Benefits of Bayesian Network Models

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.

Philippe Weber is Professor at the Engineer School of Sciences and Technologies at the University of Lorraine and at the Research Centre for Automatic Control in Nancy, France. His research concerns dependability and is mainly focused on probabilistic graphical models.

Christophe Simon is Associate Professor at the Research Centre for Automatic Control in Nancy, France. His research concerns dependability and is mainly focused on modeling engineering and uncertainties.

Foreword by J.-F. Aubry ix

Foreword by L. Portinale  xiii

Acknowledgments  xv

Introduction xvii

Part 1. Bayesian Networks 1

Chapter 1. Bayesian Networks: a Modeling Formalism for System Dependability  3

1.1. Probabilistic graphical models: BN  5

1.1.1. BN: a formalism to model dependability  5

1.1.2. Inference mechanism  7

1.2. Reliability and joint probability distributions 8

1.2.1. Multi-state system example  8

1.2.2. Joint distribution  9

1.2.3. Reliability computing  9

1.2.4. Factorization 10

1.3. Discussion and conclusion 14

Chapter 2. Bayesian Network: Modeling Formalism of the Stucture Function of Boolean Systems 17

2.1. Introduction 17

2.2. BN models in the Boolean case  19

2.2.1. BN model from cut-sets  20

2.2.2. BN model from tie-sets 23

2.2.3. BN model from a top-down approach 25

2.2.4. BN model of a bowtie 26

2.3. Standard Boolean gates CPT  29

2.4. Non-deterministic CPT 31

2.5. Industrial applications  38

2.6. Conclusion  41

Chapter 3. Bayesian Network: Modeling Formalism of the Structure Function of Multi-State Systems  43

3.1. Introduction 43

3.2. BN models in the multi-state case 43

3.2.1. BN model of multi-state systems from tie-sets 44

3.2.2. BN model of multi-state systems from cut-sets  49

3.2.3. BN model of multi-state systems from functional and dysfunctional analysis 52

3.3. Non-deterministic CPT 58

3.4. Industrial applications  59

3.5. Conclusion  62

Part 2. Dynamic Bayesian Networks 65

Chapter 4. Dynamic Bayesian Networks: Integrating Environmental and Operating Constraints in Reliability Computation 67

4.1. Introduction 67

4.2. Component modeled by a DBN  69

4.2.1. DBN model of a MC  70

4.2.2. DBN model of non-homogeneous MC  71

4.2.3. Stochastic process with exogenous constraint  72

4.3. Model of a dynamic multi-state system  75

4.4. Discussion on dependent processes  79

4.5. Conclusion  81

Chapter 5. Dynamic Bayesian Networks: Integrating Reliability Computation in the Control System  83

5.1. Introduction 83

5.2. Integrating reliability information into the control 84

5.3. Control integrating reliability modeled by DBN  85

5.3.1. Modeling and controlling an over-actuated system  86

5.3.2. Integrating reliability  88

5.4. Application to a drinking water network 90

5.4.1. DBN modeling 91

5.4.2. Results and discussion 92

5.5. Conclusion 95

5.6. Acknowledgments  96

Conclusion 97

Bibliography  101

Index 113