Hierarchical Multimodal Orthogonal Attention Fusion Framework for Lithium-Ion Battery State-of-Charge Estimation

Accurate state-of-charge estimation for lithium-ion batteries remains challenging due to nonlinear dynamics and the complexity of interpreting multimodal data. To address these challenges, this article presents a flexible sensing circuit layer attached to the battery surface to acquire electrical, mechanical, and ultrasonic signals, which are integrated via a proposed multimodal hierarchical orthogonal attention fusion framework. The modalities are encoded with gated recurrent units and fused through a stage-wise hierarchy, where an attention mechanism combined with an orthogonal constraint effectively suppresses modal redundancy and noise. Model interpretability is validated through the dynamic evolution of attention weights and cross-verified using Shapley additive explanations. This combined analysis reveals a scenario-dependent mechanism in which electrical modalities dominate during steady states, while mechanical and acoustic features are adaptively upweighted to compensate for information loss during highly dynamic load variations. Experiments on different types of batteries demonstrate that the framework delivers superior accuracy and stability with millisecond-level inference latency, achieving errors below 1% in most cycles and remaining within 2.7% even under strongly nonstationary dynamics and low-temperature environments.