*3.3. State of Health Estimation*

Another interesting application is the estimation of the SoHC with respect to the capacity (SoHC). Therefore, three cells were aged and characterized (EIS and capacity) and used to train the ANN. The cells which were aged and used for the investigation of the temperature estimation were characterized afterwards and used to test the SoHC estimation. Figure 12 shows the estimated cell SoHC and the measured SoHC. The RMSE for every SoHC estimation was below 2%.

A Bayesian regularization-backpropagation neural network with one hidden layer consisting of four neurons was used. Both the real and the imaginary part of the impedance were used as input parameters. We were unable to estimate the SoHC at the very beginning of life because the shape and the value of the EIS spectrum varies strongly for the first cycles. The impedance spectrum first decreases and than increases. After a number of cycles, stabilization of impedance growth was achieved, as shown in Figure 2. Only the data of cells which performed 100 or more cycles were used. Since the cells that were used to collect the training data were characterized only for 1400 cycles, data from cells with more cycles could not be used for testing, because the ANN is not able to extrapolate. The aging profiles of the cells that were used to collect training data and the cells for the test data were partially comparable. After aging, the testing cells experienced further aging during measurements at different temperatures and currents. Nevertheless, to generalize this system it will be necessary to investigate the presented state estimation method with data from different aging profiles. The advantage of the SoHC estimation method compared to other algorithms is the ability to estimate the total utilizable capacity from an EIS spectrum within a few seconds. Unlike the current pulse method where only one data point is determined, the impedance spectrum offers many data points belonging to a single state. That increases the estimation accuracy and reduces other influences, such as that of contact resistances.

**Figure 12.** SoHC estimates for Samsung INR18650-15L1 cells by a neural network using EIS data as input are presented. Here the SoHC is defined as the actual capacity related to the nominal capacity. The estimated SoHC is plotted over the measured SoHC. The black line is a guide to the eye of the target values. The overall RMSE was less than 2%. The legend shows the RMSE for each cell.

#### *3.4. Further Discussion*

We have developed a sensorless ANN-method based on EIS data to estimate the temperature of a lithium ion cell. The temperature estimation was performed with different SoCs, SoHCs and discharge currents. Furthermore, we have given a perspective on the possibility of using the presented method to estimate the SoC and the SoHC. One of the biggest advantages of the presented method is that a well-known ANN with a very simple architecture which requires little computational effort is able to estimate the cell temperature successfully. This fact makes it even more interesting and practical for industrial applications. The ANN was trained within minutes for each system. The time needed to train the ANN depends on the availability of supplementary input data, such as SOC, SOH or applied DC current. Once the ANN is trained, the calculations for the state estimation by the ANN are performed within milliseconds. The EIS measurement from 1 Hz to 10 kHz was performed in less than 1 min. However, we predict that the measurement time could be reduced to milliseconds by selecting suitable frequencies. The calculations for the state estimation by the ANN were performed in less than a second.

Further, we showed that the presented model is independent of the cell geometry by investigating cylindrical and prismatic cells. The focus of this study lay in the investigation of 18,650 lithium ion cells. To generalize the presented method, we will investigate larger cells with higher capacity in future work. Furthermore, we will use temperature sensors in the cell core for data acquisition and investigate connected cells in battery modules. Due to its data-driven nature, we suggest that it is possible to adapt the model to every other cell chemistry, as long as there is a strong correlation between the EIS spectrum and the investigated state. We were able to achieve reasonable results with LFP cells. As our data-driven model is easily applicable to other systems, it is attractive for practical applications, since cell manufacturers usually do not reveal exact cell chemistry.
