A framework for evaluating the impact of structural health monitoring on bridge management

1. IABMAS 2010 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

2. 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.

3. 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. 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.

5. 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

6. cost per state and action Undamaged Damaged Do Nothing Inspection

7. cost per state and action Undamaged Damaged Do Nothing Long downtime (CL) 0 Inspection Short downtime (CS) 0

8. 2 states, 2 outcomes possible states possible responses “Damage” “Alarm” D A “no Damage” “no Alarm” U ¬A

9. ideal monitoring system states responses D A U ¬A

10. ideal monitoring system states responses D A U ¬A modus tollens: [(p→q),¬q] →¬p

11. ideal monitoring allows the manager to always follow the optimal path value of information VoI = C - C* C = operational cost w/o monitoring C* = operational cost with monitoring=0

12. D U DN decision tree w/o monitoring action state cost LEGEND action: state: DN Do Nothing D Damaged I Inspection U Undamaged

13. c/s-a matrix D U CL CL DN 0 0 I 0 CS decision tree w/o monitoring action state cost D U DN LEGEND action: state: DN Do Nothing D Damaged I Inspection U Undamaged

14. c/s-a matrix D U CL DN 0 I 0 CS decision tree w/o monitoring action state cost probability CL P(D) D U 0 P(U) DN LEGEND action: state: DN Do Nothing D Damaged I Inspection U Undamaged

15. decision tree w/o monitoring action state cost probability CL P(D) D U 0 P(U) DN CDN = P(D) · CL expected cost LEGEND action: state: DN Do Nothing D Damaged I Inspection U Undamaged

16. I D U decision tree w/o monitoring action state cost probability CL P(D) D U 0 P(U) DN CDN = P(D) · CL expected cost LEGEND action: state: DN Do Nothing D Damaged I Inspection U Undamaged

17. decision tree w/o monitoring action state cost probability CL P(D) D U 0 P(U) DN CDN = P(D) · CL expected cost I 0 P(D) D U CS P(U) LEGEND CI = P(U) · CS expected cost action: state: DN Do Nothing D Damaged I Inspection U Undamaged

18. CI < CDN ? n y DN I decision tree w/o monitoring action state cost probability decision criterion CL P(D) D U 0 P(U) DN CDN = P(D) · CL I 0 P(D) D U CS P(U) LEGEND CI = P(U) · CS action: state: DN Do Nothing D Damaged I Inspection U Undamaged

19. decision tree w/o monitoring action state cost probability decision criterion CL P(D) CI < CDN ? D n y DN I U 0 P(U) DN CDN = P(D) · CL Optimal cost I 0 P(D) D C = min { CDN , CI } = min { P(D)·CL , P(U)·CS } U CS P(U) LEGEND CI = P(U) · CS action: state: DN Do Nothing D Damaged I Inspection U Undamaged

20. ideal monitoring allows the manager to always follow the optimal path value of information (VoI) VoI = C - C* min { P(D)·CL , P(U)·CS } C = C* = 0 depends on: • prior probability of scenarios • consequence of action

21. non-ideal monitoring system likelihood P(D) P(A|D) D A P(¬A|D) a priori P(A|U) P(U) U ¬A P(¬A|U) states responses

22. decision tree with monitoring outcome A ¬A

23. decision tree with monitoring action state cost test outcome probability CL P(D|A) D CDN | A = P(D|A) · CL U ALARM! 0 P(U|A) DN A I 0 D P(D|A) CI | A = P(U|A) · CS U CS P(U|A) C|A= min { CDN| A, CI| A}

24. decision tree with monitoring action state cost test outcome probability CL P(D|A) D CDN | A = P(A|D) · P(D) · CL U ALARM! 0 P(U|A) P(A) DN A I 0 D P(D|A) CI | A = P(A|U) · P(U) · CS U P(A) CS P(U|A) C|A= min { CDN| A, CI| A}

25. decision tree with monitoring cost given outcome probability of outcome outcome min { P(D)·P(A|D)·CL , P(U)·P(A|U)·CS } C|A P(A) A ¬A min { P(D)·P(¬A|D)·CL , P(U)·P(¬A|U)·CS } C|¬A P(¬A) C* = min { P(D)·P(A|D)·CL , P(U)·P(A|U)·CS } + min { P(D)·P(¬A|D)·CL , P(U)·P(¬A|U)·CS }

26. 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 { P(D)·CL , P(U)·CS } C* = min { P(D)·P(A|D)·CL , P(U)·P(A|U)·CS } + min { P(D)·P(¬A|D)·CL , P(U)·P(¬A|U)·CS }

27. 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

28. 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

29. 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

30. 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

31. 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.

32. 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

33. Bridge the Bill Emerson Memorial Bridge Located approximately 50 miles (80 km) from the New Madrid Seismic Zone.

34. Bridge the Bill Emerson Memorial 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.

35. damage assessment scheme PENN PARAMETER EVALUATOR NEURAL NETWORK ENN EMULATOR NEURAL NETWORK k+1 k DAMAGE INDICES X BRIDGE RESPONSE - RMS k+1

36. 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

37. damage assessment scheme PENN PARAMETER EVALUATOR NEURAL NETWORK ENN EMULATOR NEURAL NETWORK k+1 k DAMAGE INDICES X BRIDGE RESPONSE - RMS k+1

38. 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 . estimation of the VoI Undamaged Damaged

39. 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) estimation of the VoI Undamaged Damaged

40. x 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) estimation of the VoI Undamaged Damaged

41. Application of the VoI Two decision options: - Do-Nothing - Inspection. Assumptions: - prior probability of damage prob(D); - inspection cost CI and undershooting cost CUS. Undamaged Damaged Do Nothing Undershooting Cost (CUS) 0 Inspection Inspection Cost (CI) Inspection Cost (CI)

42. Application of the VoI Two decision options: - Do-Nothing - Inspection. Assumptions: - prior probability of damage prob(D); - inspection cost CI and undershooting cost CUS. Undamaged P(U)=70% Damaged P(D)=30% Do Nothing $ 2M 0 Inspection $ 700k $ 700k

43. decision tree w/o monitoring action state cost probability CUS P(D) D U 0 P(U) DN CDN = P(D) · CL expected cost I CI P(D) D U CI P(U) LEGEND CI expected cost action: state: DN Do Nothing D Damaged I Inspection U Undamaged

44. decision tree w/o monitoring action state cost probability 2M 30% D U 0 70% DN CUS= $ 600k expected cost I 700k 30% D U 700k 70% LEGEND CI= $ 700k expected cost action: state: DN Do Nothing D Damaged I Inspection U Undamaged

45. value of information (VoI) VoI = C - C* C = min{∑kP(sk)·ci,k}= $ 600 k C* = ∫Dx min{∑kP(sk)· PDF(x|sk)· ci,k}dx

46. Likelihoods and evidence Application of the VoI

47. Likelihoods and evidence Application of the VoI Updated probabilities

48. Likelihoods and evidence Application of the VoI Updated probabilities Updated costs

49. value of information (VoI) VoI = C - C* C = min{∑kP(sk)·ci,k}= $ 600 k C* = ∫Dx min{∑kP(sk)· PDF(x|sk)· ci,k}dx= $500k VoI = C - C*= $600k-$500k=$100k

50. conclusions • an economic evaluation of the impact of SHM on BM 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