Research Papers

Development of a Multistage Reliability-Based Design Optimization Method

[+] Author and Article Information
Eric J. Paulson

Air Force Research Laboratory,
Edwards AFB, CA 93524
e-mail: eric.paulson.1@us.af.mil

Ryan P. Starkey

University of Colorado,
Boulder, CO 80309
e-mail: rstarkey@colorado.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 29, 2013; final manuscript received August 23, 2013; published online November 7, 2013. Assoc. Editor: David Gorsich.

This material is declared a work of the US Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited; PA-13468.

J. Mech. Des 136(1), 011007 (Nov 07, 2013) (8 pages) Paper No: MD-13-1140; doi: 10.1115/1.4025492 History: Received March 29, 2013; Revised August 23, 2013

Complex system acquisition and its associated technology development have a troubled recent history. The modern acquisition timeline consists of conceptual, preliminary, and detailed design followed by system test and production. The evolving nature of the estimates of system performance, cost, and schedule during this extended process may be a significant contribution to recent issues. The recently proposed multistage reliability-based design optimization (MSRBDO) method promises improvements over reliability-based design optimization (RBDO) in achieved objective function value. In addition, its problem formulation more closely resembles the evolutionary nature of epistemic design uncertainties inherent in system design during early system acquisition. Our goal is to establish the modeling basis necessary for applying this new method to the engineering of early conceptual/preliminary design. We present corrections in the derivation and solutions to the single numerical example problem published by the original authors, Nam and Mavris, and examine the error introduced under the reduced-order reliability sampling used in the original publication. MSRBDO improvements over the RBDO solution of 10–36% for the objective function after first-stage optimization are shown for the original second-stage example problem. A larger 26–40% improvement over the RBDO solution is shown when an alternative comparison method is used than in the original. The specific implications of extending the method to arbitrary m-stage problems are presented, together with a solution for a three-stage numerical example. Several approaches are demonstrated to mitigate the computational cost increase of MSRBDO over RBDO, resulting in a net decrease in calculation time of 94% from an initial MSRBDO baseline algorithm.

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Nam, T., 2007,“A Generalized Sizing Method For Revolutionary Concepts Under Probabilistic Design Constraints,” Ph.D. thesis, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA.
Nam, T., and Mavris, D. N., 2008, “Multi-Stage Reliability-Based Design Optimization for Aerospace System Conceptual Design,” 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Apr. 7–10, 2008, Schaumburg, IL.
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Paulson, E. J., and Starkey, R. P., 2011, “Methodology for Variable Fidelity Multistage Optimization Under Uncertainty,” 13th AIAA Non-Deterministic Approaches Conference, Apr. 4–7, 2011, Denver, CO.
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Fig. 1

System performance measures/uncertainties over acquisition timeline [3]

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Fig. 2

Comparison of decision/realization in RBDO and MSRDO

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Fig. 3

Plots of RBDO solutions for x3 = (a) 0, (b) 1, and (c) 2

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Fig. 11

3SRBDO test problem objective function and reliability vs. x3

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Fig. 13

Hybrid gradient optimization computational costs

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Fig. 10

Decreasing effectiveness of pre-SORS point elimination near region of optima

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Fig. 9

Test problem 1 code speed improvement results

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Fig. 8

2SRBDO test problem first-stage objective function and reliability values for ξ2

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Fig. 7

2SRBDO test problem first-stage objective function and reliability values for ξ1

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Fig. 6

SORS reliability loop logic

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Fig. 5

FORS reliability loop logic

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Fig. 4

FOOFS objective function loop logic

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Fig. 12

E[x2], E[x3], and E[f(x)] vs. x1




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