Adaptive sparse polynomial chaos expansions for uncertainty propagation and sensitivity analysis

This thesis takes place in the context of uncertainty propagation and sensitivity analysis of computer simulation codes for industrial application. It is aimed at carrying out such probabilistic studies while minimizing the number of model evaluations which may reveal time consuming. The present work relies upon the expansion of the model response onto the polynomial chaos (PC) basis, which allows the analyst to perform post-processing at a negligible cost. However fitting the PC expansion may require a high number of calls to the model if the latter depends on a large number of input parameters, say more than 10. To circumvent this problem, two algorithms are proposed in order to select only a low number of significant terms in the PC approximation, namely a stepwise regression scheme and a procedure based on Least Angle Regression (LAR). Both approaches eventually provide PC representations with a small number of coefficients which may be computed using a reduced number of model evaluations. The methods are first tested and compared on various academic examples. Then they are applied to the industrial problem of the assessment of a pressure vessel of a nuclear power plant. The obtained results show the efficiency of the proposed procedures to carry out uncertainty and sensitivity analysis of high-dimensional problems. (author)