Operational Modal Identification Of Civil Structures Based On Under-determined Blind Source Separation Technique

Structural modal parameters,including frequencies,mode shapes and damping ratios,are the primary dynamic characteristics of structures.Operational modal analysis is of great practical importance for modal identification of large civil engineering structures since no incentive information is required.Up to now,many operational modal identification methods have been proposed.The blind source separation theory has achieved rapid development in the field of modal identification because it does not require parametric models,and is simple and efficient.Existing methods mainly focus on modal identification based on determined blind source separation,however,underdetermined problems are often encountered in practical applications.In this paper,underdetermined blind source separation method are studied focusing on determination of mode number,real mode identification,complex modal identification and modal identification for high damping structures.The benchmark model provided by American Society of Civil Engineers and an actual bridge are used to verify the performances of the proposed methods.The detailed research contents are as follows:(1)Considering that the number of active modes involved in the actual structure is often unknown,a method for determining the number of modes is proposed.Firstly,three statistics are given by using the statistical properties of the response in the time-frequency domain.Then the weighted average technique is used to smooth the discrete probability values.Finally,the number of modes is determined adaptively through automatically picking the peaks of the probability curve.The results of the examples show that the proposed method can adaptively determine the number of modes and improve the accuracy of the underdetermined blind modal identificatio.(2)In view of the accuracy of modal identification will decrease when the number of sensors is less,a sparse component analysis method modified by time-frequency method is proposed.This method establishes the relationship between the power spectrum and the single source point in sparse component analysis,and proposes a single source point detection method based on power spectrum amplitude statistics.Furthermore,the time-frequency coefficients are used to construct a generalized spectral matrix.Moreover,frequencies and damping ratios are directly identified in the time-frequency domain from the singular value decomposition of generalized spectral matrix.The results indicate that the single source point detection procedure can improve the accuracy of the mode estimation greatly,and the frequencies and damping ratios can be identified without reconstructing the modal responses.The accuracy can be improved in the case of large underdetermined problem.(3)Considering the issue that complex modes will be generated from non-proportional damping,a complex modal identification method based on extended sparse component analysis is proposed.A blind source separation model for complex modal identification is established by the analytical signals and a single source point detection method which is suitable for complex modes is proposed.Subsequently the relationships between vibration responses and vibration mode coefficients are established,and the estimation method of complex mode shapes is presented.The frequencies and damping ratios are then extracted by reconstructing the modal responses.The results of the numerical examples reveal that the proposed method is suitable for real and complex modal identification in underdetermined conditions.(4)Influenced by the structural high damping level,the statistical independence of the modal response are not satisfied,which results in the decrease of accuracy.In this paper,the modal identification method based on frequency domain independent component analysis is proposed.The method analyzes the statistical characteristics of time domain signals and frequency domain signals,and establishes a blind source separation model in the frequency domain.The fast independent component analysis and the over-completed independent component analysis method are used for the identification of modal parameters.The analysis results of the example prove that the proposed method is suitable for modal identification of dependent modes.