Global point-selection strategy based on the MF-discrepancy for stochastic response analysis of structures with independent random variables

Randomness widely exists in engineering systems, and it is a great challenge to precisely analyze the stochastic response and dynamic reliability of engineering structures.Some methods based on the high-efficacy global point sets have been proved to be effective.Reasonably measuring and improving the efficacy of the global point sets are of great importance in order to further improve the accuracy of these methods.To measure the efficacy of a point set with an acceptable computational cost even for high-dimensional cases, a new MF-discrepancy is introduced in the present paper.An extended Koksma-Hlawka inequality for error estimation in terms of the MF-discrepancy is established first, providing theoretical basis for the proposal of both the MF-discrepancy and the MF-discrepancy based pointselection strategy.Then the analytic expression of the MF-discrepancy is presented, giving deeper insights into its quantitative properties, and the lowest bound of the MF-discrepancy is rigorously derived and proven as a result.A unified theoretical framework for the MFdiscrepancy-based point-selection strategy, which can greatly reflect the physical properties of the system, is established.The widely applied GF-discrepancy-based point-selection method is included in the framework as a method focusing on the local minimization of the MFdiscrepancy, and a novel point-selection method focusing on the global minimization of the MF-discrepancy is introduced.In the global point-selection method, the composition and the correlation rank of a point set are separated: the composition of each dimension is first determined based on the lowest bound of MF-discrepancy, then the correlation rank is determined according to some certain rules and the final representative point set can be obtained.Several numerical examples are studied to verify the high efficacy of the MFdiscrepancy-based point-selection strategy.