# Asphalt Pavement Transverse Cracking Detection Based on Vehicle Dynamic Response
## 5 Data Analysis and Discussion  
Based on the optimized STFT algorithm, the study chooses 30 manually labeled samples (transverse crack: 15, normal: 15) to explore their time-frequency features. It was found that the power spectral density of the mutation feature caused by transverse cracks was above 100 dB/Hz (yellow highlight entry). While the normal pavement samples are below 80 dB/Hz (Figure 8). However, it was noted that the highlights of the three crack samples are not obvious. This results in an unreliable judge when only a feature has been mutated. The STFT algorithm demonstrates time-varying characteristics of the frequency domain brought about by signal mutations. A mutation at the cracked section causes a change in a certain frequency range. To verify this idea, we convert a two-dimensional time-frequency picture (the \(x\)-axis is time, the y-axis is frequency, and color depth denotes the power spectrum density) into a three-dimensional time-frequency map (the \(x\)-axis is time, the y-axis is frequency, and the \(z\)-axis is the power spectrum density). It was found that there are obvious differences between the cracked section and the normal section in the three-dimensional time-frequency diagram (Figure 9). All of the signals have a characteristic frequency range in the 0-50 Hz range. The PSD in the 0-0.1 s range is less than 30 dB/Hz for a transverse crack sample. When a signal is mutated (0.1-0.2 s), the power spectral density in the 0-50 Hz range increases rapidly, up to 102.2 Hz. As the mutation disappears (0.2-0.36 s), the PSD returns below 30 dB/Hz. The maximum power spectral density for the entire signal segment range (0-0.36 s) for the intact pavement samples is 42.5 dB/Hz. The maximum power spectral density (PSD\({}_{\text{max}}\)) of the STFT is expected to be a good classification indicator. To validate the above idea, the PSDmax of 15 transverse cracks and 15 normal pavements were calculated as shown in Figure 10. As can be seen in Figure 10a, the transverse crack's PSDmax distribution range is from 100 dB/Hz to 340 dB/Hz, with a maximum of 338.7 dB/Hz and a minimum of 102.2 dB/Hz. As shown in Figure 10b, the normal pavement's PSDmax distribution range is from 29 dB/Hz to 63 dB/Hz, with a maximum of 62.0 dB/Hz and a minimum of 29.8 dB/Hz. The mean, standard deviation, and variation coefficients are shown in Table 3. Based on comparison of the standard deviation and coefficient of variation, the transverse crack's PSDmax distribution is more discrete than the normal pavement. Figure 8: The 2D STFT spectrogram at cracked section or normal section. (**a**) Transverse crack; (**b**) normal pavement. In addition, it can be seen that the minimum value of the transverse crack's PSDmax is greater than the maximum value of the intact pavement sample, PSDmax. So, it is reasonable to select the PSDmax as a classification indicator. It should be noted that the standard deviation of the crack's PSDmax is much higher than that of the normal pavement. This can be explained by the field measurement affecting the crack's vibration response more. This is due to the varying degrees of pavement cracking (length, width, and depth), which leads to different transient shocks when the vehicle passes. This also results in a different degree of signal mutation at the cracked sections. This variability is strengthened by pavement roughness and the influence of sand and gravel. A sample of normal pavement's signal features is likely to be similar to transverse cracks, especially in the time-frequency domain. A cracked section is more easily mistaken for a normal section because it is difficult to cause a significant signal mutation due to its poor level. This ignores the structural damage of the pavement at the site and will make it difficult to carry out conservation activities in time. Figure 10: PSDmax at cracked sections and normal sections. (**a**) Transverse crack; (**b**) normal pavement.