## 3 Numerical Evaluations and Experimental Analyses
### Simulation Results and Analysis
After 100 iterations, 1-coverage and 2-coverage reaches 63.03% and 26.34%, respectively, while the covered hole is reduced to 8.62%. When node numbers increase from 25 to 50 in increments of 5, the coverage hole is 55.26%, 46.19%, 41.81%, 40.83%, 27%, and 27.19%, respectively. After 100 iterations, the coverage hole decreased from 33.38% to 23.05%, 17,72%,13.69%, 8.62%, and 5.40%. Data analysis shows that the proposed algorithm can expand the effective coverage area and improve the overall performance and service level of the network. This is because the  
Figure 7: Node motion trajectory and final coverage diagram. algorithm is based on the virtual force applied to the node, which promotes the underwater node to move to the uncovered area, reduces the probability of overlapping node coverage, makes it reach the optimal position effectively, and improves the node utilization rate. In addition to validating the proposed algorithm using different node numbers, coverage efficiencies, node motion trajectories, coverage holes, and other aspects, the complexity of the algorithm is also an important performance index for evaluating the quality of the coverage algorithm. The computational complexity of BES, 3D-IVFA, DABVF, and the proposed algorithm in this study is \(O(KN)\), \(O\big{(}KN^{2}\big{)}\), \(O\big{(}KN^{2}\big{)}\), and \(O\big{(}KN^{2}\big{)}\), respectively, where \(K\) represents the number of iterations the algorithm runs, and \(N\) represents the number of sensor nodes. Compared with 3D-IVFA and DABVF, the proposed algorithm improves the coverage of the network without increasing the complexity of the algorithm. Figure 11 shows changes in the average residual energy of nodes of the proposed algorithm and the other three algorithms as network time changes. We can see that the network running time and the average residual energy of nodes increase and decrease in the same direction. With 45 underwater nodes as the research object, the average residual energy of BES-DBR, 3D-IVFA-DBR, DABVF-DBR, and the proposed coverage algorithm are 57.67 J, 48.59 J, 45.30 J, and 72.74 J, respectively, when the simulation time is 200 s. The proposed algorithm is significantly better than BES-DBR, 3D-IVFA-DBR, and DABVF-DBR in terms of the average residual energy performance of nodes during network operation. At the same time, it also extends the network life cycle. This is because the algorithm adopts the DBR routing protocol, which is based on location clustering. Based on the location of nodes obtained using the coverage algorithm, the monitoring area is divided into four equal areas using clustering. To reduce information transmission energy loss between nodes, the method is first used to optimize the residual energy of nodes in each local small area. The average residual energy of nodes is then taken as the standard for comprehensive calculation. Figure 8: Comparison of average iteration steps of different algorithms. Figure 10: Comparison of \(k\)-coverage before and after optimization of the proposed algorithm. Figure 9: Three-dimensional view of four algorithms for node movement.