General Realization Algorithm for Modal Identification of Linear Dynamic Systems

The general realization algorithm GRA is developed to identify modal parameters of linear multi-degree-of-freedom dynamic systems subjected to measured known arbitrary dynamic loading from known initial conditions. The GRA extends the well known eigensystem realization algorithm ERA based on Hankel matrix decomposition by allowing an arbitrary input signal in the realization algorithm. This generalization is obtained by performing a weighted Hankel matrix decomposition, where the weighting is determined by the loading. The state-space matrices are identified in a two-step procedure that includes a state reconstruction followed by a least-squares optimization to get the minimum prediction error for the response. The statistical properties i.e., bias, variance, and robustness to added output noise introduced to model measurement noise and modeling errors of the modal parameter estimators provided by the GRA are investigated through numerical simulation based on a benchmark problem with nonclassical damping. DOI: 10.1061/ ASCE 0733-9399 2008 134:9 712 CE Database subject headings: Modal analysis; Linear systems; Earthquakes; Algorithms; Dynamic loads.