## 4 Proposed 3D-UWSN Design
### Data Gathering
The throughput for each CH in the route is involved in fairness prediction. Then, the synthesis speed of the AUV near the CH is predicted using:  
\[S_{sp}=|cos\bigg{(}\beta+arccos\bigg{(}\frac{V_{f}}{V_{AUV}}.cos\beta\bigg{)} \bigg{)}.V_{AUV}/cos\beta| \tag{14}\]  
\[\beta=arccos\bigg{(}\frac{Vc.V_{f}}{|Vc|.|V_{f}|}\bigg{)} \tag{15}\]  
Here, \(\beta\) is the angle that exists between the CH and the heave velocity \(V_{f}\), the initial velocity of AUV is represented as \(V_{AUV}\) and \(Vc\) is the vector between the AUV and the CH. Simply, the synthesis speed is defined as the summation of the heave velocity and the initial velocity of the AUV. Then, node efficiency is determined from the following equation:  
\[N_{e}=100*\frac{T_{p}-RT_{p}}{T_{p}} \tag{16}\]  
Figure 2: Three-step, inter-Cluster routing with route validation in fuzzy–LeNet. \(T_{p}\) and \(RT_{p}\) are the transmitted number of packets and retransmitted number of packets, respectively. When computing these four parameters for each CH in the route, the convolutional layer is handled and then the values are converted into a fuzzy set in the pooling layer. As a result, the validated best route is preferred for inter-cluster data transmission. The fuzzy membership functions are modeled as shown in Table 1, with which the route is validated. A set of 16 rules is defined by taking into account the four constraints. The route with higher energy, fairness and efficiency and lower speed of AUV is predicted to be the best route in the validation. A potential CH forwarder is appointed as suitable if its energy consumption is lower with a high node efficiency in data transmission and higher route fairness and a lower speed of AUV in the area of a CH, because the CHs included in the route are those that exceed the waiting time for the AUV arrival. This inter-cluster routing is performed in some instances, since the movement of AUV is optimally performed with DACP prediction. This DACP is an intelligent reinforcement learning algorithm that identifies the path by estimating the current ability of the CHs with two factors. A CH, along with its three other one-hop neighboring CHs, is taken for evaluation, and so the data can be collected from these four CHs at one time. This DACP is suitable for performing continuous control tasks, and it concurrently learns the policies. The first and second factor, \(F_{1}\) and \(F_{2}\), are estimated as:  
\[F_{1}=(Bf,(C_{T}+V_{T}+W_{T})) \tag{17}\]  
\[F_{2}=(S_{s},D_{s}) \tag{18}\]  
The buffer of the CHs is represented as \(Bf\), computation time as \(C_{T}\), visiting time as \(V_{T}\), waiting time as \(W_{T}\), RSSI as \(S_{s}\) and data size as \(D_{s}\). Using the di-factors, a state value function and soft Q-function are represented as \(V_{\psi}(S_{t})\) and \(Q_{\theta}(A_{t})\). The default parameters involved in the network are \(\psi\), \(\theta\) and \(\phi\); here, the policy in the actor-critic network is given as \(\pi_{\phi}(A_{t}|S_{t})\). The states \(S_{t}\) are defined from the estimated factors \(F_{1}\) and \(F_{2}\) of the CH. The state-value function is formulated as:  
\[V_{\psi}(S_{t})=\mathbb{E}_{A_{t}\sim\pi}[Q(S_{t},A_{t})-log\pi(S_{t}|A_{t})] \tag{19}\] \begin{table}
\begin{tabular}{c c c c c} \hline \(A_{EC}\) & \(RF_{s}\) & \(S_{sp}\) & \(N_{e}\) & **Output** \\ \hline
0.5–1 & 0.5–1 & 0.5–1 & 0.5–1 & Medium \\
0.5–1 & 0.5–1 & 0.5–1 & 0–0.5 & Low \\
0.5–1 & 0.5–1 & 0–0.5 & 0.5–1 & High \\
0.5–1 & 0.5–1 & 0–0.5 & 0–0.5 & Medium \\
0–0.5 & 0.5–1 & 0.5–1 & 0–0.5 & Very low \\
0–0.5 & 0.5–1 & 0–0.5 & 0.5–1 & Medium \\
0–0.5 & 0–0.5 & 0–0.5 & 0–0.5 & Very low \\  & & 0–0.5 indicates low, and 0.5–1 indicates high & \\ \hline \end{tabular}
\end{table} 
Table 1: Fuzzy membership functions. The \(\pi\) is the policy; here, including an approximate into the state value is not required due to the formulation of the soft-value function. This soft-value function is trained and then the gradient is estimated.