The Number Theoretical Method in Response Analysis of Nonlinear Stochastic Structures

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Strategy for selecting representative points via tangent spheres in the probability density evolution method (2008, unknown): “In this case, it is reasonable that only the points inside a prescribed hyperball are selected as the final representative points [21].”
Probability density evolution analysis of engineering structures via cubature points (2012, methodology): “For instance, the application of the number theoretical method to PDEM achieved satisfactory results, especially when the points were used as the basic points in the partitioning of probability-assigned space [3,19].”
Advances of the probability density evolution method for nonlinear stochastic systems (2012, methodology): “Though some strategies have been well investigated on such methods as the dimension-reduction strategy via mapping [32], strategy via tangent spheres [35], and the number theoretical method [36], the methods applicable to problems involving very high-dimensional random variables (say, beyond 18) are”