Pozzi, zonta, wang & chen evaluating the impact of SHM on BMS A framework for evaluating the impact of structural health monitoring on bridge management

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


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.


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?


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.


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


cost per state and action

Do Nothing

Inspection

Damaged Undamaged


cost per state and action

Longdowntime

(CL)0Do Nothing

Inspection

Damaged Undamaged

Shortdowntime

(CS)0


2 states, 2 outcomes

possible states possible responses

D

“Damage”

“no Damage”

“Alarm”

“no Alarm”

U

A

¬A


ideal monitoring system

D

U

A

¬A

states responses


ideal monitoring system

D

U

A

¬A

states responses

modus tollens: [(p→q),¬q] →¬p


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


decision tree w/o monitoring

DN

D

U

action state cost

Do Nothing

Inspection

Damaged

Undamaged

DN D

U

action: state:

LEGEND

I



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



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



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



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



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



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



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



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


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)


decision tree with monitoring

A

outcome

DN

D

U

D

U

I

DN

D

U

D

U

I

¬ A



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



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)



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)



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 }


C=min { P(D)·CL , P(U)·CS }


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



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

...

...

...

...



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

...

...



VoI = C - C*


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


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.



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



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

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.


PENNPENNPARAMETER EVALUATORPARAMETER EVALUATOR

NEURAL NETWORKNEURAL NETWORK

damage assessment scheme

ENNENNEMULATOREMULATOR


-- RMSRMS

k k+1

k+1

DAMAGE DAMAGE INDICESINDICES

XX

BRIDGE BRIDGE RESPONSERESPONSE


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


PENNPENNPARAMETER EVALUATORPARAMETER EVALUATOR


damage assessment scheme

ENNENNEMULATOREMULATOR


-- RMSRMS

k k+1

k+1

DAMAGE DAMAGE INDICESINDICES

XX

BRIDGE BRIDGE RESPONSERESPONSE


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






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






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


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)



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



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



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



VoI = C - C*

C = min { ∑k P(sk)·ci,k }= $ 600 k

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



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



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)


Updated probabilities



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)


Updated probabilities

Updated costs



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


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


Thanks. Questions?

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Pozzi, zonta, wang & chen evaluating the impact of SHM on BMS A framework for evaluating the impact of structural health monitoring on bridge management