Non-polynomial expansion for stochastic problems with non-classical pdfs

Abstract : In this study, some preliminary results about the possibility to extend the classical polynomial Chaos (PC) theory to stochastic problems with non-classical probability distributions of the variables, i.e. outside the framework of the classical Wiener-Askey scheme, are presented. The proposed strategy allows to obtain an analytical representation of the solution in order to build a metamodel or to compure conditional statistics. Various numerical results obtained on some analytical problems are then provided to demonstrate the correctness of the presented approach.