A collocation scheme for deep uncertainty treatment

Considering an uncertain correlation length of the input random fields described by a Karhunen-Loève expansion leads to a probability-box approach for the stochastic finite element computation. But, these computations are highly costly. Then, a stochastic collocation method using sparse grids within a Smolyak algorithm is proposed to reduce the computational cost, particularly in the context of non-linear computations. The interest and the development of the Smolyak algorithm for stochastic model with non-linear finite element methods regarding mixed, aleatory and epistemic, uncertain inputs are here introduced. The limitations of Smolyak algorithm are critically discussed and suggestions for improvement are made

Development of fuzzy probability based random fields for the numerical structural design

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