streicker bridge: the impact of monitoring on decision daniele zonta university of trento
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SPIE Smart Structures / NDE • San Diego, Mar 15, 2012. Streicker Bridge: The impact of monitoring on decision Daniele Zonta University of Trento Branko Glisic, Sigrid Adrianssens Princeton University. impact of monitoring on decision?. - PowerPoint PPT PresentationTRANSCRIPT
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
Streicker Bridge: The impact of Streicker Bridge: The impact of monitoring on decisionmonitoring on decision
Daniele ZontaDaniele ZontaUniversity of TrentoUniversity of Trento
Branko Glisic, Sigrid Adrianssens Branko Glisic, Sigrid Adrianssens Princeton UniversityPrinceton University
SPIE Smart Structures / NDE • San Diego, Mar 15, 2012
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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.
we propose a rational frameworkrational framework to quantitatively estimate the monitoring systems, taking into account their impact on decision making.
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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?
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
value of information (VoI)
VoI = C - C*operational cost w/o monitoringC =operational cost with monitoringC* =
recast the problem in the general framework of decision decision theorytheory [Pozzi et. al 2010, Pozzi & De Kiureghian 2011]
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 to actions in reaction to monitoringmonitoring response
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
Streicker Bridge at PU campus New pedestrian bridge being built at Princeton University campus over the
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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"
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
Tom's cost estimate
Pay nothing!!
Do Nothing No damageAND
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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=$881,600
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
cost per state and action
CF
k$ 881.6 0Do Nothing
Close bridge
Damage No Damage
CDT
k$ 139.8CDT
k$ 139.8
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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)
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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()+
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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 }
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
Likelihoods and evidence
CDT=k$139.8
CDN = P(D|) · CF
c*()=min { P(D|)CF , CDT }
C*=∫ c*()PDF()d= k$ 84.6
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
Thank you for your attention!Acknowledgments
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, UC Berkeley Ivan Bartoli, 'Tom', Drexel University
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
Thanks. Questions?
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
...
...
...
...
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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
...
...
zonta, glisic & adriaenssens • streicker bridge: the impact of monitoring on decision
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