Compressed sensing based on dictionary learning for underdetermined modal identification

With the engineering structures becoming more complicated, it is difficult to obtain complete measurement responses with limited sensors. Thus, carrying out the underdetermined modal identification will have practical engineering application values. In this paper, a new approach for underdetermined blind modal identification based on dictionary learning in the framework of compressed sensing (CS) is proposed. The principal idea is to estimate modal shapes using a clustering technique, and recover modal responses combing the estimated mode shapes matrix and the learned dictionary. The experiment results on a typical cantilever beam structure illustrate that the proposed method can perform accurate dynamic parameters identification whether in underdetermined case or determined case.