无失效数据场合智能换刀机器人中轴承的可靠性评估
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摘要
在目前无失效数据可靠性评估方法中,采用一个模型很难同时得到参数的点估计和置信区间估计。如果采用不同方法分别进行点估计和区间估计,则会造成结果的一致性问题。为此在无失效数据情况下对某型号智能换刀机器人系统中转动关节处的滚动轴承进行可靠性分析,提出一种新的无失效数据可靠性评估模型。新模型采用E-Bayes方法推导出产品寿命概率分布曲线,进而得到产品可靠度的点估计。再利用参数Bootstrap法从寿命概率分布中重新抽取新样本,通过新样本获得产品可靠度的区间估计。在不降低结果可信度的情况下,同时得到产品可靠度的点估计和区间估计。算例分析结果表明,在威布尔分布条件下,新模型不仅能够满足可靠性评估的要求,还可以提高可靠度区间估计精度。所提模型已经验证在进行无失效数据可靠性评估过程中具有良好的可行性,且便于工程应用。
It is difficult to obtain the point estimation and confidence interval estimation of the parameters simultaneously by using asingle model in the current reliability evaluation method of zero-failure data. If different methods are used for point estimation andinterval estimation, the consistency of the results will be caused. In order to solve this problem, the reliability analysis of rolling bearingsat rotating joints in an intelligent tool changing robot system without failure data is carried out, and a new reliability evaluation modelbased on zero-failure data is proposed. The E-Bayes method is adopted by the new model to derive the probability distribution curve ofproduct life, and then the point estimation of product reliability is obtained. Then, the parameter Bootstrap method is used to re-extractnew samples from the life probability distribution, and the interval estimation of product reliability is obtained from the new samples. Thepoint estimation and interval estimation of product reliability are obtained simultaneously without reducing the credibility of the result.The case analysis shows that the new model not only meets the requirements ofreliability assessment, but also improves the accuracy ofreliability interval estimation under Weibull distribution. The proposed model is validated to be feasible in the process of reliabilityevaluation of zero-failure data, and it is also convenient for engineering application.
It is difficult to obtain the point estimation and confidence interval estimation of the parameters simultaneously by using asingle model in the current reliability evaluation method of zero-failure data. If different methods are used for point estimation andinterval estimation, the consistency of the results will be caused. In order to solve this problem, the reliability analysis of rolling bearingsat rotating joints in an intelligent tool changing robot system without failure data is carried out, and a new reliability evaluation modelbased on zero-failure data is proposed. The E-Bayes method is adopted by the new model to derive the probability distribution curve ofproduct life, and then the point estimation of product reliability is obtained. Then, the parameter Bootstrap method is used to re-extractnew samples from the life probability distribution, and the interval estimation of product reliability is obtained from the new samples. Thepoint estimation and interval estimation of product reliability are obtained simultaneously without reducing the credibility of the result.The case analysis shows that the new model not only meets the requirements ofreliability assessment, but also improves the accuracy ofreliability interval estimation under Weibull distribution. The proposed model is validated to be feasible in the process of reliabilityevaluation of zero-failure data, and it is also convenient for engineering application.
引文
[1]LEI Jingtao,YU Huangying,WANG Tianmiao.Dynamic bending of bionic flexible body driven by pneumatic artificial muscles(PAMs)for spinning gait of quadruped robot[J].Chinese Journal of Mechanical Engineering,2016,29(1):11-20.
[2]DING Feng,YIN Liucheng,DANG Liuqiang.Reliability assessment of the small sample aero-engine bearings[J].Advanced Materials Research,2014,986-987:858-861.
[3]LIU Jianfeng,YIN Yichao,FU Guozhong,et al.Notice of retraction a fusion method of zero-failure data in different environments for reliability assessment of success-failure type products[C]//International Conference on Quality,Reliability,Risk,Maintenance,and Safety Engineering.IEEE,2013:1102-1105.
[4]韩明.无失效数据情形可靠性参数的估计和调整[J].应用数学,2006,19(2):325-330.HAN Ming.Estimation and rectification of reliability parameters in the case of zero-failure data[J].Mathematica Applicata,2006,19(2):325-330.
[5]NAGATA H,LI Yagang,MAACK D R,et al.Reliability estimation from zero-failure LiNbO3,modulator bias drift data[J].IEEE Photonics Technology Letters,2004,16(6):1477-1479.
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[10]茆诗松,夏剑锋,管文琪.轴承寿命试验中无失效数据的处理[J].应用概率统计,1993(3):326-331.MAO Shisong,XIA Jianfeng,GUAN Wenqi.The reliability analysis of zero-failure data for bearing life test[J].Chinese Journal of Applied Probability and Statistics,1993(3):326-331.
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[12]刘海涛,张志华.威布尔分布无失效数据的Bayes可靠性分析[J].系统工程理论与实践,2008,28(11):103-108.LIU Haitao,ZHANG Zhinhua.Bayesian reliability analysis of Weibull zero-failure data[J].System Engineering Theory and Practice,2008,28(11):103-108.
[13]韩明.多层先验分布的构造及其应用[J].运筹与管理,1997(3):31-40.HAN Ming.The structure of hierarchical prior distribution and application[J].Operations Research and Management Science,1997(3):31-40.
[14]韩明.产品无失效数据的综合处理[J].机械工程学报,2003,39(2):129-132.HAN Ming.Synthesized process for zero-failure data of the products[J].Journal of Mechanical Engineering,2003,39(2):129-132.
[15]蔡国梁,吴来林,唐晓芬.双超参数无失效数据的E-Bayes可靠性分析[J].江苏大学学报,2010,31(6):736-739.CAI Guoliang,WU Laifen,TANG Xiaofen.E-Bayes reliability analysis of double hyper parameters zero failure data[J].Journal of Jiangsu University,2010,31(6):736-739.
[16]傅惠民,张勇波.Weibull分布定时无失效数据可靠性分析方法[J].航空动力学报,2010,25(12):2807-2810.FU Huimin,ZHANG Yongbo.Method of reliability analysis for time truncated zero-failure databased on Weibulldistribution[J].Journal of Aerospace Power,2010,25(12):2807-2810.
[17]HAN Ming.Confidence limit of reliability parameters in the case of zero-failure data[J].Chinese Journal of Engineering Mathematics,2004,21(2):245-244.
[18]JIANG Renbin,JIANG Danyu.Fiducial lower confidence limits of reliability for a standby system based on zero-failure data.[J].J.Zhejiang Univ.Sci.Ed,2010(6):629-632.
[19]韩明.Weibull分布可靠性参数的置信限[J].机械强度,2009,31(1):59-62.HAN Ming.Confidence limits of reliability parameters for Weibull distribution Journal[J].Journal of Mechanical Strength,2009,31(1):59-62.
[20]贾祥,王小林,郭波.极少失效数据和无失效数据的可靠性评估[J].机械工程学报,2016,52(2):182-188.JIA Xiang,WANG Xiaolin,GUO Bo.Reliability assessment for very few failure data and zero-failure data[J].Journal of Mechanical Engineering,2016,52(2):182-188.
[21]罗巍,张春华,谭源源,等.基于Bootstrap的可修系统贮存可用度近似置信下限评估方法[J].兵工学报,2010,31(3):391-395.LUO Wei,ZHANG Chunhua,TAN Yuanyuan,et al.Estimating method of the approximate confidence lower limit of repairable system storage availabilitybased on Bootstrap[J].Acta Armamentarii,2010,31(3):391-395.
[22]夏新涛,叶亮,李云飞,等.基于多层自助最大熵法的可靠性评估[J].兵工学报,2016,37(7):1317-1329.XIA Xintao,YE Liang,LI Yunfei,et al.Reliability evaluation based on hierarchical Bootstrap maximum entropy method[J].Acta Armamentarii,2016,37(7):1317-1329.
[23]LIANG R,WU W,YU F,et al.Simplified method for evaluating shield tunnel deformation due to adjacent excavation[J].Tunnelling and Underground Space Technology,2018,71:94-105.
[24]杨晓蔚.滚动轴承疲劳寿命威布尔分布三参数的研究[D].合肥:合肥工业大学,2003.YANG Xiaowei.Study on three parameters of Wipur distribution for fatigue life of rolling bearings[D].Hefei:Hefei University of Technology,2003.
[25]宁江凡,鄢小清,张士峰.液体火箭发动机无失效条件下的可靠性分析方法[J].国防科技大学学报,2006,28(5):22-25.NING Jiangfan,YAN Xiaoqing,ZHANG Shifeng.Study on reliability analysis method for liquid rocketengine in the case of zero-failure data[J].Journal of National University of Defense Technology,2006,28(5):22-25.
[26]茆诗松,王玲玲,濮晓龙.威布尔分市场合无失效数据的可靠性分析[J].应用概率统计,1996(1):94-107.MAO Shisong,WANG Lingling,PU Xiaolong.Reliability analysis for Weibull zero-failure data[J].Chinese Journal of Applied Probability and Statistics,1996(1):94-107.
[27]BERGER J O.Statistical decision theory and Bayesian analysis[J].Springer,2002,83(401):266.
[28]韩明.失效概率的E-Bayes估计及其性质[J].数学物理学报,2007,27A(3):488-495.HAN Ming.E-Bayes estimation of failure probability and its properties[J].ActaMathematicaScientia,2007,27A(3):488-495.
[29]JOSHI M,SEIDEL-MORGENSTERN A,KREMLING A.Exploiting the bootstrap method for quantifying parameter confidence intervals in dynamical systems[J].Metabolic Engineering,2006,8(5):447.
[30]FLYGARE M E,AUSTIN J A,BUCKWALTER M.Maximum likelihood estimation for the 2-parameter Weibulldistribution based on interval-data[J].IEEETransactions on Reliability,2009,R-34(1):57-59.
[31]HONG HP.Selection of regressand for fitting the extreme value distributions using the ordinary,weighted and generalized least-squares methods[J].Reliability Engineering&System Safety,2013,118(10):71-80.
[32]BAIN L.Inferences based on censored sampling from the Weibull or extreme-value distribution[J].Technometrics,1972,14(3):693-702.
[33]高攀东,沈雪瑾,陈晓阳,等.无失效数据下航空轴承的可靠性分析[J].航空动力学报,2015,30(8):1980-1987.GAO Pandong,SHEN Xuejin,CHEN Xiaoyang,et.Reliability analysis for aircraft bearing with zero-failure data[J].Journal of Aerospace Power,2015,30(8):1980-1987.
[34]STENSRUD E,FOSS T,KITCHENHANM B,et al.An empirical validation of the relationship between the magnitude of relative error and project size[C]//Software Metrics,2002.Proceedings.Eighth IEEE Symposium on IEEE,2002:3-12.
[2]DING Feng,YIN Liucheng,DANG Liuqiang.Reliability assessment of the small sample aero-engine bearings[J].Advanced Materials Research,2014,986-987:858-861.
[3]LIU Jianfeng,YIN Yichao,FU Guozhong,et al.Notice of retraction a fusion method of zero-failure data in different environments for reliability assessment of success-failure type products[C]//International Conference on Quality,Reliability,Risk,Maintenance,and Safety Engineering.IEEE,2013:1102-1105.
[4]韩明.无失效数据情形可靠性参数的估计和调整[J].应用数学,2006,19(2):325-330.HAN Ming.Estimation and rectification of reliability parameters in the case of zero-failure data[J].Mathematica Applicata,2006,19(2):325-330.
[5]NAGATA H,LI Yagang,MAACK D R,et al.Reliability estimation from zero-failure LiNbO3,modulator bias drift data[J].IEEE Photonics Technology Letters,2004,16(6):1477-1479.
[6]ALI J B,CHEBEL-MORELLO B,SAILDI L,et al.Accurate bearing remaining useful life prediction based on Weibull distribution and artificial neural network[J].Mechanical Systems&Signal Processing,2015,56-57:150-172.
[7]MA Meng,CHEN Xuefeng,WANG Shibin,et al.Bearing degradation assessment based on weibull distribution and deep belief network[C]//International Symposium on Flexible Automation,IEEE,2016:382-385.
[8]YANG Jianwei,WANG Jinhai,XIE Yidong.Bayesian method for reliability assessment based on zero-failure data under small sample size:Application for high speed railway vehicle[J].Information Technology Journal,2013,12(21):6203-6207.
[9]BREMERMAN M V.Practical Bayesian methods for determining device failure rates from zero-failure data[C]//Reliability and Maintainability Symposium,IEEE,2013:1-6.
[10]茆诗松,夏剑锋,管文琪.轴承寿命试验中无失效数据的处理[J].应用概率统计,1993(3):326-331.MAO Shisong,XIA Jianfeng,GUAN Wenqi.The reliability analysis of zero-failure data for bearing life test[J].Chinese Journal of Applied Probability and Statistics,1993(3):326-331.
[11]HAN Ming.Bayesian estimation and hierarchical Bayesian estimationof zero-failure data[J].Chinese Quarterly Journal of Mathematics,2001,16(1):65-70.
[12]刘海涛,张志华.威布尔分布无失效数据的Bayes可靠性分析[J].系统工程理论与实践,2008,28(11):103-108.LIU Haitao,ZHANG Zhinhua.Bayesian reliability analysis of Weibull zero-failure data[J].System Engineering Theory and Practice,2008,28(11):103-108.
[13]韩明.多层先验分布的构造及其应用[J].运筹与管理,1997(3):31-40.HAN Ming.The structure of hierarchical prior distribution and application[J].Operations Research and Management Science,1997(3):31-40.
[14]韩明.产品无失效数据的综合处理[J].机械工程学报,2003,39(2):129-132.HAN Ming.Synthesized process for zero-failure data of the products[J].Journal of Mechanical Engineering,2003,39(2):129-132.
[15]蔡国梁,吴来林,唐晓芬.双超参数无失效数据的E-Bayes可靠性分析[J].江苏大学学报,2010,31(6):736-739.CAI Guoliang,WU Laifen,TANG Xiaofen.E-Bayes reliability analysis of double hyper parameters zero failure data[J].Journal of Jiangsu University,2010,31(6):736-739.
[16]傅惠民,张勇波.Weibull分布定时无失效数据可靠性分析方法[J].航空动力学报,2010,25(12):2807-2810.FU Huimin,ZHANG Yongbo.Method of reliability analysis for time truncated zero-failure databased on Weibulldistribution[J].Journal of Aerospace Power,2010,25(12):2807-2810.
[17]HAN Ming.Confidence limit of reliability parameters in the case of zero-failure data[J].Chinese Journal of Engineering Mathematics,2004,21(2):245-244.
[18]JIANG Renbin,JIANG Danyu.Fiducial lower confidence limits of reliability for a standby system based on zero-failure data.[J].J.Zhejiang Univ.Sci.Ed,2010(6):629-632.
[19]韩明.Weibull分布可靠性参数的置信限[J].机械强度,2009,31(1):59-62.HAN Ming.Confidence limits of reliability parameters for Weibull distribution Journal[J].Journal of Mechanical Strength,2009,31(1):59-62.
[20]贾祥,王小林,郭波.极少失效数据和无失效数据的可靠性评估[J].机械工程学报,2016,52(2):182-188.JIA Xiang,WANG Xiaolin,GUO Bo.Reliability assessment for very few failure data and zero-failure data[J].Journal of Mechanical Engineering,2016,52(2):182-188.
[21]罗巍,张春华,谭源源,等.基于Bootstrap的可修系统贮存可用度近似置信下限评估方法[J].兵工学报,2010,31(3):391-395.LUO Wei,ZHANG Chunhua,TAN Yuanyuan,et al.Estimating method of the approximate confidence lower limit of repairable system storage availabilitybased on Bootstrap[J].Acta Armamentarii,2010,31(3):391-395.
[22]夏新涛,叶亮,李云飞,等.基于多层自助最大熵法的可靠性评估[J].兵工学报,2016,37(7):1317-1329.XIA Xintao,YE Liang,LI Yunfei,et al.Reliability evaluation based on hierarchical Bootstrap maximum entropy method[J].Acta Armamentarii,2016,37(7):1317-1329.
[23]LIANG R,WU W,YU F,et al.Simplified method for evaluating shield tunnel deformation due to adjacent excavation[J].Tunnelling and Underground Space Technology,2018,71:94-105.
[24]杨晓蔚.滚动轴承疲劳寿命威布尔分布三参数的研究[D].合肥:合肥工业大学,2003.YANG Xiaowei.Study on three parameters of Wipur distribution for fatigue life of rolling bearings[D].Hefei:Hefei University of Technology,2003.
[25]宁江凡,鄢小清,张士峰.液体火箭发动机无失效条件下的可靠性分析方法[J].国防科技大学学报,2006,28(5):22-25.NING Jiangfan,YAN Xiaoqing,ZHANG Shifeng.Study on reliability analysis method for liquid rocketengine in the case of zero-failure data[J].Journal of National University of Defense Technology,2006,28(5):22-25.
[26]茆诗松,王玲玲,濮晓龙.威布尔分市场合无失效数据的可靠性分析[J].应用概率统计,1996(1):94-107.MAO Shisong,WANG Lingling,PU Xiaolong.Reliability analysis for Weibull zero-failure data[J].Chinese Journal of Applied Probability and Statistics,1996(1):94-107.
[27]BERGER J O.Statistical decision theory and Bayesian analysis[J].Springer,2002,83(401):266.
[28]韩明.失效概率的E-Bayes估计及其性质[J].数学物理学报,2007,27A(3):488-495.HAN Ming.E-Bayes estimation of failure probability and its properties[J].ActaMathematicaScientia,2007,27A(3):488-495.
[29]JOSHI M,SEIDEL-MORGENSTERN A,KREMLING A.Exploiting the bootstrap method for quantifying parameter confidence intervals in dynamical systems[J].Metabolic Engineering,2006,8(5):447.
[30]FLYGARE M E,AUSTIN J A,BUCKWALTER M.Maximum likelihood estimation for the 2-parameter Weibulldistribution based on interval-data[J].IEEETransactions on Reliability,2009,R-34(1):57-59.
[31]HONG HP.Selection of regressand for fitting the extreme value distributions using the ordinary,weighted and generalized least-squares methods[J].Reliability Engineering&System Safety,2013,118(10):71-80.
[32]BAIN L.Inferences based on censored sampling from the Weibull or extreme-value distribution[J].Technometrics,1972,14(3):693-702.
[33]高攀东,沈雪瑾,陈晓阳,等.无失效数据下航空轴承的可靠性分析[J].航空动力学报,2015,30(8):1980-1987.GAO Pandong,SHEN Xuejin,CHEN Xiaoyang,et.Reliability analysis for aircraft bearing with zero-failure data[J].Journal of Aerospace Power,2015,30(8):1980-1987.
[34]STENSRUD E,FOSS T,KITCHENHANM B,et al.An empirical validation of the relationship between the magnitude of relative error and project size[C]//Software Metrics,2002.Proceedings.Eighth IEEE Symposium on IEEE,2002:3-12.