Research Papers

Reliability-Based Multidisciplinary Design Optimization Using Probabilistic Gradient-Based Transformation Method

[+] Author and Article Information
Po Ting Lin

Assistant Professor
Department of Mechanical Engineering,
Research and Development Center
for Microsystem Reliability,
Chung Yuan Christian University,
Chungli City,
Taoyuan County, Taiwan 32023
e-mail: potinglin@cycu.edu.tw

Hae Chang Gea

Department of Mechanical and
Aerospace Engineering,
The State University of New Jersey,
Piscataway, NJ 08854
e-mail: gea@rci.rutgers.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received January 16, 2012; final manuscript received October 19, 2012; published online December 10, 2012. Assoc. Editor: Wei Chen.

J. Mech. Des 135(2), 021001 (Dec 10, 2012) (12 pages) Paper No: MD-12-1052; doi: 10.1115/1.4023025 History: Received January 16, 2012; Revised October 19, 2012

Recently, solving the complex design optimization problems with design uncertainties has become an important but very challenging task in the communities of reliability-based design optimization (RBDO) and multidisciplinary design optimization (MDO). The MDO algorithms decompose the complex design problem into the hierarchical or nonhierarchical optimization structure and distribute the workloads to each discipline (or subproblem) in the decomposed structure. The coordination of the local responses is crucial for the success of finding the optimal design point. The problem complexity increases dramatically when the existence of the design uncertainties is not negligible. The RBDO algorithms perform the reliability analyses to evaluate the probabilities that the random variables violate the constraints. However, the required reliability analyses build up the degree of complexity. In this paper, the gradient-based transformation method (GTM) is utilized to reduce the complexity of the MDO problems by transforming the design space to multiple single-variate monotonic coordinates along the directions of the constraint gradients. The subsystem responses are found using the monotonicity principles (MP) and then coordinated for the new design points based on two general principles. To consider the design uncertainties, the probabilistic gradient-based transformation method (PGTM) is proposed to adapt the first-order probabilistic constraints from three different RBDO algorithms, including the chance constrained programming (CCP), reliability index approach (RIA), and performance measure approach (PMA), to the framework of the GTM. PGTM is efficient because only the sensitivity analyses and the reliability analyses require function evaluations (FE). The optimization processes of monotonicity analyses and the coordination procedures are free of function evaluations. Several mathematical and engineering examples show the PGTM is capable of finding the optimal solutions with desirable reliability levels.

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Fig. 1

Different MDO optimization structures: (a) Hierarchical; (b) nonhierarchical; and (c) GTM [24]

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Fig. 2

Probabilistic design optimization of each subsystem in the hierarchical and nonhierarchical MDO structure

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Fig. 3

The unit constraint gradients and the first-order probabilistic constraints for (a) CCP, (b) PMA, and (c) RIA

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Fig. 4

Flow chart of the PGTM

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Fig. 5

Iteration histories of the design variables in three different PGTM approaches: (a) x1 in PGTM-CCP, (b) x2 in PGTM-CCP, (c) x1 in PGTM-RIA, (d) x2 in PGTM-RIA, (e) x1 in PGTM-PMA, and (f) x2 in PGTM-PMA

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Fig. 6

Iteration processes of the example 2 using (a) PGTM-CCP, (b) PGTM-RIA, and (c) PGTM-PMA

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Fig. 7

Vertical impinging CVD of silicon [55]

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Fig. 8

Performance functions of silicon deposition: (a) MDR, (b) RMS, and (c) PWA [54]

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Fig. 9

Reliability-based optimal experimental parameters for the maximum performance and the sustainable design

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Fig. 10

The structure of the anchor design [29,56-59]




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