基于PSO 的三参数威布尔分布参数的联合估计方法.doc

基于PSO的三参数威布尔分布参数的
联合估计方法*
罗航,王厚军,黄建国,龙兵
(电子科技大学自动化工程学院成都 610054)
摘要:针对图估计及双线性回归估计存在的弊端,将双线性回归估计和极大似然估计(MLE)结合起来,形成一种对三参数威布尔分布参数的联合估计。详细分析了联合优化的核心工具——粒子群优化(PSO)算法的特点、实现和收敛指标,并对基于双线性回归的初值获取作了分析。以仿真和实际例证为基础,详细评析了联合估计参数的优点和缺陷。结果表明:基于PSO优化的联合估计在一定程度上对三参数威布尔分布参数的搜索具有良好的性质,其具体体现为搜索准确和稳定。
关键词:联合估计;威布尔分布;粒子群优化;线性回归;极大似然估计
中图分类号:TP202+.1 文献标识码:A 国家标准学科分类代码:
Method of united estimation to the parameters of three-parameter Weibull
distribution based on PSO
Luo Hang, Wang Houjun, Huang Jianguo, Long Bing
(Automation Engineering College, University of Electronic Science and Technology of China, Chengdu 610054, China)
Abstract:In this paper, the methods of double-linear regression and maximum likelihood estimation (MLE) bined to form a method of united-estimation to the parameters of three-parameter Weibull distribution, which aims at the drawback of merely using figure-estimation or double-linear regression estimation. Taken as a core tool, the algorithm of Particle swarm optimization (PSO) and its characteristics, realization and convergence index are analyzed in detail, and how to get initial value based on double-linear regression is analyzed too. Then the advantage and disadvantage of the united-estimation are evaluated, which is based on simulation and actual cases. The result shows that the presented united optimization method used for searching the parameters of three-parameter Weibull distribution based on PSO algorithm has good characteristics in certain extend, namely, the searching is correct and robust.
Key words:united estimation; Weibull distribution; particle swarm optimization (PSO); linear regression; maximum likelihood estimation (MLE)
1 引言
在可靠性技术分析中,威布尔分布是较为常用但又比较复杂的一种寿命分布[1-4]。因此,如何准确计算威布尔分布参数显得非常重要。
收稿日期:2008-10 Received Date:2008-10
*基金项目:国防基础科研项目(A1420061264);总装预研基金(9140A17030308DZ02)、NSFC(60673011) 、UESTC(JX0756)资助项目
本文的主要目的是:将粒子群优化算法[5](particle swarm optimization,PSO)计算三参数威布尔分布的极大似然估计(maximum likelihood estimation, MLE)参数。这样做的原因