## 4 Actuators/Sensors Position Configuration
### Location Optimization Design Based on Improved PSO
The linear adaptive PSO algorithm adopts the form of piecewise function, that is, when the number of iterations is less than n times, the value of \(\omega\) decreases linearly. When the number of iterations is greater than \(N\), the value of \(\phi\) is adjusted in real time with the fitness correlation. The function segment points are matched and adjusted according to the engineering complexity, which is taken as \(n=50\). The cycle termination condition of population evolution is designed as Equation (33), that is, the standard deviation of the optimal fitness that satisfies more than 90 iterations and 30 consecutive iterations is less than 0.001. \[k\geq 90\&std(y(k-30:k))<0.001 \tag{33}\]  
The modal concentration plane in the search space is divided into nine regions, as seen in Figure 8. On the one hand, it prevents the concentration of ideal values, and on the other, it increases the algorithm's accuracy and search effectiveness. Figure 8 shows the plan division of the position selection points, where Figure 8a-c, represent the division of the rear inner surface at 20 Hz, 45 Hz and 75 Hz, while Figure 8d-f, represent the division of the ceiling at 45 Hz, 75 Hz and 157 Hz, respectively. Using the improved LA-PSO algorithm, the active control device's optimal position matching is performed, and the optimal coordinate combination as shown in Figure 9 is obtained, meaning that the objective function value is maximized when the 9 actuators/sensors are arranged at the corresponding coordinates. The system achieves the best active control result. Figure 9 shows the final actuator/sensor coordinates and corresponding modal shapes, where Figure 9a-c represent the division of the rear inner surface at 20 Hz, 45 Hz and 75 Hz, while Figure 9d-f represent the division of the ceiling at 45 Hz, 75 Hz and 157 Hz, respectively. The diagram illustrates the coincidence of the coordinate points of the device and the vibration modes of each order, in which the position of the yellow aperture is the position of the active control device, and its spatial geometric coordinate combination is  
Figure 7: PSO-based location optimization process. shown in Table 2. The analysis shows that the position of the device is close to the peak points of the main mode shapes of the body roof and rear, and there is a strong correlation between the combination distribution and the four mode shapes. The rationality of the selection of active control devices for multiorder modal compound control is verified from the point of view of geometry. Figure 8: Plane division of location selection points: rear inner surface corresponds to (**a**) f = 20 Hz, (**b**) 45 Hz and (**c**) 75 Hz; ceiling corresponds to (**d**) 45 Hz, (**e**) 75 Hz and (**f**) 157 Hz. Figure 9: Final actuator/sensor coordinates and corresponding modal shapes: rear inner surface corresponds to (**a**) f = 20 Hz, (**b**) 45 Hz and (**c**) 75 Hz; ceiling corresponds to (**d**) 45 Hz, (**e**) 75 Hz and (**f**) 157 Hz. In summary, through the improved LA-PSO adaptive optimization algorithm, combined with co-simulation, the actuator/sensor position combination with the highest efficiency for active acoustic and vibration suppression of the body structure is obtained, and a 9 \(\times\) 9 multichannel is constructed. The multichannel control system is the premise of the establishment of the active control system.