## 1 Introduction  
Structural Health Monitoring (SHM) is dedicated to evaluating the health and performance of engineering structures, such as buildings, bridges, airplanes, ships, etc. Among the various parameters inspected by SHM, structural displacement is one of the most valuable pieces of information when evaluating both safety and serviceability [1, 2]. By observing the long-term displacement history of a structure, the degree of deterioration and damage can be determined [3]. Given these considerations, the researchers have explored different methods to measure the displacement of structures. The methods of structural displacement measurement can be classified into two main categories: direct and indirect methods. Direct methods involve the utilization of devices such as laser displacement sensors, micrometers, radar, GPS, and digital cameras to directly capture structural displacement data [4, 5]. Indirect methods generally rely on easily accessible parameters such as velocity, acceleration, and strain, which can be converted to displacement [6]. Strain is one of the most easily measurable parameters of the structure using various strain sensors, such as strain gauges and fiber Bragg grating (FBG) sensors. The FBG sensors are particularly useful for measuring strain due to their high resolution and accuracy. Moreover, the FBG strain sensors are less susceptible to environmental factors and minimally impact the structural responses. The aim of this study is to develop a method for real-time displacement reconstruction with FBG-based strain gauges. The techniques for reconstructing displacement from surface strain measurements on a structure have been extensively studied. There are five main methods for strain-based displacement reconstruction, including the Ko method [7; 8], curvature method [9; 10], modal-based method [11; 12], inverse finite element method (iFEM) [13; 14], and deep learning method [3; 15; 16]. The Ko method is based on Euler-Bernoulli beam theory and reconstructs the displacement by integrating the strain segment by segment [7]. The performance of the Ko method is constrained by the assumption that the strain is linearly distributed in each segment of the beam. The curvature method reconstructs the displacement of the structure by transforming the strain information into curvature information [10], and the reconstruction accuracy is significantly influenced by the accumulated error. The modal-based method links the discrete strain with the displacement through the transformation relationship between strain and displacement mode shapes [12]. However, the modal-based method necessitates the assistance of finite element models to improve the reconstruction accuracy in most scenarios [17]. The iFEM is based on the conventional finite element method (FEM) and the weighted least-squares variational principle to reconstruct the displacement via strain [14]. This necessitates sophisticated designs of inverse finite element and measurement layout, as well as a complex programming process. In real applications, sensors cannot be applied to the entire structure due to practical constraints and economic limitations, and the insufficiently described strain field on the structure limits its implementation in accurate displacement field computations. Furthermore, the sophisticated calculations in iFEM make the real-time monitoring of structural displacement impossible [18]. In recent years, notable advancements have been achieved in the field of deep learning. [PERSON] et al. [16] employed a back-propagation network to directly fit the relationship between strain and displacement for carbon fiber composite laminates. [PERSON] [3] reconstructed the vertical displacement of a bridge from strains using an artificial neural network. The strain-based displacement reconstructions obtained through the deep learning method can eliminate the dependence on mechanical properties and increase computational efficiency.