Operational Modal Parameters Identification Using the ARMAV Model

Applied system identification is an important issue in science and engineering. Experimental modal analysis is used to describe the dynamical behavior of structures, in general, for a given set of input and output data. This article deals with multidimensional modal parameters identification valid for output-only data—operational modal analysis (OMA). This approach is interesting when the input is not known or difficult to be measured. A linear, time-invariant and finite dimensional mechanical system is considered, which is described mathematically by an autoregressive-moving-average-vector (ARMAV) model, excited by unknown operating forces assumed to be a white Gaussian process—a persistent excitation. The focus of the study is, both, theoretical and practical aspects, of the use of the ARMAV model in OMA. Specifically, it discusses the need of using an output-vector as reference for output-only parameters identification scheme. The model order is identified by inspection of the most significant singular values of a block Hankel matrix derived directly from the formulation of the model. The AR parameters matrices of the ARMAV model, contained in a companion matrix, are determined via least-squares technique. Natural frequencies, damping factors and modal shapes are identified by means of eigenvalues and eigenvectors of that companion matrix. Examples using computational simulated data are presented.