贝叶斯理论的可靠性评估方法及在数控系统评估中的运用  

Reliability Estimation of CNC System Based on Bayes Method

作　　者：游达章[1,2] 唐小琦[1] 戴怡[3] 郑小年[1] 金健[1] 

机构地区：[1]华中科技大学国家数控系统工程技术研究中心,武汉430074 [2]湖北工业大学,武汉430068 [3]天津工程师范学院,天津300222

出　　处：《中国机械工程》2011年第3期314-317,共4页China Mechanical Engineering

基　　金：国家自然科学基金资助项目(50875186);国家科技重大专项(2009ZX04009-011;2009ZX04014-013-02);武汉市科技局资助项目(200951830559)

摘　　要：数控系统故障概率符合威布尔分布,如果以威布尔分布来构造似然函数,运用Bayes方法进行可靠性估计,将涉及大量的积分运算,并且不便于选择合适的先验分布。为了减小计算工作量和提高评估效率,将威布尔分布转化为指数分布,并取倒伽玛分布为先验分布;采用先验矩的方法估计先验分布的超参数;利用伽玛函数性质进行指数分布参数的估计,并转化为威布尔分布特征寿命参数的点估计和区间估计,进一步推导计算其他可靠性指标。给出数字实例,证明该方法可行。Weibull distribution was used to describe the times-to-failure of a CNC system.Lots of integral operation would be involved in Bayes estimation with using Weibull distribution to construct likelihood function.To reduce the amount of calculation,the Weibull distribution was transformed to exponential distribution,and the obverse-Gamma distribution was chosen as the prior distribution.Then the hyper-parameters of the prior distribution were estimated by moment method,lastly the parameter of the exponential distribution was be estimated,which was transformed into the size parameter and the other reliability parameters of the Weibull distribution.An example was given to show that the result is proper and the method is feasible.

关 键 词：威布尔分布 指数分布 可靠性评估 贝叶斯 

分 类 号：TH17[机械工程—机械制造及自动化]