Statistical system identification of structures using ARMA models
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The present study focuses on the estimation of the modal properties, i.e., natural modal frequencies, modal damping ratios, and mode shapes, of a structural system under ambient vibration based on the response data of the structure and the statistical properties of the stationary loading process. The corresponding input-output system is represented by a covariance-equivalent ARMA model which is univariate in the case of multiple input - single output and multivariate in the case of multiple input - multiple output. The mapping between the physical modal parameters and the ARMA parameters is established. Two different algorithms are used to estimate the covariance-equivalent ARMA models, namely the maximum-likelihood algorithm and a two-stage least-squares algorithm. An augmented system approach including both a fictitious "load" system and a structural system is formulated to account for the non-whiteness of most realistic loading processes. Examples of its application are provided for the cases of earthquake, wave, and wind excitations.
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Kumar, Satyendra. "Statistical system identification of structures using ARMA models." (1993) Master’s Thesis, Rice University. https://hdl.handle.net/1911/13750.