Response probability density function for non-bijective transformations

Abstract

This work deals with a new version of the probabilistic transformation method (PTM). In particular, it aims to report a new version of the PTM able to treat those systems in which input and output variables are linked with each other by means of non-bijective transformations. The formulation proposed allows to derive firstly the characteristic function (CF) of any response element in a very simple way without any kind of saturation; secondly, it allows to evaluate the probability density function (PDF) using the inverse Fourier transform. The work presents a brief overview of the classical version of the PTM and the new theoretical aspects are rigorously justified with extensive use of distributions; a numerical application is performed to verify the reliability of the proposed approach.