基于主动学习的树状高斯过程建模与参数优化

doi:10.12305/j.issn.1001-506X.2025.06.23

Abstract

Abstract:

Under the framework of treed Gaussian process (TGP) modeling, a robust parameter optimi-zation model based on an active learning algorithm for robust parameter design problems with non-stationary responses is proposed. Firstly, by comprehensively applying the D-optimal and Expected Improvement design strategies, an active learning algorithm is constructed to improve the spatial filling performance and optimization performance of the design points. Secondly, the Bayesian hierarchical modeling approach is used to construct the model structure to estimate the non-stationary functional relationship between inputs and outputs. Finally, based on the output of the TGP model, a robust parameter optimization model is constructed based on quality loss function. The genetic algorithm (GA) is used for global optimization to obtain the optimal input parameter settings. The simulation results show that the optimal solution obtained by the proposed method has a smaller quality loss and prediction bias. Therefore, the proposed method improves the prediction accuracy in the potential optimal solution region, reduces the uncertainty of the predicted response, and further enhances the effectiveness of robust optimization results for non-stationary responses.

Key words: non-stationary response, robust parameter design, treed Gaussian process (TGP) model, active learning algorithm, quality loss

CLC Number:

TP273.2

Zebiao FENG, Xu YANG, Jianjun WANG. Modeling and parameter optimization based on active learning treed Gaussian process[J]. Systems Engineering and Electronics, 2025, 47(6): 1950-1963.

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方法	RMSE
方法	整体	最优	非线性	线性	非平稳
LHS	0.086 5	0.047 2	0.114 7	0.032 3	0.129 2
DO	0.079 7	0.047 4	0.106 8	0.027 1	0.118 4
本文方法	0.053 3	0.020 1	0.068 4	0.025 1	0.070 8

方法	RMSE			时间/s
方法	整体	最优	非平稳	时间/s
LHS	0.064 9	0.152 5	0.052 3	1.58
DO	0.075 3	0.110 8	0.074 3	31.73
本文方法	0.035 8	0.017 5	0.028 0	30.93

方法	RMSE		时间/s
方法	整体	最优	时间/s
LHS	0.041 4	0.083 6	6.04
DO	0.056 5	0.151 2	95.55
本文方法	0.017 6	0.012 8	93.74

方法	输出响应		预测方差	质量损失
方法	预测值	真实值	预测方差	质量损失
LHS	0.083 7	1.974 8	2.078 0	10.583 1
DO	1.528 4	2.028 2	0.715 5	2.881 2
本文方法	2.581 9	2.666 0	1.062 9	1.237 8

输入参数	符号	类别	最小值	最大值
光束宽度/mm	x₁	连续型	0.15	0.3
扫描速度/mm/s	x₂	连续型	1 000	2 000
层厚度/mm	x₃	连续型	0.1	2
功率/W	x₄	两水平	200	1 000

Modeling and parameter optimization based on active learning treed Gaussian process

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序号	光束宽度/mm	扫描速度/m	层厚度/mm	功率/W	总体形变/mm
1	0.188	1 046	0.155	200	0.412 14
2	0.282	1 606	0.733	200	0.133 27
3	0.215	1 686	1.114	1 000	1.077 72
4	0.207	1 965	1.338	1 000	0.992 92
5	0.234	1 933	1.625	1 000	0.765 07
6	0.275	1 374	0.653	200	0.147 92
7	0.157	1 834	1.244	1 000	1.540 99
8	0.245	1 146	0.277	200	0.241 13
9	0.259	1 199	1.720	1 000	0.888 81
10	0.251	1 542	1.460	1 000	0.769 47
11	0.268	1 402	0.553	200	0.173 95
12	0.172	1 746	1.868	1 000	1.459 93
13	0.219	1 862	1.572	1 000	0.834 16
14	0.161	1 270	0.379	200	0.478 60
15	0.173	1 494	0.423	200	0.359 53
16	0.297	1 220	1.931	1 000	0.777 81
17	0.201	1 065	1.025	1 000	1.536 95
18	0.185	1 761	0.930	200	0.264 06
19	0.290	1 339	0.818	200	0.127 85
20	0.226	1 584	1.205	1 000	0.998 54
21	0.296	1 444	1.001	1 000	0.656 56
22	0.257	1 655	0.748	200	0.152 71
23	0.225	1 802	0.867	200	0.182 09
24	0.256	1 117	0.228	200	0.221 61
25	0.224	1 723	0.539	200	0.183 51
26	0.243	1 513	0.566	200	0.172 92
27	0.247	1 446	0.484	200	0.222 94
28	0.251	1 299	0.287	200	0.213 86
29	0.276	1 021	0.444	200	0.213 72
30	0.234	1 470	0.434	200	0.200 40

方法	输入参数			预测响应	预测方差	真实响应	预测偏差	质量损失
方法	x₁	x₂	x₃	预测响应	预测方差	真实响应	预测偏差	质量损失
LHS	0.223	1 697	1.090	0.956 4	0.010 7	0.886 3	0.070 1	0.582 8
DO	0.225	1 495	0.987	0.706 0	0.186 6	0.216 9	0.455 9	0.442 6
本文方法	0.245	1 425	0.283	0.197 7	0.013 8	0.199 96	0.002 3	0.013 8

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