A new discrepancy for sample generation in stochastic response analyses of aerospace problems with uncertain parameters

Good distribution of samples and weights can improve the computational accuracy and efficiency in the stochastic response analyses of aerospace problems with uncertain parameters. This work proposes a new Generalized L2 Discrepancy based on a General Point (GL2D-GP) for generating samples and their corresponding weights. The proposed GL2D-GP is an extension of the existing discrepancy by introducing the non-same weights and a smaller box to measure probability errors. Minimizing the GL2D-GP can yield a weight optimization formula that generates a set of optimal non-identical weights for a given sample set. Through minimizing the GL2D-GP assigned to the set of optimal non-same weights, a new sample and weight generation method is developed. In the proposed method, the samples can be easily generated in terms of the generalized Halton formula with a series of optimal permutation vectors which are found by the intelligent evolutionary algorithm . Once the sample set is obtained, the optimal weights can be generated in terms of the weight optimization formula. Five numerical examples are presented to verify the high accuracy, efficiency, and strong robustness of the proposed sample generation method based on GL2D-GP.