Possibility-Based Design Optimization Method for Design Problems With Both Statistical and Fuzzy Input Data

[+] Author and Article Information
Liu Du

Department of Mechanical & Industrial Engineering, College of Engineering, The University of Iowa, Iowa City, IA 52242

K. K. Choi

Department of Mechanical & Industrial Engineering, College of Engineering, The University of Iowa, Iowa City, IA 52242kkchoi@ccad.uiowa.edu

Byeng D. Youn

Department of Mechanical Engineering, College of Engineering, University of Detroit Mercy, Detroit, MI 48219

David Gorsich

AMSTA-TR-N (MS 263), U.S. Army National Automotive Center, Warren, MI 48397

J. Mech. Des 128(4), 928-935 (Nov 23, 2005) (8 pages) doi:10.1115/1.2204972 History: Received July 13, 2005; Revised November 23, 2005

The reliability based design optimization (RBDO) method is prevailing in stochastic structural design optimization by assuming the amount of input data is sufficient enough to create accurate input statistical distribution. If the sufficient input data cannot be generated due to limitations in technical and/or facility resources, the possibility-based design optimization (PBDO) method can be used to obtain reliable designs by utilizing membership functions for epistemic uncertainties. For RBDO, the performance measure approach (PMA) is well established and accepted by many investigators. It is found that the same PMA is a very much desirable approach also for the PBDO problems. In many industry design problems, we have to deal with uncertainties with sufficient data and uncertainties with insufficient data simultaneously. For these design problems, it is not desirable to use RBDO since it could lead to an unreliable optimum design. This paper proposes to use PBDO for design optimization for such problems. In order to treat uncertainties as fuzzy variables, several methods for membership function generation are proposed. As less detailed information is available for the input data, the membership function that provides more conservative optimum design should be selected. For uncertainties with sufficient data, the membership function that yields the least conservative optimum design is proposed by using the possibility-probability consistency theory and the least conservative condition. The proposed approach for design problems with mixed type input uncertainties is applied to some example problems to demonstrate feasibility of the approach. It is shown that the proposed approach provides conservative optimum design.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

RBDO history of mathematical problem

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Figure 2

PBDO history of mathematical problem

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Figure 3

PBDO history of mixed variable problem

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Figure 4

Vehicle side impact model



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