## 3 Experimental Results and Analysis
### Practical Experiment  
The practical experiments described in this section empirically tested the simulation-based findings. This is essential in evaluating the practicality, accuracy, and reliability of the proposed method when subjected to real-world complexities and uncertainties. The experiment comprises the utilization of GB-SAR for the acquisition of dynamic-deflection data from three closely spaced points beneath the Qixia Bridge. This provides the essential observational signals for our study. The Qixia Bridge is located on Qixia Avenue within the inner ring of Nanjing City, and has a total length of 843.54 m. The main bridge is a three-span lower-through-type steel-pipe concrete tied-arch bridge with spans of 80 m + 90 m + 80 m, and the bridge deck is 34 m wide, with a total of six lanes, with traffic moving both directions. The GB-SAR was positioned at the mid-span beneath the bridge, with the radar's angular sampling frequency set at 199.4 Hz and its range resolution to 0.75 m. A schematic diagram of the experimental area and layout of GB-SAR is shown in Figure 12.  
Figure 11: De-noised signals of \(g_{5}(t)\) acquired from **(a)** I-SOBI and **(b)** the proposed method. Figure 12: (**a**) Experimental area of the Qixia Bridge and **(b)** the layout of the GB-SAR. In Figure 13, signal II represents the temporal displacement variation of observation point X2 on the side of the Qixia Bridge (Figure 12b). Signal I represents the time displacement variation at observation point X1, and signal III represents the time displacement variation at observation point X2. Due to the influence of the surrounding environment and the equipment itself, the obtained temporal displacement data inevitably contain noise. Therefore, to improve the accuracy of the temporal displacement data for observation point X2, two additional observation signals (signals I and III in Figure 13) were used. These signals correspond to the temporal displacement variations of two adjacent observation points (Figure 12b), X1 and X3, which have noise characteristics similar to those of observation point X2. Traditional SOBI, I-SOBI, and our proposed gradual de-noising method were applied to Signal II, with the results shown in Figure 14. Furthermore, to validate the effectiveness of the de-noising methods, four objective metrics, namely, Standard Deviation (STD), RMSE, Receiver Operating Characteristic with Variance (RVR), and Normalized Cross-Correlation (NCC), were selected to quantitatively assess the de-noising outcomes, as presented in Table 2.  
From Figure 14 and Table 2, the following conclusions can be drawn: (1) Figure 14 illustrates the comparison of Signal II before and after noise reduction. The blue curve represents the raw signal II obtained by GB-SAR acquisition, the red curve represents the de-noised signal II processed by the traditional SOBI method signal, and the green curve represents the de-noised signal II processed by the method proposed in this paper. Signal II, representing the original radar monitoring signal of the bridge when no vehicles are present, is expected to remain stable under normal conditions. However, due to environmental high-frequency noise, the original signal may exhibit spurious amplitude variations, leading to signal instability. After noise reduction using the SOBI method and the new approach proposed in this study, the signal amplitude is reduced, resulting in a significant difference between the original and de-noised signal amplitudes. This indicates that the proposed method effectively reduces noise, mitigates abnormal amplitude fluctuations caused by noise, and efficiently eliminates high-frequency noise components, thereby restoring the signal to its true physically based characteristics. Consequently, the significant reduction in signal amplitude following noise reduction is a reasonable and expected outcome, further validating the effectiveness of the noise reduction techniques employed. (2) When applying the traditional SOBI algorithm, the impact of noise can be reduced to some extent.