HARDCORE: H-field and power loss estimation for arbitrary waveforms with residual, dilated convolutional neural networks in ferrite cores

TL;DR

This work tackles waveform-agnostic estimation of steady-state power losses in ferrite cores by introducing HARDCORE, a residual CNN with physics-informed extensions. A key intermediate layer reconstructs the $bh$ curve and uses the polygon area, via the shoelace formula, to derive the hysteresis-based loss while a residual correction accounts for non-hysteresis losses, yielding a physically interpretable and compact model. The approach uses extensive feature engineering and a scheduled loss weighting to jointly optimize the $h$ sequence and the power loss $p$, achieving a Pareto-optimal trade-off with as few as 1755 parameters and, given sufficient data, a 95th percentile error below 8%. The method demonstrates material-specific training with a fixed topology across multiple ferrite cores, offering a scalable, interpretable pathway for data-driven power loss estimation in magnetic components.

Abstract

The MagNet Challenge 2023 calls upon competitors to develop data-driven models for the material-specific, waveform-agnostic estimation of steady-state power losses in toroidal ferrite cores. The following HARDCORE (H-field and power loss estimation for Arbitrary waveforms with Residual, Dilated convolutional neural networks in ferrite COREs) approach shows that a residual convolutional neural network with physics-informed extensions can serve this task efficiently when trained on observational data beforehand. One key solution element is an intermediate model layer which first reconstructs the bh curve and then estimates the power losses based on the curve's area rendering the proposed topology physically interpretable. In addition, emphasis was placed on expert-based feature engineering and information-rich inputs in order to enable a lean model architecture. A model is trained from scratch for each material, while the topology remains the same. A Pareto-style trade-off between model size and estimation accuracy is demonstrated, which yields an optimum at as low as 1755 parameters and down to below 8\,\% for the 95-th percentile of the relative error for the worst-case material with sufficient samples.

Figures (9)

• Figure 1: Visualization of the shoelace formula applied to a $bh$ polygon.
• Figure 2: Relative error $(\hat{p}_\text{hyst} - p) / p$ histogram between provided scalar $p$ and $\hat{p}_\text{hyst}$ calculated from the likewise provided $bh$ polygon area.
• Figure 3: Overview of the physics-inspired HARDCORE modeling toolchain.
• Figure 4: Exemplary samples of the normalized $b$ and $h$ curves.
• Figure 5: Magnetic flux density examples and their first and second order derivatives for a sinusoidal, triangular and one unclassified waveform with a circuit-based interpretation in terms of their proportionality to magnetic flux, voltage and the voltage slew rate.