三重以上混合威布尔分布参数估计方法的研究
PDF下载 (56)陈文鹏,吕 阳,屠建飞,王钢明.三重以上混合威布尔分布参数估计方法的研究[J].宁波大学学报(理工版),2025,38(5):105-112.DOI:10.20098/j.cnki.1001-5132.2024.1216
CHEN Wenpeng,LÜ Yang,TU Jianfei,WANG Gangming.A study of parameter estimation method for more than threefold mixed Weibull distributions[J].Journal of Ningbo University(Natural Science & Engineering Edition),2025,38(5):105-112.DOI:10.20098/j.cnki.1001-5132.2024.1216
| Title: | A study of parameter estimation method for more than threefold mixed Weibull distributions |
| 作者: | 陈文鹏, 吕 阳, 屠建飞, 王钢明 |
| Author(s): | CHEN Wenpeng, LÜ Yang, TU Jianfei, WANG Gangming |
| 关键词: | 模糊C均值聚类; 可靠性建模; 遗传算法; 威布尔分布 |
| Keywords: | fuzzy C-means clustering; reliability modeling; genetic algorithm; Weibull distribution |
| 分类号: | TB114.3 |
| DOI: | 10.20098/j.cnki.1001-5132.2024.1216 |
| 文献标识码: | A |
| 摘要: | 针对三重以上的两参数混合威布尔分布卷入参数过多导致求解困难的问题，使用模糊C均值聚类算法与最小二乘线性回归法相结合的方法，求出形状参数与尺度参数的初值，通过KS检验（Kolmogorov-Smirnov test）证明该方法得出的初值具有良好的精度。根据得出的初值制定合理的参数待估范围，以最小化标准均方根误差为优化目标，使用遗传算法求解不同重数混合威布尔分布的参数值。实例分析证明该方法有效解决了传统方法初值依赖性较强的问题，增加重数可以有效改善拟合效果，求出的概率密度函数能够准确反映数据的实际分布规律。 |
| Abstract: | To address the problem that the two-parameter mixed Weibull distribution with more than three-time folds is difficult to be solved due to the reason that too many parameters are involved, this paper employs the fuzzy C-mean clustering algorithm combined with the least squares linear regression method to find out the initial values of the shape parameters and the scale parameters, which are proved to have good accuracy by using the KS test (Kolmogorov-Smirnov test). Based on the initial values obtained, the parameters to be estimated are specified with reasonable ranges respectively, and the parameter values of different reweighted mixed Weibull distributions are solved by using genetic algorithm, with its optimization objective being set as minimizing the standard root mean square error. Example analysis proves that the proposed method is effective in solving the problem of those traditional methods for their strong dependency on the initial values. By increasing the number of the weights, the fitting effect can be effectively improved. The probability density function can accurately reflect the actual distribution law of the data. |
| 参考文献 /References: | [1] 吴雨婷, 陆中, 宋海靖, 等. 面向多重耗损失效的民用飞机运行风险评估[J]. 北京航空航天大学学报, 2023, 49(10):2807-2816. [2] 孟景辉. 基于影响因子聚类与分布拟合的补偿电容剩余寿命预测[J]. 铁道科学与工程学报, 2024, 21(7): 2897-2906. [3] GU D W, GAO J H, ZHONG Y H, et al. Scale parameter assessment based on pivot quantity for reliability analysis of a complex system[J]. Journal of mechanical science and technology, 2021, 35(3):1007-1015. [4] WU Y T, LU Z, WU J Y, et al. Reliability evaluation of components with multiple failure modes based on mixture Weibull distribution using expectation maximization algorithm[J]. Journal of mechanical science and technology, 2024, 38(2):649-660. [5] JIANG S, KECECIOGLU D. Graphical representation of two mixed-Weibull distributions[J]. IEEE transactions on reliability, 1992, 41(2):241-247. [6] JIANG S, KECECIOGLU D. Maximum likelyhood estimates, from censored data, for mixed-Weibull distributions[J]. IEEE transactions on reliability, 1992, 41(2):248-255. [7] TOUW A E. Bayesian estimation of mixed Weibull distributions[J]. Reliability engineering & system safety, 2009, 94(2):463-473. [8] 凌丹, 黄洪钟, 张小玲, 等. 混合威布尔分布参数估计的L-M算法[J]. 电子科技大学学报, 2008, 37(4):634- 636, 640. [9] KHAN M S A, KHALIQUE A, ABOUAMMOH A M. On estimating parameters in a discrete Weibull distribution[J]. IEEE Transactions on reliability, 1989, 38(3):348-350. [10] 董力, 陆中, 周伽. 基于遗传算法的混合威布尔分布参数最小二乘估计[J]. 南京航空航天大学学报, 2019, 51(5):711-718. [11] ACITAS S, ALADAG C H, SENOGLU B. A new approach for estimating the parameters of Weibull distribution via particle swarm optimization: an application to the strengths of glass fibre data[J]. Reliability engineering & system safety, 2019, 183:116- 127. [12] 刘巧斌, 史文库, 陈志勇, 等. 混合可靠性模型参数的核密度和引力搜索估计[J]. 吉林大学学报(工学版), 2019, 49(6):1818-1825. [13] BUČAR T, NAGODE M, FAJDIGA M. Reliability approximation using finite Weibull mixture distributions [J]. Reliability engineering & system safety, 2004, 84(3): 241-251. [14] 王继利, 杨兆军, 李国发, 等. 基于改进EM算法的多重威布尔可靠性建模[J]. 吉林大学学报(工学版), 2014, 44(4):1010-1015. [15] 游达章. 最小二乘法在威布尔分布的可靠性评估[J]. 湖北工业大学学报, 2009, 24(4):34-35, 45. [16] 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):28-31. [17] NOCEDAL J, WRIGHT S J. Numerical optimization[M]. Berlin: Springer, 1999. [18] PRABHAKAR MURTHY D N, BULMER M, ECCLESTON J A. Weibull model selection for reliability modelling[J]. Reliability engineering & system safety, 2004, 86(3):257-267. [19] WANG Y F, AO C L. Non-parameter estimation of failures intensity of tractor based on bootstrap[J]. International journal of smart home, 2016, 10:181-190. [20] 丛明, 王冠雄, 谢书文, 等. 加工中心早期故障的两重威布尔模型研究[J]. 组合机床与自动化加工技术, 2015(4):78-82. [21] 赵继俊, 邹经湘, 张锡清. 混合威布尔分布的参数优化估计[J]. 机械科学与技术, 2001, 20(1):14-16. [22] LING D, HUANG H Z, LIU Y. A method for parameter estimation of mixed Weibull distribution[C]//2009 Annual Reliability and Maintainability Symposium. Fort Worth, TX. IEEE, 2009:129-133. [23] ELMAHDY E E, ABOUTAHOUN A W. A new approach for parameter estimation of finite Weibull mixture distributions for reliability modeling[J]. Applied mathematical modelling, 2013, 37(4):1800-1810. |
| 备注/Memo: | 收稿日期：2024−12−27 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ 基金项目：国家自然科学基金（22078164）；宁波市重点研发计划（2023Z153, 2023Z061） 第一作者：陈文鹏，硕士研究生，主要研究方向为可靠性建模。E-mail: c15298@foxmail.com *通信作者：王钢明，高级实验师，主要研究方向为数字化制造。E-mail: wanggangming@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
