基于Bootstrap的小样本可靠性评估方法

兰州理工大学学报 ›› 2022, Vol. 48 ›› Issue (1): 39-44.

基于Bootstrap的小样本可靠性评估方法

张震^1,2, 刘俭辉^*1, 赵成¹, 剡昌锋¹

1.兰州理工大学机电工程学院, 甘肃兰州 730050;
2.林德液压(中国)有限公司, 山东潍坊 261061

收稿日期:2020-09-30 出版日期:2022-02-28 发布日期:2022-03-09
通讯作者: 刘俭辉(1985-),男,河南睢县人,博士,副教授.Email:liujh@lut.edu.cn
基金资助:
国家自然科学基金青年基金(51605212)

A small sample reliability assessment method based on Bootstrap

ZHANG Zhen^1,2, LIU Jian-hui¹, ZHAO Cheng¹, YAN Chang-feng¹

1. School of Machanical and Electrical Engineering, Lanzhou Univ. of Tech., Lanzhou 730050, China;
2. Linde Hydraulic (China) Co., Ltd., Weifang 261061, China

Received:2020-09-30 Online:2022-02-28 Published:2022-03-09

摘要/Abstract

摘要： 针对小样本情况下,采用极大似然估计Mle法求解分布参数会产生较大误差的问题,基于Bootstrap数据扩充的思想提出了B-mle法,减小了参数估计的误差.首先,利用Bootstrap法对小样本数据重抽样产生多组再生样本,达到扩充数据样本的目的;其次,对再生样本采用极大似然估计求解分布参数,得到多组参数的极大似然估计值,并采用核密度估计方法直接从参数估计值求解得到概率密度函数;最后,在给定置信水平下,确定参数的置信区间,得到可靠度的置信区间,并通过Monte Carlo法验证B-mle法的可行性和可信性.利用B-mle法对柱塞泵失效数据进行可靠性的评估,得到不同置信水平下Weibull分布形状参数、尺度参数以及可靠度的置信区间.

关键词: 极大似然估计, Bootstrap法, 核密度估计, 概率密度函数, Monte Carlo模拟

Abstract: In order to solve the problem that the maximum likelihood estimation method (Mle) may produce large errors in solving the distributed parameters in the case of small data samples, the B-MLE method is proposed based on Bootstrap data expansion. Firstly, the Bootstrap method was used to resample the small sample data to generate multiple groups of regenerated samples, so as to expand the data sample. Secondly, the maximum likelihood estimation is used to solve the distribution parameters of the regenerated samples, and the maximum likelihood estimation of multiple parameters is obtained. The probability density function is obtained directly from the parameter estimation by using the kernel density estimation method. Finally, at a given confidence level, the confidence interval of parameters is determined to obtain the confidence interval of reliability. The feasibility and credibility of the proposed method are verified by Monte Carlo method. The results show that the proposed method can reduce the error of maximum likelihood estimation.

Key words: maximum likelihood estimation, bootstrap method, kernel density estimation, probability density function, Monte Carlo simulation

中图分类号:

TH114

张震, 刘俭辉, 赵成, 剡昌锋. 基于Bootstrap的小样本可靠性评估方法[J]. 兰州理工大学学报, 2022, 48(1): 39-44.

ZHANG Zhen, LIU Jian-hui, ZHAO Cheng, YAN Chang-feng. A small sample reliability assessment method based on Bootstrap[J]. Journal of Lanzhou University of Technology, 2022, 48(1): 39-44.

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