A Graph Theoretic Approach in Combination With Dynamic Mode Decomposition With Control (DMDc) to Analyze Battery Degradation

TL;DR

This paper introduces a novel data-driven framework combining graph theory and dynamic mode decomposition with control (DMDc) to analyze lithium-ion battery degradation, capturing complex evolving dynamics from operational data.

Contribution

It integrates graph-theoretic analysis with DMDc to represent battery degradation as an evolving network, providing interpretable insights into aging processes.

Findings

Network connectivity decreases as degradation progresses.

Structural fragmentation increases with battery aging.

Graph measures effectively reflect degradation stages.

Abstract

Accurate monitoring of lithium-ion battery (LIB) degradation is essential, yet it remains challenging due to the complex, nonlinear, and time-varying nature of electrochemical aging processes. Conventional equivalent circuit models (ECMs) provide simplified representations of battery behavior using fixed electrical components, but they cannot capture evolving internal degradation mechanisms and structural changes over time. In this study, a data-driven framework is developed by integrating dynamic mode decomposition with control (DMDc) with graph-theoretic analysis to characterize battery degradation from operational data alone. The mode matrix ($\mathbf{\phi}$) obtained from DMDc is transformed into a weighted adjacency matrix, enabling the representation of battery dynamics as an evolving network of interacting states. Graph-based measures, including connectivity and a modularity (proxy), are then used to quantify structural changes in the system across degradation stages. The results show a clear transition from a highly connected and coherent network in the healthy state to a progressively weaker and more fragmented structure as degradation advances, accompanied by increasing heterogeneity. This work demonstrates that graph-theoretic representations can effectively capture the evolving dynamics of battery degradation and provide interpretable insights into system-level aging behavior.