Information Updating in Infrastructure Systems

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1 University of Washington, Seattle Civil and Environmental Engineering April 10, 2008 Information Updating in Infrastructure Systems Subject to Multiple Hazards Daniel Straub University of California, Berkeley Civil and Environmental Engineering g

2 Vajont Dam, Northern Italy,

3 3

4 Dam failure example: Multi-hazards engineering through Bayesian network 4

5 Dam failure example: Multi-hazards engineering through Bayesian network Bayesian network: nodes are defined through their conditional probability 5

6 Dam failure example: Multi-hazards engineering through Bayesian network Explicitily include additional model parameters These introduce dependence among the hazards 6

7 Dam failure example: Multi-hazards engineering through Bayesian network Include earthquake hazard This introduces additional dependences 7

8 Dam failure example: Multi-hazards engineering through Bayesian network Introduce deterioration hazard 8

9 Dam failure example: Multi-hazards engineering through Bayesian network Include dam inspection 9

10 How does the information updating work? 10

11 How does the information updating work? Rule of Bayes: f ( θ e) Pr ( e θ) f ( θ) 11

12 Dam failure example: Multi-hazards engineering through Bayesian network Hazards : 12

13 Dam failure example: Multi-hazards engineering through Bayesian network Information: 13

14 Avalanche risk analysis Avalanche model: 14

15 Avalanche risk analysis Parameter uncertainty E.g. friction parameter μ 15

16 Avalanche risk analysis Parameter uncertainty E.g. friction parameter μ 16

17 Avalanche risk analysis Observations available (here 50 years) 17

18 Avalanche risk analysis Observations available (here 50 years) 18

Combine (a) & (b) using Bayesian updating Model parameters Avalanche Observation

19 Avalanche risk analysis Probabilistic hazard model from: a) Semi-empirical models are available (FE) b) Observations of past events are available (here: 50 years) Combine (a) & (b) using Bayesian updating Model parameters Avalanche Observation Straub D., Grêt-Regamey A. (2006). Cold Regions Science and Technology, 46(3), pp

20 Avalanche risk analysis Information updating 20

21 Avalanche risk analysis Resulting hazard model (annual exceedance probability) Straub D., Grêt-Regamey A. (2006). Cold Regions Science and Technology, 46(3), pp

22 Avalanche risk assessment Modeling consequences through a Bayesian network Grêt-Regamey A., Straub D. (2006). Natural Hazards and Earth System Sciences, 6(6), pp

23 Avalanche risk assessment Implementation in a GIS environment Regional risk analysis Grêt-Regamey A., Straub D. (2006). Natural Hazards and Earth System Sciences, 6(6), pp

24 Modeling spatial dependences in seismic risk assessment Electrical substation equipement: Performances of individual system components (transformers, circuit it breakers, etc ) exhibit statistical dependence Why? Common uncertain factors introduce dependence, e.g., Local site conditions Characteristics of ground motion beyond PGA Age & condition of system components Identical capacity in subsequent events 24

25 Modeling spatial dependences in seismic risk assessment Results for seismic fragility of electrical substation components Components: Straub D., Der Kiureghian A. (2008). Structural Safety, 30(4), pp

26 Modeling spatial dependences in seismic risk assessment Results for seismic fragility of electrical substation components Redundant system: 10 0 Parallel system TR System fra agility Including dependence Neglecting dependence 10 6 Straub D., Der Kiureghian A. (2008). Structural Safety, 30(4), pp PGA [g] 26

27 Modeling spatial dependences in seismic risk assessment Risk assessment of spatially distributed infrastructure system: 27

28 Modeling spatial dependences in seismic risk assessment Bayesian Probabilistic Hazard Assessment Common factors Spatial random field ed Different locations (bridges, structures, measurements, etc ) Straub D., Bensi M., Der Kiureghian A. (2008). Proc. EM 08 28

29 Modeling spatial dependences in seismic risk assessment Bayesian PSHA result examples: distribution of PGA conditional on observations: Observation: PGA at site 4 equal to 0.75g Straub D., Bensi M., Der Kiureghian A. (2008). Proc. EM 08 29

30 Modeling spatial dependences in seismic risk assessment Examples of Bayesian PSHA results (System failure probabilities) Compare different models (unconditional case): Model Pr(F) No dependence Neglecting error correlation Full model Probability of system failure conditional on observations: Observation Pr(F) Earthquake occurred PGA at site 4 = 0.75g Failure of bridge Straub D., Bensi M., Der Kiureghian A. (2008). Proc. EM 08 30

31 Break What have we seen so far? How to represent uncertainty in complex systems How to use information to update the model Need to explicitly model dependences What will I talk about in the remainder? How much information do we want? Multi-hazard example involving deterioration Where do we go from here? 31

32 How much information do we want? Information is not free We want to optimize the amount of information gathered Example: Inspection planning for structures t subject to fatigue 32

33 Modeling the uncertainty in the physical process Probabilistic model for fatigue deterioration Loads Structural response Fatigue model b 17 d T P [s] /p F = 25yr 1/p F = 100yr 1/p F = 250yr 1/p F = 1000yr H S [m] S da CPa, K a, c dn = dc CPc, Kc a, c dn = Δ ( Δ a( )) ( ( )) m fm m fm 33

34 Modeling the uncertainty in the physical process Probabilistic model of the crack depth at times t: Probability of failure: 34

35 Quality of information Probability of detection model: CRIS JIP (University College London) PoD trials PoD (a) Crack depth a [mm] Straub D. (2002). Proc. PhD Symposium, TU Munich 35

36 Information updating The updated probability of failure after the inspections: Straub D., Faber M.H. (2006). Computer-Aided Civil and Infrastructure Engineering, 21(3), pp

37 Decision modeling Identify decision alternatives Determine consequences (of failure, inspection, repair) Optimal decision: Minimizing the total expected consequences (cost) E n = [ C] Pr( ) i=1 E C i i Straub D., Faber M.H. (2006). Computer-Aided Civil and Infrastructure Engineering, 21(3), pp

38 Optimal inspection effort Straub D., Faber M.H. (2004). J. of Offshore Mechanics and Arctic Engineering, 126(3), pp

39 Practical application through IT implementation iplan software 39

failures A function of structural redundancy

(2008). To be submitted. Straub D., Faber M.H.

40 Multi-hazard: Deterioration and extreme environmental loads Consequence of deterioration failures A function of structural redundancy Complex problem because structural details need to be considered jointly Approach using equivalent systems: Straub D., Der Kiureghian A. (2008). To be submitted. Straub D., Faber M.H. (2005). J. of Offshore Mechanics and Arctic Engineering, 127(2), pp

41 Multi-hazard engineering: Where do we go from here? Today 41

42 Multi-hazard engineering: Where do we go from here? 42

43 Multi-hazard engineering: Where do we go from here? 43

44 Thank you for your attention (Theorist in practice) 44

Bayesian Networks for Modeling and Managing Risks of Natural Hazards

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