Accurate battery capacity forecasting is crucial for ensuring safe operation and effective maintenance scheduling. However, capacity prediction remains challenging due to the complex, nonlinear degradation processes influenced by diverse operational conditions and usage patterns. Existing operational condition analysis methods either treat voltage, current, and temperature independently, losing cross-variable coupling effects, or aggregate exposure durations without preserving temporal ordering, discarding transition dynamics that influence degradation pathways. This work addresses both limitations through a transition-aware encoding method that discretizes measurements into joint operational bins, tracking the sequence of transitions between bins and preserving both coupled effects and temporal dynamics. An encoder–decoder neural network processes these compact representations to generate capacity forecasts over extended horizons. Based on experimental data from lithium–iron–phosphate (LFP) cells undergoing nonlinear degradation, the proposed transition-aware encoding forecasts absolute capacity with a mean absolute percentage error of 1.68% and captures cycle-to-cycle capacity variation to within 0.16%, while simultaneously compressing raw time-series data by 94.3%. Compared to methods that discard temporal ordering or treat measurements independently, the proposed approach reduces worst-case capacity prediction errors by more than 50%.

Developing accurate models for batteries, capturing ageing effects and nonlinear behaviors, is critical for the development of efficient and effective performance. Due to the inherent difficulties in developing physics-based models, data-driven techniques have been gaining popularity. However, most machine learning methods are black boxes, lacking interpretability and requiring large amounts of labeled data. In this paper, we propose a physics-informed encoder–decoder model that learns from unlabeled data to separate slow-changing battery states, such as state of charge (SOC) and state of health (SOH), from fast transient responses, thereby increasing interpretability compared to conventional methods. By integrating physics-informed loss functions and modified architectures, we map the encoder output to quantifiable battery states, without needing explicit SOC and SOH labels. Our proposed approach is validated on a lithium-ion battery ageing dataset capturing dynamic discharge profiles that aim to mimic electric vehicle driving profiles. The model is trained and validated on sparse intermittent cycles (6 %–7 % of all cycles), accurately estimating SOC and SOH while providing accurate multistep ahead voltage predictions across single and multiple-cell based training scenarios.

For reliable and safe battery operations, accurate and robust State of Charge (SOC) and model parameters estimation is vital. However, the nonlinear dependency of the model parameters on battery states makes the problem challenging. We propose a Moving-Horizon Estimation (MHE)-based robust approach for joint state and parameters estimation. Dut to all the time scales involved in the model dynamics, a multi-rate MHE is designed to improve the estimation performance. Moreover, a parallelized structure for the observer is exploited to reduce the computational burden, combining both multi-rate and a reduced-order MHEs. Results show that the battery SOC and parameters can be effectively estimated. The proposed MHE observers are verified on a Simulink-based battery equivalent circuit model.