uc berkeley, mar 11, 2013 bridge managers on the verge of a nervous breakdown daniele zonta
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UC Berkeley, Mar 11, 2013 Bridge managers on the verge of a nervous breakdown Daniele Zonta University of Trento – Italy. impact of monitoring on decision?. permanent monitoring of bridges is commonly presented as a powerful tool supporting transportation agencies’ decisions - PowerPoint PPT PresentationTRANSCRIPT
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 ZontaUniversity of Trento – Italy
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
2 states, 2 outcomes, 2 actionspossible statespossible observations
D
“Damage”
“no Damage”
“Alarm”
“no Alarm”
U
A
¬A
possible actions
“intervention”
“do nothing”
DN
I
d. zonta • bridge managers on the verge of a nervous breakdown
structural engineer's naïf perspectivepossible states
D
“Damage”
“no Damage”
U
possible responses
“Alarm”
“no Alarm”
A
¬A
possible actions
“intervention”
“do nothing”
DN
I
d. zonta • bridge managers on the verge of a nervous breakdown
observed real-life manager's behaviorpossible states
D
“Damage”
“no Damage”
U
possible responses
“Alarm”
“no Alarm”
A
¬A
possible actions
“intervention”
“do nothing”
DN
I
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
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?
d. zonta • bridge managers on the verge of a nervous breakdown
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)
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
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"
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
Tom's cost estimate
Pay nothing!!
Do Nothing No damageAND
d. zonta • bridge managers on the verge of a nervous breakdown
Tom's cost estimate
Do Nothing AND SevereDamage
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=$881,600
d. zonta • bridge managers on the verge of a nervous breakdown
cost per state and action
CF
k$ 881.6 0Do Nothing
Close bridge
Damage No Damage
CDT
k$ 139.8CDT
k$ 139.8
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
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
C = min { P(D)·CF , CDT }
Optimal cost
decision criterion
CDT < CDN ?yn
DN
d. zonta • bridge managers on the verge of a nervous breakdown
Tom's prior expectation
CF
k$ 881.6 0Do Nothing
Close bridge
DamageP(D)=30%
No DamageP(U)=70%
CDT
k$ 139.8CDT
k$ 139.8
d. zonta • bridge managers on the verge of a nervous breakdown
decision tree w/o monitoring
DN
D
U
action state cost
0
k$881.6
probability
30%CDN = P(D) · CF= k$264.5
Do Nothing
Close Bridge
Damaged
Undamaged
DN D
U
action: state:LEGEND
expected loss70%
CDT = k$ 139.8downtime cost
d. zonta • bridge managers on the verge of a nervous breakdown
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)
d. zonta • bridge managers on the verge of a nervous breakdown
5.182m 5.232m 5.232m 6.147m5.232m 5.232m6.147m
P3 P4 P5 P6 P7 P8 P9 P10
FBG Strain Sensor
BOTDA Distributed Strain & Temperature Sensor Junction Box
A;BC;D
E
A;B
C;D;E
C;D
E
A;BA;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 NP9
1.524m 1.524m1.249m1.249m
Sensor location in main span
d. zonta • bridge managers on the verge of a nervous breakdown
5.182m 5.232m 5.232m 6.147m5.232m 5.232m6.147m
P3 P4 P5 P6 P7 P8 P9 P10BOTDA 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
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
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(D|) =
P(|U) · P(U)
P()
P(|U) · P(U) P(|D) · P(D)
P(|D) · P(D) =
P(|D) · P(D)
P()+
d. zonta • bridge managers on the verge of a nervous breakdown
decision tree with monitoring
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
d. zonta • bridge managers on the verge of a nervous breakdown
Likelihoods and evidence
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
d. zonta • bridge managers on the verge of a nervous breakdown
Likelihoods and evidence
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
c*()=min { P(D|)CF , CDT }
d. zonta • bridge managers on the verge of a nervous breakdown
Likelihoods and evidence
CDT=k$139.8
CDN = P(D|) · CF
c*()=min { P(D|)CF , CDT }
C*=∫ c*()PDF()d= k$ 84.6
d. zonta • bridge managers on the verge of a nervous breakdown
value of information (VoI)
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
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
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!!
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
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
d. zonta • bridge managers on the verge of a nervous breakdown
general case
ci,kai
sk
scenarioac
tions
a1
aM
s1 sN
M available actions: from a1 to aM
N possible scenario: from s1 to sNcost per state and action
matrix
d. zonta • bridge managers on the verge of a nervous breakdown
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
...
...
...
...
d. zonta • bridge managers on the verge of a nervous breakdown
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
...
...
d. zonta • bridge managers on the verge of a nervous breakdown
value of information (VoI)
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
d. zonta • bridge managers on the verge of a nervous breakdown
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 for the informationthe 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
d. zonta • bridge managers on the verge of a nervous breakdown
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