## 4 Selection and Simulation Analysis for Wavelet Packet
### The AVC Simulation Analysis for MIMO System  
In Section 4.1, the optimal wavelet base of the multi-frequency input signal is chosen by simulation. On this basis, in order to verify the effectiveness and control effect of the M-FxLMS and WPTDDM-FxLMS algorithms, the vibration isolation platform in Figure 1 is taken as the research object, and the offline identification is carried out to acquire four primary paths and sixteen secondary paths, and these models are 500-order and 128-order FIR filters, respectively. In this process, in order to improve identification accuracy and speed up convergence, a low-band white noise excitation is input to the upper-layer exciter and the four integrated actuators in sequence, and the noise and the error signals are synchronously collected. The identification results are presented in Figures 8 and 9, respectively. Based on the above analysis, the \(\hat{P}_{p1}(n)\),\(\hat{P}_{p2}(n)\), \(\hat{P}_{p3}(n)\), and \(\hat{P}_{p4}(n)\) are the identification results for the primary path in Figure 8, and the other ones are shown for the secondary path in Figure 9. Among them, \(\hat{S}_{ij}(n)  
ficients of the main secondary path are slightly larger than those of the other non-adjacent secondary path, so the main diagonal identification for the secondary paths dominates the control process. However, the coupling effects of other non-adjacent secondary paths also cannot be overlooked, which is caused by the coupling effect between the non-proximity sensors and actuators. On this basis, with the combination of the offline identification in Figures 8 and 9, the numerical simulations are carried out to verify two algorithms with the sym20 wavelet base and 37 Hz/60 Hz/110 Hz excitation comprising white noise, and the control effect in 1#-4# error signals are shown in Figures 10-13 and Table 1 below. Figure 9: _Cont._  
Figure 11: (**a**) The time domain acceleration signal in measuring point 2#, (**b**) The acceleration signal spectrum in measuring point 2#. Figure 10: (**a**) The time domain acceleration signal in measuring point 1#; (**b**) the acceleration signal spectrum in measuring point 1#. Figures 10-13 show the comparisons in error signals 1\(\#\)-4\(\#\) for passive vibration isolation, the M-FxLMS and the WPTDDM-FxLMS algorithms, respectively. Table 1 shows the damping effect for each line spectrum. It can be seen that two algorithms have a certain effect on the time domain, while the coupling paths led to a slowing convergence and an inconspicuous control effect for the traditional algorithm on each measurement point. In particular, the vibration is even intensified in error signal 1\(\#\), which is mainly due to the failure of the 60 Hz and 110 Hz line spectrum vibration. Compared with passive vibration isolation, the traditional algorithm obtains 7.14 dB, \(-1.55\) dB, \(-2.37\) dB; 9.70 dB, 5.70 dB, 5.99 dB; 7.14 dB, 8.76 dB, 10.73 dB; and 9.61 dB, 1.47 dB, 3.05 dB at the three line spectrum in each error signal, respectively. While the improved algorithm obtains 14.97 dB, 27.86 dB, 10.73 dB, and 9.61 dB, 1.47 dB, 3.05 dB at the three line spectrum in each error signal, respectively, while the improved algorithm obtains 14.97 dB, 27.86 dB, 10.73 dB, and 9.61 dB, 1.47 dB, 3.05 dB at the three line spectrum in each error signal, respectively. While the improved algorithm obtains 14.97 dB, 27.86 dB, 10.73 dB, and  
21.14 dB; 21.05 dB, 36.16 dB, 32.52 dB; 16.96 dB, 33.58 dB, 29.52 dB; and 16.98 dB, 20.27 dB, 20.39 dB, respectively. Obviously, the M-FxLMS algorithm has a better effect at 37 Hz in error signals 1#-4#, while its effect at 60 Hz and 110 Hz is more general. The average attenuation is 8.39 dB, 3.59 dB, and 4.35 dB in the three line spectrum. Correspondingly, the WPTDDM- FxLMS algorithm has compensated for the path secondary coupling and simplified the system into a parallel single-path control loop; every error signal has a better control effect. The average attenuation is 17.49 dB, 29.46 dB, and 25.89 dB in the three line spectrum, respectively.