Data-Driven Optimization of Aspect Ratio in Permanent Magnet Machines Using Deep Learning and SHAP Analysis

The aspect ratio, defined as the ratio of the outer diameter to the stack length, is a critical parameter in permanent magnet (PM) machine design, with a profound impact on motor performance. This study presents a novel framework integrating deep learning and Shapley additive explanations (SHAP) to analyze the influence of design variables on the optimal aspect ratio. To achieve this, extensive datasets are generated using a metaheuristic optimization algorithm, covering diverse scenarios and objectives to ensure robust generalization and accuracy. A deep learning model is then trained on these datasets to capture the complex, nonlinear relationships between design variables and the aspect ratio. To enhance the interpretability of the “opaque model”, SHAP is employed, providing a detailed attribution analysis of each design variable contribution to the aspect ratio. This dual approach successfully uncovers the complex relationships between the aspect ratio and design variables across diverse design scenarios, thereby enabling actionable guidelines for sizing the outer diameter and height of the motor in the early design phase. Furthermore, the proposed methodology offers a scalable framework for analyzing other key ratios in motor design, establishing itself as a foundational tool for future advancements in this field.