*6.5. Prediction Results from ANFIS Models*

*6.5. Prediction Results from ANFIS Models*  The comparison of experimental and ANFIS predicted results of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using the triangular membership function is shown in Figure 10a. The triangular with 4-membership function shows higher prediction accuracy with R2, RMSE and COV of 0.99998, 0.02209 and 0.50106, respectively and the prediction accuracy decreases in order of triangular with 5-, 2- and 3-membership functions for The comparison of experimental and ANFIS predicted results of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using the triangular membership function is shown in Figure 10a. The triangular with 4-membership function shows higher prediction accuracy with R<sup>2</sup> , RMSE and COV of 0.99998, 0.02209 and 0.50106, respectively and the prediction accuracy decreases in order of triangular with 5-, 2- and 3-membership functions for the current of the thermoelectric generator system for waste heat recovery. For the power of the

25 0.99996 0.01050 0.73183

the current of the thermoelectric generator system for waste heat recovery. For the power of the

thermoelectric generator system for waste heat recovery, the triangular with 4-membership function shows a good agreement with the experimental results with R<sup>2</sup> , RMSE and COV of 0.99973, 0.13024 and 1.87522, respectively. The prediction accuracy of the triangular with 5- and 3-membership functions shows a good agreement within ±5%, but the prediction accuracy of the triangular with 2-membership function shows over ±15% from the corresponding experimental which are not a permissible limit. In the case of the thermal efficiency of the thermoelectric generator system for waste heat recovery using the triangular with 4-membership function shows the peak prediction accuracy and this prediction accuracy decreases in an order with the triangular with 5- and 3-membership functions. The values of R<sup>2</sup> , RMSE and COV for the thermal efficiency of the thermoelectric generator system for waste heat recovery using the triangular with 4-membership function are 0.99968, 0.02955 and 2.05980, respectively. The thermal efficiency of the thermoelectric generator system for waste heat recovery using the triangular with a 2-membership function shows the errors over ±15% from the corresponding experimental thermal efficiency as shown in Figure 10a.

The comparison of experimental and ANFIS predicted results of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using trapezoidal membership function is shown in Figure 10b. The prediction accuracy for the current and power of the thermoelectric generator system for waste heat recovery using the trapezoidal with 5-membership function shows the best. The values of R<sup>2</sup> , RMSE and COV for the trapezoidal with 5-membership function are 0.99998, 0.02333 and 0.52922, respectively, for the current and 0.99982, 0.10528 and 1.51577, respectively, for the power. In the case of the thermal efficiency of the thermoelectric generator system for waste heat recovery, the trapezoidal with a 4-membership function shows higher prediction accuracy than the trapezoidal with 5-membership function and the values of R<sup>2</sup> , RMSE and COV for the trapezoidal with 4-membership function are 0.99978, 0.02424 and 1.68948, respectively, for thermal efficiency. However, the current, power and thermal efficiency predicted by the trapezoidal with 2- and 3-membership functions show the errors above ±15% from the experimental which are not within permissible limit.

The comparison of experimental and ANFIS predicted results of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using a gbell membership function is shown in Figure 10c. The prediction accuracy of the gbell with a 4-membership function for the current of the thermoelectric generator system for waste heat recovery shows the best and decreases with 5-, 3- and 2-membership functions. The values of R<sup>2</sup> , RMSE and COV for gbell with 4-membership function are 0.99998, 0.02266 and 0.51393, respectively, for the current. For the power and thermal efficiency of the thermoelectric generator system for waste heat recovery, the gbell with 3-membership function shows a better agreement than gbell with 5- and 4-membership functions. The values of R<sup>2</sup> , RMSE and COV for gbell with 3-membership function are 0.99996, 0.04812 and 0.69281, respectively, for the power but 0.99994, 0.01241 and 0.86506, respectively for the thermal efficiency. However, the prediction accuracy of the power and thermal efficiency of the thermoelectric generator system for waste heat recovery using gbell with a 2-membership function show the errors above ±15% from the corresponding experimental which are not the permissible limit.

The comparison of experimental and ANFIS predicted results of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using a gauss membership function is shown in Figure 10d. For the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery, the prediction accuracy of the gauss with a 5-membership function shows the best and decreases with 4-, 3- and 2-membership functions. The values of R<sup>2</sup> , RMSE and COV for the gauss with 5-membership function are 0.99998, 0.02165 and 0.49110, respectively for the current, 0.99997, 0.04429 and 0.63770, respectively, for the power and 0.99997, 0.00911 and 0.63516, respectively, for the thermal efficiency. However, the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using gauss with 2-membership function show the errors above ±15% from the corresponding experimental which are not a permissible limit.

The comparison of experimental and ANFIS predicted results of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using a gauss 2-membership function is shown in Figure 10e. For the current and thermal efficiency of the thermoelectric generator system for waste heat recovery, the gauss2 with 4-membership function shows higher prediction accuracy than gauss2 with a 5-membership function, but the gauss2 with 5-membership function shows higher prediction accuracy than gauss2 with 4-membership function for the power. The values of R<sup>2</sup> , RMSE and COV for the gauss2 with 4-membership function are 0.99998, 0.02377 and 0.53902, respectively, for the current and 0.99992, 0.01437 and 1.0012, respectively, for the thermal efficiency. In addition, the values of R<sup>2</sup> , RMSE and COV for gauss2 with a 5-membership function are 0.99992, 0.06965 and 1.00285, respectively, for the power. However, the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using gauss2 with 2- and 3-membership function show the errors above ±15% from the corresponding experimental which are not the permissible limit.

The comparison of experimental and ANFIS predicted results of current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using a pi membership function is shown in Figure 10f. For the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery, the pi with 5-membership function shows higher prediction accuracy than pi with a 4-membership function. The values of R<sup>2</sup> , RMSE and COV for pi with a 5-membership function are 0.99998, 0.02469 and 0.55991, respectively, for the current, 0.99997, 0.04029, and 0.58006, respectively, for the power and 0.99997, 0.00931, and 0.64890, respectively, for the thermal efficiency. However, the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using pi with 2 and 3-membership functions show the errors above ±15% from the corresponding experimental which are not a permissible limit.

The comparison of experimental and ANFIS predicted results of current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using a dsig membership function is shown in Figure 10g. For the current of the thermoelectric generator system for waste heat recovery, dsig with a 4-membership function shows higher prediction accuracy than dsig with a 5-membership function. In addition, for the power and thermal efficiency of the thermoelectric generator system for waste heat recovery, dsig with a 5-membership function shows higher prediction accuracy than dsig with 4-membership function. The values of R<sup>2</sup> , RMSE and COV for dsig with a 4-membership function are 0.99998, 0.02360 and 0.53534, respectively, for the current. In addition, the values of R<sup>2</sup> , RMSE and COV for dsig with a 5-membership function are 0.99990, 0.07853 and 1.13067, respectively, for the power and 0.99989, 0.01704 and 1.18732, respectively, for the thermal efficiency. However, the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery using dsig with 2 and 3-membership functions show the errors above ±15% from the corresponding experimental, which are not a permissible limit.

The same number of the membership functions results in almost the same prediction cost. As the number of the membership functions increases, it results in a higher prediction cost. When the prediction accuracy plays a crucial role, the ANFIS model with a pi-5-membership function or a gauss-5-membership function could be recommended to predict the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery [40]. The prediction accuracy of the ANFIS model for the current, power and thermal efficiency is shown in Table 4a for pi membership function and Table 4b for gauss membership function, respectively. When the prediction cost plays a crucial role, the ANFIS model with gbell-3-membership function could be suggested to predict the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery as shown in Table 4c. Table 4c shows the prediction accuracy of an ANFIS model with a gbell membership function for the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery. The proposed ANFIS model with pi-5 or gauss-5 and gbell-3 show better prediction accuracy than the coupled numerical approach for the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery [41].

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**Figure 10.** *Cont*.

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**Figure 10.** *Cont*.

**Figure 10.** *Cont*.

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**Figure 10.** *Cont*.

**Figure 10.** The comparison of experimental and ANFIS predicted results of current, power and thermal efficiency for (**a**) triangular membership function, (**b**) trapezoidal membership function, (**c**) gbell membership function, (**d**) gauss membership function, (**e**) gauss2-membership function, (**f**) pi membership function, and (**g**) dsig membership function. **Figure 10.** The comparison of experimental and ANFIS predicted results of current, power and thermal efficiency for (**a**) triangular membership function, (**b**) trapezoidal membership function, (**c**) gbell membership function, (**d**) gauss membership function, (**e**) gauss2-membership function, (**f**) pi membership function, and (**g**) dsig membership function.

**Table 4.** (a) The prediction accuracy of ANFIS model with pi membership function for current, power and thermal efficiency; (b) The prediction accuracy of ANFIS model with a gauss membership function for current, power and thermal efficiency; (c) The prediction accuracy of ANFIS model with a gbell membership function for current, power and thermal efficiency. **Table 4.** (a) The prediction accuracy of ANFIS model with pi membership function for current, power and thermal efficiency; (b) The prediction accuracy of ANFIS model with a gauss membership function for current, power and thermal efficiency; (c) The prediction accuracy of ANFIS model with a gbell membership function for current, power and thermal efficiency.


240

5 0.99997 0.00931 0.64890


**Table 4.** *Cont*.

Additionally, the developed ANN and ANFIS models could accurately predict the performances like the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery with less computational time and cost because the experimental and coupled numerical approaches could be expensive and time consuming. Therefore, the proposed methodology to develop the ANN and ANFIS models could be applicable to accurately predict the performances of the various physical systems like solar based systems, refrigeration systems, heat exchanger systems, thermoelectric coolers, etc.
