General Realization Algorithm for Modal Identification of Linear Dynamic Systems

• Published in: Journal of engineering mechanics Vol. 134; no. 9; pp. 712 - 722
• Main Authors: De Callafon, R. A, Moaveni, B, Conte, J. P, He, X, Udd, E
• Format: Journal Article
• Language: English
• Published: Reston, VA American Society of Civil Engineers 01.09.2008
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Measurement and testing methods; Physics; Solid mechanics; Structural and continuum mechanics; TECHNICAL PAPERS; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Measurement; Linear systems; Statistical analysis; Modal analysis; Initial condition; Dynamic loads; State space method; Matrix decomposition; Optimization; Weight; Hankel matrix; System with n degrees of freedom; Algorithms; Least squares method; Earthquakes; System identification; State estimation; Measurement error; Dynamic load
• ISSN: 0733-9399; 1943-7889
• DOI: 10.1061/(ASCE)0733-9399(2008)134:9(712)

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.