An Efficient Sampling Method for Regression-Based Polynomial Chaos Expansion (Communications in Computational Physics, 2013)
The polynomial chaos expansion (PCE) is an efficient numerical method forperforming a reliability analysis. It relates the output of a nonlinear system with theuncertainty in its input parameters using a multidimensional polynomial approximation (the so-called PCE). Numerically, such an approximation can be obtained by usinga regression method with a suitable design of experiments. The cost of this approximation depends on the size of the design of experiments. If the design of experimentsis large and the system is modeled with a computationally expensive FEA (Finite Element Analysis) model, the PCE approximation becomes unfeasible. The aim of thiswork is to propose an algorithm that generates efficiently a design of experiments of asize defined by the user, in order to make the PCE approximation computationally feasible. It is an optimization algorithm that seeks to find the best design of experimentsin the D-optimal sense for the PCE. This algorithm is a coupling between genetic algorithms and the Fedorov exchange algorithm. The efficiency of our approach in terms ofaccuracy and computational time reduction is compared with other existing methodsin the case of analytical functions and finite element based functions.