Strategy of selecting points via number theoretical method in probability density evolution analysis of stochastic response of structures

The newly developed probability density evolution method(PDEM) is capable of capturing instantaneous probability density functionand its evolution of linear and/or nonlinear stochastic response ofstructures. In the occasions that multiple random parameters are involved inthe structural properties and external excitations, the strategy ofselecting representative points required in the PDEM is of paramountimportance to the accuracy and efficiency. Enlightened by the NumberTheoretical Method successfully employed in high-dimensional numericalintegration, the strategy of selecting points via Number Theoretical Methodis proposed in the present paper. Further, making use of the sphericallysymmetric properties or the radial attenuation properties of the jointprobability density function, the points scattered over themulti-dimensional hypercube selected by the Number Theoretic Method aresieved once again such that only the points inside the multi-dimensionalhyper-ball are retained. With the proposed strategy of selecting points, thestochastic response analysis involving multiple random parameters is almostas efficient as the problem involving only one single random parameter.