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

Abstract

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

CLC Number:

U270.18

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.

Figures/Tables 10

Fig. 1

Fig.2

Fig.3

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Fig.5

Fig.6

Table 1

Results of mixed model parameter estimation"

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	$α 1 = 34.887 ? 7, β 1 = 4.758 ? 9, γ 1 = 187.728 ? 2; α 2 = 89.960 ? 7, β 2 = 8.551 ? 6, γ 2 = 164.981 ? 8; α 3 = 48.771 ? 8, β 3 = 16.953 ? 6, γ 3 = 231.885 ? 0$

Table 1

Fig.7

Fig.8

Table 2

Comparison of goodness of fit results"

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

Table 2

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Parameter estimation of mixed reliability model based on kernel density optimal grouping and gravity search algorithm

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