**3. Artificial Neural Network (ANN)**

In recent times, ANNs are used for the performance prediction, forecasting, modeling, simulation and optimization of various physical systems. The working principle of ANN is based on a biological neural network [37]. When the input and output parameters with a larger data set is interrelated in a nonlinear relationship with each other, in those cases the ANN is the efficient tool to relate these parameters with less complexity than the conventional mathematical techniques [38]. The structure of the ANN model includes three layers namely, an input layer, a hidden layer and an output layer [39]. Each layer comprises a suitable number of neurons: the number of neurons in the input layer is equal to the number of input parameters, the number of neurons in the output layer is equal to the number output parameters and the number of neurons in the hidden layer is adjusted based on the training error [40]. Neurons in one layer are connected with the other layer's neurons using weights and two neurons are connected by a single weight value [41]. The structure of the ANN model including layers, neurons and weights is trained using a training algorithm. The construction of training algorithm includes training variant and transfer function [39]. The maximum training error and maximum number of epochs are set as stopping criteria for training. The structure of the ANN model is trained using the selected training algorithm until the desired output or permissible error is obtained [42]. In the training process, the weights assigned between neurons are adjusted to achieve the

desired output. If the desired output or the permissible errors is not achieved, then the different combination of training algorithm, training variant, transfer function, number of hidden layers and hidden neurons is used for further training. The trained ANN model that shows a higher prediction accuracy, with a predicted output closer to the actual results, is suggested as the optimum ANN model. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 6 of 25

> In the present study, an ANN model with various algorithms is developed for the prediction of battery and HVAC heating performances of the integrated system with a serial circuit and with a parallel circuit. The formulated structure of an ANN model for the integrated system with serial and parallel circuits is presented in Figure 2. The aim of the development of ANN models is to predict the battery and HVAC heating performances, which are indicated by battery out temperature and HVAC temperature difference. The battery out temperature and HVAC temperature difference are most affected by heater power and flow rate, which vary in real time. Therefore, the ANN model for the integrated system with serial and parallel circuits is formulated to predict the battery out temperature and HVAC temperature difference as the output parameters, for various conditions of heater power, flow rate and time as the input parameters. The training algorithm comprises of back-propagation algorithm, Levenberg-Marquardt (LM) training variant, Tan-Sigmoidal (Tan) and Log-Sigmoidal (Log) transfer functions, one hidden layer and 10, 15 and 20 number of hidden neurons [38]. The maximum training error and maximum number of epochs are set to 10−<sup>6</sup> and 1000, respectively. The ANN model is trained for the selected algorithm with various combinations, until the maximum training error and the maximum epochs are reached. In the present study, an ANN model with various algorithms is developed for the prediction of battery and HVAC heating performances of the integrated system with a serial circuit and with a parallel circuit. The formulated structure of an ANN model for the integrated system with serial and parallel circuits is presented in Figure 2. The aim of the development of ANN models is to predict the battery and HVAC heating performances, which are indicated by battery out temperature and HVAC temperature difference. The battery out temperature and HVAC temperature difference are most affected by heater power and flow rate, which vary in real time. Therefore, the ANN model for the integrated system with serial and parallel circuits is formulated to predict the battery out temperature and HVAC temperature difference as the output parameters, for various conditions of heater power, flow rate and time as the input parameters. The training algorithm comprises of back-propagation algorithm, Levenberg-Marquardt (LM) training variant, Tan-Sigmoidal (Tan) and Log-Sigmoidal (Log) transfer functions, one hidden layer and 10, 15 and 20 number of hidden neurons [38]. The maximum training error and maximum number of epochs are set to 10−6 and 1000, respectively. The ANN model is trained for the selected algorithm with various combinations, until the maximum training error and the maximum epochs are reached.

**Figure 2.** Artificial neural network (ANN) model for integrated system with serial and parallel circuits. **Figure 2.** Artificial neural network (ANN) model for integrated system with serial and parallel circuits.

**4. Data Reduction** 

mass of battery and specific heat of battery, as presented by Equation (3).

perature rise rate is presented in °C/min [4].

The battery temperature rise rate is calculated using Equation (2). The battery tem-

The battery heating capacity is calculated using the battery temperature rise rate,

௧௧ ௧ (2)
