Fourier-enhanced reduced-order surrogate modeling for uncertainty quantification in electric machine design

TL;DR

This paper introduces a Fourier-enhanced reduced-order surrogate modeling framework that efficiently predicts torque in electric machine design under geometric variations, significantly reducing computational costs for uncertainty quantification.

Contribution

It combines Fourier-based dimension reduction with machine learning response surfaces, notably Gaussian processes, to improve torque prediction accuracy and efficiency.

Findings

Fourier-based dimension reduction preserves physical torque information.

Gaussian process response surfaces provide the best predictive accuracy.

Surrogate models significantly reduce computational costs in uncertainty quantification.

Abstract

This work proposes a data-driven surrogate modeling framework for cost-effectively inferring the torque of a permanent magnet synchronous machine under geometric design variations. The framework is separated into a reduced-order modeling and an inference part. Given a dataset of torque signals, each corresponding to a different set of design parameters, torque dimension is first reduced by post-processing a discrete Fourier transform and keeping a reduced number of frequency components. This allows to take advantage of torque periodicity and preserve physical information contained in the frequency components. Next, a response surface model is computed by means of machine learning regression, which maps the design parameters to the reduced frequency components. The response surface models of choice are polynomial chaos expansions, feedforward neural networks, and Gaussian processes. Torque inference is performed by evaluating the response surface model for new design parameters and then inverting the dimension reduction. Numerical results show that the resulting surrogate models lead to sufficiently accurate torque predictions for previously unseen design configurations. The framework is found to be significantly advantageous compared to approximating the original (not reduced) torque signal directly, as well as slightly advantageous compared to using principal component analysis for dimension reduction. The combination of discrete Fourier transform-based dimension reduction with Gaussian process-based response surfaces yields the best-in-class surrogate model for this use case. The surrogate models replace the original, high-fidelity model in Monte Carlo-based uncertainty quantification studies, where they provide accurate torque statistics estimates at significantly reduced computational cost.