# Study of the Dynamic Response of a Rigid Runway with Different Void States during Aircraft Taxing
## 4 Analysis of Results and Discussion
### Analysis of Vibration Acceleration Response Signal of Road Panel
For monitor point 3, which was located in the corner of the pavement slabs in the void area, compared with monitor points 1 and 2, from Figure 15a,b, it can be seen that the vibration acceleration signal energy was concentrated in bands 1-4, i.e., 12.5-62.5 Hz, with the WPERs of frequency bands 1 and 3 being relatively large and the sum of the WPERs of each group of frequency bands 1 and 3 all reaching more than 65% of the total energy. From Figure 15c,d, it can be seen that the WPEEs were larger in frequency bands 1-4, and the WPEEs were smaller in frequency band 0, as well as frequency bands 5-7. This indicates that the signal energy and frequency distribution were more scattered in the 12.5-62.5 Hz range, and the signal energy and frequency distribution were relatively stable in the range of 0-12.5 Hz and the high-frequency band (transverse analysis). After analyzing the wavelet packet energy of the signal at monitor point 3, the WPERs of frequency bands 1 and 3 and the WPEEs of frequency bands 1-3 were more thoroughly studied. When the pavement was slightly void, \(\xi\) decreased from 1 to 0.0001. According to Figure 15a, the WPER of frequency band 1 decreased monotonically from 51.01% to 37.84%, with a variation of 13.17%. The WPER of frequency band 3 increased monotonically from 15.16% to 21.48%, with a variation of 6.32%. According to Figure 15c, the WPEE of frequency band 1 increased monotonically from 0.3434 to 0.3677, with a variation of 0.0243, and that of frequency band 3 increased monotonically from 0.2860 to 0.3304, with a variation of 0.0444. When the pavement was seriously void, \(S_{VA}\) increased from 0 m\({}^{2}\) to 4.75 m\({}^{2}\). From Figure 15b, the WPER of frequency band 1 decreased monotonically from 51.01% to 22.91%, with a variation of 28.1%, whereas the WPER of frequency band 3 increased monotonically from 15.16% to 48.50%, with a variation of 33.34%. From Figure 15d, When \(S_{VA}\) increased from 0 m\({}^{2}\) to 4.75 m\({}^{2}\), the WPEE in frequency band 2 decreased monotonically from 0.2988 to 0.1366, with a variation of 0.1622, whereas the WPEEs of frequency bands 1 and 3 did not change monotonically, showing a monotonic increase at first and then a monotonic decrease, reaching the maximum at \(S_{VA}\) values of 3 m\({}^{2}\) and 3.75 m\({}^{2}\), respectively. This demonstrates that, as \(S_{VA}\) increased from 0 to 3.75 m\({}^{2}\), the degree of the dispersion of the vibration signal energy distribution in frequency bands 1 and 3 gradually increased. The vibration signal energy distribution tended to be stable as SVA increased from 3.75 m\({}^{2}\). For the signals collected at monitor point 3, the results of the wavelet packet energy analysis were analyzed. P\({}_{3,1}\) and P\({}_{3,3}\) represent the energy ratios of frequency bands 1 and 3. A regression analysis was performed on them with 1 and 2, respectively. The regression results are shown in Figure 16a,b. P\({}_{3,1}\) and P\({}_{3,3}\) were logarithmic with \(\xi\), and the coefficients of determination were 0.9749 and 0.9763, respectively. P\({}_{3,1}\) and P\({}_{3,3}\) had a cubic curve relation with \(S_{VA}\), and the coefficients of determination were 0.9922 and 0.9948, respectively. Figure 17 shows the change in the WPEEs of frequency bands 1-4 of the signal at monitor point 3 considering different void states. Combined with the comprehensive analyses of Figure 16a,b and Figure 17a,b, it can be seen that when the vibration acceleration monitor point was located at the corner of the plate, after the wavelet packet energy analysis of the collected signal, the DEM of the base layer in the void area decreased, and the energy ratio and energy entropy of the first and third frequency bands had obvious gradient changes, with the changing trend being monotonous. In the case of the severe void of the pavement slab, with the increase in the void area, the energy ratios of frequency bands 1 and 3 and the energy entropies of the wavelet packet of frequency band 2 changed more obviously, showing a monotonous trend.