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KAN-Koopman Based Rapid Detection Of Battery Thermal Anomalies With Diagnostics Guarantees

Sanchita Ghosh, Tanushree Roy

TL;DR

This work proposes a Kolomogorov-Arnold network (KAN) in conjunction with a Koopman-based detection algorithm that leverages the unique advantages of both methods and derives analytical conditions that provide diagnostic guarantees on the KAN-Koopman detection scheme.

Abstract

Early diagnosis of battery thermal anomalies is crucial to ensure safe and reliable battery operation by preventing catastrophic thermal failures. Battery diagnostics primarily rely on battery surface temperature measurements and/or estimation of core temperatures. However, aging-induced changes in the battery model and limited training data remain major challenges for model-based and machine-learning based battery state estimation and diagnostics. To address these issues, we propose a Kolomogorov-Arnold network (KAN) in conjunction with a Koopman-based detection algorithm that leverages the unique advantages of both methods. Firstly, the lightweight KAN provides a model-free estimation of the core temperature to ensure rapid detection of battery thermal anomalies. Secondly, the Koopman operator is learned in real time using the estimated core temperature from KAN and the measured surface temperature of the battery to provide a prediction for diagnostic residual generation. This online learning approach overcomes the challenges of model changes, while the integrated structure reduces the dependence on large datasets. Furthermore, we derive analytical conditions that provide diagnostic guarantees on our KAN-Koopman detection scheme. Our simulation results illustrate a significant reduction in detection time with the proposed algorithm compared to the baseline Koopman-only algorithm.

KAN-Koopman Based Rapid Detection Of Battery Thermal Anomalies With Diagnostics Guarantees

TL;DR

This work proposes a Kolomogorov-Arnold network (KAN) in conjunction with a Koopman-based detection algorithm that leverages the unique advantages of both methods and derives analytical conditions that provide diagnostic guarantees on the KAN-Koopman detection scheme.

Abstract

Early diagnosis of battery thermal anomalies is crucial to ensure safe and reliable battery operation by preventing catastrophic thermal failures. Battery diagnostics primarily rely on battery surface temperature measurements and/or estimation of core temperatures. However, aging-induced changes in the battery model and limited training data remain major challenges for model-based and machine-learning based battery state estimation and diagnostics. To address these issues, we propose a Kolomogorov-Arnold network (KAN) in conjunction with a Koopman-based detection algorithm that leverages the unique advantages of both methods. Firstly, the lightweight KAN provides a model-free estimation of the core temperature to ensure rapid detection of battery thermal anomalies. Secondly, the Koopman operator is learned in real time using the estimated core temperature from KAN and the measured surface temperature of the battery to provide a prediction for diagnostic residual generation. This online learning approach overcomes the challenges of model changes, while the integrated structure reduces the dependence on large datasets. Furthermore, we derive analytical conditions that provide diagnostic guarantees on our KAN-Koopman detection scheme. Our simulation results illustrate a significant reduction in detection time with the proposed algorithm compared to the baseline Koopman-only algorithm.
Paper Structure (14 sections, 4 theorems, 33 equations, 2 figures)

This paper contains 14 sections, 4 theorems, 33 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Kolomogorov-Arnold network
  4. Koopman operator
  5. Thermal Anomalies in Battery
  6. KAN-Koopman Diagnostic Algorithm
  7. KAN-based estimation
  8. Koopman-based prediction
  9. Diagnostic guarantees
  10. Simulation Results
  11. Details of KAN-Koopman implementation
  12. Case study I: Incipient thermal fault
  13. Case study II: Battery charging cyberattack
  14. Conclusion

Key Result

Theorem 1

Let us consider a bounded multi-variate function $f(\boldsymbol{\alpha})$ for $\boldsymbol{\alpha} = (\alpha_1, \cdots, \alpha_n)$ that can be expressed with finite additive compositions of $\kappa+1$ times differentiable univariate functions $\varphi_{d,b,a}$ such that $f(\boldsymbol{\alpha}) = (\p where, the constant $\mathcal{D}$ depends on the function and its representation, and $\lvert \cdot

Figures (2)

  • Figure 1: Under an incipient thermal fault, top plot shows $T_1$, $T_2$, and $\mathbb{T}_1$; second plot shows $I$; third plot shows $\dot{Q}$; fourth and fifth plots, respectively, shows the diagnostic residuals and the thermal anomaly flag generated by proposed and the baseline Koopman algorithm.
  • Figure 2: Under battery charging cyberattack, top plot shows $T_1$, $T_2$, and $\mathbb{T}_1$; second plot shows nominal and corrupted $I$; third plot shows $\dot{Q}$; fourth and fifth plots, respectively, shows the diagnostic residuals and the thermal anomaly flag generated by proposed and the baseline Koopman algorithm.

Theorems & Definitions (8)

  • Theorem 1: Approximation Theory liu2024kan
  • Lemma 1: Lipschitz continuity of error with anomalies
  • proof
  • Remark 1
  • Theorem 2: Upper bound on residual under no anomaly
  • proof
  • Theorem 3: Reliable detection of thermal anomalies
  • proof