NERO Transformer: Energy Regulated Newton Optimization for Lithium Ion Battery State of Health Estimation

Accurate lithium-ion battery state-of-health (SOH) estimation requires effective temporal degradation modeling and reliable hyperparameter optimization. This study proposes NERO-Transformer, an integrated framework combining a Newton Energy Regulation Optimizer (NERO) with a multi-cycle Transformer for high-accuracy SOH estimation. Twelve charging-derived health indicators are organized into 20-cycle sequences to capture degradation evolution and temporal dependencies. NERO incorporates dynamic energy regulation, adaptive operator selection, and Newton-based refinement to coordinate global exploration and local exploitation while optimizing the Transformer learning rate, attention-head configuration, and L2 regularization coefficient. The proposed optimization strategy is systematically evaluated through mechanism ablation, 16 benchmark functions, and comparisons with nine representative optimizers. Experimental results on four CALCE batteries demonstrate that NERO-Transformer achieves R² values of 0.994, 0.901, 0.951, and 0.931, respectively, with an average R² of 0.944. The corresponding MAPE values range from 0.25% to 0.27%, demonstrating high relative estimation accuracy. Further evaluation on four NASA batteries extends the experimental assessment to an additional battery dataset. Model-level comparisons with Transformer, LSTM, BiLSTM, GRU, and Gaussian process regression provide complementary evidence of the framework’s predictive capability. Additionally, repeated-run analyses characterize cycle-level prediction consistency through empirical percentile ranges. The results demonstrate the effectiveness of integrating energy-regulated optimization with temporal attention-based modeling, providing a promising approach for accurate and reliable lithium-ion battery health assessment.