Matching the principal deformation mode method with the probability transformation method for the analysis of uncertain systems

This paper deals with the probabilistic description of the random response of linear uncertain structural system when the uncertainties are modeled as random variables with assigned probability density function (pdf). In particular, a novel approach is presented that allows the direct evaluation of the response pdf starting from the joint pdf characterizing the structural uncertainties. It consists in matching adequately two methods, recently proposed by the authors, which are the Approximated Principal Deformation Modes method and the Probability Transformation Method. The proposed approach, obtained by this coupling, reveals to have good levels of accuracy, even for relatively high uncertainties, and of computational efficiency, as the reported numerical applications show.