**3. The Proposed Method**

This paper proposes a moving load identification method based on MobileNetV2 and transfer learning, which identify the moving load information from responses of bridge, respectively. The training of DCNNs needs to optimize a large number of parameters and construct sufficient samples, and it will take a lot of time to train the model from scratch. Therefore, this paper adopts transfer learning strategy. The implementation process of this method is shown in Figure 4, including the following steps:

**Figure 4.** Overview of the proposed method.

(1) Responses acquisition and pre-processing. By solving the VBI dynamic equation, the responses of bridge corresponding to different vehicle parameters are obtained. In order to meet the input requirements of DCNN, the CWT is applied to transform the response into a time-frequency map. The formula of CWT is as follows:

$$WT(a,b) = \frac{1}{\sqrt{a}} \int\_{-\infty}^{\infty} x(t) \cdot \psi\left(\frac{t-b}{a}\right) dt\tag{13}$$

where *a* is the scaling factor which can control the expansion of wavelet, *b* denotes the shifting factor that identifies its location, and *ψ* denotes the mother wavelet. In this paper, Complex Morlet wavelet is used as the mother wavelet *ψ* because it has good resolution in both time and frequency domains [36]. Both the scaling factor *a* and the shifting factor *b* are set to 3.

(2) Dataset construction. The size of normalized image samples is adjusted to the input size of the MobileNetV2 model. On this basis, all image samples are labelled with the corresponding VBI system parameters, thus forming the sample library of displacement, velocity, and acceleration responses for the moving load identification task. Then, the samples are divided into the training set, validation set and test set with the ratio as 8:1:1. The network is trained by the training set, the network is verified by the validation set, and the performance of the network is evaluated by the test set.


#### **4. Case Study**

In order to verify the feasibility of the proposed method, the VBI system with single degree of freedom is taken as the object in this paper. According to the VBI dynamic equation, a sufficient sample database is constructed to perform moving load identification tasks.

#### *4.1. The Numerical Model*

In this paper, a 30 m concrete simply supported, single-span bridge is established to verify the method, as shown in Figure 5. The main beam is simulated by beam188 element [37–39] with concrete specification of C50. The elastic modulus is 3.40 × <sup>10</sup><sup>4</sup> MPa, and Poisson ratio is 0.2, mass density is 2600 kg/m3. The single-wheeled vehicle model is simulated by spring element. The spring stiffness of vehicle is set to *kv* = 190 kN/m and the damping of the vehicle is *cv* = 5 kN·m/s. The information for the vehicle is designed according to the required load conditions.

**Figure 5.** Vehicle-bridge system with single degree of freedom.
