Physically constrained multi-task CNN–GRU framework for simultaneous SOC and SOH estimation

Reliable estimation of the state of charge (SOC) and state of health (SOH) is essential for the safe and efficient operation of lithium-ion battery management systems. Although recent deep-learning methods have improved estimation accuracy, many approaches treat SOC and SOH as independent tasks and may produce SOH trajectories that are inconsistent with the expected degradation behavior under controlled aging conditions. This study proposes a structured estimation framework based on a multi-task CNN–GRU architecture for the simultaneous estimation of window-level SOC and cycle-level SOH from voltage, current, and temperature measurements. Rather than introducing new prediction modules, the proposed methodology integrates shared feature learning, monotonicity-aware optimization, and deterministic post-processing within a hierarchical estimation pipeline whose individual components are evaluated independently. The framework is assessed using the NASA Prognostics Center of Excellence battery dataset through comparative experiments including single-task and multi-task learning, ablation analyses of the physical-consistency mechanisms, sensitivity analyses of the principal hyperparameters, robustness assessment across three controlled random initializations, and computational complexity evaluation. The experimental results indicate that multi-task learning provides consistent improvements in joint battery-state estimation across the evaluated initializations, whereas the proposed physical-consistency mechanisms primarily enhance the monotonic behavior of SOH trajectories with only minor changes in prediction accuracy. These findings support the proposed structured estimation methodology while demonstrating the respective contributions of shared learning and deterministic physical-consistency mechanisms under the adopted NASA PCoE evaluation protocol.