State-of-Charge Estimation of Lithium-Ion Batteries Using Ultrasonic-Based Uncertainty-Aware Learning Models

Accurate and reliable estimation of the state of charge (SOC) is critical for the safe operation and lifetime management of lithium-ion batteries, especially in implantable medical devices where invasive sensing and frequent replacement are highly undesirable. Ultrasonic sensing provides a unique non-invasive solution with low power consumption and high integration potential. However, most existing ultrasonic-based SOC estimation methods rely on time-domain echo signals, hand-crafted features, or deterministic learning models, while few studies address estimation uncertainty, an essential requirement in safety-critical applications. This study proposes a single-frequency ultrasonic SOC estimation framework based on the phase and amplitude variations of the reflected ultrasonic signal, enabling direct prediction of SOC distributions and confidence intervals. To capture local temporal dynamics, a compact differential feature representation is constructed using the local temporal gradients of amplitude and phase. Five deterministic baseline models, including Linear Regression, ElasticNet, Linear SVR, Gradient Boosting, and Random Forest, are implemented for comparison. Moreover, three probabilistic learning models, Natural Gradient Boosting (NGBoost), Monte Carlo (MC) Dropout neural networks, and Gaussian Process Regression (GPR), are employed to enable simultaneous SOC prediction and uncertainty quantification. The performance of the proposed method is validated using multi-cycle ultrasonic measurement data of lithium-ion batteries. Results show that the proposed uncertainty-aware models achieve competitive deterministic accuracy while providing reliable prediction intervals. Overall, the proposed method provides an effective and hardware-efficient solution for non-invasive and uncertainty-aware SOC monitoring, particularly suited for implantable batteries.