Magnetic field estimation using Gaussian process regression for interactive wireless power system design

Abstract

Wireless power transfer (WPT) with coupled resonators offers a promising solution for the seamless powering of electronic devices. Interactive design approaches that visualize the magnetic field and power transfer efficiency based on system geometry adjustments can facilitate the understanding and exploration of the behavior of these systems for dynamic applications. However, typical electromagnetic field simulation methods, such as the Method of Moments (MoM), require significant computational resources, limiting the rate at which computation can be performed for acceptable interactivity. Furthermore, the system's sensitivity to positional and geometrical changes necessitates a large number of simulations, and structures such as ferromagnetic shields further complicate these simulations. Here, we introduce a machine learning approach using Gaussian Process Regression (GPR), demonstrating for the first time the rapid estimation of the entire magnetic field and power transfer efficiency for near-field coupled systems. To achieve quick and accurate estimation, we develop 3D adaptive grid systems and an active learning strategy to effectively capture the nonlinear interactions between complex system geometries and magnetic fields. By training a regression model, our approach achieves magnetic field computation with sub-second latency and with an average error of less than 6% when validated against independent electromagnetic simulation results.

Figures (8)

• Figure 1: Magnetic field estimation in a wireless power transfer system and its estimation pipeline. a The magnetic field in a wireless power transfer system is rapidly estimated using machine learning techniques. This approach facilitates interactive exploration and design of system geometries by adjusting the shield's position and geometry. b An overview of the estimation method. User input includes details about the shield geometry and the relative positioning of the transmitter and receiver. For wireless power transfer, we use coils equipped with a ferromagnetic shield. The shield geometries are represented using the proposed aligned-edge polycube mesh, which accommodates various geometries expressed in fixed-length compact vectors. Furthermore, estimation points are modeled using our proposed adaptive exterior grid. This grid alleviates nonlinearities and discontinuous relationships between geometric inputs and magnetic field outputs, essential for precise estimation via GPR. The GPR model's training data is efficiently curated using active learning, enabling the development of reliable models with fewer data points. This method allows for the rapid estimation and visualization of the magnetic field's magnitude and vector, as well as power transfer efficiency.
• Figure 2: Aligned-edge polycube and adaptive exterior grid. a Cross-sectional view for generating the aligned-edge polycube. The polycubes (green) are arranged around the shield geometry (gray) and are fitted to the surface of the geometry. Initial points consist of corner points and surface points forming shield-fitting cubes. The mesh is subdivided by interpolating points. By aligning them to the edges of the geometry, the aligned-edge polycube minimizes the number of points needed to represent the shield geometry. b Generation process for the adaptive exterior grid. Exterior cubes (blue) are positioned around shield-fitting polycubes and adjusted to match the geometry representation. These polycubes are further subdivided by interpolation relative to the exterior cubes. c Adjusting the adaptive exterior grid to coil positioning. It is modified to maintain its relative position to the coils, taking into account the transmitter and receiver's relative positions. This adjustment helps prevent abrupt changes in the magnetic field due to position variations.
• Figure 3: Principle of continuity and linearity enhancement using an adaptive exterior grid. a Shows the fixed grid estimation point transitioning between inside and outside the ferromagnetic shield, leading to discontinuous changes in the magnetic field. The proposed adaptive grid, on the other hand, adjusts its position in response to changes in geometry, thereby maintaining continuity. b Demonstrates how changes in shield position can cause discontinuous and non-linear variations in the magnetic field when using fixed exterior grids. The proposed adaptive exterior grid mitigates these effects by adapting to the geometry, thereby minimizing changes in the magnetic field magnitude at the estimated points.
• Figure 4: Generated aligned-edge polycube and adaptive exterior grid. The aligned-edge polycubes are specifically aligned with the corners of the shield geometry, while the adaptive exterior grid points are created to interface with the polycube meshes. After analyzing the resulting mesh, it was concluded that a level 3 aligned-edge polycube sufficiently represents the geometry, and a level 2 adaptive exterior grid effectively captures the magnetic field. Additional evaluations at level 3 were conducted to determine the effect on processing time by examining more detailed aspects of the field distribution.
• Figure 5: Training dataset construction using active learning for GPR. a Overview of the active learning process using GPR. Initially, we created an unlabeled dataset consisting of 169 relative positions for each of the 372 shields. From this dataset, 744 data points were simulated to form the initial training dataset, while the remaining data points were left unlabeled. The entire unlabeled dataset was then analyzed to identify six data points corresponding to GPR model instances showing the highest average deviation, and these were used throughout the active learning process. For each cycle, we calculated the deviation of each data point using these GPR instances, selected those with significant deviations to add to the training set, and repeated the cycle until the training dataset size was doubled to 1,488 data points. b Distribution of the relative positions in the initial training dataset ($N_0=744$). c Distribution of the relative positions in the training dataset after active learning ($N_\mathrm{t}=1488$). d,e Relationship between training dataset size, maximum deviation, and maximum error of selected GPR model instances at the start of active learning. Both maximum deviation and maximum error decrease as the training dataset size increases.