## 4 Parameters for the Optimal Election of CH
### Energy Model  
The chief issue related to WSNs is the exploitation of energy [33]. The re-energizing method is not applied for the WSN battery, and consequently, providing energy is impossible if the battery drops down. In addition, data transmitted to the BS from whole SNs is capably made via supplementary resources. Energy exploitation is very important to transmit data. The network needs supplementary energy owing to varied functions that comprise transmission, reception, aggregation, and sensing. Conventionally, the required energy for the overall broadcast of data is implied by Equation (1); however, as per the proposed energy model, the required energy for an overall broadcast of data is implied by Equation (2), where \(E^{i}\) denotes initial energy. As per the specified modules, the electronic energy is implied as \(E_{el}\), in which \(E_{ea}\) denotes the energy for data time aggregation. \(E_{el}\) is implied by Equation (4). \(E_{TX}(Z:di)\) indicates the whole deployed energy needed to communicate \(Z\) bytes of packets at \(di\) distance. For a good system, energy must be high. Figure 1: Pictorial representation of the proposed method. Different color star denotes three cluster groups, where cluster head is selected and connected with the base station. The receiver energy, \(E_{RX}\), required to obtain \(Z\) bytes of packets at \(di\) is shown in Equation (5), which indicates the energy necessary for amplification, \(E_{am}\). \[E_{TX}(Z:di)=E\left\{ \begin{array}{l}E_{el}\times Z+E_{rs}\times Z\times di^{2},if\ di<di_{0}\\ E_{el}\times Z+E_{pw}\times Z\times di^{2},if\ di\geq di_{0}\end{array} \right. \tag{1}\]  
\[E_{TX}(Z:di)=E\left\{ \begin{array}{l}E^{i}-E_{el}\times Z+E_{rs}\times Z\times di ^{2},if\ di<di_{0}\\ E^{i}-E_{el}\times Z+E_{pw}\times Z\times di^{2},if\ di\geq di_{0}\end{array} \right. \tag{2}\]  
\[E_{el}=E_{TX}+E_{ea} \tag{3}\]  
\[E_{RX}(Z:di)=E_{el}Z \tag{4}\]  
\[E_{am}=E_{fr}di^{2} \tag{5}\]  
\[di_{0}=\sqrt{\frac{E_{fr}}{E_{pam}}} \tag{6}\]  
In the above equations,  
\(di_{0}\) represents threshold distance;  
\(E_{pam}\) represents energy of PA;  
\(E_{fr}\) represents requisite energy as employing free space approach;  
\(E_{1}\) represents energy for entire idle state;  
\(E_{C}\) represents energy cost for whole sense phase. The overall energy to transmit data is indicated by Equation (8). \[E_{total}=E_{TX}+E_{RX}+E_{1}+E_{C} \tag{7}\]  
After computing the energy, the energy level prediction can be performed using improved DCNN. Based on this \(di\), the energy of SN can be predicted. For prediction, DCNN is used, which has \(di\) as the input to predict the energy. The DCNN detects significant features with no human intermission. However, it requires large amounts of training data. Therefore, an improvisation is performed to enhance the performance of DCNN. DCNN covers three layers, namely, the Pooling layer, the Fully connected layer, and the Convolution layer. All neurons are connected with closer neurons in the preceding layer. At position \((r,t)\) in the \(l\)th layer of correlated \(w\)th feature map, the features were designed as in Equation (8). \[B^{l}_{r,t,w}=W^{l\ T}_{w}P^{l}_{r,t}+D^{l}_{w} \tag{8}\]  
In Equation (8), \(W^{l}_{w}\) represents weight and \(D^{l}_{w}\) represents the bias of \(w\)th filter linked to the \(l\)th layer. At the center location \((r,t)\) of the \(l\)th layer, the patch input is indicated as \(PI^{l}_{r,t}\). The activation value \(\left(act^{l}_{r,t,w}\right)\) related to convolutional features, and \(B^{l}_{r,t,w}\) is calculated as in Equation (9). \[act^{l}_{r,t,w}=act\left(B^{l}_{r,t,w}\right) \tag{9}\]  
Pooling layer: For each pooling function, \(pool\) (\(\bullet\)), related to \(act^{l}_{m,h,w}\), the \(C^{l}_{r,t,w}\) value is considered, as in Equation (10), in which \(NN_{r,t}\) represents neighbor's close location \((r,t)\). The DCNN loss, \(PL\), is exposed in Equation (11).