Underdetermined Blind Identification of Structures by Using the Modified Cross-Correlation Method

Abstract

The modified cross-correlation (MCC) blind identification method is extended to handle the underdetermined case of structural system identification. The underdetermined case is one in which the number of sensors is less than the number of identifiable modes. The basic framework of the modified cross-correlation method is retained in cases in which multiple covariance matrices constructed from the correlation of the responses are diagonalized. The solution to the underdetermined blind identification consists of two stages: the generation of intrinsic mode functions (IMFs) from the measurements by using empirical mode decomposition (EMD) and the application of the modified cross-correlation method to the decomposed signals. The available measurements are first decomposed into IMFs by using the sifting process of EMD. Subsequently, the IMFs are used as initial estimates for the sources, and the MCC method is implemented in an iterative framework. Initial estimates for the mixing matrix necessary to start the iterative process are selected using assumed shape functions that satisfy the essential boundary conditions. The need for sensor measurements at all the relevant degrees of freedom (DOF) to identify the mode shapes is alleviated in this approach. This is the main advantage of the proposed method. Vibration responses collected from the apron control tower located at the Toronto Pearson International Airport are used for demonstration.