ESMD-WSST High-Frequency De-Noising Method for Bridge Dynamic Deflection Using GB-SAR

Ground-based synthetic aperture radar (GB-SAR), as a new non-contact measurement technique, has been widely applied to obtain the dynamic deflection of various bridges without corner reflectors. However, it will cause some high-frequency noise in the obtained dynamic deflection with the low signal-to-noise ratio. To solve this problem, this paper proposes an innovative high-frequency de-noising method combining the wavelet synchro-squeezing transform (WSST) method with the extreme point symmetric mode decomposition (ESMD) method. First, the ESMD method is applied to decompose the observed dynamic deflection signal into a series of intrinsic mode functions (IMFs), and the frequency boundary of the original signal autocorrelation is filtered by the mutual information entropy (MIE) for each IMF pair. Second, the high-frequency IMF components are fused into a high-frequency sub-signal. WSST is performed to remove the influence of noise to reconstruct a new sub-signal. Finally, the de-noised bridge dynamic deflection is reconstructed by the new sub-signal, the remaining IMF components, and the residual curve R. For the simulated signal with 5 dB noise, the signal-to-noise ratio (SNR) after noise reduction is increased to 11.13 dB, and the root-mean-square error (RMSE) is reduced to 0.30 mm. For the on-site experiment for the Wanning Bridge, the noise rejection ratio (NRR) is 5.48 dB, and ratio of the variance root (RVR) is 0.05 mm. The results indicate that the proposed ESMD-WSST method can retain more valid information and has a better noise reduction ability than the ESMD, WSST, and EMD-WSST methods.