## 1 Introduction  
Bridge structures are essential to the modern transportation infrastructure. Their safety and functionality are paramount, and their condition and maintenance are of great concern to governments [1]. In the realm of structural health monitoring (SHM), reconstructing structural responses is crucial for assessing the properties of structures and making informed maintenance decisions [2]. With data from multiple cross-sections, it is feasible to establish a mapping function that correlates the response at one specific cross-section with those at other locations. If the reconstructed data significantly diverges from the monitored data, it could signal severe damage at the particular cross-sections. Data reconstruction methods in current research can generally be divided into two primary strategies: model-based approaches [3] and data-driven approaches [4; 5]. The model-based approach relies heavily on accurate finite element simulations [3; 6]. After constructing a finite element model, one can calculate the global stiffness and mass matrices, estimate the mode shape vector, and subsequently determine the target mapping function to calculate responses. To enhance precision, an iterative model updating process is often necessary to refine physical parameters such as mass, stiffness, and damping ratio [7]. However, this process can be exceedingly time-consuming, as it involves building finite element models and processing numerical simulations. The parameters and their variations can lead to a vast number of combinations. Furthermore, in long-term monitoring, the properties of construction materials may change due to factors like structural aging and temperature fluctuations. An updated finite element model may not always accurately reflect the current state of a target bridge under varying conditions, necessitating even more frequent updates. These limitations diminish the practical applicability of the model-based approach in real-world engineering scenarios. In contrast to the model-driven method, the data-driven approach leverages existing monitoring data directly, which tends to be more time-efficient without any finite element modelling. Fundamentally, data-driven approaches begin by mapping the monitoring data onto a specific space. Subsequently, the responses at various cross-sections are transformed into a linear combination of bases of this space. Ultimately, the reconstruction process evolves into an estimation of the transformation matrix that connects the weights of these bases across different cross-sections. [PERSON] et al. [8] introduced the concept of the restricted isometry property (RIP) and showed that the compressive sensing (CS) method could effectively reconstruct data from incomplete frequency information. [PERSON] et al. [9] adapted the CS method for mobile wireless sensing systems to approximate the original signal, allowing responses to be reconstructed by estimating weights through normalization techniques. In recent years, machine learning techniques such as convolutional neural networks (CNNs) [10] and generative adversarial networks (GANs) [11] have been increasingly applied in the field of structural health monitoring (SHM) for data reconstruction. These methods utilize adaptive neural network structures, offering greater flexibility in modeling temporal and frequency characteristics compared with the CS method, which necessitates a predefined basis such as Fourier or wavelet transforms. Furthermore, these machine learning methods [12; 13; 14; 15; 16] directly aim to simulate the mapping function between inputs and outputs, providing a more dynamic and responsive approach to data reconstruction in SHM. Concentrating on the reconstruction of bridge responses under traffic loading, typical processes using the aforementioned machine learning methods [17] involve initially segregating the responses into low-frequency and high-frequency components [18]. These components are then trained separately to emulate the transfer matrices for different cross-sections.