UC Berkeley, Mar 11, 2013 Bridge managers on the verge of a nervous breakdown Daniele Zonta

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

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

3. 2 states, 2 outcomes, 2 actions possible actions possible observations possible states “intervention” “Alarm” “Damage” D A I “do nothing” “no Alarm” “no Damage” U DN ¬A

4. structural engineer's naïf perspective possible states possible responses possible actions “Alarm” “Damage” “intervention” D A I “no Alarm” “do nothing” “no Damage” ¬A U DN

5. observed real-life manager's behavior possible responses possible states possible actions “Alarm” “Damage” “intervention” D A I “no Alarm” “do nothing” “no Damage” ¬A U DN

6. are bridge manages crazy? • Not necessarily... • 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: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

7. 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?

8. impact of monitoring on decision? • introducing a rational 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 logic • their concen with consequences of wrong action recast the problem in the more general framework of decision theory • benefit of monitoring evaluated using the concept of Value of Information (VoI)

9. Value of Information: 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 value of information (VoI) VoI = C - C* C = operational cost w/o monitoring C* = operational cost with monitoring

10. 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

11. introducing 'Tom' "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

12. possible states of the bridge Severe Damage • 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 No damage

13. Tom's options Do Nothing • 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 Close bridge

14. Tom's cost estimate Close bridge • 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

15. Tom's cost estimate Do Nothing AND No damage • Pay nothing!!

16. Tom's cost estimate Do Nothing AND Severe Damage

17. cost per state and action No Damage Damage Do Nothing CF k$ 881.6 0 Close bridge CDT k$ 139.8 CDT k$ 139.8

18. decision tree w/o monitoring action state cost probability CF P(D) D U 0 P(U) DN CDN = P(D) · CF expected loss CDT downtime cost LEGEND action: state: DN Do Nothing D Damaged Close Bridge U Undamaged

19. decision tree w/o monitoring action state cost probability decision criterion CF P(D) CDT < CDN ? D n y DN U 0 P(U) DN CDN = P(D) · CF expected loss Optimal cost CDT C = min { P(D)·CF , CDT } downtime cost LEGEND action: state: DN Do Nothing D Damaged Close Bridge U Undamaged

20. Tom's prior expectation Damage P(D)=30% No Damage P(U)=70% Do Nothing CF k$ 881.6 0 Close bridge CDT k$ 139.8 CDT k$ 139.8

21. decision tree w/o monitoring action state cost probability k$881.6 30% D CDN = P(D) · CF= k$264.5 U 0 70% expected loss DN CDT = k$ 139.8 downtime cost LEGEND action: state: DN Do Nothing D Damaged Close Bridge U Undamaged

22. 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)

23. Sensor location in main span Junction Box BOTDA Distributed Strain & Temperature Sensor 6.147m 5.232m 5.232m 5.182m 5.232m 5.232m 6.147m P10 P3 P9 P4 P8 P7 P5 P6 A;B C;D C;D A;B A;B A;B A;B E C;D;E E C;D;E C;D FBG Temp. Sensor FBG Strain & Temp. Sensor FBG Strain Sensor 2.178m 2.178m 1.524m 1.524m 1.524m 1.524m 2x0.741m S N S N P8 Close to P10 1.249m 1.524m 1.524m 1.249m S N P7 P9 1.524m 1.524m 2x0.487 P9 S N

24. Sensor location in main span Junction Box BOTDA Distributed Strain & Temperature Sensor 6.147m 5.232m 5.232m 5.182m 5.232m 5.232m 6.147m P10 P3 P9 P4 P8 P7 P5 P6 A;B FBG Strain & Temp. Sensor P7 1.524m 1.524m 2x0.487 S N

25. decision tree with monitoring action state cost posterior probability CF P(D|e) D U 0 P(U|e) DN CDN = P(D|e) · CF e expected loss CDT downtime cost LEGEND action: state: DN Do Nothing D Damaged Close Bridge U Undamaged

26. Likelihoods and evidence P(e|U) · P(U) P(e) P(e|D) · P(D) P7 1.524m 1.524m 2x0.487 S N

27. Likelihoods and evidence P(e|U) · P(U) P(e) P(e|D) · P(D) P(e|D) · P(D) P(e|D) · P(D) P(D|e) = = P(e|U) · P(U) P(e|D) · P(D) P(e) +

28. decision tree with monitoring action state cost posterior probability decision criterion CF D P(D|e) CDT < CDN ? n y DN U 0 P(U|e) DN CDN = P(D|e) · CF e expected loss Optimal cost CDT C = min { P(D|e)·CF , CDT } downtime cost LEGEND action: state: DN Do Nothing D Damaged Close Bridge U Undamaged

29. Likelihoods and evidence P(e|U) · P(U) P(e) P(e|D) · P(D) CDN = P(D|e) · CF DN c*(e)=min { P(D|e)CF , CDT } CDT=k$139.8

30. P(e|U) · P(U) Likelihoods and evidence U D P(e|U) · P(U) P(e|D) · P(D) CDN = P(D|e) · CF DN c*(e)=min { P(D|e)CF , CDT } CDT=k$139.8

31. Likelihoods and evidence c*(e)=min { P(D|e)CF , CDT } C*=∫ c*(e)PDF(e)de= k$ 84.6 CDN = P(D|e) · CF CDT=k$139.8

32. maximum price Tom (the rational agent) is willing to pay for the information from the monitoring system value of information (VoI) VoI = C - C* C=min { P(D)·CF , CDT }= k$ 139.8 C*=∫ c*(e)PDF(e)de= k$ 84.6 VoI = C - C*= k$ 55.2

33. discussion VoI depends on: (i) the expected financial impact of a collapse CF (ii) sensor sensitivity to damage: pdf(e|D) (iii) the prior knowledge of the structure state P(D)

34. 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(e|U) and pdf(e|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

35. strong prior type 1 Trust me, no need to close the bridge, nothing will happen!! • "projected Supermansyndrome" • Tom believe the bridge is invulnerable

36. 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

37. no consequence to the manager I’ll close it – it costs me nothing!! • 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

38. general case M available actions: from a1 to aM cost per state and action matrix N possible scenario: from s1 to sN scenario sk s1 sN a1 ai ci,k actions aM

39. action state cost probability expected cost decision criterion decision tree w/o monitoring c1,1 P(s1) s1 ... c1,k sk P(sk) ... sN c1,N ∑kP(sk)·c1,k P(sN) a1 ... ci,1 P(s1) s1 ... ai ci,k sk P(sk) ... C = min{∑kP(sk)·ci,k} ... i sN ∑kP(sk)·ci,k P(sN) ci,N aM cM,1 P(s1) s1 ... cM,k P(sk) sk ... sN ∑kP(sk)·cM,k P(sN) cM,N

40. outcome action state cost probability expected cost decision criterion decision tree with monitoring c1,1 P(s1|x) s1 ... c1,k sk P(sk|x) ... sN c1,N ∑kP(sk|x) ·c1,k P(sN|x) a1 ... ci,1 P(s1|x) s1 ... X ai ci,k sk P(sk|x) ... C|x = min{∑kP(sk|x)·ci,k} ... sN ∑kP(sk|x)·ci,k i ci,N P(sN|x) aM cM,1 P(s1|x) s1 ... P(sk|x) cM,k sk ... ∑kP(sk|x)·cM,k sN P(sN|x) cM,N

41. maximum price the rational agent is willing to pay for the information from the monitoring system value of information (VoI) VoI = C - C* C = min{∑kP(sk)·ci,k} C* = ∫Dx min{∑kP(sk)· PDF(x|sk)· ci,k}dx depends on: • prior probability of scenarios • consequence of action • reliability of monitoring system

42. conclusions • an economic evaluation of the impact of SHM on decision has been performed • utility of monitoring can be quantified using VoI • VoI is the maximum price the owner is willing to payfor the information from the monitoring system • implies the manager can undertake actions in reaction to monitoring response • depends on: prior probability of scenarios; consequence of actions; reliability of monitoring system

43. 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