Modelling parametric uncertainties in vibroacoustics using a DEA approach

Dynamical Energy Analysis (DEA) is an approach for studying the vibroacoustic response of complex systems in the high frequency limit. DEA is a transfer operator method for the modelling of phase-space densities (or ray densities) arising in the ray-tracing approximation of a linear wave problem. It can also be viewed within the same family of methods as Statistical Energy Analysis, since DEA naturally incorporates non-parametric uncertainties by modelling mean energy densities; that is, the mean energy density is approximated without any knowledge of the specific sources of uncertainty affecting the underlying wave problem. In this work we describe a generalisation of the DEA approach as a stochastic transfer operator method. We discuss the design of appropriate probability density functions, which appear within the stochastic transfer operator, for the modelling of a number of sources of parametric uncertainty that may arise in vibroacoustic applications.