Estimation of modal correlation coefficients from background and resonant responses

A new simple relation for the estimation of modal correlation coefficients is presented. It is obtained from the decomposition of covariances of modal responses into background and resonant contributions, as it is commonly done for the variances. Thanks to appropriate assumptions, the modal correlation coefficients are estimated as weighted sums of two limit values, corresponding to the background and resonant responses respectively. The weighting coefficients are expressed as functions of the background-to-resonant ratios, which makes the proposed formulation convenient and easily accessible. The simplicity of the mathematical formulation facilitates the physical interpretation. It is for example proved that modal correlation coefficients can be non negligable even in case of well separated natural frequencies, which is sometimes unclear in the litterature. The new relation is mainly efficient in case of large finite element models. It is applied and validated on a finite element buffeting analysis of the Viaduct of Millau, the highest bridge deck ever built so far.