*4.2. Vehicle Weight Identification*

Acquisition of vehicle weight information is critical to the safe operation of bridges. In this section, vehicle weight is classified into 5 categories from light to heavy (i.e., A, B, C, D, E), and the vehicle weight classification table is shown in Table 1.

**Table 1.** Classification of vehicle weight.


A total of 500 weight samples are randomly generated, including 100 samples per grade. Then, the bridge responses of each weight sample are calculated when both the speed and road roughness class are fixed. By the aforementioned preprocessing procedure, the response of the VBI dynamic system is converted into images, which were divided into training set, validation set and test set for model training, selection, and evaluation, respectively. Figures 6 and 7 show the displacement sample and acceleration sample images corresponding to five randomly selected vehicle weights, respectively. Visible discrepancy

can be observed from those images, which suggests the possibility of accurate identification results. Then, those samples are used as the input of the network model for model training and vehicle weight identification evaluation.

**Figure 6.** Displacement sample images of five randomly selected vehicle weights.

**Figure 7.** Acceleration sample images of five randomly selected vehicle weights.

The trained MobileNetV2 model is used to identify vehicle weight information. Because the data characteristics of the target domain are quite different from those of the source domain, the MobileNetV2 model is transferred in the form of fine-tuning. The first 12th Bottlenecks of the MobileNetV2 model are frozen, the rest of the bottlenecks are retrained, and the original 1000-class target classifier are replaced with the 5-class target classifier required for moving load identification in this paper.

In this paper, the stochastic gradient descent algorithm is used to train the model. The learning rate is set to 0.0001. According to the scale of sample data, batch size is set to 64 and epoch is set to 50. Based on Pytorch 2.0, the MobileNetV2 model is trained under the operating system of Windows 10 and CPU of AMD Ryzen 53550H @ 2.10 GHz.

The accuracy and loss curves of the model training to convergence process are shown in Figure 8, and the accuracy and loss at the end of training are shown in Table 2. The vehicle weight is identified by using the test set samples. The identification results and confusion matrix are shown in Table 3 and Figure 8. After careful analysis of Figures 8 and 9 and Tables 2 and 3, the following conclusions can be drawn:


small number of samples. The above analysis shows that the information of vehicle weight is most efficiently identified from displacement responses.

**Figure 8.** Results of vehicle weights identification: (**a**) Training accuracy curves of response samples; (**b**) Training loss curves of the response samples; (**c**) Validation accuracy curves of the response samples; (**d**) Validation loss curves of response samples.


**Table 2.** Train results of vehicle weights identification after 50 epochs.

**Table 3.** Identification results of vehicle weights.


**Figure 9.** Confusion matrix for vehicle weight identification results: (**a**) Test results of acceleration samples; (**b**) Test results of speed sample; (**c**) Test results of displacement sample.
