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基于分位点的广义Pareto分布函数最小二乘拟合方法

赵刚 李刚

赵刚, 李刚. 基于分位点的广义Pareto分布函数最小二乘拟合方法[J]. 应用数学和力学, 2018, 39(4): 415-423. doi: 10.21656/1000-0887.380196
引用本文: 赵刚, 李刚. 基于分位点的广义Pareto分布函数最小二乘拟合方法[J]. 应用数学和力学, 2018, 39(4): 415-423. doi: 10.21656/1000-0887.380196
ZHAO Gang, LI Gang. A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles[J]. Applied Mathematics and Mechanics, 2018, 39(4): 415-423. doi: 10.21656/1000-0887.380196
Citation: ZHAO Gang, LI Gang. A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles[J]. Applied Mathematics and Mechanics, 2018, 39(4): 415-423. doi: 10.21656/1000-0887.380196

基于分位点的广义Pareto分布函数最小二乘拟合方法

doi: 10.21656/1000-0887.380196
基金项目: 国家重点基础研究发展计划(973计划)(2016CB046506)
详细信息
    作者简介:

    赵刚(1987—),男,博士生(E-mail: zhaogang54@126.com);李刚(1966—),男,教授,博士生导师(通讯作者. E-mail: ligang@dlut.edu.cn).

  • 中图分类号: O302

A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles

Funds: The National Basic Research Program of China(973 Program)(2016CB046506)
  • 摘要: 广义Pareto分布函数(GPD, generalized Pareto distribution)是一种针对随机参数尾部进行渐进插值的方法,能够对高可靠性问题进行评估.应用该函数进行随机参数尾部近似时,需要对函数中的两个重要未知参数进行拟合确定.最常用的拟合方法是最大似然拟合和最小二乘拟合,需要将所有的尾部样本进行计算;需要大量尾部样本,计算效率低.该文提出依据少量的分位点进行最小二乘拟合,既保证了尾部样本空间足够大,同时又降低了计算成本;进一步提出了Kriging模型的两阶段更新,实现了分位点求解的快速收敛.算例表明,该文提出的方法能够快速提高模型精度,求得指定的分位点,而且与基于大量尾部样本的最大似然拟合结果精度一致.
  • [1] 赵劲彪, 郑香伟, 冯蕴雯, 等. 飞机起落架应急放机构可靠性分析[J]. 机械设计与制造, 2014,8: 31-33.(ZHAO Jinbiao, ZHENG Xiangwei, FENG Yunwen, et al. Reliability analysis of landing gear mechanism during emergency extending[J]. Machinery Design & Manufacture,2014,8: 31-33.(in Chinese))
    [2] 武晓全, 薛军. 民机结构疲劳损伤可靠性分析[J]. 装备制造技术, 2014,10: 201-203.(WU Xiaoquan, XUE Jun. Structural reliability analysis of fatigue damage of civil aircraft[J]. Equipment Manufacturing Technology,2014,10: 201-203.(in Chinese))
    [3] YOO D, LEE I, CHO H. Probabilistic sensitivity analysis for novel second-order reliability method(SORM) using generalized chi-squared distribution[J]. Structural and Multidisciplinary Optimization, 2014,50(5): 787-797.
    [4] LI Gang, ZHANG Kai. A combined reliability analysis approach with dimension reduction method and maximum entropy method[J]. Structural and Multidisciplinary Optimization,2011,43(1): 121-134.
    [5] EZZATI G, MAMMADOV M, KULKARNI S. A new reliability analysis method based on the conjugate gradient direction[J]. Structural and Multidisciplinary Optimization,2015,51(1): 89-98.
    [6] MARTINO L, ELVIRA V, LUENGO D, et al. Layered adaptive importance sampling[J]. Statistics and Computing,2017,27(3): 599-623.
    [7] FAN Haijian, LIANG R. Importance sampling based algorithm for efficient reliability analysis of axially loaded piles[J]. Computers and Geotechnics,2015,65: 278-284.
    [8] DUBOURG V, SUDRET B, BOURINET J-M. Reliability-based design optimization using Kriging surrogates and subset simulation[J]. Structural and Multidisciplinary Optimization, 2011,44(5): 673-690.
    [9] LI Hongshuang, MA Yuanzhuo, CAO Zijun. A generalized subset simulation approach for estimating small failure probabilities of multiple stochastic responses[J]. Computers & Structures,2015,153: 239-251.
    [10] RAMU P, KIM N H, HAFTKA R T. Multiple tail median approach for high reliability estimation[J]. Structural Safety,2010,32(2): 124-137.
    [11] TANG Zhangchun, LU Zhenzhou, PAN Wang, et al. A mean extrapolation technique for high reliability analysis[J]. Applied Mathematics and Computation,2013,222: 82-93.
    [12] PICKANDS J. Statistical-inference using extreme order statistics[J]. The Annals of Statistics,1975,3(1): 119-131.
    [13] TORII A J, LOPEZ R H, MIGUEL L F F. A general RBDO decoupling approach for different reliability analysis methods[J].Structural and Multidisciplinary Optimization,2016,54(2): 317-332.
    [14] JEONG S, MURAYAMA M, YAMAMOTO K. Efficient optimization design method using Kriging model[J]. Journal of Aircraft,2005,42(2):413-420.
    [15] 谢延敏, 于沪平, 陈军, 等. 基于Kriging模型的可靠度计算[J]. 上海交通大学学报, 2007,41(2): 177-180.(XIE Yanmin, YU Huping, CHEN Jun, et al. The reliability estimation based on Kriging model[J].Journal of Shanghai Jiaotong University,2007,41(2): 177-180.(in Chinese))
    [16] BALESDENT M, MORIO J, MARZAT J. Kriging-based adaptive importance sampling algorithms for rare event estimation[J].Structural Safety,2013,44: 1-10.
    [17] SANTOS S R, MATIOLI L C, BECK A T. New optimization algorithms for structural reliability analysis[J]. Computer Modeling in Engineering and Sciences,2012,83(1): 23-55.
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出版历程
  • 收稿日期:  2017-07-14
  • 修回日期:  2018-01-09
  • 刊出日期:  2018-04-15

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