is not reliable.
Pumping is adding noise to data.
An understimation of evaporation is anyway evident in the data by Enel.
These data can be corrected by removing from them the evaporation that can be obtained from Piaganini, based on the many similarities between the two reservoirs.
17
Some difficulties in the scheme
1. Piaganini: there is no way to compute the indicator for the water works
2. Campotosto: the contribution from the natural cacthment is not accounted for.
3. Provvidenza e Piaganini: understimation of snow-melting in spring and evaporation in summer.
18
Campotosto
this is impossible: at 40° max evap. 3m3/s
1Cta
Estimate is not reliable.
Oscillation are wider than in Provvidenza:
Pumping, but also the instrument precision (1cm) is amplifying the error
The contribution from the natural catchment is evident, but not easily quantifiable.
Inflow from Enel (blue) and from water balance (red) are not usable. What can we do?
Estimate is not reliable.
Oscillation are wider than in Provvidenza:
Pumping, but also the instrument precision (1cm) is amplifying the error
The contribution from the natural catchment is evident, but not easily quantifiable.
Inflow from Enel (blue) and from water balance (red) are not usable. What can we do?
19
Natural inflow to Campotosto
Interceptors1350 mProvvidenza
Montorio
CAMPOTOSTOReservoir
Piaganini
Can we evaluate the significancy of the inflow contribution from the natural Campotosto’s catchment?
Water balance for the i-th year in Montorio
- Internal pumping to the system
- Error on the level negligible
From which
The valure for each year is obtained
The estimate is an annual value: how to move to a daily one?
The estimate is an annual value: how to move to a daily one?
20
0,00
0,50
1,00
1,50
2,00
2,50
3,00
3,50
4,00
4,50
5,00
0,00 0,50 1,00 1,50 2,00 2,50 3,00
afflusso medio annuo gronde 1350 (mc/s)
affl
uss
o m
edio
an
nu
o c
om
ple
ssiv
o (
mc/
s )
Inflow estimate in Campotosto
evaporation
21
Some difficulties in the scheme
1. Piaganini: there is no way to compute the indicator for the water works
2. Campotosto: the contribution from the natural cacthment is not accounted for.
3. Provvidenza e Piaganini: understimation of snow-melting in spring and evaporation in summer.
22Adriatic Sea
Fucino
VILLA VOMANO
PIAGANINI
PROVVIDENZA
CAMPOTOSTO
MONTORIO (M)
SAN GIACOMO (SG)
Irrigation District(CBN)
S. LUCIA (SL)
PROVVIDENZA (P)
Topological SchemeTopological Scheme
23
Identifying the Model
Definining the components and the system scheme
Identifying the models of the components Aggregated model
24Adriatic Sea
Fucino
VILLA VOMANO
PIAGANINI
PROVVIDENZA
CAMPOTOSTO
MONTORIO (M)
SAN GIACOMO (SG)
Irrigation District(CBN)
S. LUCIA (SL)
PROVVIDENZA (P)
25
Campotosto lake
Simplification
Let’s assume that only one criterion needs to be satisfied: flood reduction in the town of
Campotosto (on the lake shores)
26
The (lake’s) domainThe whole set of quantities and information about the lake: inflow release level water characteristics biota algae ... batimetry topography stage-discharge function of the spillway ... Consorzio dell‘Adda (lake manager) Regione Lombardia (water authority) ...
(at)
(rt) (ht)
The domain is the first level of abstraction of reality. It does not require any assumption
about the mathematical relationships linking the variables.
It is not a representaton of reality, but a partition of knowledge.
The domain is the first level of abstraction of reality. It does not require any assumption
about the mathematical relationships linking the variables.
It is not a representaton of reality, but a partition of knowledge.
Models are a simplified representation of reality;
They should reproduce those features of the system that are important for the scope of the Project.
The first step to create a model is to select the essential variables within the domain.
Models are a simplified representation of reality;
They should reproduce those features of the system that are important for the scope of the Project.
The first step to create a model is to select the essential variables within the domain.
27
The (lake’s) domainThe whole set of quantities and information about the lake: inflow release level water characteristics biota algae ... batimetry topography stage-discharge function of the spillway ... Consorzio dell‘Adda (lake manager) Regione Lombardia (water authority) ...
(at)
(rt) (ht)
1tt
th
1ta
An important convention
The subscript of a variable is the time instant at which it takes deterministically known value.
28
Are the variables well defined?
Inflow at+1: total inflow in the interval [t,t+1)
It is better to divide it into:
t+1 = inflow from the natural catchment
wt = pumping from hydropower plant downstream
at+1t+1
wt Which unit of measurement? m3/s or m3 ?
Are the variables well defined?
YES, as long as we do not find errors: only falsification is possible.
It is very important that the domain is defined in strict collaboration with the concerned Stakeholders.
Sharing and agreeing on the assumptions made at this point is key to obtain a “trusted” model of the system.
It is very important that the domain is defined in strict collaboration with the concerned Stakeholders.
Sharing and agreeing on the assumptions made at this point is key to obtain a “trusted” model of the system.
29
Identifying the model:the causal network
Is it a good representation of the real cause-effect relationships?
Release decision
30
1ts
Causal network of the lake
Is it a good model of reality?NO, evaporation is missing....
Loops are not allowed. An effect can not cause itself!!
Loops are not allowed. An effect can not cause itself!!
31
- A priori: good sense, Analyst’s intuition
- A posteriori: accuracy of the model
identified starting from the network
How to check if the network is a good model?
Causal network of the lake
32
input
input
input
Classification of the variables
state
output
control
disturbance
disturbance
deterministicdisturbance
randomdisturbance
internalvariables
The state is composed of all the variables that are necessary to describe the past history of the system, and, once these are known, the future evolution of the system is completely defined by the sole inputs.
1ts
33
The model structure
1ts
state transition function
output transformation function
set of the feasible controls
These two equations include all the information available in the network.
In the network the internal variables are explicitely considered.
These two equations include all the information available in the network.
In the network the internal variables are explicitely considered.
34
In general: variables
state xt
ut control
up planning decision
wt deterministic disturbancet +1 random disturbance
From now on vectors will be in bold, e.g. xt is the state vector!
input
ouptut yt
with the following associated expressions Models are OBJECTS in the
computer-science meaning of the
word
Models are OBJECTS in the
computer-science meaning of the
word
output transformation function
proper model
35
In general: structure
state transition function
time-varying modelModels interact with the outside only through inputs and ouputs. What happens inside is important only as far as it affects
the ouptuts.
Models interact with the outside only through inputs and ouputs. What happens inside is important only as far as it affects
the ouptuts.
This is a
DYNAMIC SYSTEM
improper model
36
Not always systems are dynamic
Not always the state appears in the system dynamics.
E.g.: diversion dam
t+1 incoming flow
ut withdrawal decision
only the output transformation function
yt=ht(ut,t+1)
model
yt diverted flowthis is a non-dynamic
model
Time-varying is not a synonymus of dynamic!
37
Simulation
simulation is aimed at computing
established a time horizon H (starting from time 0 and ending at time h)
giventhe initial state
the input trajectories
the state trajectories
the output trajectories
38
Simulation
established a time horizon H (starting from time 0 and ending at time h)
giventhe initial state
the input trajectories
381
using the model recursively
20 h
39
Conclusions
domain mental model causal network
Next step:
implicitly or explicitly define- the state transition function
- the output transformation function
How to classify model ?
with respect to
the nature
of their functions
the aumount of a priori information one has to know about the ongoing processes
40
Bayesian Believe Networks Mechanistic models Empirical models Markov models
Readings
IPWRM.Theory Ch. 4
41
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