Stacking integrated learning model via ELM and GRU with mixture correntropy loss for robust state of health estimation of lithium-ion batteries

Accurate estimation of the state of health (SOH) is crucial for the safe and stable operation of lithium-ion batteries. However, since the labeled values may contain non-Gaussian noise which may lead to a decrease in the effectiveness of traditional data-driven based estimation methods. Therefore, a novel robust stacking integrated learning model (ILM) is proposed to enable accurate SOH estimation under non-Gaussian noises (or outliers) conditions. The mixture correntropy loss (MCL) is used in original extreme learning machine (ELM) and the gated recurrent unit (GRU) frameworks to develop novel robust learning models, i.e MCL-ELM and MCL-GRU, and they are used as the sub-models of the proposed ILM, which takes into account the generalization performance of the model and the overall trend of SOH over the time series. In addition, the entropy weighting method that can well reflect the differences between the sub-models is utilized to reduce the complexity of the stacked ILM. Furthermore, the local tangent space alignment is used to capture the local relationships between different loops to enhance the effectiveness of the extracted health features. Several numerical experiments are performed under different cases to validate the estimation effect of the proposed model by using two publicly available datasets, and the experimental results demonstrate that the maximum RMSE, MAE, and MAPE values of the proposed model are 1.391%, 0.932%, and 1.480%, respectively, under non-Gaussian noises conditions.