## 4 Analysis of Low Velocity Impact Experimental Results  
### Establishment of a Low Velocity Impact Energy Feature Set for Variable Thickness Laminates  
Because the classical spectrum analysis can provide less effective signal feature information and more aliasing, the improved whitening EMD can be used to analyze the impact signals of variable thickness composite laminates. Taking the impact signals at position a, b, c, and d in Figure 6 as an example. Figure 7 shows the decomposition result of the whitening EMD algorithm, from the above to bottom are the IMF components obtained after decomposition and one residual component. Cross-correlation calculation of each order IMF component with the impact response signals shown in Figure 5(a) is carried out respectively, and get the following conclusion in Table 4: The correlation coefficient \(q\) of the first three components of whitening EMD algorithm is relatively larger, and the coefficients are all less than 0.1 from the first four components onward; all the components of the whitening EMD algorithm better cover the frequency range of the band where the original signal is located and are more independent. Figure 6: Impact response signals and spectrogram of sensor No. 5 with 2 J.  
Spectral analysis of the first three components of the whitening EMD algorithm is shown in Figure 8. The spectrogram shows that: (1) The trend of the change of the sensor spectrum and the distance between the sensor position and the impact point is basically the same, and the thickness of the laminate at the position where the sensor is located has the same tendency as the change of the sensor spectrum; (2) The frequency range of the band is gradually reduced from the high frequency component to the low frequency component, and the low frequency amplitude of the high frequency component is lower than the corresponding amplitude of the low frequency component; (3) The peak number of high frequency part of the spectrum increases with the decrease of the thickness of the \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline
**IMF1** & **IMF2** & **IMF3** & **IMF4** & **IMF5** & **IMF6** & **IMF7** & **IMF8** & **IMF9** & \(r\) \\ \hline
0.4013 & 0.2785 & 0.2130 & 0.0916 & 0.0852 & 0.0747 & 0 & 0 & 0 & 0.0365 \\
0.3822 & 0.2857 & 0.2219 & 0.0963 & 0.0817 & 0.0709 & 0 & 0 & 0 & 0.0348 \\
0.3276 & 0.2449 & 0.1901 & 0.0911 & 0.0786 & 0.0693 & 0.0447 & 0 & 0 & 0.0298 \\
0.2548 & 0.1905 & 0.1479 & 0.0709 & 0.0611 & 0.0539 & 0.0384 & 0.0317 & 0.0287 & 0.0232 \\ \hline \end{tabular}
\end{table} 
Table 4: Correlation table for each order IMF of the whitening EMD algorithm. Figure 7: The whitening EMD algorithm component graph of the impact signals at point a, b, c, d.  
laminate at the position where the sensor is located, which is related to the characteristics of variable thickness composite laminates. For example, the layer thickness of the laminate at the impact points a, b, c, d were 45.25 mm, 46.25 mm, 45.75 mm, 45.25 mm, then the peak number of high frequency component of impact signals were 4, 2, 3, 4 (Due to the fact that the aliasing condition of the \(S_{1}(t)\)-component, i.e., IMF1, still exists, the number of peaks is obtained from the \(S_{2}(t)\)-component, i.e., IMF2, and the threshold for defining the peak value is \(f_{k}/a\)). Therefore, by using the improved whitening EMD algorithm, the impact energy feature extraction of variable thickness composite laminate can be better; and need to select a component \(S_{3}(t)\) with larger spectral correlation and less aliasing to extract the spectral feature peak \(f_{k}\). Take the sensor network signals at the impact point (60 mm, 160 mm) with three impact energies (1 J, 2 J, 3 J) in Figure 5 as an example, the signal is whitening EMD decomposed, and obtain the sets of integrated thickness coefficient \(J_{a1}\), \(J_{a2}\), \(J_{a3}\) from the peak number sets \(B_{a1}\), \(B_{a2}\), \(B_{a3}\) when the impact energy is 1 J, 2 J and 3 J, respectively.