*3.2. 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 α 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 7.** The middle-span strain influence line of (**a**) 1# beam, (**b**) 3# beam, (**c**) 5# beam.



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 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.

3.2.2. Analysis of the Identification Results Considering the Load Transverse Distribution

For the identification method considering the load transverse distribution, it was necessary to obtain the strain integral coefficient of each beam by Equation (14). Firstly, the following simulation conditions were carried out with the vehicle load of 10 kg: (1) Vehicle driving in the left of the first lane, (2) vehicle driving in the right of the first lane, (3) vehicle driving in the middle of the second lane, (4) vehicle driving in the left of the third lane, (5) vehicle driving in the right of the third lane. According to Equations (13) and (14), the strain integral coefficient of each beam was obtained (as shown in Table 2). It can be seen that the strain integral coefficient of each beam bottom was basically proportional to the reciprocal of the stiffness, and the reason for the error was that the load identification method considering the load transverse distribution, which ignores the influence of spatial

effect and diaphragm in the theoretical derivation. The obtained strain integral coefficient was used to identify the load of the test sample, and the results are shown in Figure 9. It can be seen that the identification accuracy was very high no matter where the vehicle was, and the error was close to zero. Therefore, compared with the identification method without considering the load transverse distribution, the identification method considering the load transverse distribution has obvious advantages.


**Table 2.** The mid-span strain integral coefficient of each beam bottom.

**Figure 9.** Identification results considering the load transverse distribution.

3.2.3. Analysis of the Anti-Noise Performance

Two kinds of noise (5% and 10%) were added to the numerical simulation to verify the anti-noise performance of the method. The strain values of the test sample were extracted, and 5% and 10% of the noise were added as condition 1 and condition 2, and the noise can be expressed as:

$$
\varepsilon'(\mathbf{x}) = \varepsilon(\mathbf{x}) + \beta \cdot rand(\mathbf{n}) \cdot var(\mathbf{x}) \tag{16}
$$

where *ε'*(*x*) is the strain output after the added noise, *ε*(*x*) is the original strain input, *β* is the noise level, rand is short for random and *rand*(*n*) is a set of values with the mean is 0 and the variance is 1, var is short for variance and *var*(*x*) is the variance of the original strain input.

When the vehicle load (20 kg) drives in the middle of the second lane, the mid-span strain time history with different kinds of noise of 3# beam bottom is shown in Figure 10. It can be seen that there is only a slight fluctuation of the strain output when the noise level is 5%, which can better simulate the environmental noise. The strain output has an obvious difference for the original value when the noise level reaches 10%, both of these two working conditions are representative. The load identification results with different levels of noise are shown in Figure 11. It can be seen that the load identification error with different noise levels was slightly larger compared with the no-noise condition. The load identification errors were nearly the same when the noise levels were 5% and 10%. In addition, the overall error was smaller than 0.5%, which showed a good identification accuracy. Therefore, the method can keep the identification accuracy under different kinds of noise, and the noise reduction for the following analysis processing can be ignored.

**Figure 10.** The mid-span strain time history of 3# beam with (**a**) 5% noise, (**b**) 10% noise.

**Figure 11.** Identification error under different levels of noise with the load of: (**a**) 20 kg, (**b**) 30 kg.
