《疲劳统计学智能化中的高镇同法》[1]这篇论文仅仅是疲劳统计学的智能化研究的开始,故有必要对其做进一步的研究。其中一个重要问题是,用什么样的标准来判断样本数据是属于高斯分布还是威布尔分布。如果是属于威布尔分布,仍然可能因为算法不同而得到并不相同的3个参数,也存在哪一个威布尔分布更合适的问题。特提出以相关系数、决定系数的大小来作为一个判断标准,同时给出了相应的智能化解决方案。还研究了3参数威布尔分布的置信区间问题,对于实际应用来讲,人们最关心的是在给定的置信度及可靠度下疲劳寿命的置信区间,因此给出了在高镇同法基础上的一个智能化解决方法。
"Gao Zhentong Method in Intelligence of Statistics in Fatigue"[1] is only the beginning of the intelligent research of fatigue statistics, so it is necessary to do further research on it. One of the important questions is, what standard is used to judge whether the sample data belongs to the Gaussian distribution or the Weibull distribution? If it belongs to the Weibull distribution, it is still possible to get three different parameters due to different algorithms. There is also the question of which Weibull distribution is more suitable. It is specially proposed to use the correlation coefficient and the size of the determination coefficient as a judgment standard, and at the same time, the corresponding intelligent solution is given. The confidence interval of the three-parameter Weibull distribution is also studied. For practical applications, people are most concerned about the confidence interval of the fatigue life under a given confidence and reliability, and an intelligent solution based on the Gao Zhentong method is given.
[1] 徐家进. 疲劳统计学智能化中的高镇同法[J]. 北京航空航天大学学报, 2021, 47(10): 2024-2033. XU J J. Gao Zhentong method in intelligentization of statistics in fatigue[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(10): 2024-2033 (in Chinese).
[2] 高镇同. 疲劳应用统计学[M]. 北京: 国防工业出版社, 1986. GAO Z T. Fatigue applied statistics[M]. Beijing: National Defense Industry Press, 1986 (in Chinese).
[3] KISHOR S T. 计算机应用与可靠性工程中的概率统计[M].第2版. 伍志韬, 张越译. 北京: 电子工业出版社, 2015: 601-602. KISHOR S T.Probability and statistics with reliability, queuing, and computer science applications probability and statistics with reliability, queuing, and computer science applications[M]. second edition.WU Z T,ZHANG Y translater. Beijing: Publishing House of Electronics Industry, 2015: 601-602(in Chinese).
[4] 徐自力, 姜兴渭. 威布尔分布3参数置信限估计及分布类型检验[J]. 航空学报, 1996, 17(4): 477-479. XU Z L, JIANG X W. The estimation of confidence limit of Weibull three parameter distribution and examination of distribution type[J]. Acta Aeronautica et Astronautica Sinica, 1996, 17(4): 477-479 (in Chinese).
[5] 陈道礼. 双参数威布尔分布的参数区间估计的直接方法[J]. 机械强度, 1996, 18(3):32-36. CHEN D L. A direct approach to interval estimation of parameters of the two-parameter weibull distribution[J]. Journal of Mechanical Strength, 1996, 18(3): 32-36(in Chinese).
[6] 傅惠民, 高镇同, 徐人平. 三参数威布尔分布的置信限[J]. 航空学报, 1992, 13(3): 153-162. FU H M, GAO Z T, XU R P. Confidence limits of three-parameter Weibull population percentiles[J]. Acta Aeronautica et Astronautica Sinica, 1992, 13(3): 153-162 (in Chinese).
[7] 费史.概率论及数理统计[M].王福保,译.上海:上海科技出版社,1962:81,84. FISZ M.Wahrscheinlichkitsrechnung und Mathematische Stastistik[M].WANG F B translater. Shanghai: Shanghai Science and Technology Press,1962: 81,84(in Chinese).
[8] 蔡玉书. 重要不等式[M]. 2版. 合肥: 中国科学技术大学出版社, 2012. CAI Y S. Important inequality[M].2nd ed. Hefei: University of Science and Technology of China Press, 2012 (in Chinese).
[9] MEYER P L.概率引论及统计应用[M]. 潘考瑞译.北京: 高等教育出版社, 1986: 385-386. MEYER P L. Introductory probability and statistical application[M]. PAN K R translater.Beijing: Higher Education Press, 1986: 385-386 (in Chinese).
[10] 道格拉斯·蒙哥马利,伊丽莎白·派克,杰弗里·瓦伊宁.线性回归分析导论[M].王辰勇,译.北京:机械工业出版社,2019:13-14. MONTGOMERY D C,PECK E A, VINING G G. Introduction to linear regression analysis[M].WANG C Y translater.Bejing: Machinery Industry Press, 2019:13-14(in Chinese).
[11] 茆诗松, 王静龙, 濮晓龙. 高等数理统计[M]. 2版. 北京: 高等教育出版社, 2006. MAO S S, WANG J L, PU X L. Advanced mathematical statistics[M].2nd ed. Beijing: Higher Education Press, 2006 (in Chinese).
[12] HOGG R V, MCKEAN J W, CRAIG A T.数理统计导论[M].7版.王忠玉,卜长江,译.北京:机械工业出版社,2015:174-175. HOGG R V, MCKEAN J W, CRAIG A T. Introduction to mathematical statistics[M].7th ed. WANG Z Y, BU C J, translater. Beijing: Machinery Industry Press, 2015:174-175(in Chinese).
[13] 张锡清.威布尔参数的最优估计[J].哈尔滨电工学院学报,1995,18(4):402-406. ZHANG X Q. Optimal estimation of Weibull parameters[J]. Journal of Harbin Electrical Engineering Institute,1995, 18(4):402-406(in Chinese).
[14] 陈道礼. 估计威布尔分布参数、可靠寿命和可靠度的置信限的新方法[J]. 机械设计, 1997, 14(10): 19-22, 50. CHEN D L. A new approach to the estimation of confidence limits on parameters and reliable life and reliability for the weibull distribution[J]. Machine Design, 1997, 14(10): 19-22, 50 (in Chinese).
[15] 邹林全. 定时截尾试验Weibull分布参数的近似置信区间[J]. 南京理工大学学报, 2001, 25(2): 215-219. ZOU L Q. Approximate confident interval of parameter for weibull distribution under fix-time censored test[J]. Journal of Nanjing University of Science and Technology, 2001, 25(2): 215-219 (in Chinese).
[16] 赵呈建.双参数威布尔分布参数区间估计的直接方法[D].天津:南开大学,2017. ZHAO C J.Direct method for estimating the interval of two-parameter Weibull distribution[D].Tianjing: Nankai University,2017(in Chinese).
[17] 张平, 王蓉华, 徐晓岭. 两参数Weibull分布参数的联合置信区间[J]. 数学理论与应用, 2010, 30(3): 58-62. ZHANG P, WANG R H, XU X L. Joint confidence interval of parameters of two-parameter Weibull distribution[J]. Mathematical Theory and Applications, 2010, 30(3): 58-62 (in Chinese).
[18] 谈嘉祯, 边新孝. 三参数威布尔分布置信限的确定和 C—R—S—N 曲线的拟合[J]. 北京科技大学学报, 1994, 16(5):425-430. TAN J Z, BIAN X X. The determination of confidence limits for Weibull distribution of three parameter and the fitting of C—R—S—N curves[J]. Journal of University of Science and Technology Beijing, 1994, 16(5):425-430 (in Chinese).
[19] 费鹤良, 徐晓岭. 三参数威布尔分布参数的联合置信域[J]. 应用概率统计, 1992, 8(4): 62-66. FEI H L, XU X L. Simultaneous confidence region of three parameters for the three-parameter Weibull distribution[J]. Chinese Journal of Applied Probability and Statistics, 1992, 8(4): 62-66 (in Chinese).
[20] 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, 28(3): 481-488. XIA X T, XU Y Z, JIN Y P, et al. Assessment of optimum confidence interval of reliability with three-parameter Weibull distribution using bootstrap weighted-norm method[J]. Journal of Aerospace Power, 2013, 28(3): 481-488 (in Chinese).
[21] XU J J. Digital experiment for estimating three parameters and their confidence intervals of Weibull Distribution[J]. International Journal of Science, Technology and Society, 2022,10(2):72-81.
CJA