# Wavelet-Based Optimum Identification of Vehicle Axles Using Bridge Measurements
## 7 Field Test on a Simply Supported Stiff Concrete Bridge
### Improved Axle Detection for Multiple Presence Loading Events  
Figure 16 shows a multiple presence loading event on the bridge in traffic flow captured by the BWIM system. A truck is clearly visible in Lane 3, with a second truck to its left in Lane 2. The corresponding FAD signals are illustrated in Figure 17a. The raw Lane 2 signals, L2-FAD-1 and L2-FAD-2, show five peaks suggesting the presence of a 5-axle vehicle in that lane. Further, the spacing of these peaks suggest a vehicle of Class 9 according to the Federal Highways Administration classification system, i.e., a steer axle followed by two tandems. However, there is considerable vibration evident in the raw Lane 3 signals and a probable contribution of strain from the adjacent Lane 2 truck. As a result, the peaks corresponding to the second Class 9 truck are present but not clearly identifiable. Figure 17b shows that, after applying Shannon entropy and the correlation process, the Lane 3 wavelet coefficients provide clear peaks corresponding to each of the five axles. However, it is found that there are two small peaks caused by the bridge vibration between tandem wheels in L3-FAD-2, similar to the peak caused by the first axle, which may interfere with axle identification. Therefore, factors such as bridge vibration, multiple presence, low signal-to-noise ratio and even vehicle deviation within its lane, may negatively impact on the system's ability to identify the passing axles. However, the proposed wavelet-based approach has shown robustness in terms of measurement noise in in the example of Figure 13.  
Table 4 presents axle spacing errors for a sample of ten calibration vehicle and lane combinations. It should be noted that the greatest percentage errors (7.0% and 7.2%) are in the rear tandem of the 5-axle vehicle where the actual spacing is small (1.32 m). The mean and standard deviation of errors in (A2-A3) are 1.45% and 4% respectively, and those for (A4-A5) are 5.24% and 2.6%, respectively. For the larger spacings, there remain some significant errors--see, for example, an error of 5.1% in Run 10. The mean and standard deviation of errors in (A1-A2) are 1.79% and 1.26% respectively, and those for (A3-A4) are 0.18% and 0.47% respectively.  
Figure 17: Case study of multiple presence loading event: (a) raw signals; (b) optimal wavelet coefficients.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Item**} & **Ade** & \multirow{2}{*}{**Spacing**} & \multirow{2}{*}{**Run 1**} & \multirow{2}{*}{**Run 2**} & \multirow{2}{*}{**Run 3**} & \multirow{2}{*}{**Run 4**} & \multirow{2}{*}{**Run 5**} & \multirow{2}{*}{**Run 6**} & \multirow{2}{*}{**Run 7**} & \multirow{2}{*}{**Run 8**} & \multirow{2}{*}{**Run 9**} & \multirow{2}{*}{**Run 10**} & \multirow{2}{*}{**Mean**} & \multirow{2}{*}{**SD**} \\  & **Spacing** & & & & & & & & & & & & & & \\ \hline Truck no. & & 3 & 3 & 3 & 3 & 4 & 2 & 2 & 2 & 1 & 1 & 1 & / & / \\ Lane & & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 2 & / & / \\ Speed (m/s) & & 30.5 & 30.5 & 29.9 & 30.5 & 30.1 & 27.7 & 28.2 & 27.8 & 28.2 & 28.2 & \\ \hline Error in axe & A1-A2 & \(-\)0.50\% & \(-\)1.10\% & \(-\)1.00\% & \(-\)1.80\% & \(-\)0.30\% & \(-\)3.80\% & \(-\)3.70\% & \(-\)3.10\% & \(-\)2.00\% & \(-\)0.60\% & \(-\)1.79\% & 1.26\% \\ spacing (relative & A2-A3 & 3.60\% & 0\% & \(-\)2.70\% & \(-\)2.40\% & \(-\)4.04\% & \(-\)4.07\% & \(-\)4.50\% & 3.40\% & 4.70\% & 5.10\% & 1.45\% & 4.00\% \\ to static & A3-A4 & \(-\)0.40\% & \(-\)0.80\% & \(-\)0.30\% & 0\% & 0.60\% & / & / & / & / & \(-\)0.18\% & 0.47\% \\ measurement) & A4-A5 & \(-\)5.40\% & \(-\)0.20\% & \(-\)7.20\% & \(-\)7.00\% & \(-\)6.40\% & / & / & / & / & / & \(-\)5.24\% & 2.60\% \\ \hline \hline \end{tabular} Note. “Ai-AJ” means spacing between axes 1 and \(\lx@sectionsign\) SD represents the standard deviation.  
\end{table}
Table 4: Vehicle speeds and errors in axe spacings.