Response statistics of nonlinear, compliant offshore structures by the path integral solution method

Abstract

The paper investigates the applicability of the path integral solution method for calculating the response statistics of nonlinear dynamic systems whose equations of motion can be modelled by the use of Ito stochastic differential equations. The state vector process associated with such a model is generally a diffusion process, and the probability density function of the process thus satisfies a Fokker-Planck-Kolmogorov equation. It is shown in the paper that the path integral solution technique combined with an appropriate numerical scheme constitutes a powerful method for solving the Fokker-Planck-Kolmogorov equation with natural boundary conditions. The method distinguishes itself by high accuracy and numerical robustness even at very low probability levels. These features are highlighted by application to example studies of nonlinear, compliant offshore structures.