## 1 Introduction
Among the many machine learning methods, ELM has the advantages of a simple structure and easy adjustment of parameters [23]. Compared with the SVM and BP neural network models, ELM has a faster training speed, it does not easily fall into local optimality, and its generalization ability is better [24; 25]. Based on a stacked denoising autoencoders ELM algorithm, [PERSON] et al. [26] proposed a big data-driven battery modeling method (SDAE-ELM). The battery data extracted from electric buses were used to validate the effectiveness and accuracy of the model. [PERSON] et al. [27] proposed a novel robust ELM model to improve the estimation capability. The mean square error (MSE) in ELM was substituted by a mixture-generalized maximum correntropy criterion. This method solved the non-Gaussian complex noise interference problem to a certain extent. [PERSON] et al. [28] proposed a novel metabolic extreme learning machine (M-ELM) framework to describe the complex battery degradation mechanism that can reflect the latest degradation trend. [PERSON] et al. [29] developed a new broad learning-ELM (BL-ELM). The feature and enhancement nodes were merged to become the new input layer of the network. This can provide the benefit of reducing the calculation time. [PERSON] et al. [30] proposed a modified biogeography-based approach to optimize ELM for pressure prediction of a spark ignition single-cylinder engine. The type of activation function, number of hidden layer nodes, and sparse connection structure were obtained using the new approach. A possible improvement in ELM design lies in attribute selection instead of using all variables in the predictive model. [PERSON] et al. [31] proposed a new hybrid ELM model combined with grey wolf optimization (WO) and hybrid particle swarm optimization (PSO) for streamflow prediction. The new model reduced the RMSE in prediction effectively. However, it was found that the PSOGWO algorithm is not very stable compared with the PSO and PSOGSA algorithms. [PERSON] et al. [32] proposed a novel hybrid of the ELM and adaptive neuroswarm intelligence techniques for the determination of the California bearing ratio of soils. The results of the hybrid model were better than other ELM-based models. To fully utilize the advantages of different algorithms, the development of a hybrid method for ELM and other optimization algorithms has become a new research direction. On the other hand, BA is a swarm intelligence optimization algorithm based on bat echolocation for hunting [33]. As a metaheuristic algorithm used for searching for the global optimal solution, the BA provides a completely different solution to the optimization problem [34; 35]. [PERSON] et al. [36] proposed an enhanced adaptive BA for optimal energy scheduling in a microgrid system. Because of the different search mechanisms applied in the early and late search stages, the search performance improved. [PERSON] et al. [37] developed a reliability-constrained cost-effective model to identify the optimal sizing of an autonomous hybrid renewable system. The bat search algorithm was used to obtain the final optimal solution. Based on a hybrid bat algorithm (BA)-harmony search algorithm technique, [PERSON] et al. [38] proposed a new two-degree freedom-tilted integral derivative with a filter controller for a two-area wind-hydro-diesel power system. A sensitivity analysis showed that the robustness of the controller was improved. Thus, the BA has global exploration and local exploitation capabilities, and it is entirely possible to use it to optimize the ELM model. Based on the above discussion, the main contributions of this study are as follows:  
1. A globally optimized BA can be used to optimize the connection weights and bias of the ELM neural network. The BA-ELM model can be creatively constructed. 2. The relevant data of the battery can be analyzed by Pearson and Spearman correlation; thus, the data can be determined scientifically and reasonably. 3.