基于Copula函数耦合性建模的二元加速退化数据统计分析方法
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摘要
以某型继电器为研究对象,提出了一种二元加速退化数据建模方法:利用Wiener过程建立性能参数的退化模型,然后结合阿伦尼斯方程建立模型参数的加速退化模型,采用Copula函数建立二元加速退化过程之间的耦合性模型;为了一体化估计二元加速退化模型中的多个参数,设计了一种基于Bayesian马尔可夫链蒙特卡罗的参数估计方法;利用继电器二元加速退化数据统计分析实例验证了所提建模方法与参数估计方法的可行性;研究工作为解决类似产品的可靠性评估问题提供了有益借鉴,为完善二元加速退化数据统计分析理论做出了一定贡献。
A modeling method of bivariate accelerated degradation data was proposed. A Wiener process was used to establish degradation models for each degradation process,and then the Arrhenius equation was applied to establish accelerated degradation models for model parameters,finally Copulas functions were adopted to construct the dependency model between bivariate accelerated the degradation processes.A parameter estimation method based on Bayesian Markov Chain Monte Carlo was designed to estimate the multiple parameters of bivariate accelerated degradation model. A case application of a certain type of relay was provided to validate the feasibility of the proposed methods. The research work may help solve other reliability assessment problems for similar products,and makes some contributions to develop the theory of statistically analyzing bivariate acceleration degradation data.
A modeling method of bivariate accelerated degradation data was proposed. A Wiener process was used to establish degradation models for each degradation process,and then the Arrhenius equation was applied to establish accelerated degradation models for model parameters,finally Copulas functions were adopted to construct the dependency model between bivariate accelerated the degradation processes.A parameter estimation method based on Bayesian Markov Chain Monte Carlo was designed to estimate the multiple parameters of bivariate accelerated degradation model. A case application of a certain type of relay was provided to validate the feasibility of the proposed methods. The research work may help solve other reliability assessment problems for similar products,and makes some contributions to develop the theory of statistically analyzing bivariate acceleration degradation data.
引文
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[2]滕飞,王浩伟,陈瑜,等.加速度计加速退化数据统计分析方法[J].中国惯性技术学报,2017,25(2):275-280.
[3]WANG H W,XU T X,MI Q L.Lifetime prediction based on Gamma processes from accelerated degradation data[J].Chinese Journal of Aeronautics,2015,28(1):172-179.
[4]王浩伟,奚文骏,冯玉光.基于退化失效与突发失效竞争的导弹剩余寿命预测[J].航空学报,2016,37(4):1240-1248.
[5]王浩伟,滕克难,李军亮.随机环境应力冲击下基于多参数相关退化的导弹部件寿命预测[J].航空学报,2016,37(11):3404-3412.
[6]WANG Y P,PHAM H.Modeling the dependent competing risks with multiple degradation processes and random shock using time-varying Copulas[J].IEEE Transactions on Reliability,2012,61(1):13-22.
[7]潘骏,王小云,陈文华,等.基于多元性能参数的加速退化试验方案优化设计研究[J].机械工程学报,2012,48(2):30-35.
[8]PAN Z Q,BALAKRISHNAN N.Reliability modeling of degradation of products with multiple performance characteristics based on gamma process[J].Reliability Engineering and System Safety,2011,96(8):949-957.
[9]王孟.基于Copula函数的多元加速退化试验方法研究[D].杭州:浙江理工大学,2013.
[10]TSAI T R,SUNG W Y,LIO Y L,et al.Optimal two-variable accelerated degradation test plan for Gamma degradation processes[J].IEEE Transactions on Reliability,2016,65(1):459-468.
[11]ZHANG X P,SHANG J Z,CHEN X,et al.Statistical inference of accelerated life testing with dependent competing failures based on Copula theory[J].IEEE Transactions on Reliability,2014,63(3):764-780.
[12]李文华,马思宁,沈培根,等.振动条件下铁路继电器寿命预测研究[J].电气工程学报,2017,12(7):8-15.
[13]叶雪荣,林义刚,黄晓毅,等.航天继电器贮存过程吸合时间退化机理研究[J].电工技术学报,2017,32(11):173-179.
[14]孟彦辰.基于性能参数退化的航天继电器可靠性建模与评估研究[D].哈尔滨:哈尔滨工业大学,2015.
[15]王浩伟,滕克难.基于加速退化数据的可靠性评估技术综述[J].系统工程与电子技术,2017,39(12):2877-2885.
[16]FAN M F,ZENG Z G,ZIO E,et al.Modeling dependent competing failure processes with degradation-shock dependence[J].Reliability Engineering and System Safety,2017,165(7):422-430.
[17]潘正强.加速应力下二元退化可靠性建模及其试验设计方法[D].长沙:国防科学技术大学,2011.
[18]PENG W W,LI Y F,YANG Y J,et al.Bivariate analysis of incomplete degradation observations based on inverse Gaussian processes and Copulas[J].IEEE Transactions on Reliability,2016,65(2):624-639.
[19]NTZOUFRAS I.Bayesian Modeling Using Win BUGS[M].Hoboken,New Jersey,John Wiley&Sons,2009.
[20]PAN Z Q,BALAKRISHNAN N,SUN Q.Bivariate constantstress accelerated degradation model and inference[J].Communications in Statistics-Simulation and Computation,2011,40(2):247-257.