非正态响应稳健参数设计的贝叶斯建模与优化

doi:10.12305/j.issn.1001-506X.2023.03.34

Abstract

Abstract:

A Bayesian modeling and parameter optimization method considering noise factor is proposed to deal with the robust parameter design problem of non-normal response. Firstly, considering the empirical Bayesian prior information, the Bayesian generalized linear model is used to construct the functional relationship between the design factors and the output response. Secondly, assuming that the noise factor follows the known distribution, the Bayesian sampling technique is used to obtain the analog sampling value of output response considering the variation of noise factor. Then, based on the given product specification, the posterior probability function is constructed by using the sampling value of the output response, and the constructed conformance posterior probability function is optimized by a genetic algorithm to obtain the parameter design values that are robust to the fluctuation of noise factors. Finally, the effectiveness of the proposed method is verified by an actual case. The research results show that the proposed method effectively describes the impact of noise factors fluctuation on product or process quality, and obtains more robust and reliable parameter design values.

Key words: quality design, robust parameter design, Bayesian method, generalized linear model, non-normal response

CLC Number:

F273.2

Yan MA, Jianjun WANG, Zebiao FENG. Bayesian modeling and optimization of robust parametric design with non-normal response[J]. Systems Engineering and Electronics, 2023, 45(3): 921-930.

Figures/Tables 3

References 41

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试验次数	设计因子				响应电阻率
试验次数	剂量	时间	厚度	温度	响应电阻率
1	-1	-1	-1	-1	193.4
2	1	-1	-1	-1	247.6
3	-1	1	-1	-1	168.2
4	1	1	-1	-1	205.0
5	-1	-1	-1	1	303.4
6	1	-1	-1	1	339.9
7	-1	1	-1	1	226.3
8	1	1	-1	1	208.3
9	-1	-1	1	-1	220.0
10	1	-1	1	-1	256.4
11	-1	1	1	-1	165.7
12	1	1	1	-1	203.5
13	-1	-1	1	1	285.0
14	1	-1	1	1	268.0
15	-1	1	1	1	169.1
16	1	1	1	1	208.5

方差	均方误差	符合性概率
0.06	3 273.948 0	0.997 3
0.08	4 728.055 0	0.976 3
0.10	6 830.148 0	0.936 5
0.12	9 788.466 0	0.880 3
0.14	13 897.020 0	0.817 8
0.16	19 566.700 0	0.757 3
0.18	27 370.330 0	0.706 2
0.20	38 108.290 0	0.657 0

研究方法		均方误差	符合性概率
本文方法	弱遗传	7 323.374 8	0.926 5
本文方法	强遗传	6 830.147 8	0.936 0
GLM		9 857.697 5	0.902 1

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Bayesian modeling and optimization of robust parametric design with non-normal response

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