Blind Modal Identification Using Limited Sensors through Modified Sparse Component Analysis by Time‐Frequency Method

Abstract

AbstractOutput‐only modal identification with limited sensors available may be encountered in practical applications. Sparse component analysis (SCA), which is one of the most popular methods among blind source separation (BSS) techniques, is known as its capability for handling underdetermined BSS problems and nonstationary signals. Single‐source‐points (SSPs) where only one mode makes contribution are adopted to estimate the modal matrix. However, the accuracy of SSP detection is influenced by the number of sensors, because the detecting condition for SSPs may be satisfactory for multiple‐source‐points (MSPs). Besides, the estimation of frequencies and damping ratios is based on the sparse reconstruction of time‐frequency domain modal responses, where the number of sensors will have an impact on the accuracy. To improve the performance of blind modal identification using limited sensors, a method which is called SCA‐TF by modifying SCA through time‐frequency method is proposed in this paper. The TF representation in SCA is employed to modify the SSP detection process and identify frequencies and damping ratios instead of recovering the modal responses. In order to improve the accuracy of modal matrix estimation, the result of SSP detection is used as a preliminary for further refinement. Then the false SSPs are removed from the preliminary result through the power spectra which are constructed by short‐time Fourier transform coefficients. Subsequently, the estimation of modal matrix is accomplished by clustering the refined SSPs. Frequencies and damping ratios are extracted directly from the generalized spectra matrix which is formed by the short‐time Fourier transform coefficients. Because the identification of modal parameters is implemented directly in time‐frequency domain, the reconstruction of modal responses is omitted. The results of the numerical studies show that SCA‐TF can identify the modal parameters accurately. To investigate the performance of SCA‐TF in practical structures, the acceleration measurements from Tianjin Yonghe Bridge are analyzed to identify the modal parameters. The results of the Yonghe Bridge demonstrate the effectiveness of the proposed method to perform blind modal identification in practical structures.