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Streicker Bridge: The impact of monitoring on decision Daniele Zonta University of Trento

SPIE Smart Structures / NDE • San Diego, Mar 15, 2012. Streicker Bridge: The impact of monitoring on decision Daniele Zonta University of Trento Branko Glisic, Sigrid Adrianssens Princeton University. impact of monitoring on decision?.

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Streicker Bridge: The impact of monitoring on decision Daniele Zonta University of Trento

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  1. SPIE Smart Structures / NDE • San Diego, Mar 15, 2012 Streicker Bridge: The impact of monitoring on decision Daniele Zonta University of Trento Branko Glisic, Sigrid Adrianssens Princeton University

  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. • 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. recast the problem in the general framework of decision theory [Pozzi et. al 2010, Pozzi & De Kiureghian 2011] • 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

  5. 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. 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

  7. 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

  8. 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

  9. 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

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

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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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. 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

  19. 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

  20. 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

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

  22. 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) +

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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. Thanks. Questions?

  31. 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

  32. 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

  33. 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

  34. 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

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