摘要
Reliability assessment of the braking system in a high?speed train under small sample size and zero?failure data is veryimportant for safe operation. Traditional reliability assessment methods are only performed well under conditions of large sample size and complete failure data,which lead to large deviation under conditions of small sample size and zero?failure data. To improve this problem,a new Bayesian method is proposed. Based on the characteristics of the solenoid valve in the braking system of a high?speed train,the modified Weibull distribution is selected to describe the failure rate over the entire lifetime. Based on the assumption of a binomial distribution for the failure probability at censored time,a concave method is employed to obtain the relationships between accumulation failure prob?abilities. A numerical simulation is performed to compare the results of the proposed method with those obtained from maximum likelihood estimation,and to illustrate that the proposed Bayesian model exhibits a better accuracy for the expectation value when the sample size is less than 12. Finally,the robustness of the model is demonstrated by obtaining the reliability indicators for a numerical case involving the solenoid valve of the braking system,which shows that the change in the reliability and failure rate among the di erent hyperparameters is small. The method is provided to avoid misleading of subjective information and improve accuracy of reliability assessment under condi?tions of small sample size and zero?failure data.
Reliability assessment of the braking system in a high?speed train under small sample size and zero?failure data is veryimportant for safe operation. Traditional reliability assessment methods are only performed well under conditions of large sample size and complete failure data,which lead to large deviation under conditions of small sample size and zero?failure data. To improve this problem,a new Bayesian method is proposed. Based on the characteristics of the solenoid valve in the braking system of a high?speed train,the modified Weibull distribution is selected to describe the failure rate over the entire lifetime. Based on the assumption of a binomial distribution for the failure probability at censored time,a concave method is employed to obtain the relationships between accumulation failure prob?abilities. A numerical simulation is performed to compare the results of the proposed method with those obtained from maximum likelihood estimation,and to illustrate that the proposed Bayesian model exhibits a better accuracy for the expectation value when the sample size is less than 12. Finally,the robustness of the model is demonstrated by obtaining the reliability indicators for a numerical case involving the solenoid valve of the braking system,which shows that the change in the reliability and failure rate among the di erent hyperparameters is small. The method is provided to avoid misleading of subjective information and improve accuracy of reliability assessment under condi?tions of small sample size and zero?failure data.
基金
Supported by National Natural Science Foundation of China(Grant No.51175028)
Great Scholars Training Project(Grant No.CIT&TCD20150312)
Beijing Recognized Talent Project(Grant No.2014018)
作者简介
Correspondence:Jian-Wei Yang,born in 1971,is currently a professor at Beijing University of Civil Engineering Architecture,China.He received his Ph.D.degree from China Academy of Railway Science,China,in 2006.His research interests include vehicle system dynamics,failure modeling analysis,system reliability and fault diagnosis.He is a senior member of CMES,Great Scholars Project and Beijing Recognized Talent Project.He has carried on many research work about reliability and risk assessment,e.g.,The National Science Fund Project“The theory and analytical method study based on multi-state failure for braking system in high-speed train”,China Postdoctoral Science Foundation Funded Project“Research on the reliability evaluation method of the vehicle system based on the small sample theory and GO method”and The National High Technology Research and Development Program of China“Research and verification of key equipment monitoring and early warning and emergency technology for rail transit operation safety”.He has published about 130 papers in relative research field in total.Tel:+86-10-68322515,E–mail:yangjianwei@bucea.edu.cn;Jin-Hai Wang,born in 1990,is currently a Ph.D.candidate at School of Mechanical,Electronic and Control Engineering,Beijing Jiaotong University,China.He received his Master degree from Beijing University of Civil Engineering Architecture,China,in 2015.His research interests include reliability assessment,gearbox dynamics and mechanical fault diagnose.During the master period,he assisted his supervisor for studying reliability theory under small sample size,fatigue computation for structure of vehicle and optimization work.He also took part in Formula Student China 2015 and Honda energy competition for vehicle design.E–mail:wangjinhai@bjtu.edu.cn;Qiang Huang,is a professor of China Academy of Railway Sciences,was born in 1946.He obtained his Master degree in Vehicle Engineering from China Academy of Railway Sciences,in 1981.His research interests are in vehicle system dynamics for heavy load railway vehicle,high–speed railway vehicle.He is also chief expert of China Academy of Railway Sciences and rewarded“Zhan Tianyou Railway Science and Technology award”in 2001.He carried on many research and development work for Chinese high-speed train,e.g.,“Research for the bogie of 200 km/h EMU”.E–mail:qhuang@rails.com.cn;Ming Zhou,is an associate professor at Beijing University of Civil Engineering Architecture,was born in 1966.He obtained his Ph.D.degree in Mechanical Engineering from Dalian University of Technology,China,in 2006.His research interests are nonlinear dynamics and control.E–mail:zhouming@bucea.edu.
