三参数威布尔形状参数估计方法的比较与推荐取值

doi:10.3901/JME.2024.16.367

摘要/Abstract

摘要： 机电产品寿命大多数服从威布尔分布，其形状参数与潜在的失效机制有关，在相似环境下运行的产品的寿命概率分布通常有大致相同的形状参数。然而，目前在许多实际应用中威布尔形状参数值的范围和取值是基于两参数威布尔分布估计得到，这使得威布尔形状参数范围出现了较为分散的现象。首先使用偏差和方均根误差两个统计特征比较三参数威布尔形状参数估计的相关系数法、最小二乘法和最小偏差法。通过蒙特卡洛仿真验证，表明了相关系数法估计的形状参数更加准确。收集文献中的疲劳试验数据和其他机电产品寿命数据均使用两参数威布尔分布、三参数威布尔分布和对数正态分布进行拟合并通过K-S检验，通过比较三种分布的D值，说明三参数威布尔分布拟合效果最好。使用相关系数法得到三参数威布尔分布形状参数的取值和范围，计算结果表明机电产品的形状参数范围为1.0～3.0，均值为1.774。

关键词: 三参数威布尔分布, 形状参数, 相关系数法, 最小二乘法, 最小偏差法

Abstract: The shape parameters of Weibull distribution of electromechanical products are related to potential failure mechanisms, and the life probability distributions of products operating in similar environments usually have approximately the same shape parameters. However, the ranges and values of the Weibull shape parameter values in many practical applications are currently obtained based on the two-parameter Weibull distribution estimates, which makes the Weibull shape parameter ranges appear more scattered. Correlation coefficient method is compared with least squares method, and minimum discrepancy method for the estimation of the three-parameter Weibull shape parameter by two statistical features that are bias and root mean square error. Validation by Monte Carlo simulation shows that the correlation coefficient is more accurate. The fatigue test data and other electromechanical product life data collected in the literatures are fitted by the two-parameter Weibull distribution, the three-parameter Weibull distribution and the lognormal distribution and pass the K-S test. By comparing D-values of the three distributions, it is shown that the three-parameter Weibull distribution fits best. The correlation coefficient method is used to obtain the values and ranges of the shape parameters of the three-parameter Weibull distributeon. The calculation results show that the range of shape parameters of electromechanical products is 1.0-3.0, and the mean value is 1.774.

Key words: three-parameter Weibull distribution, shape parameter, correlation coefficient method, least squares method, minimum discrepancy method

中图分类号:

TB114

杨小玉, 谢里阳, 杨奕凤, 赵丙峰. 三参数威布尔形状参数估计方法的比较与推荐取值[J]. 机械工程学报, 2024, 60(16): 367-376.

YANG Xiaoyu, XIE Liyang, YANG Yifeng, ZHAO Bingfeng. Comparison of Three-parameter Weibull Shape Parameter Estimation Methods and Its Recommended Values[J]. Journal of Mechanical Engineering, 2024, 60(16): 367-376.

参考文献

[1] 孙有朝,张永进,李龙彪. 可靠性原理与方法[M]. 北京:科学出版社,2016. SUN Youzhao,ZHANG Yongjin,LI Longbiao. Reliability principles and methods[M]. Beijing:Science Press,2016.
[2] HISADA K,ARIZINO I. Reliability tests for Weibull distribution with varying shape-parameter,based on complete data[J]. IEEE Transactions on Reliability,2002,51(3):331-336.
[3] YANG X Y,XIE L Y,ZHAO B F,et al. An iterative method for parameter estimation of the three-parameter weibull distribution based on a small sample size with a fixed shape parameter[J]. International Journal of Structural Stability and Dynamics,2022,22(12):2250125.
[4] ABERNETHY R B. The new Weibull handbook[M]. Florida:R.B. Abernethy,2010.
[5] 严晓东,马翔,郑荣跃,等. 三参数威布尔分布参数估计方法比较[J]. 宁波大学学报,2005,18(3):301-305. YAN Xiaodong,MA Xiang,ZHENG Rongyue,et al. Comparison of parameter estimation methods of three parameter Weibull distribution[J]. Journal of Ningbo University,2005,18(3):301-305.
[6] 谢里阳,吴宁祥,杨小玉. 一种威布尔分布三参数最小差异估计方法:中国,202210097281.1[P]. 2022-01-27. XIE Liyang,WU Ningxiang,YANG Xiaoyu. A three-parameter minimum discrepancy method for the Weibull distribution:China,202210097281.1[P]. 2022-01-27.
[7] CHEN D,CHEN Z. Statistical inference about the location parameter of the three-parameter Weibull distribution[J]. Journal of Statistical Computation and Simulation,2009,79(3):215-225.
[8] GUMBEL A. On the statistical interpretation of fatigue tests[J]. Proceedings of the Royal Society of London,1953,216(1126):309-332.
[9] 何成铭,梁清华,吴纬. 基于三参数威布尔分布的机械产品可靠性评估[C]//2012年全国机械行业可靠性技术学术交流会暨第四届可靠性工程分会第四次全体委员大会. 长春:全国机械行业可靠性技术学术交流会,2012:97-100. HE Chengming,LIANG Qinghua,WU Wei. Reliability assessment of mechanical products based on three-parameter Weibull distribution[C]//2012 National Academic Conference on Reliability Technology in Machinery Industry and the Fourth Plenary Meeting of the Fourth Reliability Engineering Branch. Changchun:National Academic Conference on Reliability Technology in Machinery Industry,2012:97-100.
[10] 王卫国. 轮盘低循环疲劳寿命预测模型和试验评估方法研究[D]. 南京:南京航空航天大学,2006. WANG Weiguo. Research on low cycle fatigue life prediction model and test evaluation method for wheel discs[D]. Nanjing:Nanjing University of Aeronautics and Astronautics,2006.
[11] 高镇同. 航空金属材料疲劳性能手册[M]. 北京:北京航空材料研究所,1981. GAO Zhentong. Handbook of fatigue properties of aerospace metallic materials[M]. Beijing:Beijing Institute of Aerospace Materials,1981.
[12] UPADHYAY S K,MUKHERJEE B. Assessing the value of the threshold parameter in the weibull distribution using bayes paradigm[J]. IEEE Transactions on Reliability,2008,57(3):489-497.
[13] LÜ S,NIU Z,ZHEN H,et al. Estimation of lower percentiles under a Weibull distribution[C]//Proceedings of First International Conference on Reliability Systems Engineering. Beijing:IEEE,2016:1-6.
[14] SHIMIZU S K T,KASTSUJI T K. Probabilistic stress-life (P-S-N) study on bearing steel using alternating torsion life test[J]. Tribology Transactions,2009,52(6):807-816.
[15] 凌丹,何俐萍,许焕卫,等. 基于威布尔分布的疲劳剩余寿命可靠性预测方法[J]. 机械设计,2011,28(7):50-54. LING Dan,HE Liping,XU Huanwei,et al. Fatigue residual life reliability prediction method based on Weibull distribution[J]. Machine Design,2011,28(7):50-54.
[16] 付涛,王德成,程鹏. 基于威布尔分布的圆柱螺旋压缩弹簧疲劳寿命分析[J]. 机械强度,2020,42(1):81-86. FU Tao,WANG Decheng,CHENG Peng. Fatigue life analysis of cylindrical helical compression springs based on Weibull distribution[J]. Journal of Mechanical Strength,2020,42(1):81-86.
[17] 徐人平,段小建,胡志勇,等. 滚动轴承疲劳寿命P-S-N曲线[J]. 轴承,1996(4):1-3. XU Renping,DUAN Xiaojian,HU Zhiyong,et al. Fatigue life P-S-N curves of rolling bearings[J]. Bearings,1996(4):1-3.
[18] 杨维平,李纶,徐人平,等. 钢板弹簧疲劳寿命概率分布分析[J]. 广西机械,2002(1):16-18,36. YANG Weiping,LI Lun,XU Renping,et al. Analysis of fatigue life probability distribution of steel plate springs[J]. Guangxi Machinery,2002(1):16-18,36.
[19] 伍建军,游雄雄,吴事浪,等. 两参数威布尔分布的废旧矿冶零部件再制造剩余寿命预测新方法[J]. 机械科学与技术,2016,35(4):589-593. WU Jianjun,YOU Xiongxiong,WU Shilang,et al. A new method for predicting the remaining life of remanufactured scrap mining and metallurgical parts with two-parameter Weibull distribution[J]. Mechanical Science and Technology,2016,35(4):589-593.
[20] 宋欣,沈华,陈龙宝,等. Weibull分布参数估计值对细节疲劳额定强度的影响[J]. 航空学报,2021,42(3):224759. SONG Xin,SHEN Hua,CHEN Longbao,et al. Effect of Weibull distribution parameter estimates on detail fatigue rated strength[J]. Journal of Aeronautics,2021,42(3):224759.
[21] 王亚辉. 三参数威布尔分布对国产材料DFR方法计算参数的影响研究[D]. 哈尔滨:哈尔滨理工大学,2014. WANG Yahui. Study on the influence of three-parameter Weibull distribution on the calculation parameters of DFR method for domestic materials[D]. Harbin:Harbin Institute of Technology,2014.
[22] 王艺. 航空材料性能设计许用值统计分析与软件开发[D]. 沈阳:东北大学,2012. WANG Yi. Statistical analysis and software development for the design of aerospace material performance allowances[D]. Shenyang:Northeastern University,2012.
[23] 田宇. 国产508-3钢的疲劳性能研究[D]. 沈阳:东北大学,2009. TIAN Yu. Study of fatigue properties of domestic 508-3 steel[D]. Shenyang:Northeastern University,2009.
[24] 冯振宇,诸德培. 威布尔分布的拟合优度检验[J]. 机械强度,1996,18(4):29-31. FENG Zhenyu,ZHU Depei. Goodness-of-fit test for the Weibull distribution[J]. Mechanical Strength,1996,18(4):29-31.
[25] 闻德兵. 疲劳寿命概率分布类型对比研究[D]. 南京:南京航空航天大学,2017. WEN Debing. Comparative study on the types of fatigue life probability distribution[D]. Nanjing:Nanjing University of Aeronautics and Astronautics,2017.
[26] 张茂,薛景川,张侃. 新结构细节疲劳寿命威布尔分布特征参数估计方法研究[C]//第22届全国结构工程学术会议论文集. 新疆:全国结构工程学术会议,2013:69-72. ZHANG Mao,XUE Jingchuan,ZHANG Kan. Research on the estimation method of characteristic parameters of Weibull distribution for fatigue life of new structural details[C]//Proceedings of the 22nd National Academic Conference on Structural Engineering. Xinjiang:National Academic Conference on Structural Engineering,2013:69-72.
[27] 伍建军,吴小明,谢周伟,等. 改进威布尔分布的矿冶零部件可靠性寿命预测研究[J]. 机械科学与技术,2017,36(3):436-471. WU Jianjun,WU Xiaoming,XIE Zhouwei,et al. Research on reliability life prediction of mining and metallurgical components with improved Weibull distribution[J]. Mechanical Science and Technology,2017,36(3):436-471.
[28] 王灵芝,徐宇工,张家栋. 铁路设备关键零部件的可靠性分析模型及其应用研究[J]. 铁道学报,2008,30(4):93-97. WANG Lingzhi,XU Yugong,ZHANG Jiadong. Reliability analysis model of key components of railroad equipment and its application research[J]. Journal of Railways,2008,30(4):93-97.
[29] 于晓红,张来斌,王朝晖,等. 基于新的威布尔分布参数估计法的设备寿命可靠性分析[J]. 机械强度,2007,29(6):932-936. YU Xiaohong,ZHANG Laibin,WANG Zhaohui,et al. Equipment life reliability analysis based on the new Weibull distribution parameter estimation method[J]. Mechanical Strength,2007,29(6):932-936.
[30] 郑锐. 三参数威布尔分布参数估计及在可靠性分析中的应用[J]. 振动与冲击,2015,34(5):78-81. ZHENG Rui. Three-parameter Weibull distribution parameter estimation and its application in reliability analysis[J]. Vibration and Shock,2015,34(5):78-81.
[31] 金渊源. 链式刀库及机械手可靠性综合试验与评估技术研究[D]. 南京:南京理工大学,2013. JIN Yuanyuan. Research on reliability test and evaluation technology of chain tool magazine and manipulator[D]. Nanjing:Nanjing University of Science and Technology,2013.
[32] 曹克强,胡良谋,熊申辉,等. 基于三参数威布尔分布的定量泵可靠性分析[J]. 现代制造工程,2016(12):1-4. CAO Keqiang,HU Liangmou,XIONG Shenhui,et al. Reliability analysis of quantitative pumps based on three-parameter Weibull distribution[J]. Modern Manufacturing Engineering,2016(12):1-4.
[33] 夏新涛,徐永智,金银平,等. 用自助加权范数法评估三参数威布尔分布可靠性最优置信区间[J]. 航空动力学报,2013(3):481-488. XIA Xintao,XU Yongzhi,JIN Yinping,et al. Evaluation of optimal confidence intervals for the reliability of the three-parameter Weibull distribution using the self-weighted parametric method[J]. Journal of Aerodynamics,2013(3):481-488.
[34] 孙小宇. 波音737-300飞机部件寿命分布研究[J]. 航空维修与工程,2008(6):45-47. SUN Xiaoyu. Study on the life distribution of Boeing 737-300 aircraft components[J]. Aviation Maintenance and Engineering,2008(6):45-47.
[35] 孙小宇. 可靠性在民用飞机维修工程中的应用研究[D]. 昆明:昆明理工大学,2006. SUN Xiaoyu. Application of reliability in civil aircraft maintenance engineering[D]. Kunming:Kunming University of Technology,2006.
[36] 赵威力. 三参数威布尔分布下的发动机涡轮叶片可靠性研究[C]//第十五届中国科协年会论文集. 贵阳:中国科协年会,2013:1-5. ZHAO Weili. Reliability study of engine turbine blades under three-parameter Weibull distribution[C]//Proceedings of the 15th Annual Meeting of CCSA. Guiyang:Annual Meeting of CCSA,2013:1-5.
[37] 裴峻峰,郑庆元,姜海一,等. 离心式压缩机定期维修周期及可靠性研究[J]. 中国石油大学学报,2014,38(6):127-133. PEI Junfeng,ZHENG Qingyuan,JIANG Haiyi,et al. Study on periodic maintenance intervals and reliability of centrifugal compressors[J]. Journal of China University of Petroleum,2014,38(6):127-133.
[38] 聂炜. 对某型飞机及其发动机的可靠性分析[D]. 西安:西安电子科技大学,2013. NIE Wei. Reliability analysis of a type of aircraft and its engine[D]. Xi'an:Xi'an University of Electronic Science and Technology,2013.
[39] 刘飞. 固体火箭发动机可靠性增长试验理论及应用研究[D]. 长沙:国防科学技术大学,2006. LIU Fei. Solid rocket engine reliability growth test theory and application research[D]. Changsha:National University of Defense Technology,2006.
[40] 孟勃敏. 加工中心可靠性技术研究[D]. 西安:陕西科技大学,2011. MENG Bomin. Research on reliability technology of machining center[D]. Xi'an:Shaanxi University of Science and Technology,2011.
[41] 张海波,贾亚洲,周广文. 数控系统故障间隔时间分布模型的研究[J]. 哈尔滨工业大学学报,2005,37(2):198-200. ZHANG Haibo,JIA Yazhou,ZHOU Guangwen. Research on the distribution model of fault interval time of CNC system[J]. Journal of Harbin Institute of Technology,2005,37(2):198-200.
[42] 张晓彤. 基于威布尔分布的涡扇发动机寿命预测研究[D]. 哈尔滨:哈尔滨工业大学,2019. ZHANG Xiaotong. Research on turbofan engine life prediction based on Weibull distribution[D]. Harbin:Harbin Institute of Technology,2019.
[43] 袁忠大,符双学,王大伟. 基于威布尔混合分布的航空发动机可靠性评估[J]. 航空计算技术,2015,45(5):65-67. YUAN Zhongda,FU Shuangxue,WANG Dawei. Reliability assessment of aero engines based on Weibull hybrid distribution[J]. Aviation Computing Technology,2015,45(5):65-67.
[44] 杨垒峰. 基于威布尔分布的离心泵用机械密封可靠性分析[J]. 江苏科技信息(学术研究),2011(5):124-126. YANG Leifeng. Reliability analysis of mechanical seals for centrifugal pumps based on Weibull distribution[J]. Jiangsu Science and Technology Information (Academic Research),2011(5):124-126.
[45] 段飞飞. 飞机IDG可靠性评估及寿命预测研究[D]. 沈阳:沈阳航空航天大学,2019. DUAN Feifei. Research on aircraft IDG reliability assessment and life prediction[D]. Shenyang:Shenyang University of Aeronautics and Astronautics,2019.
[46] 李淑兰. V带疲劳寿命和疲劳强度概率分布模型[J]. 昆明理工大学学报,1998,23(2):113-118. LI Shulan. Fatigue life and fatigue strength probability distribution model for V-belts[J]. Journal of Kunming University of Technology,1998,23(2):113-118.