Implications of High-Dimensional Geometry for Structural Reliability Analysis and a Novel Linear Response Surface Method Based on SVM

Alibrandi, Umberto, Alani, Amir and Koh, C.G. (2015) Implications of High-Dimensional Geometry for Structural Reliability Analysis and a Novel Linear Response Surface Method Based on SVM. International Journal of Computational Methods (ijcm), 12 (4). pp. 1-19. ISSN 0219-8762

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Abstract

The geometry of high-dimensional spaces is very different from low dimensional spaces and possesses some counter-intuitive features. It is shown that, for high dimensions, the sampling points fall far away from the origin and concentrate within an intersection between a very thin shell and a suitable equatorial slab. The well-known First-Order Reliability Method (FORM), originally formulated for low dimensions, may work well in many engineering problems of high dimension. But it is not able to reveal the level of achieved accuracy. Considering the features of high-dimensional geometry, a novel linear response surface based on Support Vector Method (SVM) is proposed for structural reliability problems of high dimension. The method is shown to outperform FORM for structural reliability problems of high dimension in terms of robustness and accuracy.

Item Type: Article
Uncontrolled Keywords: Structural reliability analysis; design point; response surface; FORM; SVM
Subjects: Construction and engineering > Built environment
Construction and engineering > Civil and structural engineering
Computing
Construction and engineering
Depositing User: Fabio Tosti
Date Deposited: 26 May 2016 13:03
Last Modified: 26 May 2016 13:03
URI: http://repository.uwl.ac.uk/id/eprint/2176

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