This paper investigates the second-order statistical properties of vibrating modal parameters (natural frequency and damping ratio) by using autoregressive (AR) model. The variance of least squares AR model for the modal parameters estimation of single/multi degree of freedom free-decay vibrating system is analyzed, based on first-order Taylor approximation. In this paper, explicit expressions for variance of natural frequency and damping ratio are derived. The dependence of the variances on number of data and signal-to-noise ratio are investigated, both analytically and numerically, for practical applications. Monte Carlo numerical simulation results are given to compare and illustrate the analytical expressions.
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