基于半参数分层贝叶斯建模与优化

doi:10.12305/j.issn.1001-506X.2023.05.35

Abstract

Abstract:

To solve the robust parameter design problem with non-normal distribution and model uncertainty, a semi-parametric hierarchical Bayesian response surface model is constructed under the framework of Polya tree hybrid modeling, and the robust parameter design is realized on this basis.Firstly, the Bayesian semi-parametric model is established and the posterior distributions of the parameters of the model are obtained. Secondly, the Markov chain Monte Carlo (MCMC) algorithm is used to obtain the estimated value of each parameter. Then, the expected quality loss function is constructed based on this, and the hybrid genetic algorithm is used for global optimization to obtain the optimal setting of controllable factors. Finally, a numerical simulation study and a real case are given to verify the effectiveness of the proposed method. The proposed method can effectively solve the problem of the influence of small sample data and model uncertainty on optimization results, so as to obtain a more robust and reliable optimal setting of controllable factors.

Key words: non-normal distribution, robust parameter design, Polya tree mixed, Markov chain Monte Carlo (MCMC) algorithm, quality loss function

CLC Number:

F273.2

Xiaoying CHEN, Jianjun WANG, Shijuan YANG. Bayesian modeling and optimization based on semi-parametric hierarchy[J]. Systems Engineering and Electronics, 2023, 45(5): 1580-1588.

Figures/Tables 9

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References 35

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方法	可控因子优化结果			EQL	RMSE
方法	x₁	x₂	x₃	EQL	RMSE
GLM方法	-0.514 1	-0.628 6	0.146 5	3.750 0	0.397 6
Bayes方法	0.341 7	1.418 4	-0.298 3	0.473 2	0.286 7
TBays方法	0.177 3	1.471 7	-0.416 0	0.508 0	0.292 3
所提方法	0.711 6	1.318 2	1.372 5	0.164 9	0.286 6

可控因子	水平
可控因子	-1.682	-1	0	1	1.682
x₁	20	24.05	30	35.95	40
x₂	0.8	1.04	1.4	1.76	2.0
x₃	0.8	1.08	1.5	1.92	2.2

序号	编码值			响应y
序号	z₁	z₂	z₃	响应y
1	1	1	1	12.938 1
2	1	1	-1	13.397 7
3	1	-1	1	13.036 8
4	1	-1	-1	13.443 3
5	-1	1	1	13.745 0
6	-1	1	-1	14.520 9
7	-1	-1	1	14.423 2
8	-1	-1	-1	15.146 0
9	1.682	0	0	11.811 2
10	-1.682	0	0	13.920 1
11	0	1.682	0	13.762 1
12	0	-1.682	0	14.365 2
13	0	0	1.682	14.070 5
14	0	0	-1.682	15.055 8
15	0	0	0	13.902 0
16	0	0	0	13.901 7
17	0	0	0	13.902 4
18	0	0	0	13.901 2
19	0	0	0	13.899 7
20	0	0	0	13.902 4

方法	可控因子优化结果			EQL	RMSE
方法	z₁	z₂	z₃	EQL	RMSE
GLM方法	0.562 4	0.266 2	0.841 2	13.600 0	0.022 4
Bayes方法	-0.764 5	0.706 4	0.751 9	0.555 4	0.013 0
TBayes方法	-0.388 7	0.604 6	0.795 2	0.560 8	0.010 5
所提方法	-0.381 4	0.629 8	0.863 9	0.001 3	0.002 4

[1]	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.
[2]	Cuihong ZHAI, Jianjun WANG, Zebiao FENG. Robust parameter design of multiple responses based on Gaussian process model [J]. Systems Engineering and Electronics, 2021, 43(12): 3683-3693.
[3]	FENG Zebiao, WANG Jianjun. Multi-response robust parameter design based on covariant characteristics of model responses [J]. Systems Engineering and Electronics, 2019, 41(9): 2048-2057.
[4]	YANG Shijuan, WANG Jianjun. Robust parameter design based on hierarchical Bayesian model [J]. Systems Engineering and Electronics, 2019, 41(10): 2293-2303.
[5]	GU Xiaoguang, MA Yizhong, LIU Jian, WANG Jianjun. Robust parameter design for multivariate quality characteristics based on process capability index with individual observations [J]. Systems Engineering and Electronics, 2017, 39(2): 362-368.
[6]	ZHANG Liu-yang, MA Yi-zhong, WANG Jian-jun, WU Feng. Robust parameter design and optimization for dynamic multi-response with the skewness characteristics [J]. Systems Engineering and Electronics, 2016, 38(2): 339-346.

Bayesian modeling and optimization based on semi-parametric hierarchy

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