Robust State of Health Prediction of Li-Ion Batteries via NARX with PSO-Selected Architecture and Bayesian Regularization

Electric vehicle (EV) safety, lifetime economics, and warranty management increasingly depend on reliable estimation of lithium-ion battery (LiB) state-of-health (SOH). During real-world operation, SOH estimation relies on standard battery management system (BMS) measurements collected under heterogeneous and time-varying conditions (irregular loads, partial cycling, and temperature variation). Because heuristic and fixed-parameter models fail to capture temporal effects and exhibit poor robustness to changing operating regimes, we introduce a Nonlinear Autoregressive network with Exogenous inputs (NARX) with Particle Swarm Optimization (PSO) based architecture selection and Bayesian Regularization (BR) for robust training. Using only standard BMS measurements, voltage, current, and temperature, the model learns temporal degradation dynamics without intrusive sensing. PSO explores input/feedback delays and hidden size; the selected NARX is then trained with BR to balance data fit and weight decay. This combination of PSO-based architecture optimization and BR represents a novel approach, where PSO adaptively identifies the most informative temporal structure for degradation dynamics, while BR ensures stable learning under noisy and limited BMS data. This synergy specifically addresses the challenge of accurate SOH estimation under highly variable operating conditions. On a representative NASA laboratory dataset, the approach show close agreement with the target SOH values (overall R ≈0.99758; test R ≈0.99755) and a minimum training MSE of 1.42 × 10⁻⁴, with narrow, unbiased residuals and stable convergence.