Lithium-ion battery state of health estimation based on a hybrid kernel adaptive selective state-space model

Given the ubiquity of lithium-ion batteries as grid-scale energy storage systems, the accurate estimation of their State of Health (SOH) is of paramount importance, serving as a key enabler for reliability and predictive maintenance. However, battery degradation is driven by highly nonlinear aging mechanisms, while internal electrochemical states are not directly observable, posing significant challenges for robust SOH assessment. To address these issues, we propose a KAN–Adaptive–Delta Mamba state-space model (KAD-Mamba), which tightly couples Kolmogorov–Arnold Network (KAN) spline representations with a Δ -adaptive Mamba state-space backbone. This fusion allows the model to inherit the expressive nonlinear functional mapping of KAN and the efficient long-range recurrence of Mamba. Through its adaptive B-spline basis functions, KAD-Mamba captures complex nonlinear degradation behaviors, including capacity-fade curvature, rate-dependent hysteresis and cycle-dependent feature distortions, all of which are challenging for traditional state-space models to represent. At the same time, the Δ -adaptive Mamba backbone models the multi-timescale temporal evolution of battery aging, enabling the state-transition dynamics to adjust to varying cycling conditions. Experimental evaluations conducted on the CALCE and APR datasets demonstrate that the proposed approach can precisely trace various battery degradation trajectories, while exhibiting improved cross-cell generalization performance within the evaluated datasets. The results demonstrate that KAD-Mamba provides an effective modeling paradigm for lithium-ion battery SOH estimation, yielding notable improvements in prediction accuracy, robustness, and temporal consistency.