Transfer learning with composite kernel sparse Gaussian process-aided model for probabilistic state of health estimation of lithium-ion batteries against multi-source coupled harsh scenarios

Accurate estimation of lithium-ion battery state of health (SOH) is crucial for ensuring safety and performance. However, SOH estimation under multi-source coupled harsh scenarios remains challenging due to the synergistic effects of incomplete constant current constant voltage (CCCV) charging data, irregular cycle intervals, sparse target battery samples, and adverse temperatures. To address these issues, this study proposes a novel transfer learning-based dual-stage framework that integrates a continuous-time attention gated recurrent unit (CTAGRU) and a composite kernel sparse Gaussian process (CSGP) to enhance adaptability. In the first stage, the CTAGRU is pre-trained using historical data under normal scenarios, where equally-interval discretized outputs of the continuous-time attention (CTA) are transmitted to the gated recurrent unit (GRU) to capture SOH degradation trajectories and supplement missing SOH. In the second stage, with sparse training samples, the CSGP-aided module is introduced to rapidly adapt to the multi-source coupled harsh scenarios. This stage employs a probabilistic compensation mechanism to mitigate residual errors caused by data distribution shifts in CTAGRU estimations while providing quantification uncertainty results. Comparative results with benchmark algorithms and ablation studies show that the proposed model generally performs better across high, low, and wide temperature range conditions. Specifically, the model achieves a maximum reduction in mean absolute percentage error (MAPE) and coverage width-based criterion (CWC) by 112.74 % and 1914.14, respectively. Additionally, the supplemented SOH aligns well with the overall degradation trends. These results validate that the proposed algorithm effectively supports SOH estimation for lithium-ion batteries against multi-source coupled harsh scenarios.