pozzi, zonta, wang & chen evaluating the impact of shm on bms a framework for evaluating the...

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

A framework for evaluating the impact of structural health

monitoring on bridge management

Matteo Pozzi & Daniele Zonta

University of Trento

Wenjian Wang

Weidlinger Associates Inc., Cambridge, MA

Genda Chen

Missouri University of Science and Technology

IABMAS 2010

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

motivationpermanent monitoring of bridges is commonly

presented as a powerful tool supporting transportation agencies’ decisions

in real-life bridge operators are very skeptical

take decisions based on their experience or on common sense

often disregard the action suggested by instrumental damage detection.

we propose a rational framework to quantitatively estimate the monitoring systems, taking into account their impact on decision making.

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

benefit of monitoring?

a reinforcement intervention improves capacity

monitoring does NOT change capacity nor load

monitoring is expensive

why should I spend my money on monitoring?

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

layout of the presentation

Theoretical basis of the approach of the Value of Information:

- overview of the logic underlying - general formulation

Application on a on a cable-stayed bridge taken as case study:

- description of the bridge and its monitoring system;

- application of the Value of Information approach.

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

value of information (VoI)

VoI = C - C*

operational cost w/o monitoringC =

operational cost with monitoringC* =

money saved every time the manager interrogates the monitoring system

maximum price the rational agent is willing to pay for the information from the monitoring system

implies the manager can undertake actions in reaction to monitoring response

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

cost per state and action

Do Nothing

Inspection

Damaged Undamaged

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

cost per state and action

Longdowntime

(CL)0Do Nothing

Inspection

Damaged Undamaged

Shortdowntime

(CS)0

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

2 states, 2 outcomes

possible states possible responses

D

“Damage”

“no Damage”

“Alarm”

“no Alarm”

U

A

¬A

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

ideal monitoring system

D

U

A

¬A

states responses

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

ideal monitoring system

D

U

A

¬A

states responses

modus tollens: [(p→q),¬q] →¬p

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

value of information

VoI = C - C*

operational cost w/o monitoringC =

operational cost with monitoring=0C* =

ideal monitoring allows the manager to always follow the optimal path

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree w/o monitoring

DN

D

U

action state cost

Do Nothing

Inspection

Damaged

Undamaged

DN D

U

action: state:

LEGEND

I

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree w/o monitoring

DN

D

U

action state cost

Do Nothing

Inspection

Damaged

Undamaged

DN D

U

action: state:

LEGEND

CL 0

0 CS

DN

I

D U

c/s-a matrix

CL

0

I

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree w/o monitoring

DN

D

U

action state cost

0

CL

probability

P(D)

P(U)

Do Nothing

Inspection

Damaged

Undamaged

DN D

U

action: state:

LEGEND

CL 0

0 CS

DN

I

D U

c/s-a matrix

I

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree w/o monitoring

DN

D

U

action state cost

0

CL

probability

P(D)

P(U)

CDN = P(D) · CL

Do Nothing

Inspection

Damaged

Undamaged

DN D

U

action: state:

LEGEND

expected cost

I

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree w/o monitoring

DN

D

U

action state cost

0

CL

probability

P(D)

P(U)

ID

U

CDN = P(D) · CL

Do Nothing

Inspection

Damaged

Undamaged

DN

I

D

U

action: state:

LEGEND

expected cost

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree w/o monitoring

DN

D

U

action state cost

0

CL

probability

P(D)

P(U)

D

U CS

0 P(D)

P(U)

CDN = P(D) · CL

CI = P(U) · CS

Do Nothing

Inspection

Damaged

Undamaged

DN D

U

action: state:

LEGEND

expected cost

expected cost

I

I

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree w/o monitoring

DN

D

U

action state cost

0

CL

probability

P(D)

P(U)

D

U CS

0 P(D)

P(U)

CDN = P(D) · CL

CI = P(U) · CS

Do Nothing

Inspection

Damaged

Undamaged

DN D

U

action: state:

LEGEND

decision criterion

CI < CDN ?yn

IDN

I

I

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree w/o monitoring

DN

D

U

action state cost

0

CL

probability

P(D)

P(U)

D

U CS

0 P(D)

P(U)

CDN = P(D) · CL

CI = P(U) · CS

C = min { CDN , CI }

= min { P(D)·CL , P(U)·CS }

Optimal cost

Do Nothing

Inspection

Damaged

Undamaged

DN D

U

action: state:

LEGEND

decision criterion

CI < CDN ?yn

IDN

I

I

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

value of information (VoI)

VoI = C - C*

C =

C* = 0

ideal monitoring allows the manager to always follow the optimal path

min { P(D)·CL , P(U)·CS }

depends on: prior probability of scenariosprior probability of scenarios consequence of action

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

non-ideal monitoring system

D

U

A

¬A

P(A|D)

P(¬A|U)

P(A

|U)

P(¬A|D

)

likelihood

states responses

a p

rio

ri

P(D)

P(U)

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree with monitoring

A

outcome

DN

D

U

D

U

I

DN

D

U

D

U

I

¬ A

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree with monitoring

DN

D

U

action state cost

0

CL

probability

A

ALARM!

test outcome

P(D|A)

P(U|A)

D

U CS

0

C|A = min { CDN | A , CI | A }

IP(D|A)

P(U|A)

CI | A = P(U|A) · CS

CDN | A = P(D|A) · CL

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree with monitoring

DN

D

U

action state cost

0

CL

probability

A

ALARM!

test outcome

P(D|A)

P(U|A)

D

U CS

0

C|A = min { CDN | A , CI | A }

IP(D|A)

P(U|A)

CI | A = P(A|U) · P(U) · CS

CDN | A = P(A|D) · P(D) · CL

P(A)

P(A)

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree with monitoring

A

outcome

DN

D

U

D

U

I

DN

D

U

D

U

I

¬ A

cost given outcome

C|A

C|¬A

C* = min { P(D)·P(A|D)·CL , P(U)·P(A|U)·CS } + min { P(D)·P(¬A|D)·CL , P(U)·P(¬A|U)·CS }

min { P(D)·P(A|D)·CL ,

P(U)·P(A|U)·CS }

min { P(D)·P(¬A|D)·CL ,

P(U)·P(¬A|U)·CS }

probability of outcome

P(A)

P(¬A)

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

value of information (VoI)

VoI = C - C*

C* = min { P(D)·P(A|D)·CL , P(U)·P(A|U)·CS }

+ min { P(D)·P(¬A|D)·CL , P(U)·P(¬A|U)·CS }

maximum price the rational agent is willing to pay for the information from the monitoring system

C=min { P(D)·CL , P(U)·CS }

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

general case

ci,kai

sk

scenarioac

tions

a1

aM

s1 sN

M available actions: from a1 to aM

N possible scenario: from s1 to sN

cost per state and action matrix

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree w/o monitoring

a1

action state cost

c1,1

probability

P(s1)

c1,k

s1

sN

sk

ai

aM

c1,N

...

ci,1

ci,k

s1

sN

sk

ci,N

...

cM,1

cM,k

s1

sN

sk

cM,N

...

P(sk)

P(sN)

P(s1)

P(sk)

P(sN)

P(s1)

P(sk)

P(sN)

C = min { ∑k P(sk)·ci,k }

...

i

decision criterion

∑k P(sk)·c1,k

∑k P(sk)·ci,k

∑k P(sk)·cM,k

expected cost

...

...

...

...

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree with monitoring

a1

state cost

c1,1

probability

P(s1|x)

c1,k

s1

sN

sk

ai

aM

...

c1,N

...

ci,1

ci,k

s1

sN

sk

ci,N

...

cM,1

cM,k

s1

sN

sk

cM,N

...

... C|x = min { ∑k P(sk|x)·ci,k }

...

i

decision criterion

∑k P(sk|x) ·c1,k

∑k P(sk|x)·ci,k

∑k P(sk|x)·cM,k

expected cost

outcome

X

P(sk|x)

P(sN|x)

P(s1|x)

P(sk|x)

P(sN|x)

P(s1|x)

P(sk|x)

P(sN|x)

action

...

...

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

value of information (VoI)

VoI = C - C*

maximum price the rational agent is willing to pay for the information from the monitoring system

C = min { ∑k P(sk)·ci,k }

C* = ∫Dx min { ∑k P(sk)· PDF(x|sk)· ci,k }dxdepends on:

prior probability of scenariosprior probability of scenarios consequence of action reliability of monitoring system

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

the Bill Emerson Memorial Bridge

It carries Missouri State Highway 34, Missouri State Highway 74 and Illinois Route 146 across the Mississippi River between Cape Girardeau, Missouri, and East Cape Girardeau, Illinois.

Opened to traffic on December, 2003.

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

the Bill Emerson Memorial Bridge

Carrying two-way traffic, 4 lanes, 3.66 m (12 ft) wide vehicular plus two narrower shoulders. Total length: 1206 m (3956 ft)Main span: 350.6 m (1150 ft)12 side piers with span: 51.8 m (170 ft) each.Total deck width: 29.3 m (96 ft).Two towers, 128 cables, and 12 additional piers in the approach span on the Illinois side

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

the Bill Emerson Memorial Bridge

Located approximately 50 miles (80 km) from the New Madrid Seismic Zone.

Bridge

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

the Bill Emerson Memorial Bridge

Bridge

Located approximately 50 miles (80 km) from the New Madrid Seismic Zone.Instrumented with 84 EpiSensor accelerometers, installed throughout the bridge structure and adjacent free field sites.

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

PENNPENNPARAMETER EVALUATORPARAMETER EVALUATOR

NEURAL NETWORKNEURAL NETWORK

damage assessment scheme

ENNENNEMULATOREMULATOR

NEURAL NETWORKNEURAL NETWORK

-- RMSRMS

k k+1

k+1

DAMAGE DAMAGE INDICESINDICES

XX

BRIDGE BRIDGE RESPONSERESPONSE

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

training of the networks

networks calibrated using a 3-D FEM of the bridge

four pairs of damage locations A, B, C and D were considered and each damage location includes two plastic hinges

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

PENNPENNPARAMETER EVALUATORPARAMETER EVALUATOR

NEURAL NETWORKNEURAL NETWORK

damage assessment scheme

ENNENNEMULATOREMULATOR

NEURAL NETWORKNEURAL NETWORK

-- RMSRMS

k k+1

k+1

DAMAGE DAMAGE INDICESINDICES

XX

BRIDGE BRIDGE RESPONSERESPONSE

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

estimation of the VoITwo scenarios:(U) undamaged;(D) 12% stiffness reduction at hinges A.

Response:x: rotational stiffness amplification factor;

x=1 : hinges are intact, x<1 : the reduced stiffness is x times the original one.

In an ideal world,U → yield x=1, D → x=0.88 .

A A

Missouri side

A

Missouri side

A

DamagedUndamaged

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

estimation of the VoITwo scenarios:(U) undamaged;(D) 12% stiffness reduction at hinges A.

Response:x: rotational stiffness amplification factor;

x=1 : hinges are intact, x<1 : the reduced stiffness is x times the original one.

In an ideal world,U → yield x=1, D → x=0.88 .

From a Monte Carlo analysis on the FEM:

PDF(x|U) = logN(x,-0.0278,0.1389)PDF(x|D) = logN(x,-0.1447,0.1328)

A A

Missouri side

A

Missouri side

A

DamagedUndamaged

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

estimation of the VoITwo scenarios:(U) undamaged;(D) 12% stiffness reduction at hinges A.

Response:x: rotational stiffness amplification factor;

x=1 : hinges are intact, x<1 : the reduced stiffness is x times the original one.

In an ideal world,U → yield x=1, D → x=0.88 .

From a Monte Carlo analysis on the FEM:

PDF(x|U) = logN(x,-0.0278,0.1389)PDF(x|D) = logN(x,-0.1447,0.1328)

A A

Missouri side

A

Missouri side

A

DamagedUndamaged

0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

1

2

3

4

PD

F

0

0.5

1

prob

abili

ty

0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

1

2

cost

[M

$]

x

PDF(xIU)

PDF(xID)

prob(UIx)

prob(DIx)

C I x

C N x

Cneat

*(x)

x

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

Application of the VoI

Two decision options:- Do-Nothing- Inspection.

Assumptions:- prior probability of damage prob(D);- inspection cost CI and undershooting cost

CUS.

InspectionCost (CI)

0Do Nothing

Inspection

Damaged Undamaged

UndershootingCost (CUS)

InspectionCost (CI)

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

Application of the VoI

Two decision options:- Do-Nothing- Inspection.

Assumptions:- prior probability of damage prob(D);- inspection cost CI and undershooting cost

CUS.

$ 700k

0Do Nothing

Inspection

DamagedP(D)=30%

UndamagedP(U)=70%

$ 2M

$ 700k

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree w/o monitoring

DN

D

U

action state cost

0

CUS

probability

P(D)

P(U)

D

U CI

P(D)

P(U)

CDN = P(D) · CL

CI

Do Nothing

Inspection

Damaged

Undamaged

DN D

U

action: state:

LEGEND

expected cost

expected cost

I

ICI

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

decision tree w/o monitoring

DN

D

U

action state cost

0

2M

probability

30%

70%

D

U

30%

70%

CUS= $ 600k

CI= $ 700k

Do Nothing

Inspection

Damaged

Undamaged

DN D

U

action: state:

LEGEND

expected cost

expected cost

I

I700k

700k

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

value of information (VoI)

VoI = C - C*

C = min { ∑k P(sk)·ci,k }= $ 600 k

C* = ∫Dx min { ∑k P(sk)· PDF(x|sk)· ci,k }dx

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

Application of the VoI

0

0.5

1

1.5

2

2.5

3

3.5

4

PD

F

C* = $ 600 K, Cneat

* = $ 500 K, VoI = $ 100 K

0

0.5

1

prob

abili

ty

0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

1

2

cost

[M

$]

x

PDF(xIU)

PDF(xID)

PDF(x)

prob(UIx)

prob(DIx)

C I x

C N x

Cneat

*(x)

0

0.5

1

1.5

2

2.5

3

3.5

4

PD

F

C* = $ 600 K, Cneat

* = $ 500 K, VoI = $ 100 K

0

0.5

1

prob

abili

ty

0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

1

2

cost

[M

$]

x

PDF(xIU)

PDF(xID)

PDF(x)

prob(UIx)

prob(DIx)

C I x

C N x

Cneat

*(x)

Likelihoods and evidence

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

Application of the VoI

0

0.5

1

1.5

2

2.5

3

3.5

4

PD

F

C* = $ 600 K, Cneat

* = $ 500 K, VoI = $ 100 K

0

0.5

1

prob

abili

ty

0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

1

2

cost

[M

$]

x

PDF(xIU)

PDF(xID)

PDF(x)

prob(UIx)

prob(DIx)

C I x

C N x

Cneat

*(x)

0

0.5

1

1.5

2

2.5

3

3.5

4

PD

F

C* = $ 600 K, Cneat

* = $ 500 K, VoI = $ 100 K

0

0.5

1

prob

abili

ty

0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

1

2

cost

[M

$]

x

PDF(xIU)

PDF(xID)

PDF(x)

prob(UIx)

prob(DIx)

C I x

C N x

Cneat

*(x)

Likelihoods and evidence

Updated probabilities

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

Application of the VoI

0

0.5

1

1.5

2

2.5

3

3.5

4

PD

F

C* = $ 600 K, Cneat

* = $ 500 K, VoI = $ 100 K

0

0.5

1

prob

abili

ty

0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

1

2

cost

[M

$]

x

PDF(xIU)

PDF(xID)

PDF(x)

prob(UIx)

prob(DIx)

C I x

C N x

Cneat

*(x)

Likelihoods and evidence

Updated probabilities

Updated costs

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

value of information (VoI)

VoI = C - C*

C = min { ∑k P(sk)·ci,k }= $ 600 k

C* = ∫Dx min { ∑k P(sk)· PDF(x|sk)· ci,k }dx= $500k

VoI = C - C*= $600k-$500k=$100k

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

conclusions

an economic evaluation of the impact of SHM on BM has been performed

utility of monitoring can be quantified using VoIVoI

VoI is the maximum priceprice the owner is willing to paywilling to pay for the informationfor the information from the monitoring system

implies the manager can undertake actions in reaction to monitoring response

depends on: prior probabilityprior probability of scenarios; consequenceconsequence of actions; reliability of monitoringreliability of monitoring system

pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS

Thanks. Questions?