Adaptive Generalized Polynomial Chaos for Nonlinear Random Oscillators

Didier Lucor · George Em Karniadakis

80 citations0/0 files storedSIAM Journal on Scientific Computing

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Probabilistic and Robust Engineering Design Mathematical functions and polynomials Model Reduction and Neural Networks

Abstract

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.

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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 1992Random Vibration of Mechanical and Structural Systems 1999Ingredients for a general purpose stochastic finite elements implementation 1999Stochastic Finite Elements with Multiple Random Non-Gaussian Properties 1998Adaptive polynomial chaos expansions applied to statistics of extremes in nonlinear random vibration

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