# Pavement Distress Initiation Prediction by Time-Lag Analysis and Logistic Regression
## 2 Data Preparation
### Detection of the pavement Distress Initiation  
The pavement surface photographs contain both the pavement distress information and coordinate information, which can be extracted from raw pavement surface images and raw GPS data. Raw pavement surface photographs were obtained by front-view cameras. Digital cameras were installed on vehicles' roofs, which can obtain original pictures at a resolution of 1344 \(\times\) 756 pixels. The input image pixel range is larger than the 512 \(\times\) 512 pixel range of the commonly used pavement distress image datasets to satisfy the model training and detection requirements, and a larger image pixel range can improve the recognition accuracy but lead to longer detection time, so the current pixel range is more applicable [34]. During image acquisition, vehicles drove through the whole study area daily. Raw GPS data including date, longitude, latitude, and azimuth were collected by the same vehicle. Pavement distress has been extracted from raw pictures by an automatic method. An automatic pavement distress recognition and segmentation neural network, based on the YOLO_v3 framework, was established and trained to detect pavement distress information [24; 34]. YOLO_v3 is a very widely used framework and is simple and robust enough to be used more easily in a variety of datasets, which means that the experimental procedure in this paper can be better reproduced. The YOLO_v3 framework uses pre-trained weights, while 45,788 images containing pavement distress collected in the same scenes are used for model training. The accuracy of cracks, potholes, and alligator cracks is 80.82%, 80.27%, and 91.38%, respectively, and the mAP of our model is 87.51%. Figure 1: Hourly traffic flow of a typical urban intersection. The detection results included pavement distress types (which contain transverse crack, longitudinal crack, alligator crack, and pothole) and bounding box (which part of the picture contains pavement distress), shown in Figure 3.  
Then, the latest distress pictures are matched and compared with the previous pictures as in the following steps. Step 1: Determine the picture's photographed direction. Calculate the absolute value of azimuth between the image and road direction. This paper defines road direction as the azimuth from origin to destination. Then, judge the photographed direction when the following criteria are satisfied:  
\[\textit{direction}=\left\{ \begin{aligned} &\textit{upstream},0^{\circ}< \left|\textit{azi}_{\textit{picture}}-\textit{azi}_{\textit{road}}\right|<45^{ \circ};\\ &\textit{downstream},135^{\circ}<\left|\textit{azi}_{\textit{ picture}}-\textit{azi}_{\textit{road}}\right|<180^{\circ}.\end{aligned} \right. \tag{1}\]  
where \(\textit{azi}_{\textit{picture}}\) and \(\textit{azi}_{\textit{road}}\) represent azimuth of picture and road direction, respectively. Step 2: Search the nearest picture obtained in the previous time step. For the pavement surface images in the same direction, calculate the Euclidean distance between the present pictures and images obtained last time. The previous images with the minimum Euclidean distance of the picture were set as the potential images containing initial distresses. Step 3: Determine the initial time of pavement distress. A recurrent method was adopted for determining the initiation of distress. In the recurrent method, each picture labeled as 'contain distress' was inspected by civil engineers. To identify the initiation of pavement distress, the engineers compared the present pictures to the last period pictures in the same place. The classifier rules for distress initiation include: (a) if a present picture  
Figure 2: Overview of the study area, time period, and distress initiation dataset format.