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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 Matteo Pozzi & Daniele Zonta University of Trento Wenjian Wang Weidlinger Associates Inc., Cambridge, MA Genda Chen Missouri University of Science and Technology IABMAS 2010

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS motivation permanent 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.

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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?

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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.

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS value of information (VoI) VoI = C - C* operational cost w/o monitoring C = operational cost with monitoring C* = 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

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS cost per state and action Do Nothing Inspection Damaged Undamaged

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS cost per state and action Long downtime (C L ) 0 Do Nothing Inspection Damaged Undamaged Short downtime (C S ) 0

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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¬A

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS ideal monitoring system D U A ¬A¬A statesresponses

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS ideal monitoring system D U A ¬A¬A statesresponses modus tollens: [(p → q),¬q] →¬p

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS value of information VoI = C - C* operational cost w/o monitoring C = operational cost with monitoring=0 C* = ideal monitoring allows the manager to always follow the optimal path

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree w/o monitoring DN D U actionstatecost Do Nothing Inspection Damaged Undamaged DND U action:state: LEGEND I

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree w/o monitoring DN D U actionstatecost Do Nothing Inspection Damaged Undamaged DND U action:state: LEGEND CLCL 0 0 CSCS DN I D U c/s-a matrix CLCL 0 I

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree w/o monitoring DN D U actionstatecost 0 CLCL probability P(D) P(U) Do Nothing Inspection Damaged Undamaged DND U action:state: LEGEND CLCL 0 0 CSCS DN I D U c/s-a matrix I

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree w/o monitoring DN D U actionstatecost 0 CLCL probability P(D) P(U) C DN = P(D) · C L Do Nothing Inspection Damaged Undamaged DND U action:state: LEGEND expected cost I

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree w/o monitoring DN D U actionstatecost 0 CLCL probability P(D) P(U) I D U C DN = P(D) · C L Do Nothing Inspection Damaged Undamaged DN I D U action:state: LEGEND expected cost

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree w/o monitoring DN D U actionstatecost 0 CLCL probability P(D) P(U) D U CSCS 0 P(D) P(U) C DN = P(D) · C L C I = P(U) · C S Do Nothing Inspection Damaged Undamaged DND U action:state: LEGEND expected cost I I

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree w/o monitoring DN D U actionstatecost 0 CLCL probability P(D) P(U) D U CSCS 0 P(D) P(U) C DN = P(D) · C L C I = P(U) · C S Do Nothing Inspection Damaged Undamaged DND U action:state: LEGEND decision criterion C I < C DN ? yn I DN I I

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree w/o monitoring DN D U actionstatecost 0 CLCL probability P(D) P(U) D U CSCS 0 P(D) P(U) C DN = P(D) · C L C I = P(U) · C S C = min { C DN, C I } = min { P(D)·C L, P(U)·C S } Optimal cost Do Nothing Inspection Damaged Undamaged DND U action:state: LEGEND decision criterion C I < C DN ? yn I DN I I

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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)·C L, P(U)·C S } depends on: prior probability of scenarios consequence of action

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS non-ideal monitoring system D U A ¬A¬A P(A|D)P(A|D) P(¬A|U)P(¬A|U) P(A|U)P(A|U) P(¬A|D)P(¬A|D) likelihood statesresponses a priori P(D) P(U)P(U)

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree with monitoring A outcome ¬ A¬ A

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree with monitoring DN D U actionstatecost 0 CLCL probability A ALARM! test outcome P(D|A) P(U|A) D U CSCS 0 C |A = min { C DN | A, C I | A } I P(D|A) P(U|A) C I | A = P(U|A) · C S C DN | A = P(D|A) · C L

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree with monitoring DN D U actionstatecost 0 CLCL probability A ALARM! test outcome P(D|A) P(U|A) D U CSCS 0 C |A = min { C DN | A, C I | A } I P(D|A) P(U|A) C I | A = P(A|U) · P(U) · C S C DN | A = P(A|D) · P(D) · C L P(A)

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree with monitoring A outcome ¬ A¬ A cost given outcome C|AC|A C|¬AC|¬A C* = min { P(D)·P(A|D)·C L, P(U)·P(A|U)·C S } + min { P(D)·P(¬A|D)·C L, P(U)·P(¬A|U)·C S } min { P(D)·P(A|D)·C L, P(U)·P(A|U)·C S } min { P(D)·P(¬A|D)·C L, P(U)·P(¬A|U)·C S } probability of outcome P(A) P(¬A)

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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)·C L, P(U)·P(A|U)·C S } + min { P(D)·P(¬A|D)·C L, P(U)·P(¬A|U)·C S } maximum price the rational agent is willing to pay for the information from the monitoring system C=min { P(D)·C L, P(U)·C S }

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS general case c i,k aiai sksk scenario actions a1a1 aMaM s1s1 sNsN M available actions: from a 1 to a M N possible scenario: from s 1 to s N cost per state and action matrix

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree w/o monitoring a1a1 actionstatecost c 1,1 probability P(s 1 ) c 1,k s1s1 sNsN sksk aiai aMaM c 1,N... c i,1 c i,k s1s1 sNsN sksk c i,N... c M,1 c M,k s1s1 sNsN sksk c M,N... P(s k ) P(s N ) P(s 1 ) P(s k ) P(s N ) P(s 1 ) P(s k ) P(s N ) C = min { ∑ k P(s k )·c i,k }... i decision criterion ∑ k P(s k )·c 1,k ∑ k P(s k )·c i,k ∑ k P(s k )·c M,k expected cost...

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree with monitoring a1a1 statecost c 1,1 probability P(s 1 |x) c 1,k s1s1 sNsN sksk aiai aMaM... c 1,N... c i,1 c i,k s1s1 sNsN sksk c i,N... c M,1 c M,k s1s1 sNsN sksk c M,N... C |x = min { ∑ k P(s k |x)·c i,k }... i decision criterion ∑ k P(s k |x) ·c 1,k ∑ k P(s k |x)·c i,k ∑ k P(s k |x)·c M,k expected cost outcome X P(s k |x) P(s N |x) P(s 1 |x) P(s k |x) P(s N |x) P(s 1 |x) P(s k |x) P(s N |x) action...

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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(s k )·c i,k } C* = ∫ D x min { ∑ k P(s k )· PDF(x|s k )· c i,k }dx depends on: prior probability of scenarios consequence of action reliability of monitoring system

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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.

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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

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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

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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.

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS PENN PARAMETER EVALUATOR NEURAL NETWORK NEURAL NETWORK damage assessment schemeENNEMULATOR NEURAL NETWORK -RMS k k+1 DAMAGEINDICESX BRIDGERESPONSE

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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

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS PENN PARAMETER EVALUATOR NEURAL NETWORK NEURAL NETWORK damage assessment schemeENNEMULATOR NEURAL NETWORK -RMS k k+1 DAMAGEINDICESX BRIDGERESPONSE

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS estimation of the VoI Two 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. Damaged Undamaged

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS estimation of the VoI Two 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) Damaged Undamaged

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS estimation of the VoI Two 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) Damaged Undamaged x

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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 C I and undershooting cost C US. Inspection Cost (C I ) 0 Do Nothing Inspection Damaged Undamaged Undershooting Cost (C US ) Inspection Cost (C I )

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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 C I and undershooting cost C US. $ 700k 0 Do Nothing Inspection Damaged P(D)=30% Undamaged P(U)=70% $ 2M $ 700k

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree w/o monitoring DN D U actionstatecost 0 C US probability P(D) P(U) D U CICI P(D) P(U) C DN = P(D) · C L CICI Do Nothing Inspection Damaged Undamaged DND U action:state: LEGEND expected cost I I CICI

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS decision tree w/o monitoring DN D U actionstatecost 0 2M probability 30% 70% D U 30% 70% C US = $ 600k C I = $ 700k Do Nothing Inspection Damaged Undamaged DND U action:state: LEGEND expected cost I I 700k

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS value of information (VoI) VoI = C - C* C = min { ∑ k P(s k )·c i,k }= $ 600 k C* = ∫ D x min { ∑ k P(s k )· PDF(x|s k )· c i,k }dx

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS Application of the VoI Likelihoods and evidence

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS Application of the VoI Likelihoods and evidence Updated probabilities

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS Application of the VoI Likelihoods and evidence Updated probabilities Updated costs

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS value of information (VoI) VoI = C - C* C = min { ∑ k P(s k )·c i,k }= $ 600 k C* = ∫ D x min { ∑ k P(s k )· PDF(x|s k )· c i,k }dx= $500k VoI = C - C*= $600k-$500k=$100k

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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 VoI utility of monitoring can be quantified using VoI pricewilling to payfor the information VoI is the maximum price the owner is willing to pay for the information from the monitoring system implies the manager can undertake actions in reaction to monitoring response prior probability consequencereliability of monitoring depends on: prior probability of scenarios; consequence of actions; reliability of monitoring system

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pozzi, zonta, wang & chen evaluating the impact of SHM on BMS Thanks. Questions?

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