Representation-Level Temporal–Frequency Symmetric Learning for Battery State-of-Charge Estimation and Voltage Reconstruction

Accurate battery state-of-charge (SOC) estimation under dynamic operating conditions remains challenging because battery responses are nonlinear, history-dependent, temperature-sensitive, and prone to transient disturbances. To address this problem, this paper proposes a representation-level temporal–frequency symmetry framework, termed the Joint Temporal–Frequency Cross-Domain Attention Network (JTFCD-Net), for joint SOC estimation and voltage reconstruction. Here, symmetry denotes aligned latent representations rather than physical invariance: temporal and frequency-aware views are derived from the same battery process, mapped into the same latent space, and kept at identical temporal resolution and hidden dimensionality. A temporal aggregation block extracts local dynamics at multiple receptive fields, and a Temporal Attention Aggregation Module (TAAM) captures long-range dependence. A Frequency-Aware Attention Module (FAM) then uses global spectral statistics to perform lightweight channel recalibration, thereby injecting coarse frequency-domain information into the temporal representation while preserving the hidden feature shape. A Cross-Domain Attention Module (CDAM) performs bidirectional cross-attention, allowing the two views to query and exchange information. The fused representation is decoded by a main SOC head and an auxiliary voltage reconstruction head, which preserves voltage-response dynamics in the shared representation. Experiments on the CALCE A123 benchmark under multiple fixed ambient temperatures and operating conditions show that JTFCD-Net yields consistently lower errors than the selected baseline methods, while ablation studies confirm the contribution of cross-domain fusion and auxiliary voltage supervision. External validation on the NASA Ames battery aging dataset is also conducted as an independent laboratory-scale cell benchmark. These results indicate that combining temporal modeling with frequency-aware representation learning is a promising direction, although deployment value still requires validation in real BMS settings.