## 2 Material and Methods
### Models Design and Evaluation
#### 2.2.3 ENN Model  
The ENN is a learning algorithm of backpropagation ANN; it is summarized in [PERSON] et al. (2014). Figure 1 proposed ENN diagram and processing. ENN includes an artificial emotion unit that used to improve the performance of network nodes, and the generated hormonal weights can be changed using the learning algorithm of the feedback loop (Figure 1) ([PERSON] et al., 2016). From Figure 1, the dynamic hormones of _Hb_, _Hv_, and _Hg_ were given at each node. _Hb_, _Hv_, and _Hg_ are produced and changed during the training phase and learning process, respectively. The hormonal coefficients, such as activation function, weights, and net function, can be determined and improved in the training stage. In Figure 1, the solid and dotted lines represent the neural and hormonal paths, respectively. Thus, the output (\(y\)) of the \(i\)th node of the ENN model with the three hormonal paths can be represented as ([PERSON] et al., 2016):  
\[\begin{split} y_{i}=\underbrace{\left(w_{i}+\sum_{h}\delta_{i,h}H _{h}\right)}_{1}\times& f(\underbrace{\sum_{j}\left(\beta_{i}+ \sum_{h}\varepsilon_{i,jh}H_{h}\right)}_{2}\times\underbrace{\left(\gamma_{i, j}+\sum_{h}\varphi_{i,j,k}H_{h}\right)}_{3}\kappa_{i,j}\\ +&\underbrace{\left(\mu_{i}+\sum_{h}\tau_{i,jh}H_{h} \right)}_{4}\end{split} \tag{9}\]  
where,  
\[H=\sum_{i}H_{i,h};\;h=(b,v,g) \tag{10}\]  
In Equation (9), part (1) represents the imposed weight to the activation function (\(f\)). It includes constant neural weight of \(w_{i}\) as well as the dynamic hormonal weight of \(\sum_{h}\delta_{i,h}H_{h}\). Section (2) consists of applied weight to the summation (net) function, part (3) contains executed weight to the input variables (\(x_{i,j}\)), and term (4) shows the bias of the summation function, both neural and hormonal weights of \(\mu_{i}\) and \(\sum_{h}\tau_{i,jh}H_{h}\), respectively, were comprised.  
Figure 1: The emotional neural network (ENN) structure network (A, B, and C are the weights to input, net and activation functions, respectively; E is glandity; I represents the hormonal unit; D, M, F, G, K, and L are weights applied on net output, hormones from input/output, activation function, net function, and input static weights, respectively).  
The effect of systems hormonal level (_Hh_) in each hormonal weight is adjusted through \(\delta_{i,h}\), \(\varepsilon_{i,h}\), \(\varphi_{i,j,k}\), _and_\(\tau_{i,h}\) parameters and in turn, the model output of ith neuron (\(y_{i}\)) gives hormonal feedback of \(H_{i,h}\) to the system as:  
\[H_{i,h}=g\textit{l}\textit{l}\textit{a}\textit{l}\textit{a}\textit{l}y_{i} \tag{11}\]  
where, the _glandity_ factor should be improved in the training stage of ENN. Herein, the anxiety factor is prepared based on the change of input data of each training sample. However, at the first stage, the confidence factor is applied to connect the anxiety factor and the network output. For that, to set the hormonal values of _Hh_, some schemes can be considered, e.g., average of input variables of learning sample [31; 32]. Here, the learning process is utilized to update the hormonal values to achieve the estimated values. Consequently, anxiety and confidence coefficients (_glandity_ factor) are significant parameters in ENN model. In this study, both parameters were used throughout the generalization and learning process. These parameters were supposed lies between 0 and 1. Furthermore, the trial-and-error method was used to determine ENN structure, neurons and layers numbers, to estimate the optimum S and CS estimation value.