# Artificial Neural Network and Adaptive Neuro-Fuzzy Interface System Modelling to Predict Thermal Performances of Thermoelectric Generator for Waste Heat Recovery

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## Abstract

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## 1. Introduction

^{o}enhances the open circuit voltage, maximum power and maximum power density of the automotive thermoelectric generator system by 7.5, 10.17 and 15.49%, respectively [9]. He et al. have shown that the plate type heat exchanger shows the maximum conversion efficiency of 5% for the louvered fins and 4.5% for the smooth and offset strip fins, respectively [10]. Lu et al. have proved that the hot heat exchanger configurations with uniform winglet vortex and non-uniform winglet vortex show higher power output of the thermoelectric generator than the hot heat exchanger without fins [11]. Rana et al. have the generated maximum power of 79.02 W by designing the heat exchanger with 0.08 m length, 1 m height, 4 mm gap size and 50 thermoelectric modules [12]. Suter et al. have proposed 1 kW thermoelectric stack with the counterflow parallel plate heat exchanger and 127 pairs of thermoelectric modules to convert the geothermal reservoir heat to electricity using the optimized stack volume of 0.0021 m

^{3}and optimized the conversion efficiency of 4.2% [13]. Zhao et al. have showed that the application of intermediate fluid improves the maximum power output and generation efficiency of the automotive thermoelectric generator system [14,15]. Lu et al. have shown that 1-inlet 2-outlet heat exchanger has improved the performance characteristics compared to 2-inlet 2-outlet and empty cavity heat exchangers [16].

## 2. Experimental Set-Up

^{5}Pa. The electric heater supplies the hot gas at the required temperature using the thermostat controller. The mass flow rate of the hot gas is measured by the mass flow indicator with an accuracy of ±0.5% installed near the thermostat controller. The airtight vacuum chamber provides the constant temperature and pressure controlled by the chamber pressure regulator. In addition, the chamber pressure regulator indicates the inlet and outlet temperatures of the hot gas. The constant temperature chiller supplies the cold water to the cold fluid channels at the required temperature and pressure. The mass flow rate of the water is measured by the mass flow indicator with an accuracy of ±0.5% installed on a tube which transfers the cold water from chiller to the cold fluid channels. The temperatures of the hot gas at the inlet and outlet of the heat exchanger, temperatures of the cold water at the inlet and outlet of the cold fluid channels, temperatures of the thermoelectric modules and the chamber are measured using nine K-type thermocouples with an accuracy ±0.1 °C. The thermocouples are connected to a KEYSIGHT 34970A data logger with an accuracy of ±0.1% for monitoring the temperatures continuously. The thermoelectric modules are connected to the KIKUSUI PLZ334L electronic loader to record the current, voltage and power data with time. The accuracy of the electronic loader is ±0.1%, ±0.2% and ±0.6% for the current, voltage and power measurements, respectively.

## 3. Numerical Method

^{3}, 1005 J/k·°C, 0.026 W/m$\xb7$K and 1.8 × 10

^{−4}kg/m·s, respectively. The density, specific heat, thermal conductivity and dynamic viscosity of the water are set as 997 kg/m

^{3}, 4182 J/kg·°C, 0.607 W/m$\xb7$K and 8.9 × 10

^{−4}kg/m$\xb7$s, respectively. For skutterudite, the density, specific heat and thermal conductivity are used as 7598 kg/m

^{3}, 350 J/kg·°C and 3.4 W/m·K, respectively. In addition, the Seebeck coefficient is set as 142.8 µV/K for p-leg and −183.5 µV/K for n-leg [22]. The continuity, momentum and energy equations are expressed with Equations (2) to (5) [23].

^{3}), $U$ is the average velocity (m/s), $\nabla $ is the nabla operator, $p$ is the static pressure (Pa), $\tau $ is the stress tensor, ${S}_{M}$ is the momentum source, $\mu $ is the dynamic viscosity (Pa$\xb7$s), $h$ is the enthalpy (J), $\lambda $ is the thermal conductivity (W/m$\xb7$K) and ${S}_{E}$ is the energy source.

^{2}), $k$ is the thermal conductivity (W/m·K), $\nabla T$ is the temperature gradient, $\overrightarrow{E}$ is the electric field intensity (V/m), $\sigma $ is the electrical conductivity (Ω

^{−1}·m

^{−1}), $\alpha $ is the Seebeck coefficient (V/K), and $\nabla \varnothing $ is the electric potential (J/C).

## 4. Artificial Intelligence Models

#### 4.1. Artificial Neural Network (ANN) Modelling

^{−6}for training to confirm the prediction accuracy of the tested model for the thermoelectric generator system for waste heat recovery. The experiments are conducted on the thermoelectric generator system for waste heat recovery at the hot gas inlet temperatures and voltage load conditions to collect the data for training. A total of 931 data points of the input and output parameters are used to train the six models. For each ANN model, the training is done until the error becomes steady and the outputs predicted by that trained model are recorded. The predicted output values of the current, power and thermal efficiency are compared with the corresponding experimental values based on three statistical parameters of the coefficient of determination (R

^{2}), root mean square error (RMSE), and coefficient of variance (COV). The ANN model with the highest value of R

^{2}and the lowest values of RMSE and COV, respectively, is selected as the optimum ANN model to predict the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery for the hot gas inlet temperatures range of 315.12 to 621.61 °C and voltage load conditions range of 0 to 10 V.

#### 4.2. Adaptive Neuro-Fuzzy Interface System Modelling (ANFIS)

^{−6}. The ANFIS models are trained until the training error becomes steady. Once the training error converges, the output values are predicted in the rule viewer by importing the input conditions of hot gas temperature and voltage conditions. The predicted values of the current, power and thermal efficiency by each ANFIS model are compared with the corresponding experimental values using three statistical parameters of R

^{2}, RMSE and COV. The ANFIS model with the optimum values of three statistical parameters is considered as the best model to predict the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery under the influence of various hot gas inlet temperatures and voltage conditions.

## 5. Data Reduction

^{2}), $t$ is the module thickness (m) and $\Delta T$ is the temperature difference (°C) of the thermoelectric module.

^{2}), root mean square error (RMSE) and coefficient of variance (COV) are calculated using Equations (13)–(15), respectively [38]:

## 6. Results and Discussion

#### 6.1. Experimental Outputs of Current, Power and Thermal Efficiency

#### 6.2. Prediction Results from the Numerical Method

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

#### 6.4. Prediction Results from ANN Models

^{2}, 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.

^{2}, 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

^{2}, RMSE and COV for LM-LogSig algorithm with 20 hidden neurons are 0.99997, 0.04632 and 0.66686, respectively for the power.

^{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

^{2}, 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.

^{2}, 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.

^{2}, 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.

^{2}, 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

^{2}, 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.

#### 6.5. Prediction Results from ANFIS Models

^{2}, 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 thermoelectric generator system for waste heat recovery, the triangular with 4-membership function shows a good agreement with the experimental results with R

^{2}, 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

^{2}, 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 $\pm $15% from the corresponding experimental thermal efficiency as shown in Figure 10a.

^{2}, 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

^{2}, 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.

^{2}, 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

^{2}, 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.

^{2}, 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.

^{2}, 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

^{2}, 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.

^{2}, 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.

^{2}, 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

^{2}, 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.

## 7. Conclusions

^{2}), root mean square error (RMSE) and coefficient of variance (COV). The ANN model with back-propagation algorithm, Levenberg–Marquardt training variant, Tan-Sigmoidal transfer function, and 25 hidden neurons is suggested as the optimum model based on optimum values of statistical parameters for the prediction of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery. The ANFIS model with gbell membership function in a number of sets of 3 is suggested as the optimum model based on optimum values of statistical parameters to predict the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery with low prediction cost and acceptable prediction accuracy. The ANFIS model with pi or gauss membership function in the number of sets of 5 is suggested as the optimum model based on optimum values of statistical parameters to predict the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery with higher prediction accuracy. The optimum ANN and ANFIS models show better prediction of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery with low computational time and cost than the coupled numerical approach.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Formulated ANN structure to predict the performances of the thermoelectric generator system for waste heat recovery.

**Figure 4.**Formulated ANFIS model to predict the performances of the thermoelectric generator system for waste heat recovery.

**Figure 5.**Variation of (

**a**) current, (

**b**) power, and (

**c**) thermal efficiency for training and testing data sets.

**Figure 6.**Temperature distributions (

**a**) Module 1-hot surface, (

**b**) Module 1-cold surface, (

**c**) Module 2-hot surface, (

**d**) Module 2-cold surface, (

**e**) Module 3-hot surface, (

**f**) Module 3-cold surface, (

**g**) Module 4-hot surface, (

**h**) Module 4-cold surface, (

**i**) Module 5-hot surface, (

**j**) Module 5-cold surface, (

**k**) Module 6-hot surface, (

**l**) Module 6-cold surface with locations (x and y coordinates) at 419.26 °C.

**Figure 7.**The comparisons of experimental and numerical results of the current, power and thermal efficiency for testing data set.

**Figure 8.**The converged training errors for (

**a**) ANN and (

**b**) ANFIS models of thermoelectric generator system for waste heat recovery.

**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 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.

Parameter | Value |
---|---|

Hot gas (air) inlet temperature (°C) | 315.12, 419.26, 521.7, 621.61 |

Coolant (water) inlet temperature (°C) | 30 |

Hot gas (air) mass flow rate (kg/s) | 0.018 |

Coolant (water) mass flow rate (kg/s) | 0.075 |

High potential voltage (V) | 0 to 10 V |

Low potential voltage (V) | 0 |

Parameter | R^{2} | RMSE | COV |
---|---|---|---|

Current | 0.99865 | 0.18633 | 4.22614 |

Power | 0.99992 | 0.07032 | 1.01243 |

Thermal efficiency | 0.99992 | 0.01422 | 0.99102 |

**Table 3.**The prediction accuracy of optimum ANN model with LM-TanSig algorithm and various numbers of hidden neurons for current, power and thermal efficiency.

Parameter | Number of Hidden Neurons | R^{2} | RMSE | COV |
---|---|---|---|---|

Current | 10 | 0.99986 | 0.06013 | 1.36373 |

15 | 0.99997 | 0.02578 | 0.58476 | |

20 | 0.99998 | 0.02507 | 0.56860 | |

25 | 0.99998 | 0.02163 | 0.49061 | |

Power | 10 | 0.99977 | 0.12180 | 1.75370 |

15 | 0.99993 | 0.06769 | 0.97459 | |

20 | 0.99993 | 0.06609 | 0.95152 | |

25 | 0.99997 | 0.04111 | 0.59192 | |

Thermal efficiency | 10 | 0.99809 | 0.07170 | 4.99773 |

15 | 0.99983 | 0.02126 | 1.48165 | |

20 | 0.99981 | 0.02277 | 1.58688 | |

25 | 0.99996 | 0.01050 | 0.73183 |

Parameter | Number of Membership Functions | R^{2} | RMSE | COV |
---|---|---|---|---|

Current | 2 | 0.94053 | 1.23658 | 28.0468 |

3 | 0.96078 | 1.00416 | 22.7752 | |

4 | 0.99997 | 0.02852 | 0.64682 | |

5 | 0.99998 | 0.02469 | 0.55991 | |

Power | 2 | 0.83830 | 3.19468 | 45.9964 |

3 | 0.71781 | 4.22023 | 60.7620 | |

4 | 0.99994 | 0.05948 | 0.85635 | |

5 | 0.99997 | 0.04029 | 0.58006 | |

Thermal efficiency | 2 | 0.87063 | 0.58791 | 41.1021 |

3 | 0.96815 | 0.29262 | 20.3952 | |

4 | 0.99994 | 0.01257 | 0.87619 | |

5 | 0.99997 | 0.00931 | 0.64890 |

Parameter | Number of Membership Functions | R^{2} | RMSE | COV |
---|---|---|---|---|

Current | 2 | 0.99250 | 0.43925 | 9.96247 |

3 | 0.99998 | 0.02366 | 0.53671 | |

4 | 0.99998 | 0.02254 | 0.51116 | |

5 | 0.99998 | 0.02165 | 0.49110 | |

Power | 2 | 0.88660 | 2.67538 | 38.5195 |

3 | 0.99957 | 0.16457 | 2.36942 | |

4 | 0.99988 | 0.08667 | 1.24784 | |

5 | 0.99997 | 0.04429 | 0.63770 | |

Thermal efficiency | 2 | 0.88430 | 0.55769 | 38.8710 |

3 | 0.99967 | 0.03002 | 2.09204 | |

4 | 0.99996 | 0.01056 | 0.73603 | |

5 | 0.99997 | 0.00911 | 0.63516 |

Parameter | Number of Membership Functions | R^{2} | RMSE | COV |
---|---|---|---|---|

Current | 2 | 0.99997 | 0.02820 | 0.63965 |

3 | 0.99998 | 0.02432 | 0.55166 | |

4 | 0.99998 | 0.02266 | 0.51393 | |

5 | 0.99998 | 0.02325 | 0.52728 | |

Power | 2 | 0.88847 | 2.65317 | 38.1999 |

3 | 0.99996 | 0.04812 | 0.69281 | |

4 | 0.99990 | 0.08003 | 1.15220 | |

5 | 0.99996 | 0.04865 | 0.70043 | |

Thermal efficiency | 2 | 0.90510 | 0.50507 | 35.2033 |

3 | 0.99994 | 0.01241 | 0.86506 | |

4 | 0.99984 | 0.02086 | 1.45405 | |

5 | 0.99987 | 0.01848 | 1.28804 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Garud, K.S.; Seo, J.-H.; Cho, C.-P.; Lee, M.-Y.
Artificial Neural Network and Adaptive Neuro-Fuzzy Interface System Modelling to Predict Thermal Performances of Thermoelectric Generator for Waste Heat Recovery. *Symmetry* **2020**, *12*, 259.
https://doi.org/10.3390/sym12020259

**AMA Style**

Garud KS, Seo J-H, Cho C-P, Lee M-Y.
Artificial Neural Network and Adaptive Neuro-Fuzzy Interface System Modelling to Predict Thermal Performances of Thermoelectric Generator for Waste Heat Recovery. *Symmetry*. 2020; 12(2):259.
https://doi.org/10.3390/sym12020259

**Chicago/Turabian Style**

Garud, Kunal Sandip, Jae-Hyeong Seo, Chong-Pyo Cho, and Moo-Yeon Lee.
2020. "Artificial Neural Network and Adaptive Neuro-Fuzzy Interface System Modelling to Predict Thermal Performances of Thermoelectric Generator for Waste Heat Recovery" *Symmetry* 12, no. 2: 259.
https://doi.org/10.3390/sym12020259