Uncertainty in Industrial Practice: A Guide to Quantitative Uncertainty Management

Preface xiii

Contributors and Acknowledgements xv

Introduction xvii

Notation – Acronyms and abbreviations xxi

Part I Common Methodological Framework 1

1 Introducing the common methodological framework 3

1.1 Quantitative uncertainty assessment in industrial practice: a wide variety of contexts 3

1.2 Key generic features, notation and concepts 4

1.2.1 Pre-existing model, variables of interest and uncertain/fixed inputs 4

1.2.2 Main goals of the uncertainty assessment 6

1.2.3 Measures of uncertainty and quantities of interest 7

1.2.4 Feedback process 9

1.2.5 Uncertainty modelling 10

1.2.6 Propagation and sensitivity analysis processes 10

1.3 The common conceptual framework 11

1.4 Using probabilistic frameworks in uncertainty quantification – preliminary comments 13

1.4.1 Standard probabilistic setting and interpretations 13

1.4.2 More elaborate level-2 settings and interpretations 14

1.5 Concluding remarks 17

References 18

2 Positioning of the case studies 21

2.1 Main study characteristics to be specified in line with the common framework 21

2.2 Introducing the panel of case studies 21

2.3 Case study abstracts 27

Part II Case Studies 33

3 CO2 emissions: estimating uncertainties in practice for power plants 35

3.1 Introduction and study context 35

3.2 The study model and methodology 36

3.2.1 Three metrological options: common features in the preexisting models 36

3.2.2 Differentiating elements of the fuel consumption models 38

3.3 Underlying framework of the uncertainty study 39

3.3.1 Specification of the uncertainty study 39

3.3.2 Description and modelling of the sources of uncertainty 40

3.3.3 Uncertainty propagation and sensitivity analysis 42

3.3.4 Feedback process 44

3.4 Practical implementation and results 44

3.5 Conclusions 47

References 47

4 Hydrocarbon exploration: decision-support through uncertainty treatment 49

4.1 Introduction and study context 49

4.2 The study model and methodology 50

4.2.1 Basin and petroleum system modelling 50

4.3 Underlying framework of the uncertainty study 54

4.3.1 Specification of the uncertainty study 54

4.3.2 Description and modelling of the sources of uncertainty 56

4.3.3 Uncertainty propagation and sensitivity analysis 57

4.3.4 Feedback process 57

4.4 Practical implementation and results 59

4.4.1 Uncertainty analysis 59

4.4.2 Sensitivity analysis 62

4.5 Conclusions 63

References 64

5 Determination of the risk due to personal electronic devices (PEDs) carried out on radio-navigation systems aboard aircraft 65

5.1 Introduction and study context 65

5.2 The study model and methodology 66

5.2.1 Electromagnetic compatibility modelling and analysis 66

5.2.2 Setting the EMC problem 67

5.2.3 A model-based approach 68

5.2.4 Regulatory and industrial stakes 69

5.3 Underlying framework of the uncertainty study 71

5.3.1 Specification of the uncertainty study 71

5.3.2 Description and modelling of the sources of uncertainty 72

5.3.3 Uncertainty propagation and sensitivity analysis 75

5.3.4 Feedback process 76

5.4 Practical implementation and results 76

5.4.1 Limitations of the results of the study 76

5.4.2 Scenario no.1: effects of one emitter in the aircraft on ILS antenna (realistic data-set) 76

5.4.3 Scenario no. 2: effects of one emitter in the aircraft on ILS antenna with penalized susceptibility 78

5.4.4 Scenario no. 3: 10 coherent emitters in the aircraft, ILS antenna with a realistic data set 79

5.4.5 Scenario no. 4: new model considering the effect of one emitter in the aircraft on ILS antenna and safety factors 79

5.5 Conclusions 80

References 80

6 Safety assessment of a radioactive high-level waste repository – comparison of dose and peak dose 81

6.1 Introduction and study context 81

6.2 Study model and methodology 82

6.2.1 Source term model 83

6.2.2 Geosphere model 83

6.2.3 The biosphere model 84

6.3 Underlying framework of the uncertainty study 84

6.3.1 Specification of the uncertainty study 84

6.3.2 Sources of uncertainty, model inputs and uncertainty model developed 85

6.3.3 Uncertainty propagation and sensitivity analysis 86

6.3.4 Feedback process 87

6.4 Practical implementation and results 87

6.4.1 Uncertainty analysis 87

6.4.2 Sensitivity analysis 91

6.5 Conclusions 95

References 96

7 A cash flow statistical model for airframe accessory maintenance contracts 97

7.1 Introduction and study context 97

7.2 The study model and methodology 97

7.2.1 Generalities 97

7.2.2 Level-1 uncertainty 98

7.2.3 Computation 98

7.2.4 Stock size 100

7.3 Underlying framework of the uncertainty study 100

7.3.1 Specification of the uncertainty study 100

7.3.2 Description and modelling of the sources of uncertainty 101

7.3.3 Uncertainty propagation and sensitivity analysis 103

7.3.4 Feedback process 104

7.4 Practical implementation and results 104

7.4.1 Design of experiments results 105

7.4.2 Sobol’s sensitivity indices 107

7.4.3 Comparison between DoE and Sobol’ methods 108

7.5 Conclusions 108

References 109

8 Uncertainty and reliability study of a creep law to assess the fuel cladding behaviour of PWR spent fuel assemblies during interim dry storage 111

8.1 Introduction and study context 111

8.2 The study model and methodology 112

8.2.1 Failure limit strain and margin 113

8.2.2 The temperature scenario 113

8.3 Underlying framework of the uncertainty study 114

8.3.1 Specification of the uncertainty study 114

8.3.2 Description and modelling of the sources of uncertainty 115

8.3.3 Uncertainty propagation and sensitivity analysis 116

8.3.4 Feedback process 116

8.4 Practical implementation and results 117

8.4.1 Dispersion of the minimal margin 117

8.4.2 Sensitivity analysis 119

8.4.3 Exceedance probability analysis 120

8.5 Conclusions 121

References 122

9 Radiological protection and maintenance 123

9.1 Introduction and study context 123

9.2 The study model and methodology 124

9.3 Underlying framework of the uncertainty study 128

9.3.1 Specification of the uncertainty study 128

9.3.2 Description and modelling of the sources of uncertainty 129

9.3.3 Uncertainty propagation and sensitivity analysis 131

9.3.4 Feedback process 131

9.4 Practical implementation and results 132

9.5 Conclusions 134

References 134

10 Partial safety factors to deal with uncertainties in slope stability of river dykes 135

10.1 Introduction and study context 135

10.2 The study model and methodology 136

10.2.1 Slope stability models 136

10.2.2 Incorporating slope stability in dyke design 137

10.2.3 Uncertainties in design process 138

10.3 Underlying framework of the uncertainty study 138

10.3.1 Specification of the uncertainty study 139

10.3.2 Description and modelling of the sources of uncertainty 142

10.3.3 Uncertainty propagation and sensitivity analysis 144

10.3.4 Feedback process 149

10.4 Practical implementation and results 150

10.5 Conclusions 153

References 153

11 Probabilistic assessment of fatigue life 155

11.1 Introduction and study context 155

11.2 The study model and methodology 155

11.2.1 Fatigue criteria 155

11.2.2 System model 156

11.3 Underlying framework of the uncertainty study 157

11.3.1 Outline of current practice in fatigue design 157

11.3.2 Specification of the uncertainty study 158

11.3.3 Description and modelling of the sources of uncertainty 160

11.3.4 Uncertainty propagation and sensitivity analysis 161

11.3.5 Feedback process 161

11.4 Practical implementation and results 162

11.4.1 Identification of the macro fatigue resistance β(N) 162

11.4.2 Uncertainty analysis 164

11.5 Conclusions 167

References 167

12 Reliability modelling in early design stages using the Dempster-Shafer Theory of Evidence 169

12.1 Introduction and study context 169

12.2 The study model and methodology 170

12.2.1 The system 170

12.2.2 The system fault tree model 171

12.2.3 The IEC 61508 guideline: a framework for safety requirements 172

12.3 Underlying framework of the uncertainty study 173

12.3.1 Specification of the uncertainty study 173

12.3.2 Description and modelling of the sources of uncertainty 176

12.4 Practical implementation and results 178

12.5 Conclusions 182

References 182

Part III Methodological Review and Recommendations 185

13 What does uncertainty management mean in an industrial context? 187

13.1 Introduction 187

13.2 A basic distinction between ‘design’ and ‘in-service operations’ in an industrial estate 188

13.2.1 Design phases 188

13.2.2 In-service operations 189

13.3 Failure-driven risk management and option-exploring approaches at company level 190

13.4 Survey of the main trends and popular concepts in industry 191

13.5 Links between uncertainty management studies and a global industrial context 192

13.5.1 Internal/endogenous context 193

13.5.2 External/exogenous uncertainty 194

13.5.3 Layers of uncertainty 195

13.6 Developing a strategy to deal with uncertainties 195

References 197

14 Uncertainty settings and natures of uncertainty 199

14.1 A classical distinction 199

14.2 Theoretical distinctions, difficulties and controversies in practical applications 202

14.3 Various settings deemed acceptable in practice 205

References 210

15 Overall approach 213

15.1 Recalling the common methodological framework 213

15.2 Introducing the mathematical formulation and key steps of a study 214

15.2.1 The specification step – measure of uncertainty, quantities of interest and setting 214

15.2.2 The uncertainty modelling (or source quantification) step 215

15.2.3 The uncertainty propagation step 218

15.2.4 The sensitivity analysis step, or importance ranking 219

15.3 Links between final goals, study steps and feedback process 220

15.4 Comparison with applied system identification or command/control classics 221

15.5 Pre-existing or system model validation and model uncertainty 222

15.6 Links between decision theory and the criteria of the overall framework  223

References 224

16 Uncertainty modelling methods 225

16.1 Objectives of uncertainty modelling and important issues 225

16.2 Recommendations in a standard probabilistic setting 227

16.2.1 The case of independent variables 228

16.2.2 Building an univariate probability distribution via expert/engineering judgement 229

16.2.3 The case of dependent uncertain model inputs 234

16.3 Comments on level-2 probabilistic settings 236

References 237

17 Uncertainty propagation methods 239

17.1 Recommendations per quantity of interest 240

17.1.1 Variance, moments 240

17.1.2 Probability density function 243

17.1.3 Quantiles 245

17.1.4 Exceedance probability 247

17.2 Meta-models 250

17.2.1 Building a meta-model 251

17.2.2 Validation of a meta-model 252

17.3 Summary 253

References 256

18 Sensitivity analysis methods 259

18.1 The role of sensitivity analysis in quantitative uncertainty assessment 260

18.1.1 Understanding influence and ranking importance of uncertainties (goal U) 261

18.1.2 Calibrating, simplifying and validating a numerical model (goal A) 262

18.1.3 Comparing relative performances and decision support (goal S) 263

18.1.4 Demonstrating compliance with a criterion or a regulatory threshold (goal C) 264

18.2 Towards the choice of an appropriate Sensitivity Analysis framework 264

18.3 Scope, potential and limitations of the various techniques 269

18.3.1 Differential methods 269

18.3.2 Approximate reliability methods 270

18.3.3 Regression/correlation 271

18.3.4 Screening methods 273

18.3.5 Variance analysis of Monte Carlo simulations 274

18.3.6 Non-variance analysis of Monte Carlo simulations 276

18.3.7 Graphical methods 278

18.4 Conclusions 280

References 281

19 Presentation in a deterministic format 285

19.1 How to present in a deterministic format? 286

19.1.1 (Partial) safety factors in a deterministic approach 286

19.1.2 Safety factors in a probabilistic approach 287

19.2 On the reliability target 290

19.3 Final comments 291

References 292

20 Recommendations on the overall process in practice 293

20.1 Recommendations on the key specification step 293

20.1.1 Choice of the system model 294

20.1.2 Choice of the uncertainty setting 294

20.1.3 Choice of the quantity of interest 296

20.1.4 Choice of the model input representation (‘x’ and ‘d’) 297

20.2 Final comments regarding dissemination challenges 297

References 298

Conclusion 299

Appendices 303

Appendix A A selection of codes and standards 305

Appendix B A selection of tools and websites 307

Appendix C Towards non-probabilistic settings: promises and industrial challenges 313

Index 329