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.