基于混合威布尔分布的加工中心可靠性评估
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摘要
针对复杂机械系统可靠性评估未考虑可靠性实验故障数据具有多故障模式的不足,建立两重混合威布尔分布模型。为解决可靠性实验小子样故障数据问题,利用模糊聚类的方法实现对故障数据的分类,求得混合威布尔分布的形状参数,以此为基础将混合威布尔分布转换为具有共轭先验分布的混合指数分布。用贝叶斯估计求解混合指数分布各参数值,然后将求得的混合指数分布各参数值转换为混合威布尔分布的各参数值。最后以某型号卧式加工中心为例,求得加工中心的可靠性评估结果。
To solve the reliability assessment's problem of complex mechanical system that not considering for the characteristics of multiple failure modes,this paper built a mixed double Weibull distribution model. To solve the small sample failure data's problem,it used fuzzy clustering method to achieve fault data classification and obtained the sub-population's shape parameter of the mixed Weibull distribution. Then the mixed Weibull distribution converted into mixed exponential distribution which had conjugate prior distribution. By using the Bayes estimation,it obtained the mixed exponential distribution's parameters,then the mixed Weibull distribution's parameters converted into the mixed exponential distribution's parameters. At last,it took an example of a certain type machining center,and obtained the result of reliability evaluation.
To solve the reliability assessment's problem of complex mechanical system that not considering for the characteristics of multiple failure modes,this paper built a mixed double Weibull distribution model. To solve the small sample failure data's problem,it used fuzzy clustering method to achieve fault data classification and obtained the sub-population's shape parameter of the mixed Weibull distribution. Then the mixed Weibull distribution converted into mixed exponential distribution which had conjugate prior distribution. By using the Bayes estimation,it obtained the mixed exponential distribution's parameters,then the mixed Weibull distribution's parameters converted into the mixed exponential distribution's parameters. At last,it took an example of a certain type machining center,and obtained the result of reliability evaluation.
引文
[1]蒋仁言.威布尔模型族[M].北京:科学出版社,1998:24-25.
[2]Bucar T,Nagode M,Fajdiga M.Reliability approximation using fi-nite Weibull mixture distributions[J].Reliability Engineering&System Safety,2004,87(3):241-251.
[3]Jiang R Y,Murthy D N P.Reliability modeling involving two Weibull distributions[J].Reliability Engineering&System Safety,1995,47(3):187-198.
[4]韩明.无失效数据可靠性参数的综合估计[J].数学理论与应用,2000,20(3):36-39.
[5]徐晓岭.数据缺失场合三参数Weibull分布的参数估计[J].上海师范大学学报:自然科学版,2002,31(2):22-30.
[6]孙庆祥,戴邵武,路燕.加权最小二乘—卡尔曼滤波算法在动基座对准中的应用[J].海军航空工程学院学报,2008,23(4):395-400.
[7]Jiang Siyuan,Kececioglu D K.Maximum likelihood estimates,from censored data,for mixed-Weibull distributions[J].IEEE Trans on Reliablity,1992,41(2):248-255.
[8]赵继俊,邹经湘.可靠性实验数据混合威布尔分布的参数优化估计[J].农业机械学报,2000,31(5):106-109.
[9]Attardi L,Guida M,Pulcini G.A mixed-Weibull regression model for the analysis of automotive warranty data[J].Reliability Engineering&System Safety,2005,87(2):265-273.
[10]凌丹,黄洪钟,张小玲,等.混合威布尔分布参数估计的L-M算法[J].电子科技大学学报,2008,37(4):635-638.
[11]金光.一种综合性能与寿命数据的Bayes-Bootstrap方法[J].宇航学报,2007,28(3):731-735.
[12]Perlstein D,Jarvis W,Mazzuchi T.Bayesian calculation of cost optimal burn-in test durations for mixed exponential populations[J].Reliability Engineeing&System Safety,2001,72(3):265-273.
[13]王微.基于信息熵法的数控机床贝叶斯可靠性评估方法研究[D].长春:吉林大学,2013.
[14]游达章,唐小琪,戴怡,等.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[J].中国机械工程,2011,22(3):314-317.
[15]张弢,纪德云.模糊聚类分析法[J].沈阳大学学报:自然科学版,2000,12(2):73-79.
[16]陆建江,徐宝文.区间数据的并行模糊聚类算法[J].东南大学学报:自然科学版,2003,33(4):53-58.
[2]Bucar T,Nagode M,Fajdiga M.Reliability approximation using fi-nite Weibull mixture distributions[J].Reliability Engineering&System Safety,2004,87(3):241-251.
[3]Jiang R Y,Murthy D N P.Reliability modeling involving two Weibull distributions[J].Reliability Engineering&System Safety,1995,47(3):187-198.
[4]韩明.无失效数据可靠性参数的综合估计[J].数学理论与应用,2000,20(3):36-39.
[5]徐晓岭.数据缺失场合三参数Weibull分布的参数估计[J].上海师范大学学报:自然科学版,2002,31(2):22-30.
[6]孙庆祥,戴邵武,路燕.加权最小二乘—卡尔曼滤波算法在动基座对准中的应用[J].海军航空工程学院学报,2008,23(4):395-400.
[7]Jiang Siyuan,Kececioglu D K.Maximum likelihood estimates,from censored data,for mixed-Weibull distributions[J].IEEE Trans on Reliablity,1992,41(2):248-255.
[8]赵继俊,邹经湘.可靠性实验数据混合威布尔分布的参数优化估计[J].农业机械学报,2000,31(5):106-109.
[9]Attardi L,Guida M,Pulcini G.A mixed-Weibull regression model for the analysis of automotive warranty data[J].Reliability Engineering&System Safety,2005,87(2):265-273.
[10]凌丹,黄洪钟,张小玲,等.混合威布尔分布参数估计的L-M算法[J].电子科技大学学报,2008,37(4):635-638.
[11]金光.一种综合性能与寿命数据的Bayes-Bootstrap方法[J].宇航学报,2007,28(3):731-735.
[12]Perlstein D,Jarvis W,Mazzuchi T.Bayesian calculation of cost optimal burn-in test durations for mixed exponential populations[J].Reliability Engineeing&System Safety,2001,72(3):265-273.
[13]王微.基于信息熵法的数控机床贝叶斯可靠性评估方法研究[D].长春:吉林大学,2013.
[14]游达章,唐小琪,戴怡,等.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[J].中国机械工程,2011,22(3):314-317.
[15]张弢,纪德云.模糊聚类分析法[J].沈阳大学学报:自然科学版,2000,12(2):73-79.
[16]陆建江,徐宝文.区间数据的并行模糊聚类算法[J].东南大学学报:自然科学版,2003,33(4):53-58.