*3.2.2 AEKF based on ANFIS combined model (ANFIS-ANFIS) performance accuracy analysis*

The performance analysis is made on the information provided by the battery SOC and terminal voltage residuals errors shown in **Figure 19a** and **b**. During the steady state, more precisely after 347 seconds, the SOC residual error is less than 1% smaller

**Figure 20.** *System-level flowchart diagram.*

than usual SOC residual error of 2% value reported in the literature field. Since the SOC residual error of AEKF based on ARX ECM battery model that is less than 1% during the steady state after 600 s, as is shown in **Figure 13c**, is obviously that the AEKF based on ANFIS battery model performs better. For a complete information about the suitability of AEKF SOC estimator based on ANFIS battery model is built in the **Table 2**, which incorporates all the statistics of criteria values RMSE (IC1), MSE (IC2), MAE (IC3), and MAPE (IC4), the most common criteria that have been used in the literature field to measure model performance and select the best model from a set of potential candidate models [7, 29, 30]. Comparing both statistics criteria values (third and fourth columns) is straightforward that the AEKF SOC estimator based on ANFIS battery model performs better than AEKF SOC estimator based on ARX battery model.

By comparing the terminal battery voltage residuals shown in **Figure 12** for AEKF based on ARX model and AEKF based on ANFIS model depicted in **Figure 19b**, they are ranged inside the intervals (�0.2, 0.3) volts and (�0.01, 0.08) volts, respectively; thus, the second SOC estimator based ANFIS battery model performs better than the first one. Based on the performance analysis of SOC accuracy, robustness to changes in SOCini value and terminal battery voltage prediction accuracy it can conclude that the AEKF SOC estimator based on ANFIS model is the most suitable SOC estimator for HEVs/EVs applications.

A system-level flowchart/flow diagram is shown in **Figure 20**. It indicates the major steps involved in the key sections of the last two chapters to provide an overview of the differences in steps between generic ECM, ARX ECM, ANFIS ECM, hybrid (ARX-ANFIS), and combined (ANFIS-ANFIS) models.

A detailed description for each small block of the overall diagram of the models along with a flow of the equations is also considered in the overall diagram shown in **Figure 20**.
