d. zonta bridge managers on the verge of a nervous breakdown UC Berkeley, Mar 11, 2013 Bridge managers on the verge of a nervous breakdown Daniele Zonta University of Trento – Italy

d. zonta bridge managers on the verge of a nervous breakdown impact of monitoring on decision? permanent monitoring of bridges permanent monitoring of bridges is commonly presented as a powerful tool supporting transportation agencies’ decisions very skeptical  in real-life bridge owners are very skeptical  take decisions based on their experience or on common sense the action suggested  often disregard the action suggested by instrumental damage detection

d. zonta bridge managers on the verge of a nervous breakdown 2 states, 2 outcomes, 2 actions possible statespossible observations D “Damage” “no Damage” “Alarm” “no Alarm” U A ¬A¬A possible actions “intervention” “do nothing” DN I

d. zonta bridge managers on the verge of a nervous breakdown structural engineer's naïf perspective possible states D “Damage” “no Damage” U possible responses “Alarm” “no Alarm” A ¬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 behavior possible states D “Damage” “no Damage” U possible responses “Alarm” “no Alarm” A ¬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...  First weight experienceprior perception  First: monitoring is affected by uncertainties so managers weight differently the outcomes of the monitoring based on their experience and prior perception of the state of the structure  Second consequences of wrong action  Second: owners are concerned with the consequences of wrong action, 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? rational framework  introducing a rational framework to quantitatively estimate the benefit monitoring systems, taking into account their impact on decision making Bayesian logic  managers' prior perception can be addressed formally by using Bayesian logic decision theory  their concen with consequences of wrong action recast the problem in the more general framework of decision theory Value of Information  benefit of monitoring evaluated using the concept of 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 monitoring C = operational cost with monitoring C* =  Value of Information  Value of Information: money saved every time the manager interrogates the monitoring system pricewilling to pay  maximum price the rational agent is willing to pay for the information from the monitoring system actions in reaction to monitoring  implies the manager can undertake actions in reaction to 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 Severe Damage 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 C DT =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 NothingNo damage AND

d. zonta bridge managers on the verge of a nervous breakdown Tom's cost estimate Do Nothing AND Severe Damage 2 month DRUC$279,600 cost of fatality: k$ 3840 chance of fatality: 15% $576,000 cost of injury: k$ 52 chance of injury: 50% $26,000 total failure costC F =$881,600

d. zonta bridge managers on the verge of a nervous breakdown cost per state and action C F k$ Do Nothing Close bridge Damage No Damage C DT k$ C DT k$ 139.8

d. zonta bridge managers on the verge of a nervous breakdown decision tree w/o monitoring DN D U actionstatecost 0 CFCF probability P(D) C DN = P(D) · C F Do Nothing Close Bridge Damaged Undamaged DND U action:state: LEGEND expected loss P(U) C DT downtime cost

d. zonta bridge managers on the verge of a nervous breakdown decision tree w/o monitoring DN D U actionstatecost 0 CFCF probability P(D) C DN = P(D) · C F Do Nothing Close Bridge Damaged Undamaged DND U action:state: LEGEND expected loss P(U) C DT downtime cost C = min { P(D)·C F, C DT } Optimal cost decision criterion C DT < C DN ? yn DN

d. zonta bridge managers on the verge of a nervous breakdown Tom's prior expectation C F k$ Do Nothing Close bridge Damage P(D)=30% No Damage P(U)=70% C DT k$ C DT k$ 139.8

d. zonta bridge managers on the verge of a nervous breakdown decision tree w/o monitoring DN D U actionstatecost 0 k$881.6 probability 30% C DN = P(D) · C F = k$264.5 Do Nothing Close Bridge Damaged Undamaged DND U action:state: LEGEND expected loss 70% C DT = k$ downtime 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 5.182m5.232m 6.147m5.232m 6.147m P3 P4 P5 P6 P7 P8 P9 P10 FBG Strain Sensor BOTDA Distributed Strain & Temperature Sensor Junction Box A;B C;D E A;B C;D;E C;D E A;BA;B A;B C;D;E A;B C;D SN P m 2x0.487 SN P m 2x0.741m SN Close to P m 2.178m 1.524m FBG Temp. Sensor FBG Strain & Temp. Sensor P9 SN 1.524m 1.249m Sensor location in main span

d. zonta bridge managers on the verge of a nervous breakdown 5.182m5.232m 6.147m5.232m 6.147m P3 P4 P5 P6 P7 P8 P9 P10 BOTDA Distributed Strain & Temperature Sensor Junction Box A;B SN P m 2x0.487 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 actionstatecost 0 CFCF posterior probability P(D|  ) C DN = P(D|  ) · C F Do Nothing Close Bridge Damaged Undamaged DND U action:state: LEGEND expected loss P(U|  ) C DT downtime cost 

d. zonta bridge managers on the verge of a nervous breakdown Likelihoods and evidence P(  |D) · P(D) P(  |U) · P(U) P(  ) SN P m 2x0.487

d. zonta bridge managers on the verge of a nervous breakdown Likelihoods and evidence P(  |D) · P(D) P(D|  ) = P(  |U) · P(U) P(  ) P(  |U) · P(U) P(  |D) · P(D) = P(  ) +

d. zonta bridge managers on the verge of a nervous breakdown decision tree with monitoring DN D U actionstatecost 0 CFCF posterior probability P(D|  ) Do Nothing Close Bridge Damaged Undamaged DND U action:state: LEGEND expected loss P(U|  ) C DT downtime cost  C = min { P(D|  )·C F, C DT } Optimal cost decision criterion C DT < C DN ? yn DN C DN = P(D|  ) · C F

d. zonta bridge managers on the verge of a nervous breakdown Likelihoods and evidence P(  |D) · P(D) P(  |U) · P(U) C DT =k$139.8 C DN = P(D|  ) · C F c*(  )=min { P(D|  )C F, C DT } P(  ) DN

d. zonta bridge managers on the verge of a nervous breakdown Likelihoods and evidence P(  |D) · P(D) P(  |U) · P(U) C DT =k$139.8 P(  |U) · P(U) DN D U C DN = P(D|  ) · C F c*(  )=min { P(D|  )C F, C DT }

d. zonta bridge managers on the verge of a nervous breakdown Likelihoods and evidence C DT =k$139.8 C DN = P(D|  ) · C F c*(  )=min { P(D|  )C F, C DT } C*=∫ c*(  )PDF(  )d  = k$ 84.6

d. zonta bridge managers on the verge of a nervous breakdown value of information (VoI) VoI = C - C* pricewilling to pay  maximum price Tom (the rational agent) is willing to pay for the information from the monitoring system C=min { P(D)·C F, C DT }=k$ 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 C F (ii) sensor sensitivity to damage: pdf(  |D) (iii) the prior knowledge of the structure state P(D)

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

d. zonta bridge managers on the verge of a nervous breakdown strong prior type 1  "projected Superman syndrome"  Tom believe the bridge is invulnerable 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 Too dangerous, I’d better close the bridge anyway!!!  over-concerned Tom  believes that the bridge is highly vulnerable to truck collision

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 I’ll close it – it costs me nothing!!

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

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

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

d. zonta bridge managers on the verge of a nervous breakdown value of information (VoI) VoI = C - C* pricewilling to pay  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

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 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

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