Fourier neural operators combined with the U-Net network for state of charge estimation of Li-ion batteries under dynamic temperatures and different operating conditions

High-precision estimation of the state of charge (SOC) in lithium-ion batteries is critical for the dynamic response performance of energy storage systems. However, under the coupled effects of dynamic temperature and complex operating conditions, fluctuations in ambient temperature and non-steady-state oscillations in input signals can lead to significant errors in parameter identification in traditional SOC models. To address this, this study proposes a hybrid U-FNO model that integrates U-Net's multi-scale feature extraction with the Fourier Neural Operator (FNO)'s global modeling. A time compensation algorithm is introduced to upscale training samples collected at 5 s/10 s intervals for sub-second online SOC prediction. Experiments established a multidimensional validation framework, where temperatures spanned six points from −5 °C to 45 °C (in 10 °C intervals), and operating conditions included six standard cycles—DST, FUDS, NEDC, US06, WLTC, and UDDS. Model performance was evaluated using Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Coefficient of Determination ( 𝑅 2 ). Results indicate that U-FNO achieved an average MAE of 0.37%, average RMSE of 0.44%, and average 𝑅 2 of 99.87% across all 36 combinations. At 25 °C, the U-FNO model consistently maintains MAE values below 0.06%, RMSE values below 0.08%, and 𝑅 2 values above 99.9992%. Compared to the FNO method, the average MAE of U-FNO decreased from 0.59% to 0.37%, representing an average improvement of approximately 37.4%. Compared to GRU, the average MAE improved by approximately 75.2%. This indicates the model's strong applicability and reliability in industrial applications that involve real-time dynamic temperature variations and operating mode transitions.