Techniques for estimating the unknown functions of incomplete experimental spectral and correlation response matrices. (February 2016) - Antunes, Jose; Borsoi, Laurent; Delaune, Xavier; Piteau, Philippe
Abstract: In this paper, we propose analytical and numerical straightforward approximate methods to estimate the unknown terms of incomplete spectral or correlation matrices, when the cross-spectra 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 methods 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 spectral estimation 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. Finally, we show the effectiveness of the proposed techniques by extracting the modal responses of the simulated flow-excited tube, using the SOBI (Second Order Blind Identification) method, from an incomplete response matrix 1 . Highlights: We propose methods to estimate unknown cross-spectra in incomplete measurement sets. The first two reconstruction methods are stated through explicit formulae. The third method is a constrained iterative technique which always converged. Convincing results were obtained for a vibrating tube subjected to flow turbulence. These estimation techniques currently apply to systems with non-degenerate modes.