Sparse component analysis method for structural modal identification when the number of sensors is incomplete

Abstract

Structural health monitoring providing sparse component analysis method for structural modal identification with incomplete number of sensors. Transforming structural acceleration response data into time frequency domain by short time Fourier transform, detecting time frequency points contributed by only one-order mode where real and imaginary parts have the same direction, and taking the detection result as the initial result of single-source-points; refining the initial result of detection of single-source-point located near the peak of power spectral density, and clustering single-source-points to obtain a mode shape matrix; constructing generalized spectral matrixes using short time Fourier transform coefficients, conducting singular value decomposition on generalized spectral matrix at a single-source-point, taking the first singular value as an auto-spectrum of single-order mode, obtaining the frequency of each order by picking the peak of auto-spectrum, and extracting damping ratio of each order by transforming the auto-spectrum into a time domain through inverse Fourier transform. By means of this method, structural modal parameters are obtained when the number of sensors is incomplete, thereby increasing the identification accuracy of the sparse component analysis method.