Adaptive generalized polynomial chaos for nonlinear random oscillators

The solution of nonlinear random oscillators subject to stochastic forcing is investigated numerically. In particular, solutions to the random Duffing oscillator with random Gaussian and non-Gaussian excitations are obtained by means of the generalized polynomial chaos (GPC). Adaptive procedures are proposed to lower the increased computational cost of the GPC approach in large-dimensional spaces. Adaptive schemes combined with the use of an enriched representation of the system improve the accuracy of the GPC approach by reordering the random modes according to their magnification by the system.