*5.2. Robustness Analysis*

Anti-noise ability is a key basis for judging the practicability of the method. Therefore, this section evaluates its robustness by considering the measurement noise. In this paper, to simulate the actual test environment, the following noise levels of white noise were added to the sample data. In accordance with the implementation steps of the proposed method, the training and testing of the models for the two identification tasks were carried out under different noise levels, with the same transfer process and parameter settings as in the absence of noise; acceleration is used to identify vehicle speed, and displacement is used to identify vehicle weight.

The training results of the vehicle weight identification task are shown in Figure 14. As can be seen from Figure 14, the accuracy and loss curves of the training set do not fluctuate much under different noise levels and the accuracy and loss curves of the validation set fluctuate in the first 20 epochs under 10 dB noise condition, but become smooth at 30 to 50 epochs. The models have converged after 50 epochs for different noise conditions.

The training results for the vehicle speed identification task are shown in Figure 15. It can be seen that the training set and validation set curves of vehicle speed identification and vehicle weight identification at different noise levels have the same pattern. The accuracy and loss curves of the training set do not fluctuate much. The accuracy and loss curves of the validation set have small fluctuations in the first 20 epochs under 10 dB noise conditions, but become smooth in 30 to 50 epochs.

**Figure 14.** Results of vehicle weights identification under different noise levels: (**a**) Training accuracy curves of response samples; (**b**) Validation accuracy curves of the response samples; (**c**) Training loss curves of the response samples; (**d**) Validation loss curves of response samples.

From the test results in Table 11, the identification accuracy of the test set of the vehicle weight identification task decreases and stabilizes at 98%. With the noise level increases, identification accuracy of test set in vehicle speed identification decreased slightly. The accuracy at 30 dB and 10 dB was 98%, and the accuracy of 20 dB was still 100%. It shows that there is no obvious downward trend in the accuracy of model test, and there is only a slight fluctuation. It can be concluded that the proposed method presents excellent, strong robustness.

**Table 11.** Model Identification results under different noise levels.


**Figure 15.** Results of vehicle speed identification under different noise levels: (**a**) Training accuracy curves of response samples; (**b**) Validation accuracy curves of the response samples; (**c**) Training loss curves of the response samples; (**d**) Validation loss curves of response samples.

#### **6. Conclusions**

This paper presents a moving load identification method based on MobileNetV2 and transfer learning. The performance of the proposed method is verified by the numerical simulation and parameter analysis. The main conclusions were obtained as follows:


Although this method has achieved satisfactory identification results on the established numerical scenarios, it cannot directly address cases where vehicles are distributed in multiple lanes and drive in opposite direction. In addition, for vehicles with multiple axles, it is difficult to identify the axle weight of each wheel. Therefore, the future work will focus on further improving the practicality of the proposed method.

**Author Contributions:** Conceptualization, Y.Q.; methodology, Y.Q.; software, Y.Q., Q.T. and J.X.; validation, Y.Q., Q.T. and J.X.; formal analysis, Q.T. and J.X.; writing—original draft preparation, Y.Q.; writing—review and editing, Y.Q., J.X., C.Y., Z.Z. and X.Y.; visualization, Q.T. and J.X.; supervision, Q.T. and C.Y.; funding acquisition, J.X. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Natural Science Foundation of China (grant Nos. 52278292, 51978111), Chongqing Technology Innovation and Application Development Special Key Project (grant No. CSTB 2022TIAD-KPX0205), Chongqing Transportation Science and Technology Project (2022-01), China Postdoctoral Science Foundation (grant No. 2022MD713699), Special Funding of Chongqing Postdoctoral Research Project (grant No. 2021XM1016), and Chongqing Zhongxian Science and Technology Plan Project (grant No. zxkyxm202202).

**Data Availability Statement:** Data available on request, due to restrictions.

**Conflicts of Interest:** The authors declare no conflict of interest.
