## 4 Simulation Analysis of 3D Network Deployment Experiments  
Generally, one sensor node will include the given sensors and movement devices (such as GPS and UAV). It will have a corresponding sensing radius. Once the target region is determined, a deployment algorithm is needed to dynamically deploy all sensor nodes to the specified positions. Since we mainly concentrate on a large-scale WSN application, as for all simulation experiments in this paper, the number of sensor nodes was set to be \(N=3000\) in the whole target space. Furthermore, the initial parameters were chosen based on the fundamental experiments by [PERSON] and [PERSON] [30]. The typical settings are \(Q=15,700e\), \(m=5.2\times 10^{-13}\) kg, \(v=2.7\) s\({}^{-1}\), \(k=2.4\times 10^{-13}\) kg/s\({}^{2}\), \(\lambda_{D}=0.0526\)\(\upmu\)m, and \(R_{S}=\sqrt{3}\lambda_{D}\). In most WSN applications, sensor communication and the corresponding routing protocol affect system performance, so they are very important topics in theoretical modeling and field tests. In this paper, we do not consider any communication and mechanical parts since our VFA-DP-3D is a theoretical node-deployment solution. However, in real applications, users can easily obtain the exact node positions based on the 3D coordinates in the target region to achieve the real node deployment. Firstly, Figure 2a-c give one typical case result of the final network deployment structure for a 3D large scale WSN application, such as the 3D node diagram, the 3D network topology and the 3D ball diagram, respectively. We also present two dimensional projection of the whole 3D network on the \(XoY\), \(XoZ\) and \(YoZ\) planes, as shown in Figure 2d-f. Generally, the overall network structure is spherical. It can be seen that, from the network topology and ball diagram, the distribution of the three dimensional spherical node network is relatively uniform. However, it still needs further evaluations for the detailed performance of the network deployment. Figure 3 shows the variation of the total moving distance from all sensor nodes depending on the calculation time steps. During the 0 to 1000 time steps, the node moving distance increases very fast because all nodes are adjusting the network structure under the action of deployment algorithm. After 1500 time steps, it tends to stabilize and grow slowly. The network deployment has been roughly completed, after which the nodes can adjust positions gently to achieve a better network state and finally reach a convergence state around 2500-3000 steps. Figure 4 gives the variation of the system utilization depending on the calculation time steps. It increases at the first 0-500 time steps. The reason is that, with the progress of the algorithm, all nodes become sparse first and a certain distance is maintained between all nodes. After 500 steps, the system utilization decreases. It can be inferred that the deployment of nodes is more regular and has a certain contraction trend, After 1500 steps, the network deployment tends to be stable, but there are still some small fluctuations. The whole 3D network reaches a convergence state after 2500-3000 steps and the utilization rate is about 0.73. It should be noted that the convergence of the system utilization is very consistent with that of the moving distance, around 1700 time steps, which can also confirm that these two performance evaluations are correct. Figure 3: The variation of the total moving distance from all sensor nodes depending on the calculation time steps. Figure 2: (**a**) 3D nodes diagram. (**b**) 3D topology. (**c**) 3D balls diagram. (**d**) The projection of the XoY plane. (**e**) The projection of the XoZ plane. (**f**) The projection of the YoZ plane. As for the system coverage rate, Figure 5 presents its variation as a function of the calculation time steps. It can be observed that the coverage rate was only 0.1 at the beginning. At 0-500 steps, the coverage rate slightly decreases and then increases.