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Research Papers: Design Automation

Multiobjective Collaborative Robust Optimization With Interval Uncertainty and Interdisciplinary Uncertainty Propagation

[+] Author and Article Information
M. Li

Department of Mechanical Engineering, University of Maryland, College Park, MD 20742

S. Azarm1

Department of Mechanical Engineering, University of Maryland, College Park, MD 20742azarm@umd.edu

As shown in this example, it appears that our robust optimization approach can handle the case in which parameters have a discrete interval of uncertainty. However, we have not fully explored this aspect of the approach.

1

Corresponding author.

J. Mech. Des 130(8), 081402 (Jul 14, 2008) (11 pages) doi:10.1115/1.2936898 History: Received May 23, 2007; Revised March 12, 2008; Published July 14, 2008

We present a new solution approach for multidisciplinary design optimization (MDO) problems that, for the first time in literature, has all of the following characteristics: Each discipline has multiple objectives and constraints with mixed continuous-discrete variables; uncertainty exists in parameters and as a result, uncertainty propagation exists within and across disciplines; probability distributions of uncertain parameters are not available but their interval of uncertainty is known; and disciplines can be fully (two-way) coupled. The proposed multiobjective collaborative robust optimization (McRO) approach uses a multiobjective genetic algorithm as an optimizer. McRO obtains solutions that are as best as possible in a multiobjective and multidisciplinary sense. Moreover, for McRO solutions, the variation of objective and/or constraint functions can be kept within an acceptable range. McRO includes a technique for interdisciplinary uncertainty propagation. The approach can be used for robust optimization of MDO problems with multiple objectives, or constraints, or both together at system and subsystem levels. Results from an application of McRO to a numerical and an engineering example are presented. It is concluded that McRO can solve fully coupled MDO problems with interval uncertainty and obtain solutions that are comparable to a single-disciplinary robust optimization approach.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) Tolerance region, (b) AOVR, and (c) ACVR

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Figure 2

Performance sensitivity analysis for (a) objective robustness and (b) feasibility robustness, using (c) robustness indices

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Figure 3

A fully coupled two-discipline system

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Figure 4

Multiobjective collaborative optimization: (a) before decomposition and (b) after decomposition

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Figure 5

Collaborative optimization with uncertainty

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Figure 6

Handling couplings with uncertainty

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Figure 7

Obtained nominal and robust optimal solutions from McRO and all-in-one formulations

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Figure 9

Nominal and robust solutions for the speed reducer using the McRO approach

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