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

摘要/Abstract

摘要：

针对非正态响应的稳健参数设计问题, 提出一种考虑噪声因子的贝叶斯建模与参数优化方法。首先, 考虑经验贝叶斯先验信息, 利用贝叶斯广义线性模型构建设计因子与输出响应之间的函数关系; 其次, 假设噪声因子服从已知的分布, 在此基础上利用贝叶斯抽样技术获得考虑噪声因子波动的输出响应模拟抽样值; 然后, 在给定产品规格的基础上, 利用输出响应的抽样值构建符合性后验概率函数, 并利用遗传算法对所构建的符合性后验概率函数进行优化, 获得对噪声因子波动具有稳健性的参数设计值; 最后, 结合实际的案例验证了所提方法的有效性。研究结果表明, 所提方法有效地刻画了噪声因子的波动对产品或过程质量的影响, 从而获得了更为稳健可靠的参数设计值。

关键词: 质量设计, 稳健参数设计, 贝叶斯方法, 广义线性模型, 非正态响应

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

中图分类号:

F273.2

马妍, 汪建均, 冯泽彪. 非正态响应稳健参数设计的贝叶斯建模与优化[J]. 系统工程与电子技术, 2023, 45(3): 921-930.

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.

图/表 3

参考文献 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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