1. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision Streicker Bridge: The impact of monitoring on decision Daniele Zonta University of Trento Branko Glisic, Sigrid Adrianssens Princeton University SPIE Smart Structures / NDE San Diego, Mar 15, 2012

2. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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. rational framework  we propose a rational framework to quantitatively estimate the monitoring systems, taking into account their impact on decision making.

3. 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?

4. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision value of information (VoI) VoI = C - C* operational cost w/o monitoring C = operational cost with monitoring C* = decision theory  recast the problem in the general framework of decision theory [Pozzi et. al 2010, Pozzi & De Kiureghian 2011]  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

5. 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

6. 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"

7. 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 Severe Damage No damage

8. 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

9. 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 C DT =4660 x 30 = $139,800 Close bridge

10. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision Tom's cost estimate  Pay nothing!! Do NothingNo damage AND

11. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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

12. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision cost per state and action C F k$ 881.6 0 Do Nothing Close bridge Damage No Damage C DT k$ 139.8 C DT k$ 139.8

13. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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

14. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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

15. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision Tom's prior expectation C F k$ 881.6 0 Do Nothing Close bridge Damage P(D)=30% No Damage P(U)=70% C DT k$ 139.8 C DT k$ 139.8

16. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision decision tree w/o monitoring DN D U actionstatecost 0 k$881.6 probability 30% C DN = P(D) · C F = k$264.5 Do Nothing Close Bridge Damaged Undamaged DND U action:state: LEGEND expected loss 70% C DT = k$ 139.8 downtime cost

17. 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)

18. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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 P7 1.524m 2x0.487 SN P8 1.524m 2x0.741m SN Close to P10 1.524m 2.178m 1.524m FBG Temp. Sensor FBG Strain & Temp. Sensor P9 SN 1.524m 1.249m Sensor location in main span

19. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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 P7 1.524m 2x0.487 FBG Strain & Temp. Sensor Sensor location in main span

20. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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 

21. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision Likelihoods and evidence P(  |D) · P(D) P(  |U) · P(U) P(  ) SN P7 1.524m 2x0.487

22. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision Likelihoods and evidence P(  |D) · P(D) P(D|  ) = P(  |U) · P(U) P(  ) P(  |U) · P(U) P(  |D) · P(D) = P(  ) +

23. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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

24. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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

25. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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 }

26. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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

27. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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$ 139.8 C*=∫ c*(  )PDF(  )d  = k$ 84.6 VoI = C - C*=k$ 55.2

28. 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 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

29. 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

30. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision Thanks. Questions?

31. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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

32. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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...

33. zonta, glisic & adriaenssens streicker bridge: the impact of monitoring on decision 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...

34. 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(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