基于马氏距离的二元退化可靠性分析
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摘要
为解决二元退化产品可靠性建模困难,提出了基于马氏距离(Mahalanobis distance,MD)的二元退化产品可靠性分析方法。首先引入MD,将二元退化数据降维至一元MD,并采用蒙特卡罗方法确定MD失效阈值;然后分别采用了Wiener过程的基本模型和3个具有随机参数的Wiener过程模型进行退化建模,运用贝叶斯方法进行参数估计,并通过模型验证、分位数图(quantile-quantile plot,QQ图)和改进的留一法交叉验证等模型选择方法综合判断确定最优模型。最后采用裂纹增长数据实例验证了所提方法的有效性。
The reliability of many highly reliable products is usually evaluated by two or more performance characteristics.To address this concern,a reliability analysis method based on Mahalanobis distance(MD)is proposed.Firstly,MD is used to transform the bivariate degradation data to one dimensional MD data.The MD threshold is obtained by the Monte-Carlo method Then,a simple wiener process model and three wiener process models with random effects are investigated.The statiscal inference is performed via Bayesian approach.An integrated method of model selection is given,which considers not only the hypothesis testing model and the quantile-quantile(QQ)plot,but also the refined leave-one-out cross-validation value.Finally,for an illustration of the proposed method,a numerical example about fatigue cracks is discussed and some results are presented.
The reliability of many highly reliable products is usually evaluated by two or more performance characteristics.To address this concern,a reliability analysis method based on Mahalanobis distance(MD)is proposed.Firstly,MD is used to transform the bivariate degradation data to one dimensional MD data.The MD threshold is obtained by the Monte-Carlo method Then,a simple wiener process model and three wiener process models with random effects are investigated.The statiscal inference is performed via Bayesian approach.An integrated method of model selection is given,which considers not only the hypothesis testing model and the quantile-quantile(QQ)plot,but also the refined leave-one-out cross-validation value.Finally,for an illustration of the proposed method,a numerical example about fatigue cracks is discussed and some results are presented.
引文
[1]刘晓娟,王华伟,徐璇.考虑多退化失效和突发失效之间竞争失效的可靠性评估方法[J].中国机械工程,2017,28(1):7-12.LIU X J,WANG H W,XU X.Reliability assessment based on competition failure considering multi-degradation and catastrophic failure[J].China Mechanical Engineering,2017,28(1):7-12.
[2]PAN Z Q,BALAKRISHNAN N,SUN Q,et al.Bivariate degradation analysis of products based on Wiener processes and copulas[J].Journal of Statistical Computation and Simulation,2013,83(7):1316-1329.
[3]WANG X L,BALAKRISHNAN N,GUO B,et al.Residual life estimation based on bivariate non-stationary gamma degradation process[J].Journal of Statistical Computation and Simulation,2015,85(2):405-421.
[4]谷梦瑶,陈友玲,罗凯.多退化变量下基于灰色生成率序列的相似性寿命预测方法[J].计算机集成制造系统,2017,23(3):525-533.GU M Y,CHEN Y L,LUO K.Multi-index modeling for the similarity-based residual life estimation based on grey generation rate sequence[J].Computer Integrated Manufacturing Systems,2017,23(3):525-533.
[5]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.WANG H W,XI W J,FENG Y G.Remaining life prediction based on competing risks of degradation failure and traumatic failure for missiles[J].Acta Aeronautica et Astronautica Sinica,2016,37(4):1240-1248.
[6]张国龙,蔡金燕,梁玉英,等.基于距离分析的多性能参数故障预测方法[J].电光与控制,2014,21(2):32-35.ZHANG G L,CAI J Y,LIANG Y Y,et al.A fault prediction approach for multiple performance measures based on distance analysis[J].Electronics Optics&Control,2014,21(2):32-35.
[7]杨绪兵,王一雄,陈斌.马氏度量学习中的几个关键问题研究及几何解释[J].南京大学学报(自然科学),2013,49(2):133-141.YANG X B,WANG Y X,CHEN B.Research on several key problems of mahalanobis metric learning and corresponding geometrical interpretations[J].Journal of Nanjing University(Natural Sciences),2013,49(2):133-141.
[8]KUMAR S,CHOW T W S,PECHT M.Approach to fault identification for electronic products using Mahalanobis distance[J].IEEE Trans.on Instrumentation and Measurement,2010,59(8):2055-2064.
[9]NIU G,SINGH S,HOLLAND S W,et al.Health monitoring of electronic products based on Mahalanobis distance and Weibull decision metrics[J].Microelectronics Reliability,2011(51):279-284.
[10]HU Z W,XIAO M Q,ZHANG L,et al.Mahalanobis distance based approach for anomaly detection of analog filters using frequency features and parzen window density estimation[J].Journal of Electronic Test,2016(32):681-693.
[11]林彬,宋东,和麟.基于马氏距离与组距估计的复杂系统健康评估[J].仪器仪表学报,2016,37(9):2022-2028.LIN B,SONG D,HE L.Complex system health assessment based on mahalanobis distance and bin-width estimation technique[J].Chinese Journal of Scientific Instrument,2016,37(9):2022-2028.
[12]谷梦瑶,陈友玲,王新龙.多退化变量下基于实时健康度的相似性寿命预测方法[J].计算机集成制造系统,2017,23(2):362-372.GU M Y,CHEN Y L,WANG X L.Multi-index modeling for similarity-based residual life estimation based on real-time health degree[J].Computer Integrated Manufacturing Systems,2017,23(2):362-372.
[13]YE Z S,XIE M.Stochastic modelling and analysis of degradation for highly reliable products[J].Applied Stochastic Models in Business and Industry,2015,31(1):16-32.
[14]TANG S J,GUO X S,YU C Q,et al.Accelerated degradation tests modeling based on the nonlinear Wiener process with random effects[J].Mathematical Problems in Engineering,2014:1-11.
[15]WANG X.Wiener processes with random effects for degradation data[J].Journal of Multivariate Analysis,2010,101(1):340-351.
[16]LI H,PAN D H,CHEN C L.Reliability modeling and life estimation using an expectation maximization based Wiener degradation model for momentum wheels[J].IEEE Trans.on Cybernetics,2015,45(5):955-963.
[17]PENG W W,LI Y F,YANG Y J,et al.Inverse Gaussian process models for degradation analysis:a Baysian perspective[J].Reliability Engineering&System Safety,2014,130(6):175-189.
[18]RODRGUEZ-PICN L.Reliability assessment for systems with two performance characteristics based on gamma processes with marginal heterogeneous random effects[J].Eksploatacja i Niezawodnosc-Maintenance and Reliability,2017,19(1):8-18.
[19]YE Z S,CHEN N.The inverse Gaussian process as a degradation model[J].Technometrics,2014,56(3):302-311.
[20]HAMADA M S,WILSON A G,REESE C S,等.贝叶斯可靠性[M].曾志国,译.北京:国防工业出版社,2014.HAMADA M S,WILSON A G,REESE C S,et al.Bayesian reliability[M].ZENG Z G,trans.Beijing:National Defense Industry Press,2014.
[21]WANG P.System reliability prediction based on degradation modeling considering field operating stress scenarios[D].New Brunswick,New Jersey:The State University of New Jersey,2003.
[2]PAN Z Q,BALAKRISHNAN N,SUN Q,et al.Bivariate degradation analysis of products based on Wiener processes and copulas[J].Journal of Statistical Computation and Simulation,2013,83(7):1316-1329.
[3]WANG X L,BALAKRISHNAN N,GUO B,et al.Residual life estimation based on bivariate non-stationary gamma degradation process[J].Journal of Statistical Computation and Simulation,2015,85(2):405-421.
[4]谷梦瑶,陈友玲,罗凯.多退化变量下基于灰色生成率序列的相似性寿命预测方法[J].计算机集成制造系统,2017,23(3):525-533.GU M Y,CHEN Y L,LUO K.Multi-index modeling for the similarity-based residual life estimation based on grey generation rate sequence[J].Computer Integrated Manufacturing Systems,2017,23(3):525-533.
[5]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.WANG H W,XI W J,FENG Y G.Remaining life prediction based on competing risks of degradation failure and traumatic failure for missiles[J].Acta Aeronautica et Astronautica Sinica,2016,37(4):1240-1248.
[6]张国龙,蔡金燕,梁玉英,等.基于距离分析的多性能参数故障预测方法[J].电光与控制,2014,21(2):32-35.ZHANG G L,CAI J Y,LIANG Y Y,et al.A fault prediction approach for multiple performance measures based on distance analysis[J].Electronics Optics&Control,2014,21(2):32-35.
[7]杨绪兵,王一雄,陈斌.马氏度量学习中的几个关键问题研究及几何解释[J].南京大学学报(自然科学),2013,49(2):133-141.YANG X B,WANG Y X,CHEN B.Research on several key problems of mahalanobis metric learning and corresponding geometrical interpretations[J].Journal of Nanjing University(Natural Sciences),2013,49(2):133-141.
[8]KUMAR S,CHOW T W S,PECHT M.Approach to fault identification for electronic products using Mahalanobis distance[J].IEEE Trans.on Instrumentation and Measurement,2010,59(8):2055-2064.
[9]NIU G,SINGH S,HOLLAND S W,et al.Health monitoring of electronic products based on Mahalanobis distance and Weibull decision metrics[J].Microelectronics Reliability,2011(51):279-284.
[10]HU Z W,XIAO M Q,ZHANG L,et al.Mahalanobis distance based approach for anomaly detection of analog filters using frequency features and parzen window density estimation[J].Journal of Electronic Test,2016(32):681-693.
[11]林彬,宋东,和麟.基于马氏距离与组距估计的复杂系统健康评估[J].仪器仪表学报,2016,37(9):2022-2028.LIN B,SONG D,HE L.Complex system health assessment based on mahalanobis distance and bin-width estimation technique[J].Chinese Journal of Scientific Instrument,2016,37(9):2022-2028.
[12]谷梦瑶,陈友玲,王新龙.多退化变量下基于实时健康度的相似性寿命预测方法[J].计算机集成制造系统,2017,23(2):362-372.GU M Y,CHEN Y L,WANG X L.Multi-index modeling for similarity-based residual life estimation based on real-time health degree[J].Computer Integrated Manufacturing Systems,2017,23(2):362-372.
[13]YE Z S,XIE M.Stochastic modelling and analysis of degradation for highly reliable products[J].Applied Stochastic Models in Business and Industry,2015,31(1):16-32.
[14]TANG S J,GUO X S,YU C Q,et al.Accelerated degradation tests modeling based on the nonlinear Wiener process with random effects[J].Mathematical Problems in Engineering,2014:1-11.
[15]WANG X.Wiener processes with random effects for degradation data[J].Journal of Multivariate Analysis,2010,101(1):340-351.
[16]LI H,PAN D H,CHEN C L.Reliability modeling and life estimation using an expectation maximization based Wiener degradation model for momentum wheels[J].IEEE Trans.on Cybernetics,2015,45(5):955-963.
[17]PENG W W,LI Y F,YANG Y J,et al.Inverse Gaussian process models for degradation analysis:a Baysian perspective[J].Reliability Engineering&System Safety,2014,130(6):175-189.
[18]RODRGUEZ-PICN L.Reliability assessment for systems with two performance characteristics based on gamma processes with marginal heterogeneous random effects[J].Eksploatacja i Niezawodnosc-Maintenance and Reliability,2017,19(1):8-18.
[19]YE Z S,CHEN N.The inverse Gaussian process as a degradation model[J].Technometrics,2014,56(3):302-311.
[20]HAMADA M S,WILSON A G,REESE C S,等.贝叶斯可靠性[M].曾志国,译.北京:国防工业出版社,2014.HAMADA M S,WILSON A G,REESE C S,et al.Bayesian reliability[M].ZENG Z G,trans.Beijing:National Defense Industry Press,2014.
[21]WANG P.System reliability prediction based on degradation modeling considering field operating stress scenarios[D].New Brunswick,New Jersey:The State University of New Jersey,2003.