5.4.1. Integrated System with Parallel Circuit

5.4.1. Integrated System with Parallel Circuit The battery out temperature of the integrated system with parallel circuit for various heater powers, flow ratios and time is predicted using various algorithms of ANN models. The experimental data of battery out temperature of the integrated system with parallel circuit at various time, flow rates and heater powers are used for the training, testing and validation of ANN models with various algorithms. The prediction accuracy of various algorithms of ANN model for battery out temperature at flow ratio of 5/5 and all heater powers is presented in Table 3. A higher prediction accuracy is obtained for other flow ratios as well. For all heater powers and hidden neurons, LM with Tan training variant shows better prediction accuracy compared to LM with Log training variant. In addition, prediction accuracy increases as the number of hidden neurons increases for all heater powers. Therefore, in respective case of each heater power, LM-Tan with 20 hidden neurons shows highest prediction accuracy for battery out temperature of the integrated system with parallel circuit. The prediction accuracy of ANN model with LM-Tan-20 algorithm for battery out temperature of the integrated system with parallel circuit is R2 with The battery out temperature of the integrated system with parallel circuit for various heater powers, flow ratios and time is predicted using various algorithms of ANN models. The experimental data of battery out temperature of the integrated system with parallel circuit at various time, flow rates and heater powers are used for the training, testing and validation of ANN models with various algorithms. The prediction accuracy of various algorithms of ANN model for battery out temperature at flow ratio of 5/5 and all heater powers is presented in Table 3. A higher prediction accuracy is obtained for other flow ratios as well. For all heater powers and hidden neurons, LM with Tan training variant shows better prediction accuracy compared to LM with Log training variant. In addition, prediction accuracy increases as the number of hidden neurons increases for all heater powers. Therefore, in respective case of each heater power, LM-Tan with 20 hidden neurons shows highest prediction accuracy for battery out temperature of the integrated system with parallel circuit. The prediction accuracy of ANN model with LM-Tan-20 algorithm for battery out temperature of the integrated system with parallel circuit is R<sup>2</sup> with 0.999971, 0.999979 and 0.999979, RMSE with 0.154166, 0.183539 and 0.201043, as well as COV with 0.536230, 0.460489 and 0.472796 for heater powers of 2 kW, 4 kW and 6 kW, respectively. The comparison of battery out temperature of the integrated system with parallel circuit for

0.999971, 0.999979 and 0.999979, RMSE with 0.154166, 0.183539 and 0.201043, as well as

respectively. The comparison of battery out temperature of the integrated system with parallel circuit for experiment and ANN model with LM-Tan-20 algorithm at various heater powers is also presented in Figure 8a. Figure 8a shows the prediction capability of

experiment and ANN model with LM-Tan-20 algorithm at various heater powers is also presented in Figure 8a. Figure 8a shows the prediction capability of suggested algorithm and closeness of predicted results by suggested algorithm with the experimental results.

The same algorithms of the ANN model are used to predict the HVAC temperature difference of the integrated system with parallel circuit. The ANN model with various algorithms is trained, tested and validated for the experimental HVAC temperature difference data at various flow rates, heater powers and time. The prediction accuracy of various algorithms of ANN models is presented at flow ratio of 5/5 and all heater powers for HVAC temperature difference in Table 3. For other flow ratios, a higher prediction accuracy is also obtained. In the case of HVAC temperature difference of the integrated system with parallel circuit, the LM with Tan training variant also shows superior prediction accuracy than the LM with Log training variant for all heater powers. Additionally, higher number of hidden neurons shows higher prediction performance for all heater powers. For the HVAC temperature difference of the integrated system with parallel circuit, the LM-Tan-20 shows R<sup>2</sup> of 0.803624, 0.956737 and 0.994077, RMSE of 0.631449, 0.549005 and 0.245819, as well as COV of 44.75612, 21.27336 and 7.909049 for heater powers of 2 kW, 4 kW and 6 kW, respectively. The prediction accuracy of the LM-Tan-20 algorithm is better for the battery out temperature than the HVAC temperature difference, because of linear trends of battery out temperature and zigzag trends of HVAC temperature difference for all heater powers. Figure 8b shows the closeness of LM-Tan-20 algorithm predicted HVAC temperature difference and corresponding actual results for all heater powers. For some points deviation between the predicted and actual results is larger because of zigzag trend of HVAC temperature difference curves at all heater powers, the suggested algorithm is not able to follow all points accurately. However, the minimum prediction accuracy is 0.8, which is an acceptable prediction performance for the suggested ANN model. Mohanraj et al. have suggested the Levenberg-Marquardt training algorithm as the optimum for the accurate performance prediction with maximum R<sup>2</sup> of 0.999 and lowest values of RMSE and COV [39].

**Table 3.** Prediction accuracy of ANN models for battery heating performance and HVAC heating performance of integrated system with parallel circuit.



**Table 3.** *Cont*. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 18 of 25

(**a**) Battery out temperature

**Figure 8.** *Cont*.

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 19 of 25

(**b**) HVAC temperature difference

**Figure 8.** Comparison of (**a**) battery out temperature and (**b**) HVAC temperature difference of parallel circuit for experimental and ANN model with LM-Tan-20 algorithm at various heater powers. **Figure 8.** Comparison of (**a**) battery out temperature and (**b**) HVAC temperature difference of parallel circuit for experimental and ANN model with LM-Tan-20 algorithm at various heater powers.

#### 5.4.2. Integrated System with Serial Circuit 5.4.2. Integrated System with Serial Circuit

The battery out temperature of the integrated system with serial circuit is predicted for various algorithms of ANN model using heater power, flow rates and time as the input conditions. The experimental battery out temperature, heater powers and flow rates at various time are considered to train, test and validate the various algorithms of ANN model. The prediction accuracy of ANN model with various algorithms for battery out temperature of the integrated system with serial circuit at various heater powers is presented in Table 4. The prediction accuracy of ANN model with LM-Tan-20 algorithm is superior for all heater powers. LM-Tan-20 algorithm shows R2, RMSE and COV values of 0.999970, 0.205704 and 0.554591, respectively, at a heater power of 2 kW, those values of 0.999980, 0.170831 and 0.479862, respectively, at a heater power of 4 kW, and those values of 0.999982, 0.158077 and 0.431001, respectively, at heater power of 6 kW. The battery out temperatures predicted by the LM-Tan-20 algorithm for various time and heater powers are compared with the corresponding experimental values in Figure 9a. A higher degree of closeness between the actual and predicted results could be observed for the suggested algorithm of ANN model. The battery out temperature of the integrated system with serial circuit is predicted for various algorithms of ANN model using heater power, flow rates and time as the input conditions. The experimental battery out temperature, heater powers and flow rates at various time are considered to train, test and validate the various algorithms of ANN model. The prediction accuracy of ANN model with various algorithms for battery out temperature of the integrated system with serial circuit at various heater powers is presented in Table 4. The prediction accuracy of ANN model with LM-Tan-20 algorithm is superior for all heater powers. LM-Tan-20 algorithm shows R<sup>2</sup> , RMSE and COV values of 0.999970, 0.205704 and 0.554591, respectively, at a heater power of 2 kW, those values of 0.999980, 0.170831 and 0.479862, respectively, at a heater power of 4 kW, and those values of 0.999982, 0.158077 and 0.431001, respectively, at heater power of 6 kW. The battery out temperatures predicted by the LM-Tan-20 algorithm for various time and heater powers are compared with the corresponding experimental values in Figure 9a. A higher degree of closeness between the actual and predicted results could be observed for the suggested algorithm of ANN model.

The experimental results of HVAC temperature difference, heater power, flow rates and time are used to train, test and validate the same algorithms of the ANN models. Trained ANN models are used to predict the HVAC temperature difference for various The experimental results of HVAC temperature difference, heater power, flow rates and time are used to train, test and validate the same algorithms of the ANN models. Trained ANN models are used to predict the HVAC temperature difference for various

heater powers with time. Table 4 shows the prediction accuracy of various algorithms of the ANN model for HVAC temperature difference of the integrated system with serial circuit at various heater powers. ANN model with LM-Tan-20 algorithm is suggested as the optimum model, which shows higher value of R<sup>2</sup> and lowest values of RMSE and COV. ANN model with LM-Tan-20 algorithm shows R<sup>2</sup> , RMSE and COV values of 0.987539, 0.128786 and 11.30589, respectively, at 2 kW heater power, those of 0.998338, 0.132884 and 4.164997, respectively, at 4 kW heater power and those of 0.998081, 0.134271 and 4.444122, respectively, at 6 kW heater power. Figure 9b shows the comparison of experimental HVAC temperature difference and LM-Tan-20 algorithm predicted HVAC temperature difference for various heater powers. For all heater powers, the predicted results show closer agreement with corresponding experimental results.

**Table 4.** Prediction accuracy of ANN models for battery heating performance and HVAC heating performance of integrated system with serial circuit.


Based on the results discussed in Sections 5.4.1 and 5.4.2, ANN model with LM-Tan-20 algorithm is suggested to accurately predict the heating performances of battery and HVAC for the integrated system with serial and parallel circuits. Kunal et al. proposed an ANN model with the optimum structure as the Levenberg-Marquardt training algorithm and Tan-sigmoidal transfer function for the accurate performance prediction [43]. 20 0.998081 0.134271 4.444122 LM-Log 10 0.997779 0.144445 4.780861 15 0.997815 0.143260 4.741652 20 0.997894 0.140671 4.655938

15 0.997864 0.141669 4.688989

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 21 of 25

(**a**) Battery out temperature

**Figure 9.** *Cont*.

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 22 of 25

(**b**) HVAC temperature difference

**Figure 9.** Comparison of (**a**) battery out temperature and (**b**) HVAC temperature difference of serial circuit for experimental and ANN model with LM-Tan-20 algorithm at various heater powers. **Figure 9.** Comparison of (**a**) battery out temperature and (**b**) HVAC temperature difference of serial circuit for experimental and ANN model with LM-Tan-20 algorithm at various heater powers.

#### **6. Conclusions 6. Conclusions**

An experimental study is conducted on the integrated system with serial and parallel circuits to investigate the heating performances of battery and HVAC for an electric vehicle. In addition, ANN models are developed to predict the battery and HVAC heating performances of the integrated system with serial and parallel circuits. The following findings are summarized from the present study. An experimental study is conducted on the integrated system with serial and parallel circuits to investigate the heating performances of battery and HVAC for an electric vehicle. In addition, ANN models are developed to predict the battery and HVAC heating performances of the integrated system with serial and parallel circuits. The following findings are summarized from the present study.


5726.33 W, respectively.

for the integrated system with serial circuit are evaluated as 1025.16 W and 5726.33 W, respectively.


**Author Contributions:** Conceptualization, T.-K.L.; K.S.G.; J.-H.S. and M.-Y.L.; methodology, T.-K.L. and K.S.G.; formal analysis, T.-K.L. and K.S.G.; investigation, T.-K.L. and K.S.G.; resources, T.-K.L.; K.S.G. and J.-H.S.; data curation, T.-K.L.; K.S.G. and J.-H.S.; writing—original draft preparation, T.-K.L.; K.S.G.; J.-H.S. and M.-Y.L.; writing—review and editing, T.-K.L.; K.S.G., J.-H.S.; M.-Y.L. and D.- Y.L.; visualization, T.-K.L.; K.S.G. and J.-H.S.; supervision, M.-Y.L. and D.-Y.L.; project administration, T.-K.L.; M.-Y.L. and D.-Y.L.; funding acquisition, T.-K.L.; M.-Y.L. and D.-Y.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study will be available on request to the corresponding author.

**Acknowledgments:** This work was supported by the Technology Innovation Program (20011622, Development of battery pack system applied high efficiency heat control polymer and part component) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea), the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2C1011555) and the 2020 Yeungnam University Research Grant.

**Conflicts of Interest:** The authors declare no conflict of interest.
