Tensor-based approach for underdetermined operational modal identification

Abstract

During these years, blind source separation (BSS) techniques have been demonstrated as a promising tool for operational modal identification of large-scale engineering structures only from output responses. However, plenty of BSS identification approaches are based on the assumption that the sources are sparse or statistically independent, limiting their application scopes. Furthermore, it has been challenging to perform operational modal identification in underdetermined cases where the number of observed sensors is less than the number of active modes. In allusion to the problems above, a novel tensor-based approach for operational modal identification with limited sensors is proposed, in which the low-rank characteristics of vibration measurements is utilized. This paper reveals the intrinsic connection between tensor decomposition and modal expansion. Firstly, a third-order tensor is constructed through a set of generated matrices, in which each observed signal is reshaped into a matrix by segmentation operation. Then, the tensorial observed signals are decomposed into multilinear rank-Lr,Lr,1 terms by block-termed decomposition (BTD). And a collection of sub-tensors that correspond to the mode shapes matrix and modal responses can be obtained, from which the modal parameters are estimated. Finally, the effectiveness of the proposed method is validated with a series of numerical studies and experimental investigations, even in closely-spaced modes. The simulation and experimental results indicate that the proposed method can identify the modal parameters accurately and robustly in both determined and underdetermined situations.