Lithium-Ion Battery SOH Estimation via Mixture Correntropy Loss-Based PCA and Kolmogorov-Arnold-Enhanced Liquid Neural Networks

Accurate state of health (SOH) estimation of lithium-ion batteries is essential for reliable battery management but is particularly challenging under mixed non-Gaussian measurement noise and data scarcity. This article proposes a robust SOH estimation framework that combines noise-resistant feature extraction with data-efficient, interpretable continuous-time dynamic modeling. A mixture correntropy loss-based principal component analysis (MCL-PCA) method is first developed, which employs a hybrid Gaussian–Laplacian correntropy criterion to adaptively suppress mixed non-Gaussian noise and extract stable low-dimensional health features (HFs). These features serve as inputs to a newly designed Kolmogorov-Arnold-enhanced liquid neural network (KLNN), which augments continuous-time liquid dynamics with structured nonlinear mappings to improve stability and nonlinear generalization under limited small-sample conditions. These two components are integrated into a unified framework that yields coherent and physically consistent SOH degradation trajectories. Experimental results on laboratory and public datasets demonstrate that MCL-PCA significantly improves feature robustness, while KLNN achieves superior SOH estimation accuracy in noisy and small-sample scenarios, resulting in notably lower prediction errors than conventional PCA-based methods and consistent advantages over baseline models.