**1. Introduction**

The pace of urban infrastructure construction was further increased with the development of the national economy, the bridge had become an indispensable structural form of transportation infrastructure. Therefore, the safety operation, long-term performance maintenance, and real-time state assessment are very important for bridges. The traditional safety inspection of bridge structures was mainly based on manual inspection. However, with the intensive and large-scale development of vehicles, the phenomenon of vehicle overloading was ubiquitous. Moreover, the safety load rating of the old bridge was relatively low, the results obtained by manual inspection may lag behind the development of the structural state, so the safety of bridges has drawn widespread concern in the society.

Therefore, it is important to install structural health monitoring (SHM) system on the bridge, which can monitor the working state and damage condition of bridge structures in a real-time manner. Li et al. [1] elaborated the efficiency and ascendancy of the proposed distributed fiber optic sensing system in SHM. Cardini et al. [2] presented an approach to use strain data from a multi-girder, composite steel bridge for long-term SHM. Brownjohn et al. [3] described the motivations for and recent history of SHM applications to various forms of civil infrastructure and provided case studies on specific types of structure. Wong et al. [4] studied the health monitoring of cable-supported bridges involving the integration of instrumentation, analytical and information technologies. Li et al. [5] described three commonly used fiber optic sensors, and presented an overview of current research and development in the field of SHM with civil engineering applications. In general, the SHM

**Citation:** Yang, J.; Hou, P.; Yang, C.; Zhang, Y. Study on the Method of Moving Load Identification Based on Strain Influence Line. *Appl. Sci.* **2021**, *11*, 853. https://doi.org/10.3390/ app11020853

Received: 8 December 2020 Accepted: 13 January 2021 Published: 18 January 2021

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system can monitor the internal response of the structure, such as strain, displacement, and other parameters as well as the external effects of the structure, such as temperature, load, etc. [6,7]. Vehicle load is the most important external effect on the bridge, and the working state of the bridge can be effectively evaluated if the actual load acting on the structure is identified. Kim et al. [8] proposed that the evaluation of vehicle loads for bridge safety assessment may be adjusted according to the traffic conditions, such as the traffic volume, the proportion of heavy vehicles, and the consecutive vehicle traveling patterns. In addition, he presented a method for evaluating the reliability of an in-service highway bridge, and the bridge performance was evaluated by considering traffic conditions [9]. Ghosh et al. [10] presented a framework for joint seismic and live-load fragility assessment of highway bridges. Therefore, it is of grea<sup>t</sup> significance to the study of load identification.

In recent years, due to the rapid development of signal processing and computer processing technologies, some load identification methods and weighing techniques with a wider application and higher accuracy have been proposed and studied. Some scholars have studied static weighing techniques with excellent accuracy. Pinkaew et al. [11] used the least-squares method based on conventional regularization to identify the static gross weight of the vehicle. Han et al. [12] presented an adaptive algorithm to improve the efficiency of static weighing. Richardson et al. [13] systematically summarized a variety of weighing techniques. However, the disadvantages of static weighing technology are: It is troublesome to install, as well as costly and time-consuming. In order to solve these disadvantages, weigh-in-motion (WIM) techniques have been widely developed and applied since the 1980s. Among them, the pavement-based WIM system required installing sensors on the road, which lead to high installation and maintenance costs as well as a grea<sup>t</sup> impact on the traffic [14,15]. The further development of the bridge weigh-in-motion (B-WIM) systems has the advantage that the installation and maintenance process has little impact on the traffic [16]. However, its defect is that it needs to add additional equipment to assist the function, which increases the operating cost, and it is greatly affected by the outside, these have limited its application [17–19]. Several methods have been developed in recent years to identify the moving loads. Zhu et al. [20] identified moving loads on top of a continuous beam using measured vibration responses and orthogonal function approximation method, but the road surface roughness and the variation of the speed lead to a large error. Yang et al. [21] used the method of the BP neural network in bridge moving loads identification, and the influences of different activation function combinations and algorithms on identification results were discussed. It was found that the transfer function in different combinations has little effect on the results, but the different training methods have a grea<sup>t</sup> influence on the results. Wang et al. [22] presented a dynamic displacement influence line method for moving load identification on bridge, and the simulation of multi-axle moving train loads was carried out, which was identified with annealing genetic algorithm, but its practical performance is questionable. Some researchers used the strain response measured by strain sensors to identify the moving load. Chen et al. [23] presented a B-WIM system to measure the vehicle velocity, wheelbase, and axial and gross weight merely based on a single set of long-gauge fiber Bragg grating (FBG) sensors. Zhang et al. [24] established the correlations among the peak values of static macrostrain curves and vehicle loads based on the macrostrain influence line theory. Wang et al. [25] used strain-monitoring data and influence line theory to identify the moving train load parameters, including train speed, gross train weight, and axle weights. They were characterized by good accuracy and easy operation but these methods were greatly affected by noise. Yang et al. [26] presented a method for moving load identification based on the influence line theory and distributed optical fiber sensing technique, and the numerical results showed that the method had excellent resistance to noise. However, the method does not consider the influence of load transverse distribution, and the experiment results of the actual bridge showed that the method had a large identification error. Zuo et al. [27] proposed a vehicle weight identification method using the measured strain responses of the T-girders caused by the passing vehicle

accordingly, and the load transverse distribution was considered. However, the study did not effectively compare the methods without considering the load transverse distribution, and the influence of speed on the load identification error was not considered.

In order to improve the accuracy of load identification and study the influence of transverse distribution, a moving load identification method was proposed based on strain influence line and the load transverse distribution under consideration. The feasibility and effect of this method were verified by numerical simulations and model bridge experiments.
