基于Kriging模型的稳健参数设计

doi:10.12305/j.issn.1001-506X.2023.07.38

摘要/Abstract

摘要：

针对复杂工程系统中的稳健参数优化问题, 提出了一种新的基于Kriging代理模型的序贯优化设计方法。首先，用Kriging模型预测均值的最小值，代替真实观测的最小响应值来考虑噪声; 然后，对该加点准则的预测方差进行修正, 使其在足够的样本量下能够收敛; 最后，通过经典的低维、高维非线性数值算例和工程算例来验证所提方法的有效性。验证结果表明, 与已有的传统加点准则相比, 所提方法能以更少的加点次数获得更好的全局解, 具有更强的全局寻优能力和稳健性。

关键词: Kriging模型, 序贯优化设计, 噪声评估, 期望改善, 稳健参数设计

Abstract:

For robust parameter optimization in complex engineering systems, a new sequential optimization design method based on Kriging surrogate model is proposed. Firstly, the minimum predicted mean value of the Kriging model is used to replace the actual observed minimum response value to consider the noise. Secondly, the prediction variance of the addition criterion is modified to make it converge with sufficient sample volume. Finally, the effectiveness of the proposed method is verified by classic low dimensional and high dimensional nonlinear numerical and engineering examples. The results show that the proposed method can obtain better global solutions with fewer addition times, and has stronger global optimization ability and robustness compared to existing traditional addition criteria.

Key words: Kriging model, sequential optimization design, noise evaluation, expected improvement, robust parameter design

中图分类号:

F273.2

丁春风, 汪建均. 基于Kriging模型的稳健参数设计[J]. 系统工程与电子技术, 2023, 45(7): 2269-2279.

Chunfeng DING, Jianjun WANG. Robust parameter design based on Kriging model[J]. Systems Engineering and Electronics, 2023, 45(7): 2269-2279.

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变量	名称	下界	上界
r_w	钻孔半径/m	0.05	0.15
r	影响半径/m	100.00	50 000.00
T_u	上部含水层渗透率/(m²/yr)	63 070.00	115 600.00
H_u	上部含水层电位头/m	990.00	1 110.00
T_l	下部含水层渗透率/(m²/yr)	63.10	116.00
H_l	下部含水层电位头/m	700.00	820.00
L	钻孔长度/m	1 120.00	1 680.00
K_w	钻孔水力传导率/(m/yr)	1 500.00	15 000.00

数值算例	优化方法	评价指标
数值算例	优化方法	OE1	OE2	OE3
算例1	EI	-0.031 1	66.466 7	0.006 2
	IECI	-0.037 4	60.666 7	0.000 7
	NIECI	-0.065 7	57.633 3	0.000 2
算例2	EI	-2.861 2	179.333 3	0.004 7
	IECI	-2.997 2	162.566 7	0.000 4
	NIECI	-3.080 9	139.300 0	0.000 4
算例3	EI	2.720 7	98.766 7	0.002 7
	IECI	2.651 9	102.300 0	0.027 2
	NIECI	2.224 6	93.700 0	4.187 6e-05

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