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

摘要/Abstract

摘要：

针对非平稳响应的稳健参数设计问题, 在树状高斯过程(treed Gaussian process, TGP)建模的框架下, 提出基于主动学习算法的稳健参数优化模型。首先, 综合运用D-optimal和Expected Improvement设计策略, 构建主动学习算法, 以改善设计点的空间填充性能和优化性能。然后, 利用贝叶斯分层建模方法构建模型结构, 以估计输入和输出之间的非平稳函数关系。最后, 利用TGP模型输出, 构建基于质量损失函数的稳健参数优化模型。利用遗传算法(Genetic algorithm, GA)进行全局优化, 以获得最优输入参数设置。仿真结果表明, 所提方法所得最优解具有更小的质量损失和预测偏差, 改善了最优解潜在区域的预测精度, 降低了预测响应的不确定性, 进而提升了非平稳响应稳健优化结果的有效性。

关键词: 非平稳响应, 稳健参数设计, 树状高斯过程模型, 主动学习算法, 质量损失

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

中图分类号:

TP273.2

冯泽彪, 杨旭, 汪建均. 基于主动学习的树状高斯过程建模与参数优化[J]. 系统工程与电子技术, 2025, 47(6): 1950-1963.

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