Reduction and interpretation of matrices of frequency response functions by Bayesian independent component analysis

Abstract

This work seeks an effective data reduction method for matrices of Frequency Response Functions (FRF) in a way that preserves, as much as possible, the physical interpretation of FRFs in the full targeted frequency range. Also, this reduction method is wished able to cope with the different sources of uncertainties linked to the definition of the mechanical system whose FRFs are processed. It is shown that a Bayesian formulation of Independent Component Analysis (ICA) serves this purpose. It is used here to decompose a FRF matrix as a sum of frequency independent matrices multiplied by a frequency dependent scalar component. On the one hand, the independence property of this processing allows the scalar component to be concentrated in a narrow frequency range, on the other hand the chosen Bayesian approach presents itself as the most natural way to take into account uncertainties in the input FRFs whether they are due to measurement errors or structural uncertainties. Moreover, the probabilistic framework is shown to provide credible intervals on the estimation of the decomposition factors, thus allowing some considerations on the reliability of the processing and the development of a straightforward thresholding method to enhance the data reduction. A first application on measured automotive vibro-acoustic transfer functions shows the reduction performance of the approach and its interest when trying to analyse the measurements. A second application on non-parametric random FRFs computed through a stochastic finite element model illustrates the capacity of the proposed approach to take into account the uncertainty of the FRFs data and to propagate it to the factors of the decomposition.