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Research Papers: Design Automation

A Sequential Robust Optimization Approach for Multidisciplinary Design Optimization With Uncertainty

[+] Author and Article Information
Tingting Xia

University of Michigan—Shanghai Jiao Tong
University Joint Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China

Mian Li

University of Michigan—Shanghai Jiao Tong
University Joint Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China;
National Engineering Laboratory for Automotive
Electronic Control Technology,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: mianli@sjtu.edu.cn

Jianhua Zhou

National Engineering Laboratory for Automotive
Electronic Control Technology,
Shanghai Jiao Tong University,
Shanghai 200240, China

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 29, 2016; final manuscript received June 8, 2016; published online September 12, 2016. Assoc. Editor: Samy Missoum.

J. Mech. Des 138(11), 111406 (Sep 12, 2016) (10 pages) Paper No: MD-16-1161; doi: 10.1115/1.4034113 History: Received February 29, 2016; Revised June 08, 2016

One real challenge for multidisciplinary design optimization (MDO) problems to gain a robust solution is the propagation of uncertainty from one discipline to another. Most existing methods only consider an MDO problem in the deterministic manner or find a solution which is robust for a single-disciplinary optimization problem. These rare methods for solving MDO problems under uncertainty are usually computationally expensive. This paper proposes a robust sequential MDO (RS-MDO) approach based on a sequential MDO (S-MDO) framework. First, a robust solution is obtained by giving each discipline full autonomy to perform optimization without considering other disciplines. A tolerance range is specified for each coupling variable to take care of uncertainty propagation in the coupled system. Then the obtained robust extreme points of global variables and coupling variables are dispatched into subsystems to perform robust optimization (RO) sequentially. Additional constraints are added in each subsystem to keep the consistency and to guarantee a robust solution. To find a solution with such strict constraints, genetic algorithm (GA) is used as a solver in each optimization stage. The proposed RS-MDO can save significant amount of computational efforts by using the sequential optimization procedure. Since all iterations in the sequential optimization stage can be processed in parallel, this robust MDO approach can be more time-saving. Numerical and engineering examples are provided to demonstrate the availability and effectiveness of the proposed approach.

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References

Cramer, E. J. , Dennis, J. E., Jr. , Frank, P. D. , Lewis, R. M. , and Shubin, G. R. , 1994, “ Problem Formulation for Multidisciplinary Optimization,” SIAM J. Optim., 4(4), pp. 754–776. [CrossRef]
Sobieszczanski-Sobieski, J. , 1988, “ Optimization by Decomposition: A Step From Hierarchic to Non-Hierarchic Systems,” Recent Advances in Multidisciplinary Analysis and Optimization, Hampton, VA, Sept. 28–30, p. 51. http://ntrs.nasa.gov/search.jsp?R=19890004052
Sobieszczanski-Sobieski, J. , Agte, J. S. , and Sandusky, R. R. , 2000, “ Bilevel Integrated System Synthesis,” AIAA J., 38(1), pp. 164–172. [CrossRef]
Braun, R. , Gage, P. , Kroo, I. , and Sobieski, I. , 1996, “ Implementation and Performance Issues in Collaborative Optimization,” AIAA Paper No. 1996-4017, pp. 295–305.
Braun, R. D. , 1996, “ Collaborative Optimization: An Architecture for Large-Scale Distributed Design,” Ph.D. thesis, Stanford University, Stanford, CA. http://dl.acm.org/citation.cfm?id=237968
Roth, B. , and Kroo, I. , 2008, “ Enhanced Collaborative Optimization,” 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Victoria, BC, Paper No. AIAA 2008-5841.
Kim, H. M. , Michelena, N. F. , Papalambros, P. Y. , and Jiang, T. , 2003, “ Target Cascading in Optimal System Design,” ASME J. Mech. Des., 125(3), pp. 474–480. [CrossRef]
Martins, J. R. , and Lambe, A. B. , 2013, “ Multidisciplinary Design Optimization: A Survey of Architectures,” AIAA J., 51(9), pp. 2049–2075. [CrossRef]
Zhou, J. , Li, M. , and Min, Xu. , 2015, “ A New Sequential Multi-Disciplinary Optimization Method for Bi-Level Decomposed Systems,” ASME Paper No. DETC2015-46307.
Taguchi, G. , 1978, “ Performance Analysis Design,” Int. J. Prod. Res., 16(6), pp. 521–530. [CrossRef]
Ben-Tal, A. , El Ghaoui, L. , and Nemirovski, A. , 2009, Robust Optimization, Princeton University Press, Princeton, NJ.
Ben-Tal, A. , and Nemirovski, A. , 2002, “ Robust Optimization—Methodology and Applications,” Math. Prog., 92(3), pp. 453–480. [CrossRef]
Beyer, H.-G. , and Sendhoff, B. , 2007, “ Robust Optimization—A Comprehensive Survey,” Comput. Methods Appl. Mech. Eng., 196(33), pp. 3190–3218. [CrossRef]
Park, G.-J. , Lee, T.-H. , Lee, K. H. , and Hwang, K.-H. , 2006, “ Robust Design: An Overview,” AIAA J., 44(1), pp. 181–191. [CrossRef]
Li, M. , Azarm, S. , and Boyars, A. , 2006, “ A New Deterministic Approach Using Sensitivity Region Measures for Multi-Objective Robust and Feasibility Robust Design Optimization,” ASME J. Mech. Des., 128(4), pp. 874–883. [CrossRef]
Gunawan, S. , and Azarm, S. , 2005, “ Multi-Objective Robust Optimization Using a Sensitivity Region Concept,” Struct. Multidiscip. Optim., 29(1), pp. 50–60. [CrossRef]
Liu, H. , Chen, W. , Kokkolaras, M. , Papalambros, P. Y. , and Kim, H. M. , 2006, “ Probabilistic Analytical Target Cascading: A Moment Matching Formulation for Multilevel Optimization Under Uncertainty,” ASME J. Mech. Des., 128(4), pp. 991–1000. [CrossRef]
Du, X. , and Chen, W. , 2002, “ Efficient Uncertainty Analysis Methods for Multidisciplinary Robust Design,” AIAA J., 40(3), pp. 545–552. [CrossRef]
Yao, W. , Chen, X. , Luo, W. , Tooren, M. V. , and Guo, J. , 2011, “ Review of Uncertainty-Based Multidisciplinary Design Optimization Methods for Aerospace Vehicles,” Prog. Aerosp. Sci., 47(6), pp. 450–479. [CrossRef]
Giassi, A. , Bennis, F. , and Maisonneuve, J.-J. , 2004, “ Multidisciplinary Design Optimisation and Robust Design Approaches Applied to Concurrent Design,” Struct. Multidiscip. Optim., 28(5), pp. 356–371. [CrossRef]
Brevault, L. , Balesdent, M. , Bérend, N. , and Le Riche, R. , 2015, “ Decoupled Multidisciplinary Design Optimization Formulation for Interdisciplinary Coupling Satisfaction Under Uncertainty,” AIAA J., 54(1), pp. 186–205. [CrossRef]
Zaman, K. , and Mahadevan, S. , 2013, “ Robustness-Based Design Optimization of Multidisciplinary System Under Epistemic Uncertainty,” AIAA J., 51(5), pp. 1021–1031. [CrossRef]
Allen, J. K. , Seepersad, C. , Choi, H. , and Mistree, F. , 2006, “ Robust Design for Multiscale and Multidisciplinary Applications,” ASME J. Mech. Des., 128(4), pp. 832–843. [CrossRef]
Du, X. , Wang, Y. , and Chen, W. , 2000, “ Methods for Robust Multidisciplinary Design,” AIAA J., 1785, pp. 1–10.
Kalsi, M. , Hacker, K. , and Lewis, K. , 2001, “ A Comprehensive Robust Design Approach for Decision Trade-Offs in Complex Systems Design,” ASME J. Mech. Des., 123(1), pp. 1–10. [CrossRef]
Li, M. , and Azarm, S. , 2008, “ Multiobjective Collaborative Robust Optimization With Interval Uncertainty and Interdisciplinary Uncertainty Propagation,” ASME J. Mech. Des., 130(8), p. 081402. [CrossRef]
Hu, W. , Azarm, S. , and Almansoori, A. , 2013, “ New Approximation Assisted Multi-Objective Collaborative Robust Optimization (New AA-McRO) Under Interval Uncertainty,” Struct. Multidiscip. Optim., 47(1), pp. 19–35. [CrossRef]
Park, G.-J. , 2007, Analytic Methods for Design Practice, Springer, Berlin.
Zhou, J. , and Li, M. , 2014, “ Advanced Robust Optimization With Interval Uncertainty Using a Single-Looped Structure and Sequential Quadratic Programming,” ASME J. Mech. Des., 136(2), p. 021008. [CrossRef]
Williams, N. , Azarm, S. , and Kannan, P. , 2008, “ Engineering Product Design Optimization for Retail Channel Acceptance,” ASME J. Mech. Des., 130(6), p. 061402. [CrossRef]

Figures

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Fig. 1

A fully coupled two-discipline system

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Fig. 2

Variable dispatching and sequential optimization

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Fig. 3

Interdisciplinary propagation of uncertainty

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Fig. 5

Flowchart of RS-MDO

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Fig. 6

System decompose of NE

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Fig. 7

Sequential RO of NE

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Fig. 9

System structure of angle grinder design

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Fig. 10

Pareto of angle grinder design

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