*6.3. Training and Testing Data Sets for ANN and ANFIS Models*

of 419.26 °C with the different voltage loads.

*6.3. Training and Testing Data Sets for ANN and ANFIS Models*  Figure 5 shows the training and testing data sets used to develop the ANN and ANFIS models of the thermoelectric generator system for waste heat recovery. Using these experimental data of both the hot gas inlet temperature and voltage condition as the input parameters and the current, power and thermal efficiency as the output parameters of the thermoelectric generator system for waste heat recovery, six ANN models and seven ANFIS models are formulated. As the training data set for training the ANN and ANFIS models of the thermoelectric generator system for waste heat recovery, a total of 931 data points of the mixtures of 225 data points at the hot gas inlet temperature of 315.12 °C, 234 data points at the hot gas inlet temperature of 419.26 °C, 236 data points at the hot gas inlet temperature of 521.70 °C and 236 data points at the hot gas inlet temperature of 621.61 °C are deducted from the experimental study. The training for the considered ANN and ANFIS models is stopped when the training error converges. The converged training errors for the considered ANN and ANFIS models are shown in Figure 8. To check the reliability and accuracy of the trained ANN and ANFIS models of the thermoelectric generator system for waste heat recovery, the additional experiment for obtaining the testing data set of 100 data is conducted at the hot gas inlet temperature Figure 5 shows the training and testing data sets used to develop the ANN and ANFIS models of the thermoelectric generator system for waste heat recovery. Using these experimental data of both the hot gas inlet temperature and voltage condition as the input parameters and the current, power and thermal efficiency as the output parameters of the thermoelectric generator system for waste heat recovery, six ANN models and seven ANFIS models are formulated. As the training data set for training the ANN and ANFIS models of the thermoelectric generator system for waste heat recovery, a total of 931 data points of the mixtures of 225 data points at the hot gas inlet temperature of 315.12 ◦C, 234 data points at the hot gas inlet temperature of 419.26 ◦C, 236 data points at the hot gas inlet temperature of 521.70 ◦C and 236 data points at the hot gas inlet temperature of 621.61 ◦C are deducted from the experimental study. The training for the considered ANN and ANFIS models is stopped when the training error converges. The converged training errors for the considered ANN and ANFIS models are shown in Figure 8. To check the reliability and accuracy of the trained ANN and ANFIS models of the thermoelectric generator system for waste heat recovery, the additional experiment for obtaining the testing data set of 100 data is conducted at the hot gas inlet temperature of 419.26 ◦C with the different voltage loads.

The current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery are predicted by ANN and ANFIS models for the hot gas inlet temperature of 419.26 °C and voltage loads of the testing data set. The predicted current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery from the ANN and ANFIS models for the testing data set are compared with the corresponding experimental data of the testing data set. Based on the degree of closeness between the experimental and predicted results of the current, power and

ANFIS models, the optimum ANN and ANFIS models with higher prediction accuracy are decided.

**Figure 8.** The converged training errors for (**a**) ANN and (**b**) ANFIS models of thermoelectric generator system for waste heat recovery. **Figure 8.** The converged training errors for (**a**) ANN and (**b**) ANFIS models of thermoelectric generator system for waste heat recovery.

*6.4. Prediction Results from ANN Models*  The comparison of experimental and ANN predicted results of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using an LM-TanSig algorithm with the various numbers of the hidden neurons is shown in Figure 9a. The increase of the hidden neurons number from 10 to 25 increases the prediction accuracy of the ANN model with an LM-TanSig algorithm. The values of R2, RMSE and COV of LM-TanSig algorithm with 25 hidden The current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery are predicted by ANN and ANFIS models for the hot gas inlet temperature of 419.26 ◦C and voltage loads of the testing data set. The predicted current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery from the ANN and ANFIS models for the testing data set are compared with the corresponding experimental data of the testing data set. Based on the degree of closeness between the experimental and predicted results of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery with ANN and ANFIS models, the optimum ANN and ANFIS models with higher prediction accuracy are decided.
