## 6 Conclusions  
This study creatively established the BA-ELM model, i.e., by simulating the echolocation hunting behavior of bats, searching for the global optimal solution, and optimizing the output connection weight, input connection weight, and value of bias of the ELM. This model was also used for the first time in the field of SOH estimation of lithium-ion batteries. Six neural network models of ELM, BP, Elman, RBF, GRNN, and BA-ELM were constructed, and the actual available capacity of the battery was estimated and compared through the test set. The following conclusions can be derived based on the results and application:  
1. The relevant data of the battery can be analyzed by Pearson and Spearman correlation. The training time of the neural network model can be reduced by removing input variables with a low absolute value of Pearson's and Spearman's correlation coefficient. 2. The value of the evaluation function dropped significantly using BA. The convergence speed was fast. The BA achieved the expected effect of optimization. We proposed a new concept, i.e., the average velocity modulus length. The bat's velocity modulus became larger during the iteration. This is consistent with the fact in nature. 3. The main advantages of the proposed BA-ELM model include a fast learning speed and high SOH estimation accuracy. The BA-ELM provided less scattered estimates, and its fit line equation was closer to the exact line (\(y=x\)) with a higher determination coefficient compared to other models. The connection weight and threshold of ELM  
Figure 22: Violin diagram of six models. were randomly set, which may cause the battery SOH estimation to be inaccurate. A globally optimized BA can be used to optimize the connection weights and bias of the ELM neural network. * The RMSE of the BA-ELM model is 0.5354%, and the MAE is 0.4326%, which is the smallest among the 6 models. The RMSE values of the other model is 2.27%, 3.53%, 3.07%, 3.86%, and 3.24%, respectively. The estimated error of the actual battery capacity estimated using BA-ELM is less than 0.02 Ah, and the maximum error is less than 1%. Compared with the other five models, the results of BA-ELM estimation show a smaller RMSE, MAE, MAX, and MIN. It can be concluded that the estimation of the actual remaining capacity of the battery through the BA-ELM model has high accuracy and feasibility, which also makes the model have a good application prospect in the field of battery SOH. Although the BA-ELM model provided promising results for estimating SOH of lithium-ion batteries, this study still has some limitations. The main limitations of this study and possible recommendations based on these limitations are listed below:  
1. In this study, the proposed model was only verified on a smaller dataset containing 165 cycles. Therefore, in the future, the performance of this model should be evaluated on larger data samples. 2. The ELM model can be combined with other optimization algorithms to form a new hybrid model. Therefore, in the future, BA-ELM can be further validated and compared with other hybrid ELM models. 3. Recently, some other variants of the ELM model have been successfully exploited, such as OSELM and OP-ELM. In the future, BA can be used with these advanced variants of ELM models. 4. In this study, the impulse emission rate increased and reached the maximum at about 18 iterations. The change law of the loudness and pulse emission rate of the standard BA did not completely fit the actual application. The rates of pulse emission and loudness can be varied in a more sophisticated manner during the iteration. This also needs to be further studied in the future. Conceptualization, D.G., Z.Z. and Z.W. ; methodology, D.G. and Z.Z. ; software, D.G. ; validation, D.G. and Z.Z. ; formal analysis, D.G., X.K. and Z.Z. ; investigation, D.G. ; resources, D.G., Z.W. and Z.Z. ; data curation, D.G. ; writing--original draft preparation, D.G., X.K. and Z.Z. ; writing--review and editing, D.G. and Z.Z. ; supervision, Z.Z. ; project administration, Z.Z. and Z.W.