System identification of linear MDOF structures under ambient excitation

Abstract

This paper introduces the eigenspace structural identification technique for tall buildings subjected to ambient excitations that are stationary and where only the response time histories are measured. Based on the forward innovation model of the Kalman filter sequence, the actual response can be constructed as a function of the measured response time history with contamination of either displacement or velocity. The response time history is decomposed into subspace matrices using QR decomposition and Quotient Singular Value Decomposition (QSVD) techniques. These are then substituted into the least-square formulation to obtain the solution which is non-unique. Similarity transformation is applied to arrive at the desired solution employing the fact that eigenvalues of self-similar systems are identical. The advantages of this eigenspace technique are that it is non-iterative, initial estimates of the parameters to the identified are not required, well-established numerical algorithm of the decomposition techniques employed are available, and the method can handle MDOF systems efficiently.