# Asphalt Pavement Transverse Cracking Detection Based on Vehicle Dynamic Response
## 7 Conclusions  
In this paper, a vehicle-cracked pavement dynamic model illustrated the pavement transverse cracking detection principle based on vehicle dynamic response. As the typical features of pavement transverse cracking cannot be revealed better in the time or frequency domain, the raw vibration signal was transformed into a time-frequency-PSD map using optimized STFT. Two key classification indices distinguished transverse cracking sections from normal sections. The detailed conclusions of this paper are as follows:  
Based on the d'Alembert principle, a vehicle-cracked pavement dynamic model was established. The model's time domain solution indicates that the vertical vibration response is affected by the characteristics of the vehicle system's driving speed, transverse cracking degree, and the vehicle-crack contact geometry feature.  
The optimized STFT algorithm parameters for detecting transverse cracking were set through a parameter optimization process. The window type was a Hanning window with a length of 32, and an overlap of 16.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **Ac** & **TPR** & **FPR** \\ \hline value & 94.62 & 92.86 & 4.80 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comprehensive evaluation indices of the classification model (%).  
Figure 16: Confusion matrix.  
It was found that the power spectral density (PSD) caused by transverse cracks was above 100 dB/Hz. The PSD at normal sections was below 80 dB/Hz. The distribution of the PSD at cracked sections is more discrete than at normal sections.  
The classification model based on the maximum power spectral density (PSDmax) and the relative power spectral density (\(\Delta\)PSD) performed well. The accuracy reached 94.96%. TPR and FPR reached 92.86% and 4.80%, respectively.  
In terms of recognition accuracy, this novel method is close to the current mainstream methods based on deep learning. In addition, this method can overcome the disadvantages of traditional signal time domain and frequency domain analysis's low accuracy. Moreover, this novel method could express small signal mutations caused by transverse cracking, including its moment.  
However, the training set used in this novel method was smaller, data processing was faster, and real-time feedback was met. It was also verified that the novel model had a better effect on pavement transverse cracking detection.  
Conceptualization, Q.Y. and W.Y. ([PERSON]); methodology, W.Y. ([PERSON]); validation, Q.Y. and W.Y. ([PERSON]); formal analysis, W.Y. ([PERSON]); investigation, W.Y. ([PERSON]); resources, W.Y. ([PERSON]); data curation, W.Y. ([PERSON]); writing--original draft preparation, W.Y. ([PERSON]); writing--review and editing, Q.Y.; visualization, W.Y. ([PERSON]); supervision, Q.Y.; project administration, W.Y. ([PERSON]); funding acquisition, W.Y. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This research was funded by the 2022 Ningbo Transportation Science and Technology Plan Project, grant number 202216.  
Not applicable.  
Data availability Statement: Data are contained within the article.  
Thanks for [PERSON]'s contributions and help on data investigations and project administration. ([PERSON], who is from the Ningbo Road and Bridge Engineering Construction Co., Ltd. Ningbo, 315000, China).  
The authors declare no conflict of interest.