Statistical asymptotic error on modal parameters in combined deterministic-stochastic identification algorithm

This paper deals with the estimation of the statistical dispersion of the modal parameters of a structure, frequencies and damping ratios obtained from subspace identification. The main objective is to apply, after some useful modifications, the theory of the covariance estimates of the poles to simulation and experimental cases and evaluate its performances in a real situation. A formulation of the asymptotic distribution of the dynamic matrix estimates given in literature is slightly modified to be directly interpretable in terms of accelerations. The method is extended to the modal parameters of a structure, which are non-linear functions of these estimates. The accuracy of the method is first analysed in simulation on the case of a spring-mass-damper system. Finally, the theory is applied to a real test case consisting of a reduced model of a two-floor building submitted to random excitation.