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Research Papers: Design Automation

Reliability-Based Design Optimization on Qualitative Objective With Limited Information

[+] Author and Article Information
Khaldon T. Meselhy

School of Mechatronic Systems Engineering,
Simon Fraser University,
250-13450 102 Avenue,
Surrey, BC V3T 0A3, Canada
e-mail: ktahmed@sfu.ca

G. Gary Wang

Professor
School of Mechatronic Systems Engineering,
Simon Fraser University,
250-13450 102 Avenue,
Surrey, BC V3T 0A3, Canada
e-mail: gary_wang@sfu.ca

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 3, 2017; final manuscript received August 1, 2018; published online September 18, 2018. Editor: Wei Chen.

J. Mech. Des 140(12), 121402 (Sep 18, 2018) (8 pages) Paper No: MD-17-1537; doi: 10.1115/1.4041172 History: Received August 03, 2017; Revised August 01, 2018

Reliability-based design optimization (RBDO) algorithms typically assume a designer's prior knowledge of the objective function along with its explicit mathematical formula and the probability distributions of random design variables. These assumptions may not be valid in many industrial cases where there is limited information on variable variability and the objective function is subjective without mathematical formula. A new methodology is developed in this research to model and solve problems with qualitative objective functions and limited information about random variables. Causal graphs and design structure matrix are used to capture designer's qualitative knowledge of the effects of design variables on the objective. Maximum entropy theory and Monte Carlo simulation are used to model random variables' variability and derive reliability constraint functions. A new optimization problem based on a meta-objective function and transformed deterministic constraints is formulated, which leads close to the optimum of the original mathematical RBDO problem. The developed algorithm is tested and validated with the Golinski speed reducer design case. The results show that the algorithm finds a near-optimal reliable design with less initial information and less computation effort as compared to other RBDO algorithms that assume full knowledge of the problem.

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Figures

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Fig. 4

Eigenvector calculation steps

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Fig. 3

Design matrix derived from causal graph for the example

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Fig. 2

An example of causal graph

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Fig. 1

The five-level Likert scale

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Fig. 5

Probability density functions of various functions of assumed random variables

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Fig. 6

Cumulative distributions comparison between the actual and triangular distribution

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Fig. 7

Golinski speed reducer configuration. The design variables are x1—gear width, x2—gear module, x3—no. of teeth of the pinion, x4—shaft 1 length, x5—shaft 2 length, x6—shaft 1 diameter, and x7—shaft 2 diameter.

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Fig. 8

Causal graph for speed reducer weight reduction problem

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Fig. 9

Design matrix for the speed reducer

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