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Covariance regression for operational modal analysis

This article proposes a covariance regression procedure for operational modal analysis. The whole work is mainly twofold. On the one hand, two identities on the covariance are presented and they reveal that the covariance at different times is linearly dependent through both scalar and matrix coefficients. On the other hand, based on the two identities, the scalar covariance regression approach and the matrix covariance regression approach are naturally invoked. In proceeding so, the scalar or matrix coefficients are first acquired through covariance regression, and then, the modal parameters are simply extracted from the coefficients. Numerical examples and a field test case are studied to see the effectiveness of the proposed covariance regression procedure, and the ability to deal with harmonic load, large damping, and closely spaced modes is clearly verified.