## 3 Numerical Evaluations and Experimental Analyses
### Simulation Results and Analysis  
Figure 2 shows the coverage effect of 45 nodes randomly distributed within the monitoring range. The number of nodes randomly placed in each part of the network is not equal, resulting in poor network coverage, with a coverage rate of only 72.02%. Figure 3 shows the network coverage optimization effect of node redeployment by the proposed algorithm. The nodes of a more balanced density distribution are obvious. The optimized network coverage rate reached 91.36%, with the coverage rate increasing by 19.34%. The main reason lies in node pre-coverage using the improved particle swarm  
optimization algorithm and then using virtual force to drive nodes to move toward the coverage blind spot, improving the balanced distribution of underwater wireless sensor nodes and effectively reducing the coverage hole. Figure 4 shows the comparisons of changes in coverage ratios of different coverage algorithms as the node number changes. When the node number increases from 25 to 50 in increments of 5, the network coverage increases successively. The network coverage of random node distributions increased from 43.80% to 53.05%, 57.12%, 57.96%, 72.02%, and 72.10%. We can see from the figure that the underwater node number is directly associated with network coverage. The network coverage value increases as the node number increases, improving the coverage effect of the network and meeting its coverage requirements. However, the cost of network coverage will also increase. With 45 underwater sensor nodes deployed as the research object, the coverage rates for BES, 3D-IVFA, DABVF, and the proposed algorithm are 83.28%, 88.85%, 89.31%, and 91.36%, respectively, after 100 iterations. The proposed algorithm is better than BES, 3D-IVFA, and DABVF in coverage by about 8.06%, 2.51%, and 2.05%, respectively. The above quantitative analysis shows that the proposed algorithm can greatly increase the coverage rate, which is also the embodiment of the superiority of the algorithm. The reason is that the algorithm combines the improved PSO and VFA algorithms to make use of their complementary advantages so that the layout of nodes can be adjusted quickly to obtain the best results and achieve the best coverage of the network. Figure 3: Final network layout. Figure 2: Initial network layout. In Figure 5, we can see that as the node number changes, both the initial coverage and the final coverage of the algorithm in this study show the same upward or downward trends. More nodes can achieve greater coverage, but if the nodes are randomly distributed, the expected coverage results cannot be achieved. The reason for the improved coverage after optimization of the proposed algorithm is that the improved PSO is used for node pre-coverage and virtual force is then introduced to mutate the optimal coverage position. In the subsequent iteration, the global interference mechanism is introduced to get a more suitable node position. These strategies overcome the defect that the previous algorithm easily falls into the optimal solution, accelerates the search speed of the target value, and achieves higher coverage. In Figure 6, we can see that the node number and coverage efficiency show opposite upward or downward trends. The reason is that the more the number of nodes, the greater the probability of overlap between nodes, resulting in network coverage redundancy increases, which reduces the utilization rate of the node. With 45 underwater sensor nodes deployed as the research object, the node coverage efficiency of the proposed algorithm is significantly better than those of BES, 3D-IVFA, and DABVF algorithms, which are  
Figure 4: Comparison of coverage rate optimization of different coverage algorithms with changes in node numbers. Figure 5: The relationship between coverage rate and node number in the proposed algorithm. improved by 1.36%, 1.67%, and 5.36%, respectively. From the above quantitative analysis, the proposed algorithm performs better, especially in making full use of the nodes.