Modal Identification of Vibrating Structures Using ARMA Model

Abstract

Identification of modal parameters of a vibrating structure is a primary concern in structural dynamics. A time‐domain method for identification of modal parameters is presented in this paper. The relationship between the eigenvalues of a vibrating structure and poles of its autoregressive, moving‐average (ARMA) model is derived. The eigenvalues are then identified by an estimate of the poles of a univariate ARMA model. The relationships between the autoregressive (AR) model and the moving‐average (MA) model of the vibrating structure are derived. The coefficient matrix sequence of the AR model is estimated using the excitation and response data and the impulse response function matrix sequence of the structure is then calculated through the relationship between the AR and MA models. The estimated impulse response function matrix sequence and poles are used for the identification of the eigenvectors of the structure. Freedecay vibration data, white‐noise excitation, or general excitation and corresponding response data can be used with this method.