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research-article

Developing Meta-Models for Fast and Accurate Prediction of the Draping of Physical Surfaces

[+] Author and Article Information
Esben T Christensen

Aalborg University, Dept. of Mechanical and Manufacturing Engineering, Fibigerstræde 16, 9220 Aalborg East, Denmark
esben@m-tech.aau.dk

Alexander I J Forrester

University of Southampton, Engineering Centre of Excellence, Burgess Road, SO16 7QF Southampton, United Kingdom
alexander.forrester@soton.ac.uk

Erik Lund

Aalborg University, Dept. of Mechanical and Manufacturing Engineering, Fibigerstræde 16, 9220 Aalborg East, Denmark
el@m-tech.aau.dk

Esben Lindgaard

Aalborg University, Dept. of Mechanical and Manufacturing Engineering, Fibigerstræde 16, 9220 Aalborg East, Denmark
elo@m-tech.aau.dk

1Corresponding author.

ASME doi:10.1115/1.4039334 History: Received April 18, 2017; Revised October 28, 2017

Abstract

In this paper, the use of methods from the meta- or surrogate modeling literature for building models predicting the draping of physical surfaces is examined. An example application concerning modeling of the behavior of a variable shape mould is treated. Four different methods are considered for this problem. The proposed methods are difference methods assembled from the methods kriging and proper orthogonal decomposition together with a spline-based underlying model. The four models, namely kriging and proper orthogonal decomposition with kriging of the coefficients in global and local variants, are compared in terms of accuracy and numerical efficiency on data sets of different sizes for the treated application. It is shown that the proper orthogonal decomposition based methods are vastly superior to models based on kriging alone, and that the use of a difference model structure is advantageous. It is demonstrated that local modeling schemes, where the complete surface behavior is modeled by a collection of locally defined smaller models, can provide a good compromise between achieving good model accuracy, and scalability of the models to large systems.

Copyright (c) 2018 by ASME
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