State-of-Health and Remaining-Useful-Life Estimation of Lithium-Ion Batteries Using Axial-Embedding Transformer–Bidirectional Long Short-Term Memory Optimized by an Improved Newton–Raphson-Based Optimizer

Accurate estimation of the state of health (SOH) and prediction of the remaining useful life (RUL) of lithium-ion batteries (LIBs) are critical for ensuring system reliability and safety across diverse energy storage applications. This paper proposes a hybrid deep learning framework that integrates an axial-embedding Transformer (AxEmbTrans) encoder and a bidirectional LSTM (BiLSTM) module for the joint estimation of SOH and RUL. The AxEmbTrans encoder employs axial attention with abstract embeddings to capture global dependencies among multidimensional health features at reduced computational complexity compared to standard self-attention, while the BiLSTM models local temporal dynamics and short-term degradation fluctuations across consecutive cycles, with its bidirectional structure enhancing robustness against transient noise. Informative health features are extracted from charge–discharge curves, grouped into temporal, energy, and thermal categories, and fused using local linear embedding (LLE) for nonlinear dimensionality reduction. An improved Newton–Raphson-based optimizer (INRBO) is introduced to automatically tune the framework’s key hyperparameters, including the hidden dimension, number of attention heads, number of BiLSTM units, and learning rate, incorporating directional similarity modulation and multi-elite guidance to overcome the convergence instability of the standard NRBO. Extensive experiments on NASA and Maryland datasets demonstrate that the proposed method consistently outperforms baselines in both SOH and RUL prediction, achieving higher accuracy, improved robustness, and better cross-condition generalization.