## 5 Theory and Field Test Verification  
### Theoretical Experimental Research  
To verify the superiority of IPSO in solving the optimal arrangement of the microseismic monitoring network, a hypothetical artificial network was studied. For the mining working face, we assume that the X direction interval of the monitoring model is [0 m, 100 m], the Y direction interval is [0 m, 50 m], and the elevation is 200 m. The key monitoring area range is [200 m, 500 m] in the X direction, [0 m, 200 m] in the Y direction, and the elevation is 200 m. The grid spacing is 100 m \(\times\) 50 m, and the sensor arrangement elevation is 0 m. The probability of shaking at all grid nodes is 1.0. The distribution of candidate points for all 18 stations is shown in Figure 2. The key monitoring area is the yellow area in Figure 2. According to the provisions of Table 1, \(F_{Q}\) of the key monitoring area is 1.5, and the \(F_{Q}\) of other monitoring areas is 1.0. To simplify the solution process, it is assumed that all vibrations in the monitoring area can be monitored, and the expected value of the P-wave velocity is 3200 m/s. The test is divided into three schemes. Scheme I selects four candidate points from the set of the optimal network layout scheme. Scheme II selects six candidate points from the set. Scheme III selects eight candidate points from the candidate point set. The three schemes are solved by using IPSO, the simulated annealing algorithm (SA), and the exhaustive algorithm (EA), respectively. IPSO parameters are set as follows: the learning factor \(c_{1}=c_{2}=2\), the group size \(N_{pop}=100\), \(w_{0}=1\), \(C=10\), \(d_{attr}=w_{attr}=0.05\), \(h_{prop}=w_{prop}=0.05\), the end condition \(\varepsilon_{0}=0.001\), and the search times \(E_{t}=50\). The parameters of SA are set as follows: the initial temperature \(t_{0}=97\), the end temperature \(t_{f}=89.9\), and the temperature drop ratio \(\lambda=0.99\). Table 2 lists the results of different network layout schemes. It can be seen that the candidate points layout schemes show multiple increases with the increase in the number of sensors. The model solution results are shown in Table 3 and Figures 3 and 4. From the results of EA, it can be seen that, except for scheme I, which has multiple solutions, both schemes II and III have unique solutions. Since the monitoring area is a cube, it can be seen that there is symmetry among the multiple solutions through rotation. Although SA and IPSO cannot obtain all the optimal solutions, the global optimal solutions are found for the three schemes. However, more importantly, the two optimization algorithms do not significantly increase the computation time as the number of combinations increases. After the number of probes increased to eight, the time-consumption of EA increased to 261.88 s, while SA needed 37.4 s and IPSO needed 27.06 s to obtain the optimal network layout. Therefore, EA and IPSO are global in the optimization of the network optimization problem, and they are also efficient in time. As can be seen from Figure 5, for scheme I, IPSO found the optimal solution when it evolved to the 10 th generation, and SA obtained the optimal solution in the 38 th generation. In scheme II and scheme III, IPSO finds the optimal solution in the 22 nd and the 6 th generations, respectively, which are better than  
Figure 2: Distributions of candidate microseismic monitoring points. the 29 th and the 31 st generations of SA. It can be seen that the time-consumption of IPSO should be shorter. Figure 3: Network configuration results solved by EA. (**a**) Solution Results of Scheme II. (**b**) Solution Results of Scheme II. (**c**) Solution Results of Scheme III. Figure 4: Network configuration results solved by IPSO and SA. (**a**) Solution Results of Scheme I. (**b**) Solution Results of Scheme II. (**c**) Solution Results of Scheme III. Figure 6: Error evaluation of different network layout schemes. (**a**) Positioning error of Scheme I. (**b**) Positioning error of Scheme II. (**c**) Positioning error of Scheme III.