Generalized Fourier Series for Representing Random Variables and Application for Quantifying Uncertainties in Optimization

Mohamed Bassi¹; José Edouardo Souza de Cursi²; Rachid Ellaia³

¹ INSA Rouen (France) and EMI Rabat (Morocco); ² INSA Rouen; ³ Mohammadia School of Engineering

doi:10.20906/CPS/USM-2016-0037

Resumo

We present a new Hilbert expansion type method for quantifying uncertainties in optimization problems. A demonstration is made in a Bochner space to determine the conditions of using this approach which is based on Generalized Fourier Series Expansion of random variables. The main advantage of this technic is the approximation of a random variable without need to determine its joint probability distribution whit another random vector, which is one of the defects of the famous Wiener Chaos Expansion based methods. Moreover, our method is more flexible and its application proves its numerical efficiency.

Palavras-chave: Optimization,; Uncertainties; Hilbert expansion; Generalized Fourier Series