Effect of systematic FRF errors on matrix inversion based vibro-acoustic analysis methods

Abstract

The establishment of a non-parametric system description in terms of a Frequency Response Function matrix is an essential step in many structural and vibro-acoustic analysis approaches such as Modal Analysis, Load Identification, Transfer Path Analysis and Substructuring. A crucial step in many of these applications is the inversion of a matrix of this FRF matrix. Several studies have been reported on the influence of stochastic FRF errors on this matrix inversion, leading to the use of a pseudo-inverse approach, SVD truncation, regularization etc. but little is known about the effect of systematic errors, such as amplitude or frequency shifts and inter-FRF inconsistencies qn the matrix inversion result. The present paper investigates the effect of selected systematic FRF measurement errors on applications involving matrix inversion, with emphasis on the Transfer Path Analysis method. The subject is reviewed through analytical considerations and through simulations on a reference numerical model (the Garteur model). In particular, the sensitivity of two Transfer Path Analysis methods with respect to the studied systematic errors is analyzed and considerations on increasing the robustness of these methods are derived.