NARX neural network optimized by polynomial chaos and forward orthogonal least squares for lithium-ion battery SOC estimation

Accurate estimation of the State of Charge (SOC) of lithium-ion batteries is crucial for optimizing battery performance, extending service life, and ensuring safe operation. In neural network-based SOC estimation, dynamic neural networks are indispensable, with the Nonlinear AutoRegressive with eXogenous inputs Neural Network (NARXNN) excelling in modeling lithium-ion batteries’ nonlinear time-varying dynamics. To enhance estimation performance, a dual-optimization framework is introduced. First, Forward Orthogonal Least Squares (FOLS) optimizes the NARXNN regression matrix through stepwise orthogonal regression, improving high-speed dynamic adaptability by selecting dominant time-delay terms. Subsequently, Polynomial Chaos (PC) optimizes NARXNN network weights via orthogonal polynomial decomposition, quantifying parameter uncertainties to boost steady-state precision. Under the UDDS, US06, and LA92 driving cycles, the FOLS-PC-NARXNN model achieved MAE values of 0.0255%, 0.0798%, and 0.0479%, respectively. These results represent a significant improvement over the 4.7276%, 1.6783%, and 1.8928% errors from the baseline NARXNN model and also surpass other mainstream methods in comparison. Furthermore, tests conducted at extended sampling intervals of 10, 15, and 30 s confirm the model’s strong robustness and maintained estimation accuracy under varied sampling conditions, collectively demonstrating the effectiveness of the dual-optimization strategy in enhancing SOC estimation.