Benchmark studies on several reliability methods based on tail estimation

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研究生：	李美麗 Merry - Natalia Maranata
論文名稱：	Benchmark studies on several reliability methods based on tail estimation Benchmark studies on several reliability methods based on tail estimation
指導教授：	卿建業 Jianye Ching
口試委員:	楊亦東 I-Tung Yang 劉家男 Chia-Nan Liu
學位類別：	碩士 Master
系所名稱：	工程學院 - 營建工程系 Department of Civil and Construction Engineering
論文出版年：	2008
畢業學年度：	96
語文別：	英文
論文頁數：	130
外文關鍵詞：	tail distribution, quantile-function
相關次數：	點閱：162 下載：0
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Failure probabilities of engineering structures are small, usually less than 0.01. Therefore, accurately estimating the tail of the distribution of the performance function is essential. This study compares several nonparametric reliability methods based on tail-fitting concept, including quantile-function (QF) methods, generalized Pareto distribution (GPD) methods and moment-matching (MM) methods.
The comparisons are made on several typical geotechnical design examples. The comparisons show that the performance of quantile-function methods is satisfactory, especially the QF method with minimum cross entropy since it effectively assumes the tail distribution to be exponential, which is roughly a correct assumption for many examples. The GPD method also provides reasonably stable results if the sampling threshold is carefully chosen. For most methods, the performance depends on the choice of threshold, which is found to perform the best when chosen to be around 80% of the failure threshold. The moment methods turn out to perform poorly due to its unrealistic assumptions.

Table of Content

Title page…………………………………………………………………………..	i
Abstract	ii
Table of Content	iii
List of Figures	vi
List of Tables	viii
Acknowledgements	x
Chapter 1 Introduction	1
1.1 Background	1
1.2 Research objectives	1
1.3 Organization of the thesis	2
Chapter 2 Review of Several Reliability Analysis Methods	3
2.1 Statement of problem	3
2.2 Reliability analysis method review	3
2.2.1 First order second moment (FOSM)	4
2.2.2 First order reliability methods (FORM)	5
2.2.3 Monte Carlo Simulation (MCS)	6
2.3 Implementation of reliability analysis method to predict tail distribution	7
Chapter 3 Review of Quantile-Function Method	9
3.1 General	9
3.2 Quantile-function	9
3.2.1 Probability Weighted Moments (PWM)	9
a. PWM and characterizing a probability distribution	11
b. Unbiased estimator of PWM	11
c. Unbiased estimator of PWM as moments of quantile-function	13
3.2.2 Information entropy	13
a. Maximum entropy principle	14
b. Minimum cross entropy principle	15
3.3 Quantile-function and varieties methodology	17
3.3.1 Quantile-function with maximum entropy	17
3.3.2 Quantile-function with minimum cross entropy	19
Chapter 4 Review of generalized Pareto distribution	23
4.1 General	23
4.2 Revised generalized Pareto distribution	23
4.2.1 Estimating GPD parameters by MLE method	24
a. Maximum likelihood principle	24
b. Application of MLE in GPD	25
4.2.2 Fitting Tail distribution by GPD	25
Chapter 5 Review of moment method	27
5.1 Review Moment Methods	27
5.2 Moment Methods	27
5.2.1 Second-moment method	27
a. Conventional second moment reliability methods	27
b. Second moment method by Zhao and Ono (2001)	28
5.2.2 Third-moment method	28
5.2.3 Fourth moment method	29
a. First Fourth Moment (FM-1)	29
b. Second Fourth Moment (FM-2)	30
c. Third Fourth Moment (FM-3)	30
Chapter 6 Geotechnical benchmark examples	33
6.1 Introduction	33
6.2. Sheet pile wall	33
6.3 Deep Excavation	34
6.4 Consolidation settlement in clay problem	36
6.5 Shallow foundation	37
6.6 Retaining Wall	39
Chapter 7 Analysis results	41
7.1 General	41
7.2 Sheet pile	41
7.2.1 Sliding limit state of sheet pile example	41
a. Quantile-function	41
b. GPD	44
c. Moment method	45
7.2.2 Overturning limit state of sheet pile	46
a. Quantile-function	46
b. GPD	49
c. Moment methods	50
7.3 Deep excavation example	51
a. Quantile-function	51
b. GPD	54
c. Moment methods	55
7.4 Consolidation example	56
a. Quantile-function	56
b. GPD	59
c. Moment methods	60
7.5 Shallow foundation	61
a. Quantile-function	61
b. GPD	64
c. Moment methods	65
7.6. Retaining wall	65
7.6.1 Sliding limit state	65
a. Quantile-function	65
b. GPD	69
c. Moment methods	70
7.6.2 Bearing limit state	70
a. Quantile-function	70
b. GPD	74
c. Moment methods	74
7.6.3 Overturning limit state	75
a. Quantile-function	75
b. GPD	77
c. Moment methods	78
Chapter 8 Conclusion	88
References	93
Appendix A	95
Appendix B	99
Appendix C	100
Appendix D	101
Appendix E	104
Appendix F	105
Appendix G	109
Appendix H	111

                                

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