## 3 Result and Discussion
### Short-Term State of Health Estimation  
In this subsection, the performance of the short-term SOH estimation is presented by employing the proposed techniques. Both the GMDH and ANFIS are trained by the collected dataset. The inputs and the outputs of the system in the training phase are the battery terminal voltage and the SOH, respectively. The beginning-of-life (BoL), corresponding to a fresh battery, is defined as a 100% SOH, and the 167 th cycle, when the capacity has reached the 1.4 Ah, is considered as the end-of-life. Moreover, the algorithm uses the unit-time-delays to consider the battery voltage at past time frames. The voltage is normalized, which is a standard procedure when such intelligent techniques are used. Thereafter, the normalized dataset after the computing and estimating procedures will be de-normalized. Owing to the capability of improvement in the read performance of the database, this technique is used. Indeed, each sample is divided by the maximum possible measurement. For instance, a measurement of 4.2 V constitutes as number 1, while 0 V is represented as number 0, and every other value is between 1 and 0. Furthermore, it should be noted that EVs are not always charged at a certain state of charge, which means that the technique should be able to estimate the SOH at different SOC levels, corresponding to different initial voltages. The proposed techniques, GMDH and ANFIS, were trained by the experimental results of battery No. 05. As mentioned previously, during the training phase, the structure and weights of GMDH and weights of ANFIS could be optimized and adjusted in terms of minimizing the error between the estimated SOH from the network, and the training targets from the experimental data. Then, the techniques are validated by employing the experimental data from battery No. 06. For the GMDH whose parameters are the maximum number of neurons in a layer, the maximum number of layers and selection pressure are set to 10, 5, and 0.6, respectively. It should be pointed out that the dataset for the training phase includes all of the voltage samples corresponding to 0% SOC to 100% SOC. The GMDH parameters, maximum number of neurons in a layer, maximum number of layers, and selection pressure are set to 250, 10, and 0.6, respectively. For validation, battery No. 06 was used, whose experimental results were used to test the estimation accuracy of the GMDH technique. The actual and estimated SOH are depicted in Figure 4. The blue line shows the actual SOH and the red line indicates the estimated SOH at first and second cycles with 0.052 mean square error, and 0.23 root mean square error. It is observed that the relationship between the battery voltage and estimated SOH closely matches the actual test dataset. Moreover, the RMSE and MSE show that the GMDH has successfully discovered the effects of aging of the battery voltage behavior. With regard to the second technique, as mentioned earlier, the combination of fuzzy logic and NNs leads to the ANFIS structure, which is classified under adaptive networks. Consequently, ANFIS has the ability to reach a conclusion from unclear and complex data, because of the fuzzy logic, with the capability to work from imprecise data [35]. In this regard, this technique is utilized to estimate the SOH from a set of curves whose shapes depend on the state of the system. Furthermore, the ANFIS cannot work without a training phase. Therefore, the battery terminal voltage during constant current charge profile at different SOH is prepared. Then, the membership functions should be adapted to the battery charge curves, which are diverse at different SOH levels. It should be pointed out that the constant-voltage sub-process is not included in the input dataset. The number of initial ANFIS rules for the first input was set to 15, these rules were generated using the fuzzy C-means (FCM) clustering method, and then the ANFIS was trained and tuned by the experimental results of battery No. 05.