基于多评价标准的代理模型综合比较研究

doi:10.3901/JME.2022.16.403

摘要/Abstract

摘要： 代理模型是指利用有限的样本信息建立结构输入与输出之间的数学关系，其在复杂装备的结构和多学科设计优化中的应用日益广泛，为了获取不同代理模型在代替仿真分析或物理试验时的表现效果，采用38个测试函数对常见的代理模型方法进行了系统对比。对九种代理模型在不同样本数量、不同非线性程度、不同维度的测试函数下的预测精度进行研究，并分析了模型在不同维度测试问题下的计算成本，最后通过两个工程实例对比了不同代理模型的预测性能。结果表明，在所有模型未进行参数优化的情况下，传统的代理模型(多项式回归，径向基函数模型，支持向量回归，克里金模型)在工程分析时能保持较好的预测性能；支持向量回归在大多数测试函数下，总能保持较好的预测精度；径向基函数在高非线性问题中鲁棒性最好，随机森林在低非线性问题中表现出更好的鲁棒性。因此，针对不同的回归问题，采用相适应的模型能进一步提高计算结果的准确性和效率，对研究回归模型在优化设计领域中的应用具有指导意义。

关键词: 代理模型, 模型对比, 非线性程度, 多评价标准, 优化设计

Abstract: The surrogate model refers to the use of limited sample information to establish the mathematical relationship between structural input and output, and it is increasingly used in the structural and multidisciplinary design optimization of complex equipment. With the purpose of obtaining performance effect of different approximate models in place of simulation analysis or physical test, systematic comparative analysis of approximate model for 38 test functions is carried out. Research the prediction accuracy of each model is calculated with the condition of different sample sizes, different nonlinearity degrees and different dimensions, and the computational time of different test functions on the model is also analyzed. Finally, two engineering examples are used to compare the predictive performance of the different approximate models. The results show that traditional approximate model (Polynomial Regression Surface, Radial Basis Function, Support Vector Regression, Kriging) maintain better prediction performance in engineering analysis without parameter optimization of the model. The accuracy of support vector regression (SVR) is better than other algorithm under most test functions. Radial basis function (RBF) has the best robustness in high non-linearity problems while random forest (RF) shows better robustness in low non-linearity. Thus, for different regression problems using suitable models can further improve the prediction accuracy and efficiency for different situations, which has guiding significance for studying the application of regression algorithm in the field of optimization design.

Key words: surrogate model, model comparison, degree of non-linearity, multiple evaluation criteria, optimization design

中图分类号:

TH122

何西旺, 杨亮亮, 冉仁杰, 朱发文, 宋学官. 基于多评价标准的代理模型综合比较研究[J]. 机械工程学报, 2022, 58(16): 403-419.

HE Xiwang, YANG Liangliang, RAN Renjie, ZHU Fawen, SONG Xueguan. Comparative Studies of Surrogate Models Based on Multiple Evaluation Criteria[J]. Journal of Mechanical Engineering, 2022, 58(16): 403-419.

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