Clustering Number Determination for Sparse Component Analysis during Output-Only Modal Identification

Output-only modal identification plays an important role in the structural health monitoring of large-scale structures. In recent years, blind source separation (BSS) has achieved great success in structural modal identification. Sparse component analysis (SCA), which is one of the most popular methods of BSS, has the capability to handle nonstationary excitation and underdetermined problems. In the process of SCA, clustering number, which is equal to the number of active modes, plays an important role in the estimation of modal matrix, in which the hierarchical clustering algorithm is used. However, the clustering number is always unknown in the clustering step, which makes application inconvenient. To fill this gap, an improved SCA method, equipped with a process of estimating the clustering number, is proposed in this paper. After transforming the signals into time-frequency (TF) domain, the single-source-points (SSPs) detection process is applied to pick out the TF points at which only one mode makes a contribution to the responses. The clustering technique is preceded by a preprocessing step to determine the clustering number. The key idea is that the clustering number is equal to the number of columns in the modal matrix, which is reflected in the number of lines in the scatter plot of two observations. A normalization method is proposed to distinguish the clusters clearly. The number of clusters is acquired through statistical analysis of the normalized vectors. After obtaining the modal matrix, the smoothed zero-norm algorithm is used to recover the modal responses in order to extract natural frequencies and damping ratios. An experimental cantilever beam and a three degree-of-freedom (DOF) numerical system with closely spaced modes were used to verify the effectiveness of the proposed method. The results showed that the improved SCA could detect the number of active modes for the beam and the numerical system. Full-scale data measured from the Green Building located at the Massachusetts Institute of Technology (MIT) campus and the Tianjin Yonghe Bridge were analyzed to verify the effectiveness of the proposed method in practical applications.