# Temporal Convolutional Network-Based Axle Load Estimation from pavement Vibration Data
## 3 Field Testing
### Data Collection  
At Site 1, 15 test scenarios were conducted based on different speeds and magnitudes of mobile loads, as shown in Tables 1 and 2. The DOVS-based vibration system was used to measure concrete pavement vibration, while the FBG sensor was used to measure dynamic strain for each mobile load. The sampling frequency was set at 2.5 kHz, and the measured vibration and strain were recorded as a time history showing the variation during loading. This resulted in the collection of 2230 data samples. When pavement conditions were unchanged, the variation in mobile load applied at a specific position was proportional to the variation in dynamic strain measured at that position. Thus, the measured time history of strain for each data sample could be considered the ground truth for the time history of mobile load. After random windows were selected and down-sampled, a total of 6690 samples were obtained. The training set and the test set were divided by a ratio of 4:1. A uniform sampling of 80% of all load level and load speed samples was used as the training set to ensure a balanced sample distribution. Finally, the training set totaled 5352 samples and the test set totaled 1338 samples. Figure 5 presents the raw vibration signals and corresponding ground-truth mobile load signal during impact. It is observed that the fluctuation time range of the vibration signals is similar to that of the mobile load signal. The vibration signal amplitude increases as the load gets heavier and is more volatile as the loading speed increases too. This may be related to the amplitude of the dynamic response of the pavement influenced by external forces and loading rates. At Site 2, the DOVS-based vibration sensing system measured vibrations induced by 335 vehicles on the concrete pavement with a sampling frequency of 2500 Hz. The axle configurations of these vehicles are shown in Table 3. When a vehicle passed by, the vibration sensing system measured the pavement vibration, and later, the commercial WIM system recorded the axle weights. These data were collected as samples. There were 335 data samples collected at Site 2. It should be noted that the ground truth of traffic loads should be in the form of time history, but the commercial WIM system was only able to provide a number representing the axle weight. Therefore, based on the recorded loading period, Gaussian distribution fitting was employed to expand the measured number to a time history. Then, the expanded time history was recorded as the ground truth of traffic loads. There were three rows of sensing loops that provided vibration data, and as they were close to each other, the ground truth of traffic loads was similar. Therefore, each row of vibration data was treated as an independent sample. The training set and the test set were also divided by a ratio of 4:1. The samples were evenly sampled according to vehicle type. The training set had 268 samples and the test set had 70 samples. After preprocessing \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Load Level**} & **No. 1 Axis** & **No. 2 Axis** & **No. 3 Axis** & **No. 4 Axis** & **No. 5 Axis** & **No. 6 Axis** & **Average Axle Load** \\  & **(kg)** & **(kg)** & **(kg)** & **(kg)** & **(kg)** & **(kg)** & **(kg)** \\ \hline \(1\) & 2200 & 1690 & 1880 & 2020 & 2240 & 1750 & 1963.33 \\ \(2\) & 5150 & 4770 & 4910 & 5080 & 5250 & 4730 & 4981.67 \\ \(3\) & 6180 & 5120 & 5990 & 5830 & 6130 & 5630 & 5813.33 \\ \(4\) & 6700 & 6720 & 6900 & 6450 & 6990 & 5820 & 6596.67 \\ \(5\) & 7800 & 7080 & 7230 & 7470 & 7000 & 6900 & 7246.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Load scenarios at Site 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No** & **Load Level** & **Loading Speed (m/s)** & **Percentage of Sample to the Total (\%)** & **Number of Samples** \\ \hline \(1\) & \(1,2,3,4,5\) & \(2\) & \(15\%\) & \(1004\) \\ \(2\) & \(1,2,3,4,5\) & \(4\) & \(40\%\) & \(2676\) \\ \(3\) & \(1,2,3,4,5\) & \(6\) & \(45\%\) & \(3010\) \\ \hline \hline \end{tabular}
\end{table}