| Bridge dynamic deflection is an important index of bridge structure safety detection.Ground based synthetic aperture radar(GBSAR)is a new technology,which has been widely used in bridge dynamic deflection measurement.In the process of GBSAR bridge dynamic deflection acquisition,it will inevitably be affected by factors such as the surrounding environment and traffic activities.The dynamic deflection of bridge will contain white noise,impulse noise,random noise and so on,which will reduce the accuracy of the data.In order to improve the accuracy of bridge dynamic deflection,it is necessary to reduce the noise of GBSAR bridge dynamic deflection data.Morphological filter(MF)method can effectively filter impulse noise and eliminate small noise,but MF method is not ideal filtering random noise and bias may appear after noise reduction.Extreme-point symmetric mode decomposition(ESMD)method can adaptively decompose the signal into a series of intrinsic mode functions(IMF)and an adaptive global mean curve(AGM),but ESMD method needs to be integrated with other methods for signal denoising.The singular value decomposition(SVD)method is based on the different effects of useful information and noise information on the singular values of the matrix.It can separate noise information from the signal by selecting appropriate singular values,which can effectively suppress random noise interference.However,the signal denoised by SVD method may appear "burr" phenomenon,and the denoising effect is affected by the strong trend term of the signal.A single noise reduction method is not ideal for GBSAR bridge dynamic deflection signal.In view of the above problems,the main research contents and achievements of this paper are as follows:(1)Aiming at the white noise and impulse noise in the GBSAR bridge deflection signal,and the noise of different frequencies and scales in the IMF decomposed by the ESMD method,a MF-ESMD signal denoising method for bridge dynamic deflection that combines the ESMD method and the MF method is proposed.First,the bridge dynamic deflection signal is decomposed into a series of IMF with different frequencies and an optimal AGM curve by ESMD method;secondly,the high frequency IMF dominated by noise is removed by Spearman correlation coefficient algorithm;finally,the residual noise in the reconstructed signal is further eliminated by using generalized mean morphological filter.The simulation experiment results show that the root mean square error of the MF-ESMD denoising method is 0.0361 mm,and the signal-noise ratio is 30.6619 d B,which is 53.3% higher.Compared with the MF and MF-EEMD denoising methods,the MF-ESMD denoising method has a better noise reduction effect on nonlinear and non-stationary signals.The denoising results of the Fengbei Bridge dynamic deflection signal show that root of variance ratio and noise rejection ratio of the MF-ESMD denoising method are better than those of the other two methods,which proves that the MFESMD denoising method can more effectively eliminate white noise and impulse noise in GBSAR bridge dynamic deflection signal.(2)Aiming at the white noise and random noise in the GBSAR bridge dynamic deflection signal,and the noise reduction effect of the SVD method will be affected by the signal trend term,a ESMD-SVD denoising method based on the ESMD method and the SVD method is proposed.The ESMD method is used to decompose the bridge dynamic deflection signal into a series of IMF and the optimal signal trend term R,and R is extracted and the IMF are reconstructed into a new signal.The SVD method is used to eliminate random noise and other noises in the reconstructed signal.Finally,R and the signal denoised by the SVD method are superimposed and reconstructed to obtain the final denoised signal.Through simulation experiments,the noise reduction effect of the ESMD-SVD denoising method and other denoising methods are compared and analyzed.The root mean square error of ESMD-SVD denoising method is 0.0212 mm,and the signal-noise ratio is 35.8441 d B.Compared with the analog signal,the signal-noise ratio increased by 79.22%,which is superior to other denoising methods.It proves the feasibility and accuracy of the ESMD-SVD denoising method.Through the noise reduction effect and comprehensive evaluation index of the measured data,it is further verified that the method has a good denoising ability on the GBSAR bridge dynamic deflection signal,and can effectively eliminate the white noise and random noise in the GBSAR bridge dynamic deflection signal.(3)The ESMD-SVD method can effectively suppress white noise and random noise,but the denoised signal still contains small impulse noise and "burr" phenomenon.To solve this problem,the ESMD-SVD-MF denoising method based on ESMD,SVD and MF three methods is proposed.The ESMD method is used to extract the optimal trend term r of the signal,and then the IMF is reconstructed into a new signal.The new signal is denoised by SVD.Then the denoised signal by SVD and R are reconstructed into a new signal,and the reconstructed signal is smoothed by the generalized mean filter to obtain the final denoised signal.Through simulation experiments,the noise reduction effects of six denoising methods and four evaluation index values are compared and analyzed.The results show that the normalized correlation coefficient of the ESMD-SVD-MF denoising method is 0.9999,the root of variance ratio is 1.0066,and the root mean square error is 0.0206 mm.And the signal-noise ratio is36.0849 d B,which is 80.42% higher.It proves that the ESMD-SVD-MF method has an ideal noise reduction effect on nonlinear and non-stationary signals.Better than the other five methods.Through the denoising effect and four evaluation indexes of the GBSAR dynamic deflection signal of the Fengbei Bridge,it is further proved that the proposed ESMD-SVD-MF denoising method has a good denoising ability on the GBSAR bridge dynamic deflection signal,and it can not only effectively reduce the white noise,impulse noise and random noise in the signal,but also effectively retain the basic characteristics of the signal. |
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