Introduction to Risk and Uncertainty in Hydrosystem Engineering (eBook)

Preface 7
Contents 10
1 Basic Concepts 13
Abstract 13
1.1…Introduction 13
1.2…Hydrosystem 14
1.3…Risk and Reliability 14
1.4…Risk Assessment and Management 15
1.5…Uncertainty 16
1.5.1 Purpose of Uncertainty Analysis 17
1.5.2 Measurement of Risk and Uncertainty 17
References 19
2 Probability Theories 20
Abstract 20
2.1…Review of Probability Theory 20
2.2…Probability Concepts 21
2.3…Random Variables 23
2.4…Moments of Distribution 25
2.4.1 Estimate Moments From Data Series 29
2.5…Two Random Variables 32
2.6…Commonly Used Probability Distributions in Hydrosystem Engineering 37
2.6.1 Binomial Distribution 37
2.6.2 Poisson Distribution 41
2.6.3 Normal Distribution 42
2.6.4 Log-Normal Distribution 45
2.6.5 Exponential Distribution 48
2.6.6 Gamma Distribution 50
2.6.7 Beta Distribution 53
2.6.8 Uniform DistributionUniform Distribution 54
References 55
3 Risk and Uncertainty Analysis 56
Abstract 56
3.1…Basic Concept of Uncertainty 56
3.2…Uncertainty Analysis 57
3.2.1 Analytical Techniques 58
3.2.1.1 Derived Distribution Technique 58
3.2.1.2 Fourier Transforms Techniques 59
3.3…Basic Concepts of Risk and Reliability 62
3.4…Safety Factor and Safety Margin 63
3.5…Performance Function 64
3.6…Reliability Index 66
3.7…First-Order Second-Moment Method 72
3.7.1 Mean-Value First-Order Second-Moment Method 72
3.8…Probabilistic Point Estimation Methods 76
3.8.1 Rosenblueth’s Point Estimation Method 76
3.8.2 Bivariate RPEM 79
3.9…Reliability Analysis of Complex System 82
3.9.1 Event-Tree 82
3.9.2 Fault-Tree 84
References 86
4 Monte Carlo Simulation 88
Abstract 88
4.1…Introduction 88
4.2…Basics of Monte Carlo Simulation 89
4.3…Generation of Random Numbers 89
4.4…CDF-inverse Method (Continuous Case) 91
4.5…Acceptance-Rejection Method 95
4.6…Generation Random Variates from Probability Distributions 97
4.6.1 Normal Distribution 97
4.6.1.1 Box-Muller Algorithm 97
4.6.1.2 The Polar Method 98
4.6.2 Lognormal Distribution 99
4.6.3 Exponential Distribution 101
4.7…Monte Carlo Integration 102
4.7.1 One-Dimensional Monte Carlo Integration 102
4.7.2 Two-Dimensional Monte Carlo Integration 104
4.8… Hit-and-Miss Method 105
4.9…Variance-Reduction Techniques 110
References 111
5 Evaluation of Dam Overtopping Risk Based on Univariate Frequency Analysis 112
Abstract 112
5.1…Introduction 112
5.2…Dam Risk Model 115
5.2.1 Risk Modeling for Flood and Wind Overtopping 116
5.3…Reservoir Routing 117
5.4…Wind Model 117
5.5…Uncertainty Analysis 119
5.5.1 Monte Carlo Simulation 119
5.5.2 Latin Hypercube Sampling 120
5.6…Overtopping Risk for an Existing Dam 121
5.6.1 Study Area and Data Collection 121
5.6.2 Flood Frequency Analysis 122
5.6.3 Wind Frequency Analysis 123
5.6.4 Uncertain Variables 124
5.6.5 Overtopping Risk Due to Different Floods 125
5.6.6 Overtopping Risk Due to Flood and Wind 126
5.7…Conclusions 128
5.8…Future Studies 131
References 131
6 Evaluation of Dam Overtopping Risk Based on Univariate and Bivariate Flood Frequency Analyses 133
Abstract 133
6.1…Introduction 133
6.2…Bivariate Frequency Analysis 135
6.3…Reservoir Routing Analysis 137
6.4…Risk and Uncertainty Analysis 137
6.5…Case Study 138
6.6…Outlier Test 139
6.7…Determination of Uncertainty Factors 139
6.8…Univariate Flood Frequency Analysis 141
6.9…Bivariate Flood Frequency Analysis 143
6.10…Overtopping Risk Based on Univariate Flood Frequency 145
6.11…Overtopping Risk Based on Bivariate Flood Frequency 145
6.12…Conclusion 148
References 150
Appendix A 152
Appendix A 152
Appendix B 158
Appendix C 161
Index 163