Modified Probability Density Evolution Method for the Solution of Multi-Degree-of-Freedom Nonlinear Stochastic Dynamical Systems

A probability density evolution based exponential polynomial regression (PDEM-EPR) method to calculate the probability density function (PDF) of the high dimensional nonlinear stochastic dynamical systems is presented in this paper. Several typical examples, such as linear oscillator and Duffing oscillator are solved by PDEM-EPR method, and the results fit well with the analytical solutions. An engineering practice problem of ship nonlinear random roll in the beam waves is involved in this paper. The results obtained by PDEM-EPR is compared with those obtained by path integral method. The later results were given by Chai Wei [3]. It shows that PDEM-EPR method has the advantages as following: 1) The multi-degree-of-freedom (MDOF) nonlinear stochastic dynamical problems can be solved by PDEM-EPR method; 2) High efficiency can be obtained by PDEM-EPR method.