Domino Effect Modeling using Bayesian Network

Transcription

1 Domino Effect Modeling using Bayesian Network Dr. Faisal Khan Associate Dean (Global Engagement) University of Tasmania, Australia Vale Research Chair Safety and Risk Engineering Memorial University, St. John s, NL, Canada

2 Outline Domino effect definition Available approaches Fundamental of Bayesian Network Application of BN to Domino Effect Modellin Conclusions

3 Domino effect History: Domino effect reported since early sixties Domino effect intensity and likelihood have increased significantly over last three decades First encounter with DE modeling: Process Safety Progress, 17 (2), , 1998 Testing of the concept, HPCL refinery, India: Process Safety Progress, 19(1), 40 57, 2000

4 Domino Effect: Definition A primary accident in a unit propagates to neighboring units (propagation), triggering secondary accidents (escalation). The consequences are much more severe than the primary accident.

5 Domino Effect: Mechanism Fire or explosion in a unit causes escalation vectors. Escalation vectors can be heat radiation, overpressure, or projectile debris. Escalation vectors cause damages to other units (propagate accident). Damaged units contribute to the primary accident.

6 Domino Effect: Modeling Primary unit and possible accident scenarios are determined using QRA methods. Escalation vectors and their intensity are determined based on the type of primary accident and the substance involved. Escalation and propagation probabilities are determined using empirical and dose effect relationships.

7 Domino Effect Modelling Approaches Analytical Empirical Analytical model for escalation Empirical model for likelihood, probit Analytical Logical Empirical Analytical model for escalation Logical model for causation and propagation Empirical model for likelihood Analytical Probabilistic Analytical model for escalation Probabilistic model for propagation

8 Bayesian Network: semantics A: Root node B: Child of A; parent of C and D C: Child of A and B; parent of D D: Leaf node

9 Bayesian Network: Definition Nodes represent random variables. Arcs represent direct dependencies. Conditional probability tables determine the type of these dependencies.

10 Bayesian Network: Formulation

11 Bayesian network: Application To model conditional dependencies and cause effect relationships. To model complex and interlinked systems To update probabilities To deal with sparse data and subjective probabilities To data mining and machine learning

12 Application of Bayesian network: Alternative to Fault tree Fault tree Bayesian network

13 Application of Bayesian network: Alternative to Event tree Event tree Bayesian network

14 Application of Bayesian network: Alternative to Bow tie Bow tie Bayesian network

15 Application of Bayesian network to domino effects

16 Application of Bayesian network to domino effects Each unit is illustrated by a node in the Bayesian network. T1 is determined as the primary unit (colored in yellow). The most credible accident scenario for T1 is considered to be a pool fire (primary accident). Escalation vector is identified as heat radiation.

17 Application of Bayesian network to domino effects Based on the threshold value for heat radiation and distances, T2 is more likely to be affected by T1. Thus, T1 is connected to T2, showing their cause effect relationship. The conditional probability of P(T2 T1) can be calculated from Probit functions.

18 Application of Bayesian network to domino effects Up to this point, the probability of 1 st level domino effect (DL1) comprising T1 and T2 can be calculated as: P(DL1) = P(T1). P(T2 T1) 1 st level domino can be accounted for by adding the node DL1 to the network. DL1 is connected to T1 and T2 by AND gate.

19 Application of Bayesian network to domino effects Considering a pool fire in T2 as a secondary accident, T1 and T2 can contribute to accident in T3 by synergistic effect. Thus, T1 and T2 are connected to T3. The conditional probability P(T3 T1,T2) can be calculated by Probit function and summing the heat radiations of T1 and T2.

20 Application of Bayesian network to domino effects Up to this point, the probability of 2nd level domino effect (DL2) comprising T1, T2, and T3 can be calculated as: P(DL2) = P(T1). P(T2 T1). P(T3 T1,T2) Or equivalently as: P(DL2) = P(DL1). P(T3 T1,T2) 2nd level domino can be accounted for by adding the node DL2 to the network. DL2 is connected to DL1 and T3 by AND gate.

21 Application of Bayesian network to domino effects: Procedure to develop the propagation pattern

22 A Numerical Example Distances between tanks Schematic of a fuel storage farm

23 A Numerical Example Overpressure Escalation Vectors Heat Radiation Escalation Vectors

24 Numerical Example D1 is selected as the primary unit. Threshold value for heat radiation is selected as Q = 15 kw/m2. Threshold value for overpressure is selected as P = 7 kpa. According to above threshold values, D2 and D4 are selected as secondary units. D1 contributes with D2 and D4 (synergistic effect) to impact D5 as tertiary unit.

25 Numerical Example Prior and posterior probabilities Complete Bayesian network to model domino effect

26 Domino Effect: Application of Bayesian Network Khakzad, N., Khan, F., Amyotte, P., Cozzani, V. Domino effect analysis using Bayesian networks. Risk Analysis Khakzad, N., Khan, F., Amyotte, P., Cozzani, V. Risk management of domino effects considering dynamic consequence analysis. Risk Analysis 2014.

27 Conclusions Bayesian Network is most effective way to model Domino effect propagation It helps analyzing dependencies of primary, secondary and tertiary effects It also help minimizing uncertainty and updating the likelihood as new evidence are get available Much work is needed to better define escalation factor and conditional probabilities