Modeling of non-linear dynamics and degradation characterization of lithium-ion batteries using delay-embedded dynamic mode decomposition

Data-driven modeling approaches offer a compelling alternative of the physics-based models that do not require explicit use of governing equations of the system. In this study, Koopman-based approaches such as dynamic mode decomposition with control (DMDc) and its extended formulation (eDMDc) are employed to construct models for predicting the non-linear voltage behavior of lithium-ion batteries from hybrid pulse power characterization (HPPC) tests. To better capture the nonlinear dynamics of the battery and perform long-horizon prediction, time-delay embedded snapshots were constructed via Hankel-delay embedding using 60% of the voltage data from a single HPPC test. By augmenting the state space with lagged observations, the embedding lifts the system’s dynamics into a higher-dimensional linear representation, enabling DMDc and eDMDc to approximate the underlying nonlinear behavior more faithfully. Optimum embedding dimensions for the input and output data were determined using residual sum of squares criteria such that both models can capture the underlying patterns without being underfitted or overfitted. Cross-cell validation and the behavior under aging were also investigated. Additionally, spectral analysis of the dynamic modes from both models reveals a monotonic decrease in modal decay coefficients with progressive cycling. This monotonic spectral evolution contrasts with the non-monotonic trends commonly observed in equivalent circuit model (ECM) parameters, suggesting that DMDc and eDMDc modal spectra could provide a reliable and interpretable signature of battery state of health.