Use of polynomial chaos expansions and maximum likelihood estimation for probabilistic inverse problems

The present paper deals with the identification of probabilistic models of input variables using response measurements. The input random variables, whose probability density function has to be identified, are represented by their polynomial chaos expansion (PCE). The proposed method allows to solve the probabilistic inverse problem using an efficient maximum likelihood approach. An advanced optimization algorithm is used to maximize this likelihood and get the optimal values of unknown PCE coefficients. The approach is illustrated by determining the variability of the loading applied to a series of similar simply supported beams when a database of measured maximum deflection is at hand