Data-Driven Intelligent Predictive Networks for Lithium-Ion Battery State of Charge Estimation

Lithium-ion batteries have the characteristics of efficient charging, large specific energy, and long cycle. The battery state of charge (SOC) is an important parameter for battery management systems and is defined as the ratio of the remaining capacity of the battery to its nominal capacity. The direct and accurate prediction of SOC is difficult due to the nonlinear dynamic characteristics and complex charging/discharging cycles. This study presents data-driven nonlinear autoregressive exogenous neuroarchitecture optimized with Levenberg-Marquardt (NARX-NA-LM) and Bayesian regularization (NARX-NA-BR) algorithms for accurate and robust SOC estimation. The performance of the proposed NARX-NA-LM and NARX-NA-BR is investigated in detail for five temperature conditions (-20 °C, - 10 °C, 0 °C, 10 °C, 25 °C) under four operating conditions. The four operating conditions are based on the data from the highway fuel economy driving schedule, urban dynamometer driving schedule profile, US06 supplemental federal test procedure, and the Los Angeles 92 profile. Accurate SOC prediction supports the proposed scheme, while the MSE-based learning plots for training/testing, error histogram results, correlation statistics, and state transition outcomes verify its convergence and reliability. Generally, the NARX-NA-LM provides better SOC prediction results than the NARX-NA-BR. The NARX-NA-LM is examined in detail for both open-loop and closed-loop configurations, as well as random and sequential data partitioning strategies. The proposed NARX-NA-LM network demonstrated high SOC prediction accuracy across four driving cycles and five operating temperatures (–20°C to 25°C), with results averaged over 10 independent runs yielding mean absolute errors (MAEs) ranging from 0.00052% to 0.00078% and root mean square errors (RMSEs) ranging from 0.00080% to 0.00181% across the investigated conditions.