Reduced order modeling for nonlinear structural analysis using Gaussian process regression

Mengwu Guo

doi:10.1016/j.cma.2018.07.017

Return

Reduced order modeling for nonlinear structural analysis using Gaussian process regression

2018-11-01

191

Mengwu Guo *

Jan S. Hesthaven

DOI：10.1016/j.cma.2018.07.017

Original

Save

View PDF

Abstract

En 中文

A non-intrusive reduced basis (RB) method is proposed for parametrized nonlinear structural analysis undergoing large deformations and with elasto-plastic constitutive relations. In this method, a reduced basis is constructed from a set of full-order snapshots by the proper orthogonal decomposition (POD), and the Gaussian process regression (GPR) is used to approximate the projection coefficients. The GPR is carried out in the offline stage with active data selection, and the outputs for new parameter values can be obtained rapidly as probabilistic distributions during the online stage. Due to the complete decoupling of the offline and online stages, the proposed non-intrusive RB method provides a powerful tool to efficiently solve parametrized nonlinear problems with various engineering applications requiring multi-query or real-time evaluations. With both geometric and material nonlinearities taken into account, numerical results are presented for typical 1D and 3D examples, illustrating the accuracy and efficiency of the proposed method. (C) 2018 Elsevier B.Y. All rights reserved.

Keywords:

Reduced basis method

Nonlinear structural analysis

Proper orthogonal decomposition

Gaussian process regression

Machine learning