PC-Kriging: A new meta-modelling method and its application to quantile estimation

The cost for solving structural reliability problems is high, e.g. when using finite element models. Meta-modelling decreases the computational effort of time-consuming computer simulations by approximating the underlying computer modelling techniques with simple and easy-to-evaluate functions. In this paper, we introduce Polynomial-Chaos-Kriging (PC-Kriging) as a new non-intrusive meta-modelling method derived from the combination of Polynomial Chaos Expansions (PCE) (Ghanem and Spanos 2003) and Kriging (Santner et al. 2003). A sparse set of orthonormal polynomials approximates the global behaviour of the computational model. An adaptive algorithm determines the optimal sparse set of polynomials according to the least angle regression algorithm (Blatman and Sudret 2011). The resulting set of orthogonal polynomials represents the trend of a universal Kriging model. The parameters of the universal Kriging model are then obtained by maximum likelihood estimation. The new approach is applied to solve quantile estimation problems using an adaptive experimental design scheme. Based on the so-called Kriging variance, i.e. a local error estimate, an iterative algorithm determines the best additional experimental design points in order to increase the accuracy of the quantity of interest. The adaptive experimental design algorithm is applied onto a benchmark analytical function and on two-degree-of-freedom damped oscillator problem.

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