Bayesian Networks - QRA in DNV

Sam Johnston and Amy Spicer

January 30, 2015

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Working Team

SAMBa: Matthew Thomas

Students: Amy Spicer, Sam Johnston

Academics: Finn Lindgren, Simon Shaw, Karim Anaya-Izquierdo

DNV: David Worthington

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The problem

QRA with Bayesian Networks

Proof of ConceptSensitivityConsequence modelling

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QRA using Bayesian Network

Is conversion easy from event trees?

What further questions does this raise?

Toy Example:

Example with 5 nodes

Further Questions:

Does this work on the scale of DNV?

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A Toy Example

Isolatable.section

Blowdown

Ignition.at.time.1

Ignition.at.time.2

Explosion.level

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QRA using Bayesian Network

Question: What happens where there is weak conditional dependence?

Consider a group of random variables X1, ...,Xn. Let Xj have valuesin Ω. Suppose that for y ∈ Ω

P[Xj = y |Xj ,1,Xj ,2, . . . ,Xj ,jk ,Xl ] ≈ P[Xj = y |Xj ,1,Xj ,2, . . . ,Xj ,jk ]

then we conclude Xj is only weakly dependent on Xl conditional onXj ,1, ...,Xj ,jk .

This corresponds to removing an arc from Xl to Xj

Kullback-Leibler divergence

DKL(P||Q) =∑y∈Ω

P(y)lnP(y)

Q(y)

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A Toy Example

Isolatable.section Blowdown

Ignition.at.time.1

Ignition.at.time.2

Explosion.level

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QRA using Bayesian Network

Further Questions:

Is this the most appropriate way to remove arcs?Which distribution do you use?What happens when you change the distribution?Continuous distibutions

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Sensitivity Analysis

Question: How sensitive is the Bayesian Network to change?

Introduce hyperpriors into the model?

How do small perturbations propagate through?

Further Questions:

How do we represent uncertainty?Penalised Complexity Priors

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Toy Example

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Consequence Modelling

How do we use this network in consequence modelling

Total Risk =∑x∈Ω

P(X = x)Cost(X = x)

Escape Route Graphs

Further Questions:

Can we reduce the total risk?Expectation vs. DistributionShortest path vs. safest path

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Toy Example

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DNV Example

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Any Questions

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