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

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.