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RESEARCH PAPERS

An Approach for Testing Methods for Modeling Uncertainty

[+] Author and Article Information
Raphael T. Haftka

Mechanical and Aerospace Engineering Department, The University of Florida, 231 MAE-A Building, Gainesville, FL 32611-6250haftka@ufl.edu

Raluca I. Rosca

Mechanical and Aerospace Engineering Department, The University of Florida, 231 MAE-A Building, Gainesville, FL 32611-6250rarosca@ufl.edu

Efstratios Nikolaidis

Mechanical, Industrial and Manufacturing Engineering, The University of Toledo, 4034 Nitschke Hall, Toledo, OH 43606enikolai@eng.utoledo.edu

J. Mech. Des 128(5), 1038-1049 (Aug 10, 2005) (12 pages) doi:10.1115/1.2214738 History: Received January 13, 2005; Revised August 10, 2005

To address the need for efficient and unbiased experimental testing of methods for modeling uncertainty that are used for decision making, we devise an approach for probing weaknesses of these methods by running numerical experiments on arbitrary data. We recommend using readily available data recorded in real-life activities, such as competitions, student design projects, medical procedures, or business decisions. Because the generating mechanism and the probability distribution of this data is often unknown, the approach adds dimensions, such as fitting errors and time dependencies of data that may be missing from tests conducted using computer simulations. For an illustration, we tested probabilistic and possibilistic methods using a database of results of a domino tower competition. The experiments yielded several surprising results. First, even though a probabilistic metric of success was used, there was no significant difference between the rates of success of the probabilistic and possibilistic models. Second, the common practice of inflating uncertainty when there is little data about the uncertain variables shifted the decision differently for the probabilistic and possibilistic models, with the latter being counter-intuitive. Finally, inflation of uncertainty proved detrimental even when very little data was available.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Approach for testing a method for decision under uncertainty

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Figure 2

Histograms of maximum built heights of domino towers

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Figure 3

Domino competition: decision/event tree

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Figure 4

Design decision for selecting location of anchor; (a) beam with boxes, (b) decision tree

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Figure 5

A comparison of the likelihood of success of probabilistic and possibilistic designs versus the handicap for the case where the decision maker has all the data in the database and the case where the decision maker knows the true probability distribution of the population of maximum heights

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Figure 6

A comparison of the likelihood of the success of probabilistic and possibilistic designs versus the handicap for the case where the decision maker has five data points and the case where the decision maker knows the true probability distribution of the population of maximum heights

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Figure 7

Triangular membership function (solid line) fitted to the sample of 5 from the Competitor’s experiments [27, 37, 37, 27, 31] and sample cumulative histogram

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Figure 8

Experimental data CDF (bars), fitted shifted gamma CDF (circles), and fitted normal CDF (asterisks) for the same data as in Fig. 7

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Figure 9

Extreme inflation of the uncertainty in the Competitor’s performance reduces the sensitivity of the probability of the Competitor’s failure to the guaranteed height, thereby reducing the optimum guaranteed height

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Figure 10

Inflation of the uncertainty in the Competitor’s performance increases the importance of the Competitor’s failure, thereby increasing the optimum guaranteed height

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Figure 11

Probabilistic and possibilistic optima when there is high uncertainty in the Competitor’s performance and little uncertainty in Rosca’s performance. The difference between the ways probabilistic and possibilistic design find the optimum guaranteed height is accentuated in this case. The probability density of the Competitor’s maximum built height is almost zero over the entire range of heights in the figure.

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