35 - The use of SVD for the study of multivariate noise and vibration problems

Abstract

This chapter deals with a global and consistent application of singular value analysis methodologies for multivariate noise and vibration problems of mechanical structures. By attributing a generic and consistent physical significance to the parameters forthcoming from the singular value decomposition (SVD) of operating response data or frequency response functions, singular value analysis is developed as a robust diagnostic approach in experimental-structural dynamics engineering. A global SVD method, referred to as principal response analysis, for multivariate operating response analysis leads to a number of diagnostic tools, such as virtual coherence analysis and principal operating field shape analysis, that are both alternative and complementary to existing approaches. A common perspective on the use of SVD for nonparametric impedance modeling, valid in the medium frequency range and based on multireference frequency response functions is explored. Using identical principles as in operating response analysis, an alternative for modeshapes, referred to as principal field shapes is developed. Case studies on the dynamic behavior of a sports car and a propeller aircraft illustrate the real world applicability of the discussed methodologies.