Two-Level W-ESMD Denoising for Dynamic Deflection Measurement of Railway Bridges by Microwave Interferometry

Aiming to reduce the influences of noise for dynamic deflection measurements of railway bridges by microwave interferometry, this paper proposes a two-level wavelet-based extreme-point symmetric mode decomposition (ESMD) denoising algorithm on the basis of the characteristics of different noise frequency scales. First, the ESMD method is adopted to decompose the obtained dynamic deflection signal into a series of intrinsic mode functions (IMFs) from high to low frequency. Second, the first-level denoising is performed to eliminate the influences of high frequency noise by integrating the heursure threshold rule, soft thresholding, and different decomposition scales for high or low frequency IMFs, respectively. Third, the reconstructed first-level denoised signal is further decomposed into a series of IMFs, from high to low frequency, by the ESMD method. Last, the second-level denoising is performed to eliminate the influences of low frequency noise and some residual high frequency noise. For the low frequency noise, by using the heursure threshold rule, soft thresholding and a lower decomposition scale, and for some residual high frequency noise by using minimax threshold rule, hard thresholding and a moderate decomposition scale, the results on both simulated and real dynamic deflection signals show that the proposed two-level denoising algorithm is superior to wavelet threshold denoising and conventional empirical mode decomposition-based denoising techniques.