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Research Papers

# Experimental Data Have to Decide Which of the Nonprobabilistic Uncertainty Descriptions—Convex Modeling or Interval Analysis—to Utilize

[+] Author and Article Information
Xiaojun Wang1

Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing, 100083, P.R.C.xjwang@buaa.edu.cn

Isaac Elishakoff

Department of Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431-0991elishako@fau.edu

Zhiping Qiu

Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing, 100083, P.R.C.zpqiu@buaa.edu.cn

1

Corresponding author.

J. Appl. Mech 75(4), 041018 (May 16, 2008) (8 pages) doi:10.1115/1.2912988 History: Received June 28, 2007; Revised March 04, 2008; Published May 16, 2008

## Abstract

This study shows that the type of the analytical treatment that should be adopted for nonprobabilistic analysis of uncertainty depends on the available experimental data. The main idea is based on the consideration that the maximum structural response predicted by the preferred theory ought to be minimal, and the minimum structural response predicted by the preferred theory ought to be maximal, to constitute a lower overestimation. Prior to the analysis, the existing data ought to be enclosed by the minimum-volume hyper-rectangle $V1$ that contains all experimental data. The experimental data also have to be enclosed by the minimum-volume ellipsoid $V2$. If $V1$ is smaller than $V2$ and the response calculated based on it $R(V1)$ is smaller than $R(V2)$, then one has to prefer interval analysis. However, if $V1$ is in excess of $V2$ and $R(V1)$ is greater than $R(V2)$, then the analyst ought to utilize convex modeling. If $V1$ equals $V2$ or these two quantities are in close vicinity, then two approaches can be utilized with nearly equal validity. Some numerical examples are given to illustrate the efficacy of the proposed methodology.

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## Figures

Figure 4

Rectangle and ellipse containing the data on uncertain parameters F1 and F2

Figure 5

Rectangle and ellipse containing the data on uncertain parameters F1 and F2

Figure 6

A 60-bar space truss structure

Figure 7

Rectangle and ellipse containing the data on uncertain parameters F1 and F2

Figure 8

Rectangle and ellipse containing the data on uncertain parameters F1 and F2

Figure 1

A seven bar planar truss structure

Figure 2

Rectangle and ellipse containing the data on uncertain parameters F1 and F2

Figure 3

Rectangle and ellipse containing the data on uncertain parameters F1 and F2

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