2014a). Combining polynomial chaos expansions and Kriging for solving structural reliability problems

science and engineering in order to predict the behaviour of systems and, in case of engineering applications, to optimize them and assess their performance. In parallel, engineers are all the more concerned with structural reliability and robust design, meaning that the quantification of uncertainties has become a key challenge. Due to the high cost of advanced computational models (CM), classical techniques such as Monte Carlo simulation are not applicable. In this respect, meta-modelling techniques allow one to build up a surrogate model from a limited number of runs of the CM. Among many available options, Kriging and Polynomial Chaos Expansions (PCE) are two popular techniques. Kriging assumes that the computational model is a realization of a Gaussian random process whose properties (mean, autocorrelation structure) are fitted from a set of computer runs. PCE aim at approximating the CM response using a set of multivariate orthogonal polynomials in the input variables. The coefficients of a PCE are computed e.g. by least-square minimization. In this paper we introduce PC-Kriging as a new non-intrusive meta-modelling technique derived from the combination of PCE and Kriging. A sparse set of orthonormal polynomials is first selected using the least angle regression algorithm as in Blatman and Sudret (2011). Then the parameters of the autocorrelation function of the underlying Gaussian field are fitted using the universal Kriging equations with the sparse PCE as a trend. Various trends and associated Kriging models ar