QUANTIFYING RESILIENCE-BASED IMPORTANCE MEASURES USING BAYESIAN KERNEL METHODS

Transcription

1 QUANTIFYING RESILIENCE-BASED IMPORTANCE MEASURES USING BAYESIAN KERNEL METHODS Hiba Baroud, Ph.D. Civil and Environmental Engineering Vanderbilt University Thursday, May 19, 2016

2 WHAT IS RESILIENCE? Photo: Marco Monetti

3 HOW DID IT START? Hosseini, S., Barker, K. and Ramirez-Marquez, J.E., A review of definitions and measures of system resilience. Reliability Engineering & System Safety, 145, pp

4 WHY IS IT IMPORTANT? 4

5 WHY IS IT IMPORTANT? Hosseini, S., Barker, K. and Ramirez-Marquez, J.E., A review of definitions and measures of system resilience. Reliability Engineering & System Safety, 145, pp

6 WHAT IS THE DEFINITION OF RESILIENCE? A resilient infrastructure sector would rapidly recover and reconstitute critical assets, operations, and services with minimum damage and disruption. Infrastructure Security Partnership Resilience is the ability of assets, networks and systems to anticipate, absorb, adapt to and/or rapidly recover from a disruptive event. Cabinet Of fice, UK Infrastructure resilience is the ability to reduce the magnitude and/or duration of disruptive events National Infrastructure Advisory Council There are almost as many definitions of resilience as there are people defining it. Congressional Research Service Report for Congress 6

7 HOW DO WE MEASURE IT? Hosseini, S., Barker, K. and Ramirez-Marquez, J.E., A review of definitions and measures of system resilience. Reliability Engineering & System Safety, 145, pp

8 BEFORE A DISRUPTION Risk Management Planning and preparedness decision making Risk mitigation Henry, D. and J.E. Ramirez-Marquez Generic Metrics and Quantitative Approaches for System Resilience as a Function of Time. Reliability Engineering and System Safety, 99(1):

9 AFTER A DISRUPTION Recover y management Post-disaster strategies Stochastic behavior of recover y Henry, D. and J.E. Ramirez-Marquez Generic Metrics and Quantitative Approaches for System Resilience as a Function of Time. Reliability Engineering and System Safety, 99(1):

10 RESILIENCE-BASED CIM Component importance measures (CIM) Commonly found in risk and reliability engineering Extended to resilience analysis Impact of a component on the resilience of the system How is the recovery of the entire system impacted by the recovery of a component? Barker, K., J.E. Ramirez-Marquez, and C.M. Rocco Resilience-Based Network Component Importance Measures. Reliability Engineering and System Safety, 117(1), Baroud, H., K. Barker, J.E. Ramirez-Marquez, and C.M. Rocco Importance Measures for Inland Waterway Network Resilience. Transportation Research Part E: Logistics and Transportation, 62(1):

11 RESILIENCE-BASED CIM CIЯ φ,i t r e j = Network performance loss due to disruption of component i φ x t 0 φ x t 0, x i t d V i j max i φ x t 0 φ x t 0, x i t d V i j Time to full network restoration T φ x t0 V i j Maximum loss among all the components 11

12 RESILIENCE WORTH INDEX Time to total network recover y Time to total network recovery when component i is invulnerable WЯ φ,i t r e j = T φ x t0 V i j T φ x t0 V i j =0 T φ x t0 V i j 0 < WЯ φ,i t r e j < 1 12

13 ASCE REPORT CARD ON AMERICA S INFRASTRUCTURE The average age of the 84,000 dams in the country is 52 years old By 2020, 70% of the total dams in the United States will be over 50 years old A S C E s R e p o r t C a r d f o r A m e r i c a s I n f r a s t r u c t u r e [ ] 13

14 WHY INLAND WATERWAYS? Over 200 lock chambers Over 566 million tons of freight (~51 million truck trips) Over $152 billion equivalence of goods Low-cost and fuel-efficient freight mode 15-barge grain tow, hauling approximately 22,500 tons of export grain, exits Lock & Dam 13 14

15 PLAN OF ACTION The dam safety engineering practice is moving towards a risk-based decision-making process for the design, rehabilitation, and operation of dams. Risk-based decisions enable the dam owner to better utilize limited funding, and prioritize projects, by focusing on repairs and operational changes that reduce risk to acceptable levels, thus improving community resilience. ASCE s Report Card for America s Infrastructure [2013] 15

16 SIMULATION APPROACH Probability distribution for the magnitude of disruption and speed of recovery Simulation Probability distribution for the resilience based CIM P a < V i j b = P t s < U i j V i j a b f v i j dv i j t r = t s t r f ui j V i j f WЯ F,i t r e j dv i j

17 STOCHASTIC RANKING OF COMPONENTS CIЯ φ,i WЯ φ,i Baroud, H., K. Barker, J.E. Ramirez-Marquez, and C.M. Rocco Importance Measures for Inland Waterway Network Resilience. Transportation Research Part E: Logistics and Transportation, 62(1):

18 DATA-DRIVEN APPROACH Lock & Dam Closure Frequency River Mile Vessels Tonnage Lockages... L&D ,397 6,747 4,406 L&D ,810 14,545 3,155 L&D ,478 6,735 2,893 L&D ,508 20,828 3,582 L&D ,280 22,476 3,486 L&D ,333 10,277 2, US Army Corps of Engineers Interactive access to website. 18

19 DATA-DRIVEN APPROACH Prior distribution (prior knowledge, expertise) Bayesian kernel model (binary historical data, attributes) Posterior distribution of the resilience worth f WЯ F,i t r e j

20 BETA BAYESIAN KERNEL MODEL Prior θ i y~beta(α, β) Posterior α = α + m k(x m i, x j ) {j yj =1} β = β + m + m {j y j= 1} k(x i, x j ) m = number of negative labels in training set m + = number of positive labels in training set m = size of training set k = kernel function of x i and x j MacKenzie, C.A., T.B. Trafalis, and K. Barker A Bayesian Beta Kernel Model for Binary Classification and Online Learning Problems Statistical Analysis and Data Mining, 7(6),

21 RISK ANALYSIS USING THE RESILIENCE WORTH Expected value of the posterior distribution WЯ φ,i t r e j = θ i = α α + β Posterior probability distribution f WЯ φ,i t r e j = WЯα 1 1 WЯ β 1 Β α, β 21

22 PREDICTION ACCURACY UNWEIGHTED MODEL TP=0.89 TN=0.48 ACC=0.55 TP=0.79 TN=0.79 ACC=0.70 TP=0.21 TN=0.96 ACC=0.26 TP=0.99 TN=0.12 ACC=

23 PREDICTION ACCURACY WEIGHTED MODEL TP=0.85 TN=0.75 ACC=0.76 TP=0.75 TN=0.86 ACC=0.68 TP=0.21 TN=0.96 ACC=0.01 TP=0.96 TN=0.27 ACC=

24 INTERPRETABILITY Rank components based on their resilience Identify critical components for resource allocation of preparedness and recovery strategies Incorporate uncertainty into the decision Integrate the decision maker s expertise and risk attitude 24

25 INTERPRETABILITY ACC=0.65 ACC=0.68 ACC=

26 POSTERIOR CUMULATIVE DISTRIBUTION Posterior cumulative distribution for the 5 most impactful locks and dams according to the posterior expected value 26

27 COPELAND SCORE METHOD Copeland score method: a multi-criteria decision analysis technique Comparing discrete objects a and b C k a, b = C k 1 a, b + 1 q k a < q k b C k 1 a, b 1 q k a > q k b C k 1 a, b q k a = q k b Copeland Score of object a CS a = b a C Ω a, b 27

28 RANKING OF COMPONENTS Different ranking of components when the entire probability distribution is considered WЯ ranking Posterior expected value Posterior Copeland score 1 L&D 24 L&D 22 2 L&D 5 L&D 27 3 L&D 27 L&D 20 4 L&D 20 L&D 5 5 L&D 22 L&D 24 28

29 CONCLUDING REMARKS Conclusions Data-driven and Bayesian methods integrate historical information with the decision maker s opinion Posterior probability distributions are more flexible, comprehensive, and informative for risk-based decision making Prediction accuracy and interpretability of results are highly sensitive to the definition of the prior distribution A better prediction accuracy does not necessarily mean a better interpretability Future Research Investigate a more realistic identification of the prior based on prior knowledge and empirical estimation Study the tradeoff between prediction accuracy and interpretability and decision making 29

30 END OF PRESENTATION contact: learn 30