## 7 Conclusions
As stand-alone EIS measurement systems are usually very large and cost-intensive, a small and low-cost measurement system was developed, which makes the integration of the measurement technology financially attractive even for smaller energy storage systems, such as those used in the private sector for intermediate storage of solar energy. Typically, the measured impedance spectra are used to parameterize an electrical equivalent circuit of the battery. However, many of the components of the equivalent circuit depend not only on the frequency but also on the operating point or the DC current component during the impedance measurement. Therefore, an exact knowledge of thecell processes is necessary to work out the influence of the DC current on the parameters. Typically, previous approaches therefore assume a fixed operating state of the cell while the measurement data are being recorded. In the article, methods of machine learning, were also used to check the capability of determining the state of charge on the basis of the EIS spectra measured at different charging currents. Artificial neural networks and SVR turned out to be particularly promising. In contrast to the common process of parameter fitting, both methods use the raw measured data of the measured impedance spectra as input data, so an exact knowledge of the battery model is not necessary and they can be applied particularly easily. The hyperparameters of the two methods were optimized in the grid search procedure and via a Bayesian optimization on the basis of the training data set in order to prevent data leakage. A crucial point and a highlight is that both artificial intelligence methods can also be applied to unknown DC currents during impedance measurement. A change in the charge or discharge current, for example, leads to a change in the linearized charge transfer resistance and thus to different impedance spectra. Provided that the training data contains the charging current selected from the outer limits of possible charging currents, the determination of the state of charge when interpolating the charging current within these limits is very precise. In principle, both methods are sufficiently accurate. By means of a principal component transformation, the dimensionality of the feature space was reduced with very little loss of information. Provided that a particularly strong reduction in the dimensionality is used, ANN show a better performance. Thus, the RMSEP is smaller when using one to four principal components inclusive than with SVR. The best result is obtained when using two principal components. With a higher dimensionality of the input data the SVR is ahead. Even when the principal component transformation is not used, SVR shows a smaller tendency to overfit, so that the metric is only about half as large. When considering the best results, the ANN achieves an error of 0.16% and the SVR achieves an error of 0.47% on unseen data. In practice, this success is of great relevance. Now, no predefined charge current is needed, which was trained beforehand. Thus, the current working point of the battery does not have to be left in order to start the determination of the state of charge, as long as the dc current is within the trained limits. Conceptualization, A.L., I.R.R. and P.G. ; methodology, A.L. ; software, A.L. ; validation, A.L., I.R.R. and P.G. ; formal analysis, A.L., I.R.R. and P.G. ; investigation, A.L. ; resources, I.R.R. and P.G. ; data curation, A.L. ; writing--original draft preparation, A.L. ; writing--review and editing, I.R.R. and P.G. ; visualization, A.L. ; supervision, I.R.R. and P.G. ; project administration, I.R. and P.G. ; funding acquisition, P.G. All authors have read and agreed to the published version of the manuscript. This research was funded by EFRE--LeitmarkAgentur.NRW grant numbers 0801585, KESW-1-1-006B. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to non-disclosure agreement.