Efficient and accurate health state estimation is crucial for lithium-ion battery (LIB) performance monitoring and economic evaluation. Effectively estimating the health state of LIBs online is the key but is also the most difficult task for energy storage systems. With high adaptability and applicability advantages

battery health state estimation based on data-driven techniques has attracted extensive attention from researchers around the world. Artificial neural network (ANN)-based methods are often used for state estimations of LIBs. As one of the ANN methods

the Elman neural network (ENN) model has been improved to estimate the battery state more efficiently and accurately. In this paper

an improved ENN estimation method based on electrochemical impedance spectroscopy (EIS) and cuckoo search (CS) is established as the EIS-CS-ENN model to estimate the health state of LIBs. Also

the paper conducts a critical review of various ANN models against the EIS-CS-ENN model. This demonstrates that the EIS-CS-ENN model outperforms other models. The review also proves that

under the same conditions

selecting appropriate health indicators (HIs) according to the mathematical modeling ability and state requirements are the keys in estimating the health state efficiently. In the calculation process

several evaluation indicators are adopted to analyze and compare the modeling accuracy with other existing methods. Through the analysis of the evaluation results and the selection of HIs

conclusions and suggestions are put forward. Also

the robustness of the EIS-CS-ENN model for the health state estimation of LIBs is verified.