d. zonta bridge managers on the verge of a nervous breakdown uc berkeley, mar 11, 2013 bridge...

d. zonta • bridge managers on the verge of a nervous breakdown

UC Berkeley, Mar 11, 2013UC Berkeley, Mar 11, 2013

Bridge Bridge managers on the managers on the

verge of a nervous verge of a nervous

breakdownbreakdown

Daniele Zonta

University of Trento – Italy


impact of monitoring on decision?

permanent monitoring of bridgespermanent monitoring of bridges is commonly presented as a powerful tool supporting transportation agencies’ decisions

in real-life bridge owners are very skepticalvery skeptical

take decisions based on their experience or on common sense

often disregard the action suggestedthe action suggested by instrumental damage detection


2 states, 2 outcomes, 2 actions

possible statespossible observations

D

“Damage”

“no Damage”

“Alarm”

“no Alarm”

U

A

¬A

possible actions

“intervention”

“do nothing”

DN

I


structural engineer's naïf perspective

possible states

D

“Damage”

“no Damage”

U

possible responses

“Alarm”

“no Alarm”

A

¬A

possible actions

“intervention”

“do nothing”

DN

I


observed real-life manager's behavior

possible states

D

“Damage”

“no Damage”

U

possible responses

“Alarm”

“no Alarm”

A

¬A

possible actions

“intervention”

“do nothing”

DN

I


are bridge manages crazy?

Not necessarily...

FirstFirst: monitoring is affected by uncertainties so managers weightweight differently the outcomes of the monitoring based on their experienceexperience and prior perceptionprior perception of the state of the structure

SecondSecond: owners are concerned with the consequences of wrong consequences of wrong actionaction, and so will decide keeping in mind the possible effects of the action they can undertake


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?


impact of monitoring on decision?

introducing a rational frameworkrational framework to quantitatively estimate the benefit monitoring systems, taking into account their impact on decision making

managers' prior perception can be addressed formally by using Bayesian logicBayesian logic

their concen with consequences of wrong action recast the problem in the more general framework of decision theory decision theory

benefit of monitoring evaluated using the concept of Value of Information Value of Information (VoI)


value of information (VoI)

VoI = C - C*operational cost w/o monitoringC =operational cost with monitoringC* =

Value of InformationValue of Information: money saved every time the manager interrogates the monitoring system

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

implies the manager can undertake actions in reaction actions in reaction to monitoringto monitoring response


Streicker Bridge at PU campus

New pedestrian bridge being built at Princeton University campus over the busy Washington Road

Funded by Princeton alumnus John Harrison Streicker (*64), overall design by Christian Menn, design details by Princeton alumni Ryan Woodward (*02) and Theodor Zoli (*88)

• Main span: deck-stiffened arch, deck=post-tensioned concrete, arch=weathering steel

• Approaching legs: curved post-tensioned concrete continuous girders supported on weathering steel columns


introducing 'Tom' fictitious character responsible of the imaginary Design

and Construction office in PU behaves in a rational manner aims at minimizing the operational

cost linear utility with cost no separation between direct cost to

the owner and indirect cost to the user

concerned that a truck driving on Washington Rd., could collide with the steel arch

"Tom"


possible states of the bridge

the bridge is still standing, but experienced severe damage at the steel arch structure; chance of collapse under design live load and under self-weight

the structure has either no damage or mere cosmetic damage, with no or negligible loss in capacity

SevereDamage

No damage


Tom's options

no special restriction is applied; bridge is open to pedestrian traffic; minimal repair or maintenance works con be carried out

both Streicker bridge and Washington Rd. are closed to pedestrian and vehicular traffic; access to the nearby area is restricted

Do Nothing

Close bridge


Tom's cost estimate

Daily Road User Cost (DRUC)that considers the value of time per day as a monetary term (Kansas DOT 1991, Herbsman et al. 1995)

estimated DRUC for Washington Road in $4660/day

estimated downtime: 1 month total downtime cost

CDT=4660 x 30 = $139,800

Close bridge


Tom's cost estimate

Pay nothing!!

Do Nothing No damageAND


Tom's cost estimate

Do Nothing ANDSevere

Damage

2 month DRUC $279,600

cost of fatality: k$ 3840chance of fatality: 15%

$576,000

cost of injury: k$ 52chance of injury: 50%

$26,000

total failure cost CF=$881,600


cost per state and action

CF

k$ 881.60Do Nothing

Close bridge

Damage No Damage

CDT

k$ 139.8CDT

k$ 139.8


decision tree w/o monitoring

DN

D

U

action state cost

0

CF

probability

P(D)

CDN = P(D) · CF

Do Nothing

Close Bridge

Damaged

Undamaged

DN D

U

action: state:

LEGEND

expected loss

P(U)

CDT downtime cost



DN

D

U

action state cost

0

CF

probability

P(D)

CDN = P(D) · CF

Do Nothing

Close Bridge

Damaged

Undamaged

DN D

U

action: state:

LEGEND

expected loss

P(U)

CDT downtime cost

C = min { P(D)·CF , CDT }

Optimal cost

decision criterion

CDT < CDN ?yn

DN


Tom's prior expectation

CF

k$ 881.60Do Nothing

Close bridge

DamageP(D)=30%

No DamageP(U)=70%

CDT

k$ 139.8CDT

k$ 139.8



DN

D

U

action state cost

0

k$881.6

probability

30%CDN = P(D) · CF= k$264.5

Do Nothing

Close Bridge

Damaged

Undamaged

DN D

U

action: state:

LEGEND

expected loss70%

CDT = k$ 139.8

downtime cost


Streicker Bridge, instrumentation

Half of main span equipped with sensors (assuming symmetry)

• Currently two fiber-optic sensing technologies used

• Discrete Fiber Bragg-Grating (FBG) long-gage sensing technology (average strain and temperature measurements)

• Truly distributed sensing technology based on Brillouin Optical Time Domain Analysis (BOTDA, average strain and temperature measurements)


5.182m 5.232m 5.232m 6.147m5.232m 5.232m6.147m

P3 P4 P5 P6 P7 P8 P9P10

FBG Strain Sensor

BOTDA Distributed Strain & Temperature Sensor Junction Box

A;BC;D

E

A;B

C;D;E

C;D

E

A;B

A;B

C;D;E

A;B

C;D

S N

P71.524m 1.524m2x0.487

S NP8

1.524m 1.524m2x0.741mS N

Close to P10

1.524m 2.178m 2.178m 1.524m

FBG Temp. SensorFBG Strain & Temp. Sensor

P9

S N

P9

1.524m 1.524m1.249m1.249m

Sensor location in main span


5.182m 5.232m 5.232m 6.147m5.232m 5.232m6.147m

P3 P4 P5 P6 P7 P8 P9P10BOTDA Distributed Strain & Temperature Sensor Junction Box

A;B

S N

P7

1.524m 1.524m2x0.487

FBG Strain & Temp. Sensor

Sensor location in main span


decision tree with monitoring

DN

D

U

action state cost

0

CF

posterior

probability

P(D|)

CDN = P(D|) · CF

Do Nothing

Close Bridge

Damaged

Undamaged

DN D

U

action: state:

LEGEND

expected loss

P(U|)

CDT downtime cost


0

0.02

0.04

0.06

0.08

0.1

0.12

-1000 -500 0 500 1000 1500 2000 2500 3000

elongation [m]

PD

F(

|S)

Likelihoods and evidence

P(|D) · P(D)

P(|U) · P(U)

P()

S N

P71.524m 1.524m2x0.487



DN

D

U

action state cost

0

CF

posterior

probability

P(D|)

Do Nothing

Close Bridge

Damaged

Undamaged

DN D

U

action: state:

LEGEND

expected loss

P(U|)

CDT downtime cost

C = min { P(D|)·CF , CDT }

Optimal cost

decision criterion

CDT < CDN ?yn

DN

CDN = P(D|) · CF



0

0.02

0.04

0.06

0.08

0.1

0.12

-1000 -500 0 500 1000 1500 2000 2500 3000

PD

F(

|S)

P(|D) · P(D)

P(|U) · P(U)

CDT=k$139.8

CDN = P(D|) · CF

c*()=min { P(D|)CF , CDT }

P()

DN



0

0.02

0.04

0.06

0.08

0.1

0.12

-1000 -500 0 500 1000 1500 2000 2500 3000

PD

F(

|S)

P(|D) · P(D)

P(|U) · P(U)

CDT=k$139.8

DN

DU

CDN = P(D|) · CF




CDT=k$139.8

CDN = P(D|) · CF


C*=∫ c*()PDF()d= k$ 84.6



VoI = C - C*

maximum priceprice Tom (the rational agent) is willing to willing to paypay for the information from the monitoring system

C=min { P(D)·CF , CDT }= k$ 139.8

C*=∫ c*()PDF()d= k$ 84.6

VoI = C - C*= k$ 55.2


discussion

VoI depends on:(i) the expected financial impact of a collapse CF

(ii) sensor sensitivity to damage: pdf(|D)

(iii) the prior knowledge of the structure state P(D)

0

*

min P D , min pdf ε|D P D , dεF DT F DT

VoI C C

C C C C


perfect information

assume that the monitoring system provides perfect information means that Tom can always determine univocally the state of the bridge

based on the sensor measurements this happens when the two likelihood distributions pdf(|U) and pdf(|D) do

not overlap, thus only one possible state is associated to any one value of strain

cost Tom will incur for taking the wrong decision due to his lack in knowledge represents the upper bound value of VoI

* P DDTC C

* P D PDT DT DTVoI C C C C C U


strong prior type 1

"projected Superman syndrome" Tom believe the bridge is invulnerable

P D 0 0VoI

Trust me, no need to close the

bridge, nothing will happen!!


strong prior type 2

* 0VoI C C

Too dangerous, I’d better close the bridge anyway!!!

over-concerned Tom believes that the bridge is highly vulnerable to

truck collision

P D 1 * DTC C C


no consequence to the manager

an action has no direct consequence for the manager say, for example, that to Tom the indirect cost to users is irrelevant

he will always close the bridge

0VoI

I’ll close it – it costs me nothing!!

0DTC

* 0C C


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*

maximum priceprice the rational agent is willing to pay 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


conclusions

an economic evaluation of the impact of SHM on decision 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


Thank you for your attention!

Acknowledgments Branko Glisic, Sigrid Adraenssens, Princeton

University Turner Construction Company; R. Woodward

and T. Zoli, HNTB Corporation; D. Lee and his team, A.G. Construction Corporation; S. Mancini and T.R. Wintermute, Vollers Excavating & Construction, Inc.; SMARTEC SA; Micron Optics, Inc.

the following personnel from Princeton University supported and helped realization of the project: G. Gettelfinger, J. P. Wallace, M. Hersey, S. Weber, P. Prucnal, Y. Deng, M. Fok; faculty and staff of CEE; Our students: M. Wachter, J. Hsu, G. Lederman, J. Chen, K. Liew, C. Chen, A. Halpern, D. Hubbell, M. Neal, D. Reynolds and D. Schiffner.

Matteo Pozzi, CMU Ivan Bartoli, 'Tom', Drexel University

d. zonta bridge managers on the verge of a nervous breakdown uc berkeley, mar 11, 2013 bridge...

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