面向数控系统可靠性评估的最大熵先验信息解  

Maximum Entropy Prior Information Solution for Numerical Control System Reliability Assessment

作　　者：凌光[1] 戴怡[2] 王仲民[2] 

机构地区：[1]天津职业技术师范大学理学院,天津300222 [2]天津职业技术师范大学机械学院,天津300222

出　　处：《机械工程学报》2012年第6期157-161,共5页Journal of Mechanical Engineering

基　　金：国家自然科学基金(50875186);国家科技重大专项(2009ZX04014-013)资助项目

摘　　要：应用贝叶斯理论对数控系统可靠性评估方法进行研究,提出以最大熵原理求解双参数联合先验分布的方法。利用最大熵原理给出在不同约束条件下威布尔分布双参数联合先验分布的一般解析形式,针对该联合先验分布的具体求解过程,介绍通过应用自助法构造参数再生子样来确定参数矩的方法和利用非线性最小二乘法、结合牛顿迭代法求解联合先验分布中待定系数的方法,引入先验分布稳健性的概念,结合具体数控系统寿命数据,从提高参数矩的阶数和增加参数不等式约束两个方面展开讨论,分别研究这两种改进对先验分布稳健性提升的效果。研究表明基于不等式约束的最大熵二元联合先验分布,能极大地提高先验分布的稳健性,更加适用于数控系统的可靠性评估。To apply Bayesian theory to numerical control（NC） system reliability assessment,a method to get two-parameter joint prior distribution is proposed by maximum entropy principle.The general analytical two-parameter prior distribution of Weibull is obtained using maximum entropy principle under several different constraints.Then considering to solve the specific form of the joint prior distribution,a method to get the two parameters＇ moments is introduced by using bootstrap to generate two parameters＇ samples,and also how to devolve the unknown parameters of joint prior distribution is shown using nonlinear least square jointed Newton iteration method.At last the robustness of prior distribution is introduced.Combining a set of NC system life data,the robustness of the prior distribution is discussed from two aspects： one is to consider higher moments and the other is to introduce inequality restrictions.Studies show that the robustness of prior distribution is greatly improved considering inequality restrictions.It＇s fit for NC system reliability assessment to solve the joint prior distribution using maximum entropy principle with inequality restrictions.

关 键 词：贝叶斯方法 最大熵 数控系统 可靠性评估 

分 类 号：TH17[机械工程—机械制造及自动化]