机械工程

基于累积误差平方和最小的参数估计方法

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  • 数控装备可靠性教育部重点实验室//吉林大学 机械与航空航天工程学院,吉林 长春 130022
张英芝(1970-),女,博士,教授,主要从事数控装备可靠性工程研究。

收稿日期: 2020-04-08

  修回日期: 2020-05-19

  网络出版日期: 2020-05-29

基金资助

国家科技重大专项项目 (2015ZX04005005); 吉林省科技发展计划项目 (20190302104GX)

Parameter Estimation Method Based on Minimum Cumulative Error Square Sum

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  • Key Laboratory of CNC Equipment Reliability,Ministry of Education∥School of Mechanical and Aerospace Engineering,
    Jilin University,Changchun 130022,Jilin,China
张英芝(1970-),女,博士,教授,主要从事数控装备可靠性工程研究。

Received date: 2020-04-08

  Revised date: 2020-05-19

  Online published: 2020-05-29

Supported by

Supported by the National Science and Technology Major Project (2015ZX04005005) and Jilin Provincial Department of Science and Technology Foundation (20190302104GX)

摘要

针对经典最小二乘法与加权最小二乘法进行两参数威布尔模型参数估计时,虽满足无偏性但不满足有效性问题,提出一种基于累积误差平方和最小的参数估计方法。基于粒子群算法对完全样本、定时截尾样本以及定数截尾样本进行参数计算,以均方根误差为指标进行效果评价,并结合相关文献数据进行实证研究。研究表明,所提参数估计方法较经典最小二乘法与加权最小二乘法的均方根误差值低,能够较好地给出两参数威布尔模型的参数估计。

本文引用格式

张英芝, 翟粉莉, 郑玉彬, 等 . 基于累积误差平方和最小的参数估计方法[J]. 华南理工大学学报(自然科学版), 2020 , 48(11) : 49 -54 . DOI: 10.12141/j.issn.1000-565X.200159

Abstract

When using classical least squares and weighted least squares to estimate the two-parameter Weibull model parameters,it satisfies the unbiasedness well but it doesn't satisfy the validity. Aiming at this problem,a parameter estimation method based on the minimum sum of squared cumulative errors was proposed. The parameters were calculated for full samples,time-censored samples,and fixed-number censored samples. The root mean square error was used as an indicator to evaluate the effect,and an empirical study was carried out in conjunction with relevant literature data. The research shows that the RMSE value of the proposed parameter estimation method is small than that of the least squares and weighted least squares,so it can efficiently estimate the parameters of the two-parameter Weibull model.
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