## 5 Conclusions  
In this study, a novel data fusion technology was proposed. By synthesizing the measured low-frequency inclination data across multiple cross-sections with the high-frequency acceleration data from select locations, high-frequency accelerations at the other sections can be estimated. A theoretical analysis was performed to highlight the parallels between the dynamics of a VBI system and the BSS problem. Subsequently, the FastICA algorithm and discrete integration were employed to formulate surrogate inclination mode shapes, surrogate displacement mode shapes, and the surrogate inter-section transfer matrix for acceleration across different bridge cross-sections. Throughout the theoretical derivation, three key principles emerged, elucidating the rationale and methodology behind the application of our proposed data fusion approach. A comprehensive series of finite element simulations and laboratory experiments were executed to substantiate the efficacy of the proposed method. The principal findings are summarized as follows:  
1. High-frequency accelerations and low-frequency displacements share identical mode shape functions and inter-section transfer matrices. 2. The surrogate inter-section transfer matrix for various parameters, such as displacement and acceleration, derived from the FastICA algorithm, is equivalent to the actual physical inter-section transfer matrix obtained from true physical mode shape functions. 3. The surrogate displacement mode shape function can be deduced from the discrete integration of the surrogate inclination mode shape function, while the resulting surrogate inter-section transfer matrix for displacement also matches the real physical inter-section transfer matrix for displacement. 4. A series of finite element models have been constructed to validate the proposed method. The comparison between the estimation results and the simulation data demonstrates that the method in question can yield accurate outcomes for the first two vibration modes, given the current assumption that only these two modes are taken into account. However, the inconsistencies observed in the higher-mode vibrations suggest that the existing set-up is not suitable for estimating the higher-mode components. To attain more precise results, it is recommended that the method be adapted by adjusting the number of signal sources and by expanding the measurement of acceleration to include more cross-sections, corresponding to the vibration modes under consideration. * A laboratory experiment was also carried out to substantiate the efficacy of the proposed method. Consistent with the validation findings from the numerical analysis, the method exhibits satisfactory performance in estimating lower modes of vibrations. However, it falls short of accurately capturing the higher modes of vibrations under the current configuration, which is limited to considering only the first two modes and relies on acceleration data from just two cross-sections as input. To enhance the precision of higher modes' component estimation, it is imperative to augment the method by incorporating acceleration measurements from an expanded array of cross-sections, along with the requisite adjustments to the associated parameters of the method. The proposed method is anticipated to eliminate the necessity of creating finite element models. Additionally, it would obviate the need for partial measurement of the target acceleration, significantly reducing the expenditure on sensors and health monitoring equipment. Consequently, with a constrained budget, the proposed approach promises to deliver more extensive monitoring insights. It is crucial to highlight that within the scope of this study, the influence of measurement noise on the input data for the FastICA algorithm has been found to be negligible. This minimal noise level is essential for ensuring the efficacy of the separated signal sources and the mixing matrix in subsequent applications. However, in real-world engineering contexts, noise conditions may not always be as ideal.