Ambient modal identification using non-stationary correlation technique

Abstract

The topic of this paper is the modal identification from non-stationary ambient response data by applying correlation technique. It is shown theoretically that by assuming the ambient excitation to be non-stationary white noise in the form of a product model, the non-stationary response signals can be converted into free vibration data via the correlation technique. Previous studies have showed that the practical problem of insufficient data samples available for evaluating non-stationary correlation can be approximately resolved by first extracting the amplitude-modulating function from the response and then transforming the non-stationary responses into stationary ones. However, the errors involved in the approximate free-decay response would generally lead to a distortion in the modal identification. In the present paper, we propose that, if the ambient excitation can be represented by a product model with slowly time-varying function, without any additional treatment of transforming the original nonstationary responses, the non-stationary responses of the system can be treated approximately as a stationary random process; then, the nonstationary cross correlation functions of structural response evaluated at an arbitrary, fixed time instants of structural response are of the same mathematical form as that of free vibration of a structure, from which modal parameters of the original system can thus be identified. Numerical simulations, including one example of using the practical earthquake data served as the excitation input acting on a linear two-dimensional model of one-half of a railway vehicle, confirm the validity of the proposed method for identification of modal parameters from non-stationary ambient response data only.