Vibroacoustic Model’s Likelihood Computation Based on a Statistical Reduction of Random FRF Matrices

Improvement of vibroacoustic models prediction capabilities requires an adapted indicator to compare experimental measurements with the results of the computational model. When dealing with highly uncertain objects such as series production cars, a probabilistic approach is mandatory to be able to describe the dispersion of experimental results. Moreover, a probabilistic non-parametric model also account for modeling uncertainties and simplifications that are part of any engineering process. The proposed approach deals with Frequency Response Functions since FRFs are the common way to handle vibroacoustic models. When considering multiple input and output points configuration, FRFs are frequency dependent complex matrices. Since the probabilistic modeling is available in current vibroacoustic software, collections of random realizations of the FRF matrix can be computed from the existing FE model. The model’s likelihood naturally appears as the probability of a measured quantity to be part of its model. It is a single number that can advantageously be used as an indicator of the model‘s relevance regarding measurements. A novel complex FRF matrix statistical reduction is proposed, allowing the model’s likelihood computation. This reduction relies on the separation of statistically independent components such that the probability of the whole is the product of the probability of the components. The reduction is performed by a two stage Independent Component Analysis, first along the frequencies and second on frequency independent complex matrices. For each of the components, the joint probability density function of the complex coefficient is constructed from the various realization of the considered FRF matrix. The projection of any experimental or computed matrix on the components basis provides the complex coefficients which probabilities are known. The product of the component probabilities is the model’s likelihood. The proposed approach is applied to a mid-size vehicle body.