Journal of Engineering Research
Journal of Engineering Research. 2025; 4: (1) ; 10.12208/j.jer.20250003 .
总浏览量: 67
力中国际融资租赁有限公司 广东广州
*通讯作者： 徐家进,单位：力中国际融资租赁有限公司 广东广州；
三参数Weibull分布在结构疲劳、可靠性等领域起了越来越大的作用，人们根据有关数据来从不同的角度提出估计Weibull分布的三个参数提出了许多方法。这些方法各有所长，但似乎都存在这样或那样的问题：1. 估计参数的数学推导比较繁琐，得到的结果也不容易解出；2. 为简化估计的困难程度，往往假定位置参数为零或将数据取对数；3，得到的估计参数结果有时会违反Weibull分布参数的物理意义。作者最近几年提出的高镇同法以及推广了的高镇同法，在一定程度上克服了上述问题，且同时能给出估计参数的置信区间，得到了比较令人满意的结果。
The three-parameters Weibull distribution has played an increasingly important role in fields such as structural fatigue and reliability. Many methods have been proposed to estimate the three parameters of the Weibull distribution from different perspectives based on relevant data. These methods each have their own strengths, but it seems that they all have some problems: 1. The mathematical derivation of estimating parameters is quite cumbersome, and the results obtained are not easy to solve; 2. To simplify the difficulty of estimation, it is often assumed that the position parameter is zero or the data is logarithmically represented; 3. The estimated parameter results obtained sometimes violate the physical meaning of Weibull distribution parameters. In recent years, the author has proposed and promoted the Zhentong Gao method, which to some extent overcomes the above problems and can also provide confidence intervals for estimating parameters, achieving satisfactory results.
[1] 高镇同,疲劳应用统计学[M]. 北京: 国防工业出版社,1986
[2] 高镇同, 熊峻江, 疲劳可靠性[M], 北京:北京航空航天大学出版社,2000
[3] 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): 2021,4 7(10):2021-2033
[4] Ivana P and Zuzana S, Comparison of Four Methods for Estimating the Weibull Distribution Parameters[J], Applied Mathematical Sciences, Vol. 8, 2014, no. 83, 4137 – 4149,
HIKARI Ltd, www.m-hikari.com, http://dx.doi.org/10. 12988 / ams.2014.45389
[5] 傅惠民,高镇同,确定威布尔分布三参数的相关系数优化法[J], 航空学报,1990,11(7): A323-A327
[6] 严晓东,马翔,郑荣跃,吴亮[J], 三参数威布尔分布参数估计方法比较[J],宁波大学学报,2005,9, V18(3)
[7] 胡恩平,罗兴柏,刘国庆[J], 三参数Weibull 分布的参数估计方法[J],沈阳工学院学报,2000,9,V.19(3)
[8] 张平等, 两参数Weibull分布参数的联合置信区间[J], 数学理论与应用 2010, V.3, No.3]
[9] 高镇同,徐家进[M],智能疲劳统计学, 北京 : 北航出版社,2022
[10] Jiajin Xu & Zhentong Gao, From Gaussian Distribution to Weibull Distribution[J], Global Journal of Researches in Engineering: I Numerical Methods, Volume 23, Issue 1 Version 1.0 Year 2023,
Doi:10.34257/GJREIVOL23IS1PG1
[11] Gao Z T & Xu J J[M],Intelligent Fatigue Statistics, London: CRC Press, 2024 Doi:10.1201/9781003466477
[12] Xu J J[J], Generalized Zhentong Gao Method for Estimating Three Parameters of Weibull Distribution, SCIREA Journal of Computer, 8(2). 2023
[13] Xu J J[J], Using Monte Carlo method to Upgrade Zhentong Gao method, World Journal of Advanced Research and Reviews, 2024, 22(02), 633–640,
Doi: https://doi.org/10.30574/wjarr.2024.22.2.1391
[14] 徐家进&高镇同.疲劳统计学智能化进一步的研究[J], 航空学报,2022,43(8)
[15] Xu J J, Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution[J], International Journal of Science, Technology and Society, Vol. 10, No. 2, 2022, pp. 72-81, Doi: 0.11648 /j.ijsts. 20221002.16
[16] Xu J J, Generalized Zhentong Gao Method for Estimating Three Parameters of Weibull Distribution[J], SCIREA Journal of Computer, V. 8, Issue 2, 2023, Doi: 10. 54647/ computer520345
[17] 谷耀新, 三参数威布尔分布参数估计方法[J],“沈阳工业学院学报”, 1997,V.16(4)]
[18] Efron B and Hastie T[M],计算机时代的统计推断, 北京: 机械工业出版社,2019
[19] Metropolis, et al, Equation of state calculation by fast computing machines[J], J. Chemical Phys, 1953,21: 1087-1091
[20] 徐晓岭等, 恒加试验下 LED 照明灯的三参数 Weibull 分布的参数估计[J], 半导体光电,第44卷第4期,2023
[21] 张建平等 [J], Weibull分布下基于MLE的红外发光二极管寿命预测[J]. 半导体光电, Vol.32(1): 47-51. 2011
[22] 同济大学数学系编[M],高等数学,第7版,北京,高等教育出版社,2014,P115,P118