## 1 Introduction  
Bridges are a critical infrastructure that are used for the movement of goods and people, so the evaluation of their safety is very important. The real-time evaluation of the safety of such structures is called structural health monitoring (SHM). Through SHM, it is possible to quickly address urgent situations, such as the threat of collapse. In addition to extending the life of a structure, SHM can reduce its maintenance costs [1]. SHM can be divided into two categories: safety evaluation to assess the load bearing capacity of a structure and serviceability evaluation to assess the degree of deformation present [2]. In SHM, various physical data are collected. Of these, data on the displacement of structures constitute one of the most basic data types, useful in evaluating both safety and serviceability [2, 3]. From the displacements of a structure, the behavior and strength of a structure can be intuitively confirmed. In addition, by observing its long-term displacement history, the degree of deterioration and degree of damage suffered by a structure can be clearly ascertained. For these reasons, many studies have been conducted on methods of measuring the displacements of a structure [1, 2, 3, 4, 5, 6, 7]. Methods for measuring the displacements of a structure can be generally classified as contact or non-contact measurements [1, 8, 9]. Devices for contact-type measurements include linear variable differential transformers (LVDTs) and cable-type displacement transducers. These contact-type devices generally have a very high accuracy [1]. However, these devices are affected by the installation site because they require contact with the structure. For example, it is very difficult to install equipment for bridges that have very high clearance, such as bridges in valleys or bridges over rivers or oceans. Non-contact devices include laser, radar, GPS, and video or digital cameras [1] and many methods to measure displacement using non-contact devices have been studied [10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. These devices are guaranteed to be accurate within 1 mm owing to advances in technology. However, they usually need complex computer algorithms and are affected by environmental factors such as light. Furthermore, although existing equipment can measure the displacement of a structure at a given time, it is limited in its ability to continuously measure the displacement of a structure in real time. In addition to methods for directly measuring the displacement of a structure, there are studies for estimating displacement using strain and acceleration, which are relatively easy to measure [20; 21; 22; 23; 24; 25; 26]. According to Euler-Bernoulli beam theory, displacement can be calculated by integrating the strain; however, there are limitations in applying theoretical behavior to actual structures. The displacement can also be obtained by integrating the acceleration twice. When using the boundary condition to obtain the integral constant, an error occurs because the boundary condition of the actual structure does not match the theory. In this study, an artificial neural network (ANN) was used as an alternative to overcome the limitations of the above displacement estimation method. An ANN is a computer algorithm that simulates the human central nervous system, and ANNs have a strong ability to capture correlations between two variables that are difficult to formulate or have a very complex relationship [27]. An ANN can justify the correlation between the two variables by learning rather than by using conventional mathematical formulas. Due to these advantages, The ANN was used to predict displacements. In general, it is very difficult to define the relationship between longitudinal strain and vertical displacement analytically in a complex real structure. However, using the data mapping capability of ANN, the relationship between strain and displacement can be clearly defined after the training process.