A FIRST ORDER ASSEMBLE EVOLUTION METHOD FOR SOLVING GDEE
Jie Li, Weifeng Tao · 2015
Probability density evolution method (PDEM) provides a feasible approach for stochastic response analysis of general structures.The key issue of PDEM is to solve a generalized density evolution equation (GDEE).Previously, GDEE was solved in the framework of point evolution method which is in essence a zero order assemble evolution method.In this paper, a first order assemble evolution method is proposed aiming at increasing the accuracy and robustness of PDEM.The main idea of the proposed method is to extend the velocity term of the derived density evolution equation from integration of GDEE in a subdomain of the random space with a first order term with respect to the response variable.Compared to the original one, the proposed method directly introduces inherent diffusivity into PDEM which is essential in order to better reflect the evolution result of the corresponding subdomain.The same as in the point evolution case, TVD finite difference scheme is adopted to solve the new derived density evolution equation.A single-degree-of-freedom (SDOF) oscillator with random frequency is studied in the paper, and the result indicates that the proposed method performs better than the original one.