(3.238.130.97) 您好!臺灣時間:2021/05/14 19:44
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:李美麗
研究生(外文):Merry Natalia Maranata
論文名稱:Benchmarkstudiesonseveralreliabilitymethodsbasedontailestimation
論文名稱(外文):Benchmark studies on several reliability methods based on tail estimation
指導教授:卿建業卿建業引用關係
指導教授(外文):Jianye Ching
學位類別:碩士
校院名稱:國立臺灣科技大學
系所名稱:營建工程系
學門:工程學門
學類:土木工程學類
論文種類:學術論文
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:reliabilityfailure probabilitytail distributionquantile-functionentropy
相關次數:
  • 被引用被引用:0
  • 點閱點閱:98
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
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
References

Abramowitz, M. and Stegun, I.A. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. Dover, New York.

Ching, J.Y., Porter, A.K., and Beck, L.J. (2003). Uncertainty Propagation and Feature Selection for Loss Estimation in Performance-based Earthquake Engineering. Research report of Earthquake Engineering Research Laboratory, EERL 2003-03. Pasadena, California.

Ching, J.Y. (2008). Equivalence Between Reliability and Factor Safety. Journal of Probabilistic Engineering Mechanics, doi:10.1016/j.probengmech.2008.04.004.

Ching, J.Y. and Hsieh, Y.Y. (2007). Local Estimation of Failure Probability and Its Confidence Interval with Maximum Entropy Principle. Journal of Probabilistic Engineering Mechanics, 22, 39-49.

Castillo, E. (1988). Extreme Value Theory in Engineering. Academic Press, Inc

Cornell, C.A., (1969). A Probabilty-Based Structural Code. Journal of The American Concrete Institute, 66, 974-985

Djeng, J., Pandey MD. (2007). Estimation of minimum cross-entropy quantile function using fractional probability weighted moments. Journal of Probabilistic Engineering Mechanics, doi:10.1016/j.probengmech.2007.12.016.

Davison, A. C. and Smith, R. L. (1990). Models of Exceedances Over High Thresholds. Journal of the Royal Statistical Society, 52(Ser. B), 393–442.

Greenwood JA, Landwehr JM, Matalas NC. (1979). Probability weighted moments: definition and relation to parameters of several distributions expressible in inverse form. Journal of Water Resources Research, 15(5), 1049–1054.

Hosking, J.R.M. (1986). The theory of probability weighted moments. NY: IBM Research Report, RC 12210, Yorktown Heights.

Hosking, J. R. M. (1990). L-moments: analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society, 52(Series B), , 105-124.

Hosking, J. R. M., and Wallis, J. R. (1997). Regional frequency analysis: an approach based on L-moments”. Cambridge, U.K.: Cambridge University Press.

Jaynes, E.T. (1957). Information theory and statistical mechanics. Physic Review, 106, 620–630.

Kapur, J.N. and Kesavan, H.K. (1992). Entropy optimization principles with applications. San Diego, USA: Academic Press Inc..

Landwehr, J.M., Matalas, N.C. and Wallis, J.R. (1979). Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles. Journal of Water Resources Research, 15(5), 1055–1064.

Ono, T., and Idota, H. (1986). Development of high order moment standardization method into structural design and its efficiency. Journal of Structural and Construction Engineering, AIJ, 36, 5, 40-7.

Madsen, H.O., and Egeland, T. (1989). Structural Reliability – Models and Application. International Statistical Review, 57(3), 185-203.

Pandey, M.D. (2000). Direct Estimation of Quantile Functions Using the Maximum Entropy Principle. Journal of Structural Safety, 22(1), 61-79.

Pandey, M.D. (2001). Minimum Cross-Entropy Method for Extreme Value Estimation using Peaks-Over-Threshold Data. Journal of Structural Safety, 23(4), 345-363.

Pickands, J. (1975). Statistical inference using order statistics. Annals of Statistics, 3, 119–131.

Rosenblueth, E. (1975), Point estimates for probability moments, Proceeding National Academia of Science, 72(10), 3812-3814.

Shore, J.E. and Johnson, R.W. (1980). Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy. IEEE Trans. on Information Theory, 26(1), 26–37.

Tichy, M. (1994). First Order Third Moment reliability method. Journal of Structural Safety, 16, 189-200.

Zhao, Y. and Ono, T. (2001). Moment Method for Structural Reliability, Journal of Structural Safety, 23, 47-75.

Zhao, Y., Lu, Z., and Ono, T. (2006). A Simple Third-Moment Method for Structural Reliability . Journal of Asian Architecture and Building Engineering, 5(1), 129-136.

Xu, L. and Cheng, G..D. (2003). Discussion on: Moment Methods for Structural Reliability. Journal of Structural Safety, 25 (2), 193-199.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top