*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 R<sup>2</sup> , RMSE and COV of LM-TanSig algorithm with 25 hidden neurons are 0.99998, 0.02163 and 0.49061, respectively for the current, 0.99997, 0.04111 and 0.59192, respectively, for the power and 0.99996, 0.01050 and 0.73183, respectively, for the thermal efficiency.

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-LogSig algorithm with the various numbers of the hidden neurons is shown in Figure 9b. The ANN model for the current and thermal efficiency of the thermoelectric generator system for waste heat recovery with LM-LogSig algorithm and 25 hidden neurons shows the peak prediction accuracy and this prediction accuracy decreases in an order with LM-LogSig algorithm of 20, 15 and 10 hidden neurons, respectively. The values of R<sup>2</sup> , RMSE and COV for LM-LogSig algorithm and 25 hidden neurons are 0.99998, 0.02370 and 0.53755, respectively for the current and 0.99994, 0.01225 and 0.85347, respectively for the thermal efficiency. For the power of the thermoelectric generator system for waste heat recovery, LM-LogSig algorithm with 20 hidden neurons shows higher prediction accuracy than that with 25, 15 and 10 hidden neurons, respectively. The values of R<sup>2</sup> , RMSE and COV for LM-LogSig algorithm with 20 hidden neurons are 0.99997, 0.04632 and 0.66686, respectively for the power.

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 SCG-TanSig algorithm with the various numbers of the hidden neurons is shown in Figure 9c. The ANN model for the current of the thermoelectric generator system for waste heat recovery with SCG-TanSig algorithm and 25 hidden neurons shows the peak prediction accuracy and this prediction accuracy decreases in an order with SCG-TanSig algorithm of 10, 25 and 15 hidden neurons, respectively. The values of R 2 , RMSE and COV for SCG-TanSig algorithm with 25 hidden neurons are 0.99992, 0.04524, 1.02613, respectively for the current of the thermoelectric generator system for waste heat recovery. The power and thermal efficiency of the thermoelectric generator system for waste heat recovery using the SCG-TanSig algorithm with 20 hidden neurons shows higher prediction accuracy than that with 10, 25 and 15 hidden neurons, respectively. The values of R<sup>2</sup> , RMSE and COV for SCG-TanSig algorithm with 20 hidden neurons are 0.99971, 0.13652 and 1.96554, respectively, for the power and 0.99929, 0.04377 and 3.05105, respectively, for the thermal efficiency.

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 SCG-LogSig algorithm with the various numbers of the hidden neurons is shown in Figure 9d. The prediction accuracy for the current of the thermoelectric generator system for waste heat recovery with the SCG-LogSig algorithm decreases with 25, 15, 20 and 10 hidden neurons. The values of R<sup>2</sup> , RMSE and COV for SCG-LogSig algorithm with 25 hidden neurons are 0.99996, 0.03138 and 0.71178, respectively, for the current. The prediction accuracy for the power of the thermoelectric generator system for waste heat recovery with SCG-LogSig algorithm decreases with 15, 10, 25 and 20 hidden neurons but prediction accuracy for the thermal efficiency of the thermoelectric generator system for waste heat recovery with SCG-LogSig algorithm decreases with 15, 25, 10 and 20 hidden neurons. The values of SCG-LogSig with 15 hidden neurons are 0.99980, 0.11376 and 1.63783, respectively, for the power and 0.99958, 0.03359 and 2.34133, respectively, for the thermal efficiency.

The comparison of experimental and ANN predicted results of current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using the CGP-TanSig algorithm with various numbers of hidden neurons is shown in Figure 9e. The prediction accuracy of the thermoelectric generator system for waste heat recovery with the CGP-TanSig algorithm decreases with 20, 25, 10, and 15 hidden neurons for the current but 20, 10, 15 and 25 hidden neurons for the power, respectively. The values of R<sup>2</sup> , RMSE and COV for CGP-TanSig algorithm with 20 hidden neurons are 0.99989, 0.05377 and 1.21965, respectively, for the current and 0.99945, 0.18629 and 2.68213, respectively, for the power. In addition, the prediction accuracy for the thermal efficiency of the thermoelectric generator system for waste heat recovery using CGP-TanSig algorithm with 25 hidden neurons is the most accurate and decreases with 15, 20 and 10 hidden neurons, respectively. The values of CGP-TanSig algorithm with 25 hidden neurons are 0.99875, 0.05805 and 4.04596, respectively, for the thermal efficiency.

The comparison of experimental and ANN predicted results of current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using the CGP-LogSig algorithm with various numbers of hidden neurons is shown in Figure 9f. The CGP-LogSig algorithm with 25 hidden neurons predicts current values of the thermoelectric generator system for waste heat recovery closer to the corresponding experimental current values of the thermoelectric generator system for waste heat recovery with R<sup>2</sup> , RMSE and COV values of 0.99989, 0.05354 and 1.21437, respectively. The CGP-LogSig algorithm with 20, 15, and 10 hidden neurons shows the decreasing order of prediction accuracy for the current of the thermoelectric generator system for waste heat recovery. The CGP-LogSig algorithm with 15, 20, 25 and 10 hidden neurons, respectively, shows the decreasing order of prediction accuracy for the power of the thermoelectric generator system for waste heat recovery and CGP-LogSig algorithm with 15, 25, 10 and 20 hidden neurons, respectively, shows the decreasing order of prediction accuracy for the thermal efficiency of the thermoelectric generator system for waste heat recovery. The R<sup>2</sup> , RMSE and COV values for CGP-LogSig algorithm with 15 hidden neurons are 0.99953, 0.17188 and 2.47463, respectively, for power and 0.99848, 0.06391 and 4.45470, respectively, for the thermal efficiency. with 25 hidden neurons predicts current values of the thermoelectric generator system for waste heat recovery closer to the corresponding experimental current values of the thermoelectric generator system for waste heat recovery with R2, RMSE and COV values of 0.99989, 0.05354 and 1.21437, respectively. The CGP-LogSig algorithm with 20, 15, and 10 hidden neurons shows the decreasing order of prediction accuracy for the current of the thermoelectric generator system for waste heat recovery. The CGP-LogSig algorithm with 15, 20, 25 and 10 hidden neurons, respectively, shows the decreasing order of prediction accuracy for the power of the thermoelectric generator system for waste heat recovery and CGP-LogSig algorithm with 15, 25, 10 and 20 hidden neurons, respectively, shows the decreasing order of prediction accuracy for the thermal efficiency of the thermoelectric generator system for waste heat recovery. The R2, RMSE and COV values for CGP-LogSig algorithm with 15 hidden neurons are 0.99953, 0.17188 and 2.47463, respectively, for power and 0.99848, 0.06391 and 4.45470, respectively, for the thermal efficiency. The comparison of ANN models with various combinations of the training variants, transfer

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efficiency of the thermoelectric generator system for waste heat recovery using the CGP-LogSig algorithm with various numbers of hidden neurons is shown in Figure 9f. The CGP-LogSig algorithm

The comparison of ANN models with various combinations of the training variants, transfer functions and number of the hidden neurons is shown. The combination of LM training variant with TanSig and LogSig transfer functions and all numbers of the hidden neurons show better accuracy than that of SCG and CGP training variants with TanSig and LogSig transfer functions and all numbers of hidden neurons to predict current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery. In particular, the ANN model with LM-TanSig training algorithm and 25 hidden neurons shows the best prediction accuracy [29,39] and is suggested as the optimum model for predicting the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery for the hot gas temperature ranges of 315.12 to 621.61 ◦C and voltage load ranges of 0 to 10 V. The accuracy of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using the ANN model with the LM-TanSig algorithm and 25 hidden neurons are 0.99998, 0.99997 and 0.99996, respectively, as shown in Table 3. Table 3 shows the prediction accuracy of the optimum ANN model with the LM-TanSig algorithm and various numbers of the hidden neurons for the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery. functions and number of the hidden neurons is shown. The combination of LM training variant with TanSig and LogSig transfer functions and all numbers of the hidden neurons show better accuracy than that of SCG and CGP training variants with TanSig and LogSig transfer functions and all numbers of hidden neurons to predict current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery. In particular, the ANN model with LM-TanSig training algorithm and 25 hidden neurons shows the best prediction accuracy [29,39] and is suggested as the optimum model for predicting the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery for the hot gas temperature ranges of 315.12 to 621.61 °C and voltage load ranges of 0 to 10 V. The accuracy of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using the ANN model with the LM-TanSig algorithm and 25 hidden neurons are 0.99998, 0.99997 and 0.99996, respectively, as shown in Table 3. Table 3 shows the prediction accuracy of the optimum ANN model with the LM-TanSig algorithm and various numbers of the hidden neurons for the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery.

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**Figure 9.** *Cont*.

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**Figure 9.** *Cont*.

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**Figure 9.** *Cont*.

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**Figure 9.** The comparison of experimental and ANN predicted results of current, power and thermal efficiency for (**a**) LM-TanSig algorithm, (**b**) LM-LogSig algorithm, (**c**) SCG-TanSig algorithm, (**d**) SCG-LogSig algorithm, (**e**) CGP-TanSig algorithm, and (**f**) the CGP-LogSig algorithm with various numbers of hidden neurons. **Figure 9.** The comparison of experimental and ANN predicted results of current, power and thermal efficiency for (**a**) LM-TanSig algorithm, (**b**) LM-LogSig algorithm, (**c**) SCG-TanSig algorithm, (**d**) SCG-LogSig algorithm, (**e**) CGP-TanSig algorithm, and (**f**) the CGP-LogSig algorithm with various numbers of hidden neurons.


