Surrogate Modeling of Field Performance Analysis and Optimization via Hierarchical Proper Orthogonal Decomposition and Adaptive Sampling Radial Basis Function

In the pursuit of electric motor digitalization and performance enhancement, addressing the inherent complexities of multiphysics and multimodal field performance analysis is essential. Current methodologies often face limitations due to substantial computational resource demands and a tendency toward local optima in high-dimensional problems. This article proposed a self-adaptive reduced basis algorithm (SARBA), which utilizes a nonintrusive model order reduction technique to reduce computational complexity. To efficiently and accurately extract the reduced basis (RB) that is independent of the spatial distribution and parameters, a hierarchical proper orthogonal decomposition (HPOD) method was proposed as a priori dimensionality reduction, enabling the model to capture global features and achieve low dimensionality in the design space. Furthermore, to balance the tradeoff between global exploration and local exploitation in nonlinear spaces, this article combined adaptive algorithm with radial basis function (RBF) to approximate the RB expansion coefficient vectors for untrained parameters and dynamically adjusts the training dataset based on expectation improvement criteria, thereby iteratively updating the RBF model. The resulting multistep collaborative modeling framework facilitates precise field solution predictions from a limited dataset of large-scale simulations. The model’s accuracy and effectiveness were validated through tests on benchmark functions and its application in optimizing the stator magnetic field of high-speed electric motors.