Keywords: polynomial chaos, uncertainty, B-splines, hybrid optimization, separable non-linear least squares.

This study investigates a non-intrusive uncertainty quantification scheme relying on a polynomial chaos (PC) basis constructed from the available data. Instead of predefining basis functions with respect to the statistics of the uncertain input, the method introduced here realizes a proper basis function parametrization that adapts to a given input-output data set. Parameter estimation is effectively dealt with through a separable non-linear least squares procedure that allows for simultaneous estimation of both the PC basis and the corresponding coefficients of projection. The induced constrained non-quadratic optimization problem is treated through the implementation of a hybrid optimization algorithm that combines the advantages of evolutionary and deterministic schemes, combining higher convergence rates and reliability in the search for a global optimum. The method's effectiveness is examined through both numerical and experimental case studies, while comparisons with the classical PC based on the Wiener-Askey scheme and alternative data-driven methods, such as the arbitrary PC, provide indications of superior performance.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £50 +P&P)