Data-driven polynomial chaos basis estimation Spiridonakos, Minas D.; Chatzi, Eleni N.
A non-intrusive uncertainty quantification scheme based on Polynomial Chaos (PC) basis constructed from available data is introduced. The method uses properly parametrized basis functions in order to let them adapt to the given input-output data instead of predefining them based on the probability density function of the uncertain input variable. Model parameter estimation is effectively dealt with through a Separable Non-linear Least Squares (SNLS) procedure that allows the simultaneous estimation of both the PC basis and the corresponding coefficients of projection. Method’s effectiveness is demonstrated through its application to the uncertainty propagation modelling in two examples: a nonlinear differential equation with uncertain initial conditions and a nonlinear single degree-of-freedom system with an uncertain parameter. Comparisons with classical PC expansion modelling based on the Wiener-Askey scheme are used to illustrate the method’s performance and potential advantages.
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