Bayesian network for infrastructure seismic risk assessment and decision support

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1 Bayesian network for infrastructure seismic risk assessment and decision support Michelle T. Bensi Armen Der Kiureghian University of California, Berkeley Daniel Straub Technical University of Munich

Research motivation Civil infrastructure systems: Are

consequences if disrupted Are vulnerable to

spatially-distributed infrastructure differs from

Subject to multitude of hazards Requires

application of system analysis methods to assess

framework for seismic infrastructure risk assessment

2 Research motivation Civil infrastructure systems: Are logistical backbones of societies Have far-reaching consequences if disrupted Are vulnerable to natural/man-made hazards Risk assessment of spatially-distributed infrastructure differs from point-site components: Higher rate of exposure Subject to multitude of hazards Requires consideration of random field effects Requires application of system analysis methods to assess system reliability Long-term goal: Bayesian network framework for seismic infrastructure risk assessment & decisionsupport Before an event Immediately following an event In the longer term post-event recovery phase

3 Research motivation sensors health monitoring module inspections, expert knowledge, etc. Bayesian network & decision graph network connectivity & flow module hazard module monitoring of gas, power, water, transportation network services structural reliability module recordings of ground motion, shock wave, etc.

4 What is a BN? A probabilistic graphical model that encodes a set of random variables and their probabilistic (in)dependencies: A set of variables (nodes) and directed links Each variable has mutually exclusive states To each variable we attach a CPT representing discrete probabilities Facilitate information updating Highly demanding of computer memory X 1 X 2 X 4 X 3 X 5

5 What is a BN? A probabilistic graphical model that encodes a set of random variables and their probabilistic (in)dependencies: A set of variables (nodes) and directed links Each variable has mutually exclusive states To each variable we attach a CPT representing discrete probabilities Facilitate information updating Highly demanding of computer memory X 1 X 2 X 4 X 3 X 5

6 What is a BN? A probabilistic graphical model that encodes a set of random variables and their probabilistic (in)dependencies: A set of variables (nodes) and directed links Each variable has mutually exclusive states To each variable we attach a CPT representing discrete probabilities Facilitate information updating Highly demanding of computer memory X 1 X 2 X 4 X 3 X 5

7 What is a BN? x1 p(x1) A probabilistic graphical model that encodes a set of random variables and their probabilistic (in)dependencies: A set of variables (nodes) and directed links Each variable has mutually exclusive states To each variable we attach a CPT representing discrete probabilities Facilitate information updating Highly demanding of computer memory X 1 X 2 X 4 X 5 x1 1 x1 p x4 1 x4 q X 3 x5 1 x5 p p(x 5 x 4 )

8 What is a BN? A probabilistic graphical model that encodes a set of random variables and their probabilistic (in)dependencies: A set of variables (nodes) and directed links Each variable has mutually exclusive states To each variable we attach a CPT representing discrete probabilities Facilitate information updating Highly demanding of computer memory X 1 X 2 X 4 X 5 X 3 evidence

9 What is a BN? A probabilistic graphical model that encodes a set of random variables and their probabilistic (in)dependencies: A set of variables (nodes) and directed links Each variable has mutually exclusive states To each variable we attach a CPT representing discrete probabilities Facilitate information updating Highly demanding of computer memory X 1 X 2 X 4 X 5 X 3 evidence

10 What is a BN? A probabilistic graphical model that encodes a set of random variables and their probabilistic (in)dependencies: A set of variables (nodes) and directed links Each variable has mutually exclusive states To each variable we attach a CPT representing discrete probabilities Facilitate information updating Highly demanding of computer memory X 1 X 2 X 4 X 3 X 5

11 Big Picture: BN for seismic infrastructure risk assessment and decision support S C source characterization (Chapter 3) M L eq random field approximations (Chapter 4) ε m S 1 S 2 _ S 3 _ S n random field model ε r S 1 S 2 S 3 S n model of seismic demands at distributed locations (Chapter 3) C 1 C 2 C 3 C n component performance models (Chapter 5) decision support model decision support framework (Chapter 7) S sys system performance model

12 Example (23.5,22) (35,22) (37,22) (50,22) (65,22) source (20,18.5) 1 12 (68.5,18.5) sink Y (23.5,15) (35,15) (37,15) (50,15) (65,15) X (0,0) (120,0) fault Point-site components Distributed components with directed flow Ground motion prediction points

13 (1) Seismic Demand Model X e X r R L M R 1 f d,1 R i f d,i R n f d,n ln( S i ) = f ( M, Ri, fd, i, Xi ) ε m source 1 12 sink Y fault (0,0) X (120,0) ε r,1... ε r,i... ε r,n

14 (1) Seismic Demand Model X e X r R L M R 1 f d,1 R i f d,i R n f d,n ln( S i ) = f ( M, Ri, fd, i, Xi ) ε m source 1 12 sink Y fault (0,0) X (120,0) ε r,1... ε r,i... ε r,n

15 (1) Seismic Demand Model X e X r R L M R 1 f d,1 R i f d,i R n f d,n ln( S i ) = f ( M, Ri, fd, i, Xi ) ε m source 1 12 sink Y fault (0,0) X (120,0) ε r,1... ε r,i... ε r,n

16 (1) Seismic Demand Model X e X r R L M R 1 f d,1 R i f d,i R n f d,n ln( S i ) = f ( M, Ri, fd, i, Xi ) ε m source 1 12 sink Y fault (0,0) X (120,0) ε r,1... ε r,i... ε r,n

17 (1) Seismic Demand Model X e X r R L M R 1 f d,1 R i f d,i R n f d,n ln( S i ) = ln( S i ) + ε m + ε r, i ε m source 1 12 sink Y fault (0,0) X (120,0) ε r,1... ε r,i... ε r,n

18 (1) Seismic Demand Model X e X r R L M R 1 f d,1 R i f d,i R n f d,n ln( S i ) = ln( S i ) + ε m + ε r, i ε m source 1 12 sink Y fault (0,0) X (120,0) ε r,1... ε r,i... ε r,n

19 (1) Seismic Demand Model X e X r R L M R 1 f d,1 R i f d,i R n f d,n ln( S i ) = ln( S i ) + ε m + ε r, i ε m source 1 12 sink Y fault (0,0) X (120,0) ε r,1... ε r,i... ε r,n

20 (1) Seismic Demand Model X e X r R L M R 1 f d,1 R i f d,i R n f d,n Must be modeled as Gaussian random field Densely connected BN Computationally demanding (possibly intractable) ε m source 1 12 sink Y fault (0,0) X (120,0) ε r,1... ε r,i... ε r,n

21 (1) Seismic demand model: Approximation of error correlation ε r,1... ε r,i... ε r,n tt 11 tt 1mm UU 1 εε = TTUU = tt nn1 tt nnnn UU mm U 1 U 2 U 3... U n ε r,1 ε r,2 ε r,3... ε r,n

22 (1) Seismic demand model: Approximation of error correlation ε r,1... ε r,i... ε r,n tt 11 tt 1mm UU 1 εε = TTUU = tt nn1 tt nnnn UU mm U 1 U 2 U 3... U n ε r,1 ε r,2 ε r,3... ε r,n U 1 U 2 U 3... U m ss 1 0 VV 1 tt 11 tt 1mm UU 1 εε = SSSS + TTUU = + 0 ss nn VV nn UU mm tt nn1 tt nnnn ε r,1 ε r,2 ε r,3... ε r,n V 1 V 2 V 3 V... n

23 (2) Component Performance source 1 12 sink Point-site components Distributed components with directed flow Y Ground motion prediction points fault (0,0) X (120,0) Point site components: Distributed components: seismic demand model seismic demand model S 1 S 2... S i-1 S i S i+1... S n-1 S n C... C i... C n C 1,2... C i-1,i C i,i+1... C n-1,n

24 (2) Component Performance source 1 12 sink Point-site components Distributed components with directed flow Y Ground motion prediction points fault (0,0) X (120,0) Point site components: Distributed components: seismic demand model seismic demand model S 1 S 2... S i-1 S i S i+1... S n-1 S n C... C i... C n C 1,2... C i-1,i C i,i+1... C n-1,n CPTs specified using fragility functions (or other analysis methods)

25 (2) Component Performance source 1 12 sink Point-site components Distributed components with directed flow Y Ground motion prediction points fault (0,0) X (120,0) Point site components: Distributed components: seismic demand model seismic demand model S 1 S 2... S i-1 S i S i+1... S n-1 S n C... C i... C n C 1,2... C i-1,i C i,i+1... C n-1,n CPTs specified using performance functions and assuming non-homogenous Poisson process

26 (3) System performance: A collection of system performance BN formulations developed based on: Adaptation of classical systems analysis methods Ease of facilitating third party interaction Issues related to computational efficiency: (a) (b) (c) C 1 C 2... C i... C n C 1 C MLS 1 MLS 2... MLS j... MLS k C i C n C C 2 MCS 1 MCS 2... MCS j... MCS m C i C n S sys S sys S sys

27 (3) System performance: A collection of system performance BN formulations developed based on: Adaptation of classical systems analysis methods Ease of facilitating third party interaction Issues related to computational efficiency: (a) (b) (c) C 1 C 2... C i... C n C 1 C MLS 1 MLS 2... MLS j... MLS k C i C n C C 2 MCS 1 MCS 2... MCS j... MCS m C i C n S sys S sys S sys C 1 C 2... C i... C n E s,1 E s,2... E s,i... E s,n S sys

28 (3) System performance: A collection of system performance BN formulations developed based on: Adaptation of classical systems analysis methods Ease of facilitating third party interaction Issues related to computational efficiency: List of system MLSs or MCSs (obtained from system topology or other system analysis methods, e.g. fault tree) Optimization-based algorithm Efficient system performance BN formulation Heuristically augmented binary optimization algorithm: Automates generation of efficient formulations Increases computational efficiency by order(s) of magnitude C p,1 E f,1 C p,12 E f,12 C d,1,2 E f,1,2 E s,1,3 C d,1, C d,i,j E f,i,j E f,m,n C d,m,n C d,10,12 E f,10,12 E f,11,12 C d,11,12 S sys

29 (3) System Performance source 1 12 sink Y fault (0,0) X (120,0) C p,1 C p,12 C d,1,2 C d,2,4 C p,4 C d,6,8 C d,8,10 C d,10, E s,1 E s,12 E s,1,2 E s,2,4 E s,4 E s,6,8 E s,8,10 E s,10,1 2 S sys E s,5,8 C d,5,8 E s,1,3 E s,3,5 E s,5,7 E s,7 E s,7,9 E s,9,11 E s,11,1 2 C d,1,3 C d,3,5 C d,5,7 C p,7 C d,7,9 C d,9,11 C d,11,1 2

30 (3) System Performance source 1 12 sink Y fault (0,0) X (120,0) C p,1 C p,12 C d,1,2 C d,2,4 C p,4 C d,6,8 C d,8,10 C d,10, E s,1 E s,12 E s,1,2 E s,2,4 E s,4 E s,6,8 E s,8,10 E s,10,1 2 S sys E s,5,8 C d,5,8 E s,1,3 E s,3,5 E s,5,7 E s,7 E s,7,9 E s,9,11 E s,11,1 2 C d,1,3 C d,3,5 C d,5,7 C p,7 C d,7,9 C d,9,11 C d,11,1 2

31 (3) System Performance source 1 12 sink Y fault (0,0) X (120,0) C p,1 C p,12 C d,1,2 C d,2,4 C p,4 C d,6,8 C d,8,10 C d,10, E s,1 E s,12 E s,1,2 E s,2,4 E s,4 E s,6,8 E s,8,10 E s,10,1 2 S sys E s,5,8 C d,5,8 E s,1,3 E s,3,5 E s,5,7 E s,7 E s,7,9 E s,9,11 E s,11,1 2 C d,1,3 C d,3,5 C d,5,7 C p,7 C d,7,9 C d,9,11 C d,11,1 2

32 Example: Information Updating Evidence Cases: (1) A M=6.8 EQ occurs with epicenter located 30km from left end of the fault (2) EC (1) + PGV at GMPP 3 is measured to be 23cm/sec. (3) EC (2) + component is observed to have failed. (4) EC (2) + component is observed to have survived EC(1) EC(2) EC(3) EC(4) C p, C d,1, C d,1, C d,2, C d,3, C d,4, C p, C d,5, C d,5, C p, C d,6, C p, C d,7, C d,8, C d,9, C d,10, C d,11, C p, System source Y fault (0,0) X (120,0) M=6.8 sink

33 Example: Information Updating X e X r R L M R 1 f d,1 R i f d,i R n f d,n ε m S 1 S i S n ε r,1... ε r,i... ε r,n C 1... C i... C n S sys

34 Example: Information Updating X e X r R L M R 1 f d,1 R i f d,i R n f d,n ε m S 1 S i S n ε r,1... ε r,i... ε r,n C 1... C i... C n S sys

35 Example: Information Updating Evidence Cases: (1) A M=6.8 EQ occurs with epicenter located 30km from left end of the fault (2) EC (1) + PGV at GMPP 3 is measured to be 23cm/sec. (3) EC (2) + component is observed to have failed. (4) EC (2) + component is observed to have survived EC(1) EC(2) EC(3) EC(4) C p, C d,1, C d,1, C d,2, C d,3, C d,4, C p, C d,5, C d,5, C p, C d,6, C p, C d,7, C d,8, C d,9, C d,10, C d,11, C p, System source Y fault (0,0) X (120,0) M=6.8 sink

36 Example: Information Updating X e X r R L M R 1 f d,1 R i f d,i R n f d,n ε m S 1 S i S n ε r,1... ε r,i... ε r,n C 1... C i... C n S sys

37 Example: Information Updating X e X r R L M R 1 f d,1 R i f d,i R n f d,n ε m S 1 S i S n ε r,1... ε r,i... ε r,n C 1... C i... C n S sys

38 Example: Information Updating Evidence Cases: (1) A M=6.8 EQ occurs with epicenter located 30km from left end of the fault (2) EC (1) + PGV at GMPP 3 is measured to be 23cm/sec. (3) EC (2) + component is observed to have failed. (4) EC (2) + component is observed to have survived EC(1) EC(2) EC(3) EC(4) C p, C d,1, C d,1, C d,2, C d,3, C d,4, C p, C d,5, C d,5, C p, C d,6, C p, C d,7, C d,8, C d,9, C d,10, C d,11, C p, System source Y fault (0,0) X (120,0) M=6.8 sink

39 Example: Information Updating Evidence Cases: (1) A M=6.8 EQ occurs with epicenter located 30km from left end of the fault (2) EC (1) + PGV at GMPP 3 is measured to be 23cm/sec. (3) EC (2) + component is observed to have failed. (4) EC (2) + component is observed to have survived EC(1) EC(2) EC(3) EC(4) C p, C d,1, C d,1, C d,2, C d,3, C d,4, C p, C d,5, C d,5, C p, C d,6, C p, C d,7, C d,8, C d,9, C d,10, C d,11, C p, System source Y fault (0,0) X (120,0) M=6.8 sink

40 Example: Information Updating X e X r R L M R 1 f d,1 R i f d,i R n f d,n ε m S 1 S i S n ε r,1... ε r,i... ε r,n C 1... C i... C n S sys

41 Example: Information Updating Evidence Cases: (1) A M=6.8 EQ occurs with epicenter located 30km from left end of the fault (2) EC (1) + PGV at GMPP 3 is measured to be 23cm/sec. (3) EC (2) + component is observed to have failed. (4) EC (2) + component is observed to have survived EC(1) EC(2) EC(3) EC(4) C p, C d,1, C d,1, C d,2, C d,3, C d,4, C p, C d,5, C d,5, C p, C d,6, C p, C d,7, C d,8, C d,9, C d,10, C d,11, C p, System source Y fault (0,0) X (120,0) M=6.8 sink

42 Summary sensors health monitoring module inspections, expert knowledge, etc. Bayesian network & decision graph network connectivity & flow module hazard module monitoring of gas, power, water, transportation network services structural reliability module recordings of ground motion, shock wave, etc.

43 Future work Examples for future extensions and refinements may include: Expanded models Source characterization (beyond line source assumption) Liquefaction and fault rupture seismic demand models Revised heuristics for optimization (improve scalability) Discipline specific performance formulations System interdependency More extensive decision formulations Integration with external information sources E.g. structural health monitoring systems Improved algorithms/ formulations (computational issues) Multi-scale modeling Application specific inference algorithms Additional applications (hazards beyond earthquakes) Current/near term Longer term

44 sensors health monitoring module inspections, expert knowledge, etc. Bayesian network & decision graph Thank you network connectivity & flow module monitoring of gas, power, water, transportation network services structural reliability module hazard module recordings of ground motion, shock wave, etc. This material is based upon work supported under the PEER Transportation Research Program, the National Science Foundation Graduate Research Fellowship, and UCB Taisei Chair funds.

A Bayesian Network Methodology for Infrastructure Seismic Risk Assessment and Decision Support

PACIFIC EARTHQUAKE ENGINEERING RESEARCH CENTER PACIFIC EARTHQUAKE ENGINEERING A Bayesian Network Methodology for Infrastructure Seismic Risk Assessment and Decision Support Michelle T. Bensi Department