## 4 Experiment Validation
### Experimental Result Analysis
This similarity is likely due to the fact that the separated signal sources are linear combinations of the actual independent signals with distinct frequencies, as described by Equation (18a,b). Moreover, the corresponding surrogate inter-section transfer matrix of bridge displacement can be obtained. Finally, the target acceleration time history at \(-\)2.4 m was estimated through acceleration measured at +2.4 m and 0 m with the surrogate transfer matrix of bridge displacement. It is important to note that, given that the high-frequency components predominantly contribute to the acceleration time history, a high-pass filter with a 1 Hz threshold was applied to isolate these high-frequency accelerations. Additionally, the discrete modal amplitudes, as depicted in Figure 18b, on the displacement  
Figure 17: Comparison between measured inclination, reconstructed inclination from product between mixing matrix and signal sources (shown in (**a**)), and estimated inclination from transfer matrix (“TM estimation in (**b**)”). Figure 18: Surrogate inclination mode shape (**a**) and displacement mode shapes (**b**). ment mode shape curve at \(\pm\)2.4 m and 0m were utilized to construct the inter-section transfer matrix from +2.4 m and 0m to \(-\)2.4 m. Subsequently, Figures 19 and 20 present the comparisons between the estimated and measured accelerations in the time and frequency domains, respectively. As illustrated in Figure 19, it is evident that in the time domain, the estimated and measured accelerations align closely for the majority of the observed time periods. Despite potential variations in loading conditions across multiple trips, the inter-section transfer matrix is expected to remain consistent for the linear bridge structure. The validation also indicates that the time-varying loading conditions, implicitly contained within the acceleration time histories recorded at +2.4 m and 0 m,  
Figure 19: Comparison between the estimated and measured acceleration at \(-\)2.4 m. (The blue curve denotes the estimated result while the red curve denotes the measured acceleration. The rectangle marks the high-frequency low-amplitude part.) Figure 20: Comparison of frequency spectrum between estimated and measured acceleration at \(-\)2.4 m.  
have been effectively translated via the inter-section transfer matrix to accurately estimate the target acceleration at \(-\)2.4 m.  
However, when the acceleration is characterized by high-frequency, low-amplitude components--highlighted within a red rectangle in Figure 18--the estimated results do not align as closely with the measured accelerations. By checking the frequency spectra of both the estimated and measured accelerations (presented in Figure 20a,b, respectively), for the first vertical mode, the estimated acceleration amplitude is 0.0021 m/s\({}^{2}\), while the measured amplitude is 0.0022 m/s\({}^{2}\), indicating a good match. This concurrence suggests that the vibrations around 10 Hz in the acceleration time history are well correlated between the estimated and measured data. Furthermore, a significant difference is observed in the amplitudes corresponding to higher modes, which is supposed to result in the divergence of high-frequency, low-amplitude vibrations marked in Figure 19. This divergence is likely due to two detailed factors: firstly, the close proximity of the frequencies for the second (20.015 Hz) and third (21.979 Hz) modes of the target bridge, which may present challenges for the algorithm to accurately capture the vibration modes and estimate the inter-section transfer matrix; and secondly, the presence of potential high-frequency noise. In this study, a high-pass filter was solely employed to isolate high-frequency vibration signals, and high-frequency noise was not specifically filtered out, which might result in the observed discrepancies. Additionally, the limitation of the proposed method is obvious with only the first two modes being considered.