Modal identification from nonstationary ambient response data using extended random decrement algorithm

The topic of this paper is the estimation of modal parameters from nonstationary ambient vibration data by applying the random decrement algorithm. If the ambient excitation can be modeled as a nonstationary white noise in the form of a product model, then the nonstationary cross randomdec signatures of structural response evaluated at any fixed time instant are shown theoretically to be proportional to the nonstationary cross-correlation functions, which is of the same form as the free-vibration decay or impulse response of the original system. The practical problem of insufficient data samples available for evaluating nonstationary randomdec signatures can be approximately resolved by first extracting the amplitude-modulating function from the response and then transforming the nonstationary responses into stationary ones. However, the error involved in the approximate free-decay response would generally lead to a distortion in the modal identification. In the present paper, we also further propose that, if the ambient excitation can be modeled as a zero-mean nonstationary process, without any additional treatment of transforming the original nonstationary responses, the nonstationary cross randomdec signatures of structural response are shown in 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 excitation data, confirm the validity of the proposed method for identification of modal parameters from nonstationary ambient response data only.