## 5 Conclusions  
In this research, we introduce a pioneering transfer-reconstruction technique designed to reconstruct low-frequency responses from high-frequency data. Our theoretical exploration of bridge dynamics within a simple VBI system establishes a crucial physical property: the transfer matrices for both low-frequency and high-frequency bridge responses remain consistent across varying traffic conditions and temperature fluctuations. Additionally, we have developed an interception algorithm capable of distinguishing between high-frequency and low-frequency responses within monitoring data. Subsequently, we propose the application of the ResNet method to model the transfer matrix across multiple cross-sections. To substantiate the physical properties and confirm the efficacy of our proposed method, we conducted finite element simulations and field tests. The key findings of our study are summarized as follows:  
1. The theoretical analysis confirms that the transfer matrix for high-frequency responses is identical to that for low-frequency responses. This matrix is independent of time and remains stable under changing traffic conditions, which can modify the external forces acting on the bridge, and under varying air temperatures, which can influence the stiffness of the bridge's structural materials. 2. A series of numerical models was meticulously constructed. The low-frequency bridge displacement at a designated cross-section was accurately reconstructed by multiplying the regressed transfer matrix for high-frequency displacements and the low-frequency displacement input. This reconstructed outcome closely aligned with the simulation results, thereby substantiating the validity of the derived physical characteristics. Furthermore, it was confirmed that the transfer matrix maintained its constancy even amidst varying traffic conditions and alterations in the global stiffness of the bridge. 3. Through validation with monitoring data from a real continuously bridge, an example of the aforementioned constant transfer matrix representing physical characteristics was confirmed. The reconstructed low-frequency bridge responses were in close agreement with the actual values, thereby also validating the effectiveness of the proposed algorithm. Moreover, comparisons with a typical time-series prediction method such as LSTM suggest that the proposed method exhibits superior robustness. Figure 24: High\(-\)frequency strain time history at 03\(-\)S02. This study demonstrates the potential of utilizing solely high-frequency responses for the reconstruction of both high-frequency and low-frequency responses. As a result, the time expenditure required for training a neural network to simulate the transfer matrix can be significantly curtailed. Comparing with existing research, particularly in the realm of purely data-driven approaches, the proposed method stands out as markedly more efficient. Furthermore, given that this advantage is theoretically grounded in the dynamic equations of structural dynamics, it is anticipated that this method could be extensively applied across various engineering scenarios. It should be highlighted that this study method may be confined to medium-span and short-span bridges, with the simulation of the transfer matrix approached as a multiple linear regression problem. The linear structure property and constant mode shape function underpin the applicability of the proposed method. However, for long-span bridges, which exhibit nonlinear characteristics, this method may not be suitable. In particular, time-dependent factors like varying wind and traffic load must be considered. Thus, the time-irrelevant method should be adapted to include input of time-varying external load data. Furthermore, a large comprehensive database encompassing time-varying temperatures, traffic conditions, and wind forces will be essential for developing an accurate response reconstruction model.