Probabilistic transfer learning for lithium-ion battery capacity estimation based on the sparse sample case

Accurate estimation of the State of Health (SOH) for lithium-ion batteries is crucial for ensuring their safe and reliable operation. However, data-driven models often face the challenge of scarce labeled aging data in real industrial settings, which is typically difficult to obtain in industrial practice. To address this issue, this paper proposes a novel probabilistic transfer learning framework based on bayesian convolutional neural networks (PTL-BCNN). The core of this approach lies in transferring knowledge from the source domain—rich in data across diverse battery types—to the target domain, which has sparse data. Its mechanism extends beyond fine-tuning deterministic parameters to adjusting the overall probability distribution of model weights. This method inherently provides uncertainty estimation alongside capacity prediction. The framework was comprehensively validated on two public datasets (Oxford and CALCE) and a custom sparse sample dataset. The proposed PTL-BCNN achieves remarkably low Mean Absolute Percentage Error (MAPE) of 0.71%, 1.21%, and 0.79% on these datasets, significantly outperforming traditional deep learning and transfer learning benchmark models. Crucially, the model maintains robust performance even when using only partial charging segment data, demonstrating strong practical applicability. This work establishes a probabilistic transfer learning paradigm, providing a fundamental solution for achieving reliable and data-efficient battery health estimation across different battery types.