混合可靠性模型参数的核密度和引力搜索估计

doi:10.13229/j.cnki.jdxbgxb20180978

摘要/Abstract

摘要：

针对可靠性建模中广泛应用的混合分布模型的参数估计问题，为解决其重数选择主观性强、参数识别初值敏感性高、参数识别效率低等难题，融合人工智能方法，提出了一种新型参数估计方法。引入核密度估计对数据进行非参数拟合，以最小化平均积分平方误差为目标，获得核密度估计的最优带宽，以最优带宽为组距对原始数据进行分组，做出统计直方图，并由此确定分布密度函数的混合重数。采用K-均值聚类方法对统计直方图进行聚类，由聚类结果计算获得混合分布模型的权重，接着应用引力搜索算法对混合模型各重子模型的参数进行辨识。以实测商用车车桥位移谱信号为例，对其概率密度函数和累计分布函数进行混合模型建模和模型参数识别。在车桥位移谱模型参数识别的基础上，分别计算决定系数、KS值和平均相对误差3个指标，验证了本文参数估计方法的有效性，为商用车可靠性的疲劳载荷谱编制和实验室台架试验奠定了基础，同时，可以为相关可靠性建模和模型参数识别问题提供参考。

关键词: 车辆工程, 可靠性建模, 参数识别, 核密度, 引力搜索算法, 聚类

Abstract:

To estimate the parameters of the mixed distribution models which are widely used in reliability modeling, a new parameter estimation method was proposed. The kernel density estimation was introduced to non-parametric fitting of the data. With the minimized mean integration square error, the optimal bandwidth of kernel density estimation (KDE) was obtained. The original data were grouped by the optimal bandwidth of KDE as the group distance, and the statistical histogram was made. The mixed multiplicity of the distribution density function was determined by the histogram. The K-means clustering method was employed to cluster the histograms. The weights of the mixed distribution model were calculated from the clustering results. Then the gravitational search algorithm (GSA) was applied to identify the parameters of the sub-distributions' parameters for the mixed model. Taking the measured displacement signal of vehicle axle as an example, mixed reliability model was developed, in which the model parameters were estimated by the proposed method. Based on the identification results of model parameters, the determination coefficient, Kolmogorov-Smirnov coefficient and average relative error were calculated respectively, with which the effectiveness of the proposed parameter estimation method was verified. This research would lay the foundation for the fatigue load spectrum preparation and laboratory reliability bench test of commercial vehicle. Moreover, it can provide reference for related reliability modeling and model parameter identification.

Key words: vehicle engineering, reliability modeling, parameter identification, kernel density estimation, gravitational search algorithm, clustering

中图分类号:

U270.18

刘巧斌,史文库,陈志勇,骆联盟,苏志勇,黄开军. 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.

Qiao-bin LIU,Wen-ku SHI,Zhi-yong CHEN,Lian-meng LUO,Zhi-yong SU,Kai-jun HUANG. Parameter estimation of mixed reliability model based on kernel density optimal grouping and gravity search algorithm[J]. Journal of Jilin University(Engineering and Technology Edition), 2019, 49(6): 1818-1825.

图/表 10

图1

图2

图3

图4

图5

图6

表1

混合模型参数估计结果"

模型	数值
混合正态分布	$μ 1 = 220.349 ? 1, σ 1 = 7.674 ? 1; μ 2 = 252.801 ? 6, σ 2 = 11.065 ? 5; μ 3 = 280.481 ? 7, σ 3 = 2.899 ? 7$
混合威布尔分布	$α 1 = 34.887 ? 7, β 1 = 4.758 ? 9, γ 1 = 187.728 ? 2; α 2 = 89.960 ? 7, β 2 = 8.551 ? 6, γ 2 = 164.981 ? 8; α 3 = 48.771 ? 8, β 3 = 16.953 ? 6, γ 3 = 231.885 ? 0$

表1

图7

图8

表2

拟合优度结果对比"

指标	混合正态分布	混合威布尔分布
R $2$	0.992 0	0.993 6
D _max	0.034 2	0.010 0
MRE/%	12.91	5.98

表2

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