Comparative Battery State of Charge (SoC) Estimation Using Shallow and Deep Machine Learning Models

This paper evaluates neural-network approaches for lithium-ion battery state-of-charge (SoC) estimation under a unified pipeline, fixed data partitions, and identical preprocessing. We study FNNs trained with Levenberg–Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG) across three hidden sizes (10, 20, 30) and three topologies: Fitting, Nonlinear Input–Output (Nonlinear I/O), and time-series NAR/NARX. Models are assessed using test MSE and RMSE, correlation (R), generalization gap, convergence indicators (final gradient, damping factor), wall time per epoch, and a relative compute-cost index. On the Fitting task, BR-Fitting-FNN with 20 neurons provides the best accuracy-efficiency balance, while LM-Fitting-FNN with 30 neurons reaches slightly lower error at a higher cost. For Nonlinear I/O, BR-Nonlinear I/O-FNN with 30 neurons achieves the lowest test MSE with clear evidence of effective weight shrinkage; LM-Nonlinear I/O-FNN with 20 neurons is a close alternative. In time-series settings, LM-NAR-FNN with 10 neurons attains the lowest test error and fastest epochs but shows a very negative gap that suggests test-split favorability; BR-NAR-FNN with 30 neurons is more costly yet consistently strong. For NARX, LM-NARX-FNN with 20 neurons yields the best test accuracy and robust convergence. Overall, BR delivers the most reliable accuracy–robustness trade-off as networks widen, LM often achieves the best raw accuracy with careful split validation, and SCG offers the lowest training cost when resources are limited. These results provide practical guidance for selecting SoC estimators to match accuracy targets, computing budgets, and deployment constraints in battery management systems.