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    分级扩展组合代理模型建模方法及预测性能研究

    Research on Modeling Method and Prediction Performance of Hierarchical Extended Ensemble Surrogate Models

    • 摘要: 针对复杂高维非线性工程问题中单一代理模型预测精度不足及稳健性差的问题,文中提出一种分级扩展组合代理模型(Hierarchical Extended Ensemble Surrogate, HEES)建模方法,旨在通过多模型协同优化提升代理模型预测性能。首先,基于交叉验证方法筛选高精度模型库,并通过全局与局部误差准则对模型排序;其次,设计线性、多项式及指数型权重控制函数,分配组合基础代理模型和扩展代理模型权重,实现多模型优势融合;最后,通过30组涵盖低维(2维)至高维(10维)的测试函数验证模型性能。结果表明:HEES模型在全局精度与局部精度方面表现出显著性能优势,相比平均权重组合代理(Average Weight Ensemble Surrogate, AWES)模型,将R2从0.911 7提高至0.941 7,将标准化最大绝对误差从0.192 6降低至0.119 8。该研究为复杂工程系统优化设计提供了高效建模工具,具有重要应用价值。

       

      Abstract: To address the issues of insufficient prediction accuracy and poor robustness of single surrogate models in complex high-dimensional nonlinear engineering problems, a hierarchical extended ensemble surrogate (HEES) modeling approach is proposed in this paper. The HEES method first ranks the models based on their performance, then designs linear, polynomial, and exponential weight control functions to dynamically allocate weights between the base surrogate models and the extended surrogate models, thereby integrating the advantages of multiple models. Finally, the performance of the HEES model is validated through 30 test functions ranging from low-dimensional (2D) to high-dimensional (10D). The results show that the HEES model exhibits significant performance advantages in both global and local accuracy, improving the R2 from 0.911 7 to 0.941 7 and reducing the normal maximum absolute error from 0.192 6 to 0.119 8, compared to the average weight ensemble surrogate (AWES) model. This research provides an efficient modeling tool for the optimal design of complex engineering systems, which is of substantial practical importance.

       

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