**1. Introduction**

Moving load is the main external load acting on the bridge [1,2]. Due to the inefficient supervision of overweight vehicles, bridge collapse accidents caused by overweight vehicles have occurred occasionally in recent years [3–5]. Therefore, the accurate and rapid recognition of moving loads is beneficial to the early warning and control of the overweight vehicle, thereby ensuring the safe operation of the bridge [6,7]. Traditional moving loads identification method primarily rely on a bridge weigh-in-motion (WIM) system. However, WIM may harm the road surface, and the sensor is prone to be damaged under long-term moving load, which increases the operation and maintenance costs [8]. Therefore, it is urgent to indirectly identify the moving load using the dynamic response by a more efficient and economic method, i.e., moving load identification (MLI) methods.

MLI methods can roughly be classified into two categories, i.e., intelligent optimization methods and machine learning methods. Among them, intelligent optimization methods compute the optimal solution of the loss function to obtain the load parameters with the smallest loss function [9]. For example, Wang et al. [10] applied simulated annealing algorithm to identify multi-axis moving train loads, and the experimental results demonstrated that the proposed method exhibits excellent robustness and accuracy. Pan et al. [11] proposed a moving loads identification method based on the firefly algorithm, in which, vehicle load information can be accurately identified with only a small number of sensors. Liu et al. [12] recognized the constant component of the moving load with the help of

**Citation:** Qin, Y.; Tang, Q.; Xin, J.; Yang, C.; Zhang, Z.; Yang, X. A Rapid Identification Technique of Moving Loads Based on MobileNetV2 and Transfer Learning. *Buildings* **2023**, *13*, 572. https://doi.org/10.3390/ buildings13020572

Academic Editor: Jorge de Brito

Received: 4 January 2023 Revised: 13 February 2023 Accepted: 17 February 2023 Published: 20 February 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

particle swarm algorithm and used the hybrid measurement response to further improve the identification accuracy. Ali R. Vosoughi et al. [13] applied a genetic algorithm for moving load identification by defining a root mean square error function between the measured and calculated responses, and the results showed that the accuracy and efficiency of this method higher than the Newmark's method. Although the intelligent optimization methods can effectively obtain the moving load information from the bridge response, the optimization process often requires searching a huge solution space, which leads to computational inefficiency and is not conducive to the rapid identification of moving loads [14].

With the rapid development of artificial intelligence, machine learning (especially deep learning) has shown great advantages in feature extraction, target detection, and recognition [15], etc., and is also widely applied in moving load identification. For instance, Yang et al. [16] applied a neural network to acquire the information of moving load through structural dynamic strain and discussed the influence of activation function on identification accuracy. Zhou et al. [17] developed a moving load identification algorithm, which converted the bridge acceleration response into a two-dimensional map as the network input. Chen et al. [18] reconstructed and located impact load based on deep convolution recurrent neural network and feature learning, which avoided the infeasibility and ill-posedness of nonlinear structure when identifying random impact loads. Zhang [19] applied a long short-term memory neural network to obtain the information of moving loads through the dynamic responses of the bridge, and the results revealed that the information of the moving load can be recognized synchronously with great accuracy. The above literature confirms the great potential of machine learning methods in the accurate and efficient identification of moving loads. However, these machine learning methods often encounter a heavy computational burden, due to the large model parameters and complex network structure, which leads to an inefficient identification process.

Fortunately, lightweight convolutional neural network has a faster identification speed. Compared with traditional deep convolutional neural network models, separable convolution is used in lightweight convolutional neural network model, which greatly reduces the model parameters without sacrificing the accuracy of the model. As a lightweight convolutional neural network model with superior performance [20], the MobileNetV2 model has not yet been used in moving load identification. Therefore, this paper proposes a moving load identification method based on MobileNetV2 and transfer learning, which has faster identification speed and requires less computing resource. Concretely, the continuous wavelet transform (CWT) is first applied to convert the dynamic responses of vehicle-bridge interaction (VBI) system into images to construct the data set for the moving load identification task. Secondly, a pre-trained MobileNetV2 model is applied to the load identification task through transfer learning strategy to enhance the efficiency of the model. Then, the information of moving loads can be acquired through inputting responses of bridge into the completely trained model. Finally, the feasibility of the method is demonstrated in the numerical modeling case.

The major contributions of this paper in comparison with the published literature are summarized in the following.


This paper is organized as follows. In Section 2, the theoretical background involved in this paper is introduced. In Section 3, the process of this method is described. The case study of identification task is conducted in Section 4. In Section 5, the performance of this method is discussed and analyzed. In Section 6, several conclusions are described.
