## 1 Introduction
Prior research has confirmed that the transfer matrices for both low-frequency [19] and high-frequency [20] components are governed by the bridge's modal shapes. However, in this study, it is further revealed and substantiated that the transfer matrices for responses at different frequencies are identical. Consequently, the individual training approach is deemed redundant. Specifically, a simulated inter-section relationship tailored to high-frequency responses can be employed to reconstruct the low-frequency responses. This insight suggests that a unified training strategy could be more efficient and effective, eliminating the need for separate training for different frequency bands. The theoretical framework for the construction of transfer matrices is explicated through an analysis of the physical characteristics of bridge responses within vehicle-bridge interaction (VBI) systems [21]. This analysis confirms the existence of high-frequency free vibrations of the bridge, low-frequency vibrations induced by traffic forces, and responses due to temperature fluctuations within the long-term dynamics of bridges. More importantly, transfer matrices for both high-frequency and low-frequency dynamics were examined, revealing that these matrices are identical and remain consistent under varying traffic and temperature conditions. Based on the theoretical understanding of the VBI system's physical properties, an interception method was first introduced to separate these components. Subsequently, a residual network (ResNet) [22] algorithm was utilized to model the transfer matrix of high-frequency bridge responses. Furthermore, a series of finite element simulations and field tests validated that the ResNet calibrated for high-frequency responses can be directly applied to the reconstruction of low-frequency responses. In contrast to the model-based approach, the proposed data-driven methodology promises to be more time-efficient. It eliminates the need for finite element models and detailed knowledge of global stiffness matrices, mass matrices, or mode shape vectors. This data-driven approach directly estimates the mapping relationship between responses at multiple different cross-sections, enhancing efficiency in practical applications. Moreover, this method aims to simulate a physically based, time-independent transfer matrix, leveraging the findings from previous studies [19; 20]. This could potentially offer even greater time efficiency compared with conventional data-driven reconstruction techniques [10; 11; 12; 13; 14; 15; 16], which often overlook time-related factors such as traffic conditions and temperature. Additionally, the model-updating process, a staple in the model-based approach, is rendered unnecessary. Most importantly, this study demonstrates that the proposed approach eliminates the need for separate training processes for low-frequency and high-frequency responses, thereby further streamlining the data reconstruction process. Consequently, it is anticipated that the proposed method will be more suitable for practical engineering applications. Section 2 delves into the theoretical derivation of bridge dynamics within a simplified VBI system. It examines the physical characteristics associated with bridge free vibrations and vibrations related to driving forces. This section then proceeds to outline the entire algorithm, encompassing an interception method and the deployment of a residual network (ResNet). Section 3 presents a series of finite element models constructed for the VBI system, designed to substantiate the theoretical analyses. Section 4 details the validation of these theoretical analyses and the methodology for response reconstruction, utilizing field monitoring data.