## 3 System Models
### Sensing Coverage Model
Theorem 2: _The computational complexity of IQPSO is \(O(N^{2}oK)\)._

Proof: The calculation of \(TSCNS\) within a charging cycle needs to be for the charge of \(N\) nodes. The time complexity of the IQPSO is \(O(N^{2})\). The IQPSO takes \(O(N^{2}o)\) times to traverse the largest \(TSCNS\) of all particles in the inner, while the loop needs to be executed \(o\) times. Since the outer loop requires at most \(K\) iterations, the computational complexity of IQPSO is \(O(N^{2}oK))\). In addition, we used Matlab2021b simulation software to verify the IQPSO algorithm convergence. The simulation settings in this paper are based on [33], and the specific parameters are shown in Table 1.

As shown in Figure 1(a), the x-axis is the number of iteration steps and the y-axis represents the performance index. The IQPSO is proved to be convergent, converging to the maximum \(TSCNS\) value of 58.69 in about 12 steps. The maximum \(TSCNS\) value of the QPSO is 58.63 in about 19 steps; therefore, the convergence performance of IQPSO is better than that of QPSO. Similarly, as shown in Figure 1(b), IQPSO before iterating 12 steps \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline \(L\) & 100 \\ \(N\) & 80 \\ \(v_{c}\) & 40 \\ \(v_{cs}^{l}\) & 0.2–1.8 \\ \(e_{m}\) & 144 \\ \(v_{m}\) & 5 \\ \(v_{l}\) & 1 \\ \(E_{m}\) & 23,040 \\ \(R_{m}\) & 6 \\ \(e_{in}^{l}\) & 43.2–51.84 \\ \(K\) of the QPSO and IQPSO & 40 \\ \(o\) of the QPSO and IQPSO & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation settings. has a large error fluctuation to increase the iteration step size and thus converges to the maximum \(TSCNS\) faster. In order to make our conclusion more convincing, we have performed 20 comparison simulations, and the results are shown in the following Tables 2 and 3. The position distribution and initial residual energy of 80 nodes in 20 simulations are randomly set; therefore, the results are different each time. Finally, we averaged the results of 20 comparison simulations to obtain the performance indexes (60.25 and 59.16) and the convergence steps (12 and 17.6) of the IQPSO and QPSO algorithms, respectively. It is clear that the IQPSO is better than QPSO in convergence performance, especially for the convergence speed. ## 6 Comparative Performance Analysis

In this section, to evaluate the performance of the IQPSO algorithm, we will conduct three sets of fifty simulation tests. We analyzed the impact of the IQPSO algorithm performance on the network QSC; the average network coverage rate and the number of off-working nodes under different network scales; the MC charging powers; and the MC moving speeds, respectively. The simulation results are taken as the average of 50 tests to make the simulation results more persuasive. ### Experimental Details

In this paper, the simulation parameters are shown in Table 1, some details are supplemented. To increase the proposed algorithm's adaptability to different WRSNs, we \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline IQPSO & 9 & 12 & 15 & 8 & 11 & 14 & 13 & 11 & 10 & 15 \\ QPSO & 15 & 19 & 17 & 15 & 17 & 19 & 19 & 15 & 13 & 19 \\ \hline  & **11** & **12** & **13** & **14** & **15** & **16** & **17** & **18** & **19** & **20** \\ \hline IQPSO & 11 & 18 & 15 & 12 & 8 & 12 & 16 & 8 & 10 & 12 \\ QPSO & 21 & 22 & 16 & 17 & 18 & 15 & 19 & 16 & 19 & 21 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of convergence speed.