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

2024-12-09

arXiv.org

AI Summary

To address the high computational cost and low accuracy of torque prediction for permanent magnet synchronous motors (PMSMs) arising from geometric parameter uncertainties, this paper proposes a Fourier-enhanced surrogate modeling framework. First, the time-domain torque response is transformed via discrete Fourier transform (DFT), and dominant frequency-domain components are retained to achieve physics-informed dimensionality reduction. Second, Gaussian process regression (GPR) is employed to map design parameters to the reduced spectral features. Finally, the full torque signal is reconstructed via inverse DFT. This work pioneers the integration of periodic physical priors with statistical surrogate modeling. Compared to direct time-domain modeling or PCA-based reduction, the proposed method achieves significantly higher prediction accuracy, reduces uncertainty quantification overhead by over 90%, yields torque statistical errors below 2%, and demonstrates strong generalization to unseen design configurations.

Technology Category

• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

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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.

Problem

• Cost-effective torque inference under design variations
• Reduced-order modeling using Fourier transform and machine learning
• Accurate torque predictions for unseen design configurations

Innovation

• Fourier transform reduces torque signal dimensions
• Machine learning maps design to frequency components
• Gaussian processes optimize response surface modeling