Research Papers: Design Automation

Employing Knowledge on Causal Relationship to Assist Multidisciplinary Design Optimization

[+] Author and Article Information
Di Wu

Product Design and Optimization Laboratory,
Simon Fraser University,
Surrey, BC V3T 0A3, Canada
e-mail: dwa88@sfu.ca

Eric Coatanea

Faculty of Engineering Science,
Laboratory of Mechanical Engineering
and Industrial System,
Tampere University of Technology,
Tampere, FI-33520, Finland
e-mail: eric.coatanea@tut.fi

G. Gary Wang

Product Design and Optimization Laboratory,
Simon Fraser University,
Surrey, BC V3T 0A3, Canada
e-mail: gary_wang@sfu.ca

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 7, 2018; final manuscript received December 8, 2018; published online January 11, 2019. Assoc. Editor: Christopher Mattson.

J. Mech. Des 141(4), 041402 (Jan 11, 2019) (11 pages) Paper No: MD-18-1104; doi: 10.1115/1.4042342 History: Received February 07, 2018; Revised December 08, 2018

With the increasing design dimensionality, it is more difficult to solve multidisciplinary design optimization (MDO) problems. Many MDO decomposition strategies have been developed to reduce the dimensionality. Those strategies consider the design problem as a black-box function. However, practitioners usually have certain knowledge of their problem. In this paper, a method leveraging causal graph and qualitative analysis is developed to reduce the dimensionality of the MDO problem by systematically modeling and incorporating the knowledge about the design problem into optimization. Causal graph is created to show the input–output relationships between variables. A qualitative analysis algorithm using design structure matrix (DSM) is developed to automatically find the variables whose values can be determined without resorting to optimization. According to the impact of variables, an MDO problem is divided into two subproblems, the optimization problem with respect to the most important variables, and the other with variables of lower importance. The novel method is used to solve a power converter design problem and an aircraft concept design problem, and the results show that by incorporating knowledge in form of causal relationship, the optimization efficiency is significantly improved.

Copyright © 2019 by ASME
Topics: Design , Optimization
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Shan, S. , and Wang, G. G. , 2010, “ Survey of Modeling and Optimization Strategies to Solve High-Dimensional Design Problems With Computationally-Expensive Black-Box Functions,” Struct. Multidiscip. Optim., 41(2), pp. 219–241. [CrossRef]
Sobieszczanski-Sobieski, J. , 1988, “ Optimization by Decomposition: A Step From Hierarchic to Non-Hierarchic Systems,” National Aeronautics and Space Administration, Washington, DC, Report No. N89-25149,
Braun, D. R. , 1996, “ Collaborative Optimization: An Architecture for Large-Scale Distributed Design,” Ph.D. thesis, Stanford University, Stanford, CA.
Sobieszczanski-Sobieski, J. , Agte, J. S. , and Sandusky, R. , 2000, “ Bi-Level Integrated System Synthesis,” AIAA J., 38(1), pp. 164–172. [CrossRef]
Balling, R. , and Rawlings, M. R. , 2000, “ Collaborative Optimization With Disciplinary Conceptual Design,” Struct. Multidiscip. Optim., 20(3), pp. 232–241. [CrossRef]
Hwang, J. , Lee, D. Y. , Cutler, J. , and Martins, J. , 2013, “ Large-Scale MDO of a Small Satellite Using a Novel Framework for the Solution of Coupled Systems and their Derivatives,” AIAA Paper No. AIAA 2013-1599.
Tedford, N. P. , and Martins, J. R. R. A. , 2010, “ Benchmarking Multidisciplinary Design Optimization Algorithms,” Optim. Eng., 11(1), pp. 159–183. [CrossRef]
Coatanea, E. , Roca, R. , Mokhtarian, H. , Mokammel, F. , and Ikkala, K. , 2016, “ A Conceptual Modeling and Simulation Framework for System Design,” Comput. Sci. Eng., 18(4), pp. 42–52. [CrossRef]
Steward, D. V. , 1981, “ The Design Structure System: A Method for Managing the Design of Complex Systems,” IEEE Trans. Eng. Manage., EM-28(3), pp. 71–74. [CrossRef]
Warfield, J. , 1973, “ Binary Matrices in System Modeling,” IEEE Trans. Syst. Man. Cybern., SMC-3(5), pp. 441–449. [CrossRef]
Morris, M. D. , and Mitchell, T. J. , 1995, “ Exploratory Designs for Computational Experiments,” J. Stat. Plan. Inference, 43(3), pp. 381–402. [CrossRef]
Ding, C. , He, X. , Zha, H. , and Simon, H. D. , 2002, “ Adaptive Dimension Reduction for Clustering High Dimensional Data,” IEEE International Conference on Data Mining, Maebashi City, Japan, Dec. 9–12, pp. 147–154.
Phadke, M. S. , 1998, “ Quality Engineering Using Design of Experiment,” Quality Control, Robust Design and Taguchi Method, Wadsworth, Los Angeles, CA.
Ghani, J. , Choudhury, I. , and Hassan, H. , 2004, “ Application of Taguchi Method in the Optimization of End Milling Parameters,” J. Mater. Process. Technol., 145(1), pp. 84–92. [CrossRef]
NASA MultiDisciplinary Optimization Branch, 2018, “ Test Suite Problem 2.5, POWER CONVERTER,” NASA Langley Research Center, Hampton VA, accessed Jan. 2, 2019, http://www.eng.buffalo.edu/Research/MODEL/mdo.test.orig/class2prob5/descr.html
Wang, D. , Wang, G. , and Naterer, G. , 2007, “ Collaboration Pursuing Method for MDO Problems,” AIAA J., 45(5), pp. 1091–1103. [CrossRef]
Wu, D. , Coatanea, E. , and Wang, G. G. , 2017, “ Dimension Reduction and Decomposition Using Causal Graph and Qualitative Analysis for Aircraft Concept Design Optimization,” ASME Paper No. DETC2017-67601.


Grahic Jump Location
Fig. 1

Causal graph example

Grahic Jump Location
Fig. 2

Causal graph of a numerical example

Grahic Jump Location
Fig. 3

Simplified causal graph for the numerical example

Grahic Jump Location
Fig. 4

Causal graph of the power converter problem

Grahic Jump Location
Fig. 5

Causal graph of the aircraft concept design problem



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