Optimal hidden layer size for Levenberg-Marquardt based neural network for SoC estimation under different temperature conditions.

Currently, neural networks are one of the best techniques that can be used to earn the great challenge of accurate electric vehicle battery SOC estimation. Therefore, in this study, a Levenberg-Marquardt (LVA) based neural network is developed to estimate the SoC of Li-ion batteries under different temperature conditions. A comprehensive study is carried out to assess the influence of hidden layer size on model performance during the training, validation and test phases. The results reveal that increasing the layer size beyond a particular value makes the model more complex and increases simulation time, with a reduction of model precision and accuracy. An optimal architecture with 100 hidden neurons is selected based on regression measurements and error analysis. To evaluate objectively the developed LVA model's performance, the optimal architecture is also compared with the unscented Kalman filter (UKF) under different thermal conditions (0 °C, 10 °C, 25 °C and 40 °C). The obtained results show that the LVA model outperforms the UKF Filter, providing more stable and accurate SoC predictions, with error fluctuations generally remaining within ± 2%. On the other hand, the UKF exhibits larger estimation errors, particularly at low temperatures, indicating its sensitivity to heat-induced non-linearity. These results highlight the robustness and efficiency of the LVA method, making it a promising candidate for real-time battery.