| Bridges play an important role in urban transportation and shortening the distance between cities across rivers and seas in China.However,due to the impact of many factors such as service life,load overruns,and surrounding construction,the structure and stability of the bridge body have changed,increasing safety risks.Hence,effective identification of damages and ensuring safety monitoring of existing bridges is of utmost importance to ensure their stable and secure functioning.Moreover,providing comprehensive data support for bridge safety assessment holds significant significance and practical application value.Ground Based Synthetic Aperture Radar has the advantages of high precision(0.01mm),high sampling frequency(200Hz)and overall monitoring,which can realize sub-millimeter microdeformation monitoring.It is a new type of ground microwave interferometry technology,which is widely used in deformation monitoring of Bridges and other fields.Nevertheless,during the signal acquisition process,it is highly susceptible to being influenced by various factors such as environmental climate,vehicles,pedestrians and the equipment itself.The signal collected by ground-based SAR equipment inevitably contains multi-scale noise information,such as high frequency noise,low frequency noise and instantaneous noise,which seriously affects the accuracy of monitoring dynamic deflection data,and thus cannot accurately determine bridge deformation and safety status,leading to the inability to provide timely decision-making support for bridge maintenance.Therefore,in order to reduce the impact of noise on the dynamic deflection of ground-based SAR bridges and improve the accuracy of bridge dynamic deflection monitoring,this paper proposes an energy-entropy collaborative VMD-SOBI ground-based SAR bridge dynamic deflection de-noising approach,which achieves hierarchical denoising of multi-scale noise in ground-based SAR bridge dynamic deflection monitoring data.The research content and results are as follows:(1)Elaborate on modal decomposition and Blind Source Separation(BSS)time-frequency signal processing methods,including the recursive-version Empirical Mode Decomposition(EMD)algorithm,the enhanced Ensemble Empirical Mode Decomposition(EEMD)algorithm which builds upon EMD,and the non-recursive mode decomposition method,Variational Mode Decomposition(VMD).The feasibility of high-frequency de-noising using VMD is verified and effectiveness through simulation experiments.The experimental results show that after VMD de-noising,the correlation between the signal and the simulated noiseless signal reaches0.9953,which is 10.55% and 8.81% higher than that of EMD and EEMD,respectively.Aiming at the problem of scale noise other than high-frequency noise and the lack of prior information in ground-based SAR acquisition signals,the present study provides detailed introduction of the fundamental principle and algorithmic framework of a reliable BSS method,known as Second Order Blind Identification(SOBI),aimed at hierarchical de-noising of multiscale noise through VMD and SOBI.(2)Aiming at the problem of artificially setting the decomposition level K and penalty factor α for VMD high-frequency de-noising of ground-based SAR dynamic deflection signals,which leads to insufficient or excessive source signal differentiation,a VMD high-frequency de-noising method based on energy entropy synergy [K,α] optimization is proposed.First,the dynamic deflection signal is decomposed by VMD,and the optimal decomposition level K is determined by the maximum value of energy change rate in the energy conservation criterion;Determining α by utilizing the criterion of minimum sample entropy;Finally,adaptive VMD decomposition is implemented according to the optimal parameters to remove the interference of high-frequency noise.(3)Aiming at the problem that signal aliasing is difficult to eliminate due to the close signal frequency of low frequency,instantaneous noise and VMD high frequency noise after denoising,in this study,a approach for de-noising with low frequency and instantaneous effect is investigated.The approach is based on the Kernel Principal Component Analysis(K-PCA)constraint for building the SOBI Virtual multi-channel.Firstly,K-PCA method is used to identify the number of source signals of the primary de-noising signal that removes highfrequency noise,and the number of eigenvalues whose cumulative contribution rate is more than 90% for the first time is taken as the number of source signals,which is the condition to restrict the number of SOBI Virtual multi-channel;Then the IMF component dominated by useful information is combined with the original signal to complete the construction of virtual multi-channel.Finally,SOBI is used to separate the useful information and residual noise in Virtual multi-channel data,and Fast Fourier Transform is used to effectively remove the impact of residual noise on the data.(4)In order to verify the feasibility and effectiveness of the proposed VMD-SOBI hierarchical de-noising method based on energy entropy synergy,this paper verifies it through simulation experiments and real experiments.Firstly,a set of non-stationary and nonlinear data is set up to simulate real bridge data for simulation experiments.The de-noising effect is evaluated through traditional de-noising evaluation indicators such as Pearson Correlation Coefficient,Signal-to-Noise Ratio and Root-Mean-Square Error;The simulation experiment results show that both the single optimized VMD and the method proposed in this article are feasible in signal de-noising,but the evaluation indicators of the method proposed in this article are better than the single method in de-noising.Signals processed using the proposed methods exhibit a higher correlation coefficient,in a 33.30% increase in signal-to-noise ratio and a 53.62%reduction in root-mean-square-error than the single respective methods.These findings further attest to the effectiveness of the proposed approaches for de-noising.Then,taking the measured dynamic deflection signal of Fufeng Bridge in Beijing as the experimental data,the paper proposes a de-noising method which is compared with that of single EMD,EEMD,VMD and optimized VMD methods de-noising effect;Finally,the de-noising effect is described by five precision evaluation indicators: Noise Rejection Ratio,Signal Energy Ratio,Noise Mode,Ratio of the Variance Root and composite index T.The method proposed in this paper is superior to the single VMD and optimized VMD in terms of Signal Energy Ratio,Noise Mode and Ratio of the Variance Root.The Signal Energy Ratio is increased by 1.32% and 1.96% respectively,the Noise Mode exhibits an increase of 57.98% and 3.45%,while the Ratio of the Variance Root experiences a reduction of 87.07% and 9.6% than the two respective methods,and the value of the composite index T is 0.3473,which is the smallest among the five de-noising methods.The comprehensive description is superior to the above four de-noising methods,further indicating that the de-noising effect of the method proposed in this paper is the best.It not only has better anti-interference ability to high and low frequency noise and instantaneous noise,but also can well retain the characteristic information of the useful signal of the dynamic deflection of the ground-based SAR bridge. |
