Benefits of Bayesian Network Models

By Philippe Weber and Christophe Simon

The application of Bayesian Networks (BN) or Dynamic Bayesian Networks (DBN) in dependability and risk analysis is a recent development. A large number of scientific publications show the interest in the applications of BN in this field.

Unfortunately, this modeling formalism is not fully accepted in the industry. The questions facing today's engineers are focused on the validity of BN models and the resulting estimates. Indeed, a BN model is not based on a specific semantic in dependability but offers a general formalism for modeling problems under uncertainty.

This book explains the principles of knowledge structuration to ensure a valid BN and DBN model and illustrate the flexibility and efficiency of these representations in dependability, risk analysis and control of multi-state systems and dynamic systems.

Across five chapters, the authors present several modeling methods and industrial applications are referenced for illustration in real industrial contexts.

• Language: English
• Publisher: Wiley
• Release date: Aug 23, 2016
• ISBN: 9781119347446

Book preview

Table of Contents

Cover

Title

Copyright

Foreword by J.-F. Aubry

Foreword by L. Portinale

Acknowledgments

Introduction

I.1. Problem statement

I.2. Book structure

PART 1: Bayesian Networks

1 Bayesian Networks: a Modeling Formalism for System Dependability

1.1. Probabilistic graphical models: BN

1.2. Reliability and joint probability distributions

1.3. Discussion and conclusion

2 Bayesian Network: Modeling Formalism of the Structure Function of Boolean Systems

2.1. Introduction

2.2. BN models in the Boolean case

2.3. Standard Boolean gates CPT

2.4. Non-deterministic CPT

2.5. Industrial applications

2.6. Conclusion

3 Bayesian Network: Modeling Formalism of the Structure Function of Multi-State Systems

3.1. Introduction

3.2. BN models in the multi-state case

3.3. Non-deterministic CPT

3.4. Industrial applications

3.5. Conclusion

PART 2: Dynamic Bayesian Networks

4 Dynamic Bayesian Networks: Integrating Environmental and Operating Constraints in Reliability Computation

4.1. Introduction

4.2. Component modeled by a DBN

4.3. Model of a dynamic multi-state system

4.4. Discussion on dependent processes

4.5. Conclusion

5 Dynamic Bayesian Networks: Integrating Reliability Computation in the Control System

5.1. Introduction

5.2. Integrating reliability information into the control

5.3. Control integrating reliability modeled by DBN

5.4. Application to a drinking water network

5.5. Conclusion

5.6. Acknowledgments

Conclusion

Bibliography

Index

End User License Agreement

List of Tables

1 Bayesian Networks: a Modeling Formalism for System Dependability

Table 1.1. Generic definition of a conditional probability table

Table 1.2. Probability distributions of component states

Table 1.3. Joint probability distributions modeling the three-valve system, part 1

Table 1.4. Joint probability distributions modeling the three-valve system, part 2

Table 1.5. Probability distributions of E1 states

Table 1.6. Probability distributions of E2 states

Table 1.7. Probability distributions of y states

2 Bayesian Network: Modeling Formalism of the Structure Function of Boolean Systems

Table 2.1. Probability distribution of valves’ states

Table 2.2. CPT of cut-set C2

Table 2.3. CPT of y based on cut-sets

Table 2.4. CPT of L1

Table 2.5. CPT of L2

Table 2.6. CPT of y|L1, L2

Table 2.7. Probability distribution on y state

Table 2.8. CPT of a Boolean AND

Table 2.9. CPT of a Boolean OR

Table 2.10. CPT of the inhibitor of E2 = x2 ∧ x3 by B1 in a bowtie model

Table 2.11. CPT of the inhibitor of Ip1 by B2 in a bowtie model

Table 2.12. CPT of a Boolean 2-out-of-3:G system

Table 2.13. CPT of the Ci variables

Table 2.14. CPT of y in a linear consecutive-2-out-of-5:G

Table 2.15. CPT of y in a linear consecutive-2-out-of-5:G

3 Bayesian Network: Modeling Formalism of the Structure Function of Multi-State Systems

Table 3.1. Multi-state L13 tie-set

Table 3.2. Multi-state L24 tie-set

Table 3.3. Multi-state L567 tie-set

Table 3.4. Results of the computation based on multi-state and tie-sets

Table 3.5. Multi-state C1 tie-set

Table 3.6. Multi-state C2 tie-set

Table 3.7. Multi-state C3 tie-set

Table 3.8. Multi-state C4 tie-set

Table 3.9. Results of the computation based on multi-state and cut-sets

Table 3.10. Variables in the IDEF0 model representing the flow F(i)

Table 3.11. Results of the computation based on the IDEF0 model

Table 3.12. Results of the computation based on the IDEF0 model Li variables

Table 3.13. Results of the computation based on the IDEF0 model Ii variables

Table 3.14. CPT of HSB efficiency

4 Dynamic Bayesian Networks: Integrating Environmental and Operating Constraints in Reliability Computation

Table 4.1. CPT defining the transition probability matrix of a MC

5 Dynamic Bayesian Networks: Integrating Reliability Computation in the Control System

Table 5.1. Failure rates of the actuators

Table 5.2. Paths linking the sources to the demand point

Table 5.3. Variables Computing the actuator Weighting

List of Illustrations

1 Bayesian Networks: a Modeling Formalism for System Dependability

Figure 1.1. Bayesian network model

Figure 1.2. Multi-state system with three valves

Figure 1.3. Multi-state three-valve system with two stages

2 Bayesian Network: Modeling Formalism of the Structure Function of Boolean Systems

Figure 2.1. RBD of the flow distribution system

Figure 2.2. BN model for three cut-sets

Figure 2.3. BN model of two minimal cut-sets

Figure 2.4. BN modeling the two minimal tie-sets

Figure 2.5. FT of the flow distribution system

Figure 2.6. BN model of the FT of Figure 2.5

Figure 2.7. BN model of a bowtie and its barriers

Figure 2.8. BN model of the 2-out-of-3:G system

Figure 2.9. BN model of the linear consecutive-2-out-of-5:G system

Figure 2.10. BN model of the circular consecutive-2-out-of-5:G system

Figure 2.11. Noisy-OR structures

Figure 2.12. Leaky Noisy-OR structures

Figure 2.13. Structuration in organizational level and action phases relating to a bowtie model

Figure 2.14. RB unified model of the power plant risk

3 Bayesian Network: Modeling Formalism of the Structure Function of Multi-State Systems

Figure 3.1. BN structured by the minimal multi-state tie-sets

Figure 3.2. Compact BN structured by minimal tie-sets for a multi-state system

Figure 3.3. BN based on the minimal cut-sets of a multi-state system

Figure 3.4. Generic definition of a function and its flows

Figure 3.5. Generic BN pattern of a function

Figure 3.6. Functional model of the system

Figure 3.7. Model of the function (transfer the fluid)

Figure 3.8. Model of the function (circulate the fluid)

Figure 3.9. Model of the function (stop the fluid)

Figure 3.10. BN model mapped from the functional model of the system

Figure 3.11. BN model of a human safety barrier (HSB)

4 Dynamic Bayesian Networks: Integrating Environmental and Operating Constraints in Reliability Computation

Figure 4.1. DBN model developed over eight time slices

Figure 4.2. DBN of a MC

Figure 4.3. DBN of a non-homogeneous MC

Figure 4.4. Inference in the DBN of a non-homogeneous MC

Figure 4.5. DBN model of a MSM

Figure 4.6. DBN model of an IOHMM

Figure 4.7. Inference in the DBN model of the IOHMM

Figure 4.8. Unroll up the DBN model without conditional dependence between components

Figure 4.9. Unroll up the DBN model with conditional dependence between components

Figure 4.10. 2TBN of a multi-state system

Figure 4.11. Inference of a 2TBN multi-state model and state probability distribution

Figure 4.12. Multi-state system and components’ reliability

Figure 4.13. 2TBN model of a multi-state system with largely dependent processes

5 Dynamic Bayesian Networks: Integrating Reliability Computation in the Control System

Figure 5.1. Control structure of an over-actuated system integrating a reliability model

Figure 5.2. Control framework of an over-actuated system integrating a DBN reliability model

Figure 5.3. Part of the Barcelona DWN studied

Figure 5.4. DBN model of the Barcelona DWN

Figure 5.5. Actuators and DWN reliability

Figure 5.6. Simulation of control inputs and weights of the Barcelona DWN

Systems Dependability Assessment Set

coordinated by

Jean-Francois Aubry

Volume 2

Benefits of Bayesian Network Models

Philippe Weber

Christophe Simon

log

First published 2016 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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© ISTE Ltd 2016

The rights of Philippe Weber and Christophe Simon to be identified as the author of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2016943665

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-84821-992-2

Foreword by J.-F. Aubry

Systems Dependability Assessment is the title of a series of books, of which this is the third. The preface to the first series described the reasons why the authors embarked upon writing these books: in recent decades, they have made significant contributions to recent approaches to the predictive dependability of systems by considering concepts developed in other scientific fields but not yet applied to account of dependability. All these authors belong to the Automatic Control Research Center (CRAN, Centre de Recherches en Automatique de Nancy) of the