# Study on the Method of Moving Load Identification Based on Strain Influence Line
## 2 Theoretical Background
### Simulation Results Analysis  
#### 3.2.1 Analysis of the Identification Results without Considering the Load Transverse Distribution  
For the identification method without considering the load transverse distribution, it is only necessary to know the mid-span strain integral coefficient \(\alpha\) of a single beam. Firstly, the following simulation conditions were carried out: (1) Vehicle driving in the middle of the first lane with 10 kg weight at 1 m/s, (2) vehicle driving in the middle of the second lane with 10 kg weight at 1m/s, (3) vehicle driving in the middle of the third lane with 10 kg weight at 1m/s. According to each working conditions, the corresponding mid-span strain influence line (1#, 3#, 5# beam) were obtained, as shown in Figure 7, then the corresponding strain integral coefficient was obtained in Table 1.  
Figure 5: (a) Bridge model, (b) bridge section size, (c) vehicle load (unit: mm).  
Figure 6: Vehicle load position.  
Figure 8 shows the load identification results obtained according to the strain integral coefficient. Taking the strain integral coefficient of 3# beam as an example, it can be seen that the identification error was smaller than 10% when the vehicle load drove in the second lane. Especially when the vehicle load drove in the middle of the second lane, the error was almost zero. However, the identification error was large when the vehicle drove in the first and third lane. Therefore, it was not suitable for load identification. For the load identification results obtained according to the strain integral coefficient of 1# beam and 5# beam, the identification error was close to zero when the vehicle load drove in the middle of the first and third lane. However, the identification accuracy was still poor when the vehicle load drove in the second lane.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Vehicle Driving Position**} & \multicolumn{2}{c}{**The Middle of the**} & \multicolumn{2}{c}{**The Middle of the**} & \multicolumn{2}{c}{**The Middle of the**} \\  & **First Lane** & **Second Lane** & **Third Lane** \\ \hline Beam number & 1\# & 3\# & 5\# \\ Total weight (kg) & 10 & 10 & 10 \\ The integral value of strain & & & \\ influence line (10\({}^{-6}\) m) & 14.46 & 7.57 & 13.48 \\ Strain integral coefficient (10\({}^{-8}\)) & 14.75 & 7.73 & 13.75 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The strain integral coefficient.  
Figure 7: The middle-span strain influence line of (**a**) 1# beam, (**b**) 3# beam, (**c**) 5# beam.  
the vehicle load drove in the left or the right line. In addition, the farther away from the vehicle position of coefficient calibration, the worse the identification accuracy was. In summary, the load identification accuracy was closely related to the driving position of the vehicle load when the influence of load transverse distribution was not considered. The identification accuracy was relatively high when it was close to the vehicle position of coefficient calibration, conversely, the identification accuracy was poor. Therefore, it was no longer suitable for load identification.