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.

翻译：本研究提出了一种数据驱动的代理建模框架，用于经济高效地推断永磁同步电机在几何设计变化下的转矩。该框架分为降阶建模和推断两部分。给定一组转矩信号数据集，每个信号对应不同的设计参数集，首先通过对离散傅里叶变换进行后处理并保留少量频率分量来实现转矩维度的降阶。这能够利用转矩的周期性并保留频率分量中包含的物理信息。接着，通过机器学习回归方法构建响应面模型，该模型将设计参数映射至降维后的频率分量。所选的响应面模型包括多项式混沌展开、前馈神经网络和高斯过程。转矩推断通过评估新设计参数下的响应面模型，然后逆转降维过程来实现。数值结果表明，所得代理模型能够对未见过的设计配置提供足够精确的转矩预测。该框架相较于直接近似原始（未降维）转矩信号具有显著优势，与使用主成分分析进行降维的方法相比也略有优势。基于离散傅里叶变换的降维方法与基于高斯过程的响应面模型相结合，为此应用场景提供了最优的代理模型。在基于蒙特卡洛的不确定性量化研究中，这些代理模型替代了原始的高保真模型，以显著降低的计算成本提供精确的转矩统计估计。