Hybrid Sampling Strategies for a Surrogate Model in High-Dimensional Space for Electric Motor Design

This paper presents a hybrid sequential sampling (HSS) method for effectively constructing a surrogate model in the high-dimensional, multi-objective optimization of a permanent magnet-assisted synchronous reluctance motor (PMa-SynRM) designed for high-speed rail traction. Conventional finite element analysis (FEA)-based optimization requires significant computational costs, necessitating more efficient alternatives. Surrogate model-based optimization methods have been widely studied to reduce this burden while maintaining accuracy. However, traditional sampling techniques often struggle to achieve well-distributed samples in high-dimensional spaces, where the curse of dimensionality hinders accurate surrogate modeling. To address this, we propose an HSS method integrating space-filling sequential sampling (SFSS) for global exploration and residual-based adaptive sequential sampling (ASS) for local refinement. The core innovation of HSS lies in its adaptive switching mechanism, which dynamically transitions between SFSS and ASS based on the real-time improvement rate of the surrogate model’s accuracy (measured by), ensuring efficient sample allocation. The method employs extreme gradient boosting (XGBoost) as the underlying surrogate model. The effectiveness of HSS is validated using three benchmark test functions, comparing its performance against standalone ASS and SFSS methods. Finally, HSS is successfully validated on a high-speed rail traction motor design case, demonstrating its effectiveness in building accurate surrogate models from electromagnetic FEA data for complex engineering applications.