Uncertainty quantification/propagation in nonlinear models: Robust reduction – generalized polynomial chaos

Abstract

Purpose

The purpose of this paper is to develop robust metamodels, which allow propagating parametric uncertainties, in the presence of localized nonlinearities, with reduced cost and without significant loss of accuracy.

Design/methodology/approach

The proposed metamodels combine the generalized polynomial chaos expansion (gPCE) for the uncertainty propagation and reduced order models (ROMs). Based on the computation of deterministic responses, the gPCE requires prohibitive computational time for large-size finite element models, large number of uncertain parameters and presence of nonlinearities. To overcome this issue, a first metamodel is created by combining the gPCE and a ROM based on the enrichment of the truncated Ritz basis using static residuals taking into account the stochastic and nonlinear effects. The extension to the Craig–Bampton approach leads to a second metamodel.

Findings

Implementing the metamodels to approximate the time responses of a frame and a coupled micro-beams structure containing localized nonlinearities and stochastic parameters permits to significantly reduce computation cost with acceptable loss of accuracy, with respect to the reference Latin Hypercube Sampling method.

Originality/value

The proposed combination of the gPCE and the ROMs leads to a computationally efficient and accurate tool for robust design in the presence of parametric uncertainties and localized nonlinearities.

Citation

Chikhaoui, K., Bouhaddi, N., Kacem, N., Guedri, M. and Soula, M. (2017), "Uncertainty quantification/propagation in nonlinear models: Robust reduction – generalized polynomial chaos", Engineering Computations, Vol. 34 No. 4, pp. 1082-1106. https://doi.org/10.1108/EC-11-2015-0363