Simple relations for estimating the unknown functions of incomplete experimental spectral and correlation response matrices

Abstract

In this paper we suggest two simple approximate methods to estimate the unknown terms of incomplete spectral or correlation matrices, when the crossspectra or cross-correlations available from multiple measurements do not cover all pairs of transducer locations. The proposed techniques may be applied whenever the available data includes the auto-spectra at all measurement locations, as well as selected cross-spectra which implicates all measurement locations. The suggested formulae can also be used for checking the consistency between the spectral or correlation functions pertaining to measurement matrices, in cases of suspicious data. After presenting the proposed formulations, we discuss their merits and limitations. Then we illustrate their use on a realistic simulation of a multi-supported tube subjected to turbulence excitation from cross-flow.