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Explainable Functional Relation Discovery for Battery State-of-Health Using Kolmogorov-Arnold Network

Sanchita Ghosh, Tanushree Roy

Abstract

Battery health management is heavily dependent on reliable State-of-Health (SoH) estimation to ensure battery safety with maximized energy utilization. Although SoH estimation can effectively track battery degradation, it requires continuous battery data acquisition. In addition, model-based SoH estimation methods rely on accurate battery model knowledge, whereas data-driven approaches often suffer from limited interpretability. In contrast, analytical characterization of SoH will offer a direct and tractable handle on battery performance degradation, while also establishing a foundation for further analytical studies toward effective battery health management. Thus, in this work, we propose a Kolmogorov Arnold Network (KAN)-based data-driven pipeline to establish a functional relationship for SoH degradation using battery temperature data. Specifically, we learn long-term battery thermal dynamics and battery heat generation via learnable activation functions of our KAN model. We utilize the learned mapping to obtain an explicit functional relationship between SoH degradation and cycle number. The proposed pipeline was validated using real-world data, yielding a closed-form analytical formula of SoH degradation with high accuracy.

Explainable Functional Relation Discovery for Battery State-of-Health Using Kolmogorov-Arnold Network

Abstract

Battery health management is heavily dependent on reliable State-of-Health (SoH) estimation to ensure battery safety with maximized energy utilization. Although SoH estimation can effectively track battery degradation, it requires continuous battery data acquisition. In addition, model-based SoH estimation methods rely on accurate battery model knowledge, whereas data-driven approaches often suffer from limited interpretability. In contrast, analytical characterization of SoH will offer a direct and tractable handle on battery performance degradation, while also establishing a foundation for further analytical studies toward effective battery health management. Thus, in this work, we propose a Kolmogorov Arnold Network (KAN)-based data-driven pipeline to establish a functional relationship for SoH degradation using battery temperature data. Specifically, we learn long-term battery thermal dynamics and battery heat generation via learnable activation functions of our KAN model. We utilize the learned mapping to obtain an explicit functional relationship between SoH degradation and cycle number. The proposed pipeline was validated using real-world data, yielding a closed-form analytical formula of SoH degradation with high accuracy.

Paper Structure

This paper contains 10 sections, 25 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Characterizing Battery Degradation from Temperature
  3. Long-horizon battery thermal model
  4. SoH characterization using variation in heat generation
  5. Kolmogorov-Arnold Network For SoH Estimation
  6. Preliminaries on KAN
  7. Description of KAN training
  8. Relevance of KAN as an interpretable model
  9. Results and Discussions
  10. Conclusion & Future Work

Figures (5)

  • Figure 1: Overview of the data-driven pipeline used for discovering the functional relationship between battery degradation and battery cycle number.
  • Figure 2: Plot shows the converging training and validation losses during the training of the KAN model.
  • Figure 3: Plot shows the true and predicted long-term prediction of lumped battery temperature, measured at the surface.
  • Figure 4: Plot shows the baseline and three estimated $\mathrm{SoH}_p$. The true $\mathrm{SoH}_p$ is calculated using the drop in resistance. The $\mathrm{SoH}_p$ estimations are calculated from B-spline, quadratic, cubic, and quartic-based $\mathcal{A} _{2}(k)$ representation.
  • Figure 5: The top plot shows the error in $\mathrm{SoH}_p$ estimations, and the bottom plot compares the estimation error distribution using boxplots for B-spline, quadratic, cubic, and quartic-based $\mathcal{A} _{2}(k)$ representations.