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Sequential optimization and reliability assessment for multidisciplinary systems design

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Abstract

With higher reliability and safety requirements, reliability-based design has been increasingly applied in multidisciplinary design optimization (MDO). A direct integration of reliability-based design and MDO may present tremendous implementation and numerical difficulties. In this work, a methodology of sequential optimization and reliability assessment for MDO is proposed to improve the efficiency of reliability-based MDO. The central idea is to decouple the reliability analysis from MDO with sequential cycles of reliability analysis and deterministic MDO. The reliability analysis is based on the first-order reliability method (FORM). In the proposed method, the reliability analysis and the deterministic MDO use two MDO strategies, the multidisciplinary feasible approach and the individual disciplinary feasible approach. The effectiveness of the proposed method is illustrated with two example problems.

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References

  • Acton FS (1990) Numerical methods that work, 2nd edn. Mathematical Association of America, Washington, DC

    MATH  Google Scholar 

  • Agarwal H, Renaud JE, Mack JD (2003) A decomposition approach for reliability-based multidisciplinary design optimization. AIAA 2003-1778, 44th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Norfolk, VA, 7–10 April 2003

  • Ahn J, Lee J, Kim S (2004) Sequential reliability analysis framework for multidisciplinary systems, AIAA 2004-451. Proceedings of the 10th AIAA/NASA/ISSMO symposium on multidisciplinary analysis and optimization, Albany, NY, 30 Aug.–1 Sept. 2004

  • Allison J, Kokkolaras M, Papalambros P (2005) On the impact of coupling strength on complex system optimization for single-level formulations, ASME 2005 international design engineering technical conferences and computers and information in engineering conference, Long Beach, CA, 24–28 Sep 2005

  • Arian E (1997) Convergence estimates for multidisciplinary analysis and optimization, NASA/CR-201752, ICASE report no. 97-57 (Oct)

  • Autio M (2001) Optimization of coupled thermal–structural problems of laminated plates with lamination parameters. Struct Multidiscipl Optim 21(1):40–51

    Article  Google Scholar 

  • Balling RJ, Sobieski J (1994) An algorithm for solving the system-level problem in multilevel optimization. 5th AIAA/USAF/NASA/ISSMO symposium on recent advances in multidisciplinary analysis and optimization, Panama City, FL, 7–9 September 1994

  • Batill SM, Renaud JE, Gu X (2000) Modeling and simulation uncertainty in multidisciplinary design optimization. 8th AIAA/NASA/ISSMO symposium on multidisciplinary analysis and optimization, Long Beach, CA, 6–8 September 2000

  • Breitung K (1984) Asymptotic approximations for multinomial integrals. J Eng Mech 110(3):357–367

    Article  Google Scholar 

  • Chen W, Hasselman TK (1997) Reliability based structural design optimization for practical applications. 38th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference and exhibit and AIAA/ASME/AHS adaptive structural forum, Kissimmee, FL, 7–10 April 1997

  • Choi KK, Youn BD (2003) Hybrid analysis method for reliability-based design optimization. ASME J Mech Des 125(2):221–232

    Article  Google Scholar 

  • Cramer EJ, Dennis JE, Frank PD, Lewis RM, Shubin GR (1994) Problem formulation for multidisciplinary design optimization. SIAM J Optim 4:754–776

    Article  MATH  MathSciNet  Google Scholar 

  • Dennis JE, Schnabel RB (1996) Numerical methods for nonlinear equations and unconstrained optimization. SIAM, Philadelphia

    MATH  Google Scholar 

  • Der Kiureghian A, Zhang Y, Li CC (1994) Inverse reliability problem. ASCE J Eng Mech 120(5):1150–1159

    Article  Google Scholar 

  • Du X, Chen W (2000a) Towards a better understanding of modeling feasibility robustness in engineering. ASME J Mech Des 122(4):357–583

    Article  Google Scholar 

  • Du X, Chen W (2000b) An integrated methodology for uncertainty propagation and management in simulation-based systems design. AIAA J 38(8):1471–1478

    Article  Google Scholar 

  • Du X, Chen W (2001) A most probable point based method for uncertainty analysis. J Des Manuf Autom 1(1–2):47–66

    Google Scholar 

  • Du X, Chen W (2002) Collaborative reliability analysis for multidisciplinary systems design. 9th AIAA/ISSMO symposium on multidisciplinary analysis and optimization, Atlanta, GA, 4–6 Sept. 2002

  • Du X, Chen W (2004) Sequential optimization and reliability assessment for probabilistic design. ASME J Mech Des 126(2):225–233

    Article  Google Scholar 

  • Du X, Sudjianto A (2003) Reliability-based design under the mixture of random and interval variables. 2003 ASME international design engineering technical conferences and the computers and information in engineering conference, Chicago, IL, 2–6 Sept. 2003

  • Du X, Sudjianto A, Chen (2004) An integrated framework for optimization under uncertainty using inverse reliability strategy. ASME J Mech Des 126(4):561–764

    Article  Google Scholar 

  • Giesing JP, Barthelemy JM (1998) A summary of industry MDO applications and needs. 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, St. Louis, MO, 2–4 Sept. 1998

  • Hasofer AM, Lind NC (1974) Exact and invariant second-moment code format. J Eng Mech Div 100(EM1):111–121

    Google Scholar 

  • Heinkenschloss M, Hribar MB, Kokkolaras M (1998) Acceleration of multidisciplinary analysis solvers by inexact subsystem simulations, 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, St. Louis, MO, 2–4 Sept. 1998

  • Hirohata K, Hisano K, Mukai M, Takahashi H, Kawamura, N, Iwasaki H, Kawakami T, Yu Q, Shiratori M (2004) Multidisciplinary reliability design of electronics packaging based on the first order reliability method and structural equation modeling, AIAA 2004-4621, 10th AIAA/ISSMO multidisciplinary analysis and optimization conference, Albany, NY, 30 Aug.–1 Sept. 2004

  • Kelly CT (1995) Iterative methods for linear and nonlinear equations. SIAM, Philadelphia

    Google Scholar 

  • Koch PK, Wujek B, Golovidov O (2000) A multi-stage, parallel implementation of probabilistic design optimization in an MDO framework. 8th AIAA/NASA/ISSMO symposium on multidisciplinary analysis and optimization, Long Beach, CA, 6–8 September 2000

  • Kodiyalam S, Yang RJ, Gu L, Tho C-H (2004) Multidisciplinary design optimization of a vehicle system in a scalable, high performance computing environment. Struct Multidiscipl Optim 26:256–263

    Article  Google Scholar 

  • Laban M (2004) Multi-disciplinary analysis and optimization of supersonic transport aircraft wing platforms. 10th AIAA/ISSMO multidisciplinary analysis and optimization conference, Albany, NY, 30 Aug.–1 Sept. 2004

  • Li H, Foschi RO (1998) An inverse reliability method and its application. Struct Saf 20(3):257–270

    Article  Google Scholar 

  • Lund E, Moller H, Jakobsen LA (2003) Shape design optimization of stationary fluid–structure interaction problems with large displacements and turbulence. Struct Multidiscipl Optim 25:383–392

    Article  Google Scholar 

  • Maute K, Allen M (2004) Conceptual design of aeroelastic structures by topology optimization. Struct Multidiscipl Optim 27:27–42

    Article  Google Scholar 

  • Murotsu Y, Shao S, Watanabe A (1994) An approach to reliability-based optimization of redundant structures. Struct Saf 16(1–2):133–143

    Article  Google Scholar 

  • Ortega JM, Rheinboldt WC (1970) Iterative solution of nonlinear equations in several variables. Academic Press, NY

    MATH  Google Scholar 

  • Padmanabhan D, Batill S (2002a) Decomposition strategies for reliability based optimization in multidisciplinary system design. 9th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, Atlanta, GA, 4–6 Sept. 2002

  • Padmanabhan D, Batill S (2002b) Reliability based optimization using approximations with applications to multi-disciplinary system design. 40th AIAA sciences meeting and exhibit, Reno, NV, 14–17 January 2002

  • Padmanabhan D, Tappeta RV, Batill SM (2003) Monte Carlo simulation in reliability based optimization applied to multidisciplinary system design. 44th AIAA/ASME/ASCE/AHS structures, structural dynamics, and materials conference, Norfolk, VA, 7–10 April 2003

  • Patel NM, Renaud JE, Agarwal H, Tovar A (2005) Reliability based topology optimization using the hybrid cellular automation method, AIAA 2005-2134, 46th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Austin, Texas, 18–21 April 2005

  • Pettit CL, Grandhi RV (2000) Multidisciplinary optimization of aerospace structures with high reliability. Proceedings of the 8th ASCE specialty conference on probabilistic mechanics and structural reliability, PMC2000-132

  • Powell MJD (1970) A FORTRAN subroutine for solving systems of nonlinear algebraic equations. Numerical methods for nonlinear algebraic equations. Gordon and Breach, London, pp 115–161

    Google Scholar 

  • Qu X, Haftka RT (2004) Reliability-based design optimization using probabilistic sufficiency factor. Struct Multidiscipl Optim 5(27):314–325

    Google Scholar 

  • Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Stat 3(23):470–472

    Article  MathSciNet  Google Scholar 

  • Salas AO, Townsend JC (1998) Framework requirements for MDO application development. 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, St. Louis, MO, 2–4 Sept. 1998

  • Sues RH, Cesare MA (2000) An innovative framework for reliability-based MDO. 41st AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Atlanta, GA, 3–6 April 2000

  • Sues RH, Oakley DR, Rhodes GS (1995) Multidisciplinary stochastic optimization. 10th conference on engineering mechanics, Boulder, CO, 21–24 May 1995

  • Sues RH, Aminpour MA, Shin Y (2001) Reliability-based MDO for aerospace systems, 42nd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference and exhibit, Seattle, WA, 16–19 April 2001

  • Tu J, Choi KK, Young HP (1999) A new study on reliability-based design optimization. ASME J Mech Des 121(4):557–564

    Google Scholar 

  • Ugural AC, Fenster SK (1975) Advanced strength and applied elasticity. American Elsevier, NY

    Google Scholar 

  • Wu Y-T, Wang W (1998) Efficient probabilistic design by converting reliability constraints to approximately equivalent deterministic constraints. J Int Des Proc Sci 2(4):13–21

    Google Scholar 

  • Wu Y-T, Shin Y, Sues R, Cesare M (2001) Safety-factor based approach for probabilistic-based design optimization. 42nd AIAA/ASME/ASCE/ AHS/ASC structures, structural dynamics, and materials conference, Seattle, WA, 16–19 April 2001

  • Xiao Q, Sues RH, Rhodes S (1999) Multi-disciplinary shape optimization with uncertain parameters, AIAA 1999-1601. Proceedings of the 40th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference and exhibit

  • Xiong Y, Miscinski M, Frontera M, Yin S, Dede M, Paradis M (2004) Multidisciplinary design optimization of full combustor structure. 10th AIAA/ISSMO multidisciplinary analysis and optimization conference, Albany, NY, 30 Aug.–Sept.

  • Zang TA, Hemsch MJ, Hilburger MW, Kenny SP, Luckring JM, Maghami P, Padula SL, Stroud WJ (2002) Needs and opportunities for uncertainty-based multidisciplinary design methods for aerospace vehicles. NASA/TM-2002-211462

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  1. Department of Mechanical and Aerospace Engineering, University of Missouri–Rolla, 1870 Miner Circle, Rolla, MO, 65409-4494, USA

    Xiaoping Du, Jia Guo & Harish Beeram

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  1. Xiaoping Du
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  2. Jia Guo
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  3. Harish Beeram
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Correspondence to Xiaoping Du.

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Du, X., Guo, J. & Beeram, H. Sequential optimization and reliability assessment for multidisciplinary systems design. Struct Multidisc Optim 35, 117–130 (2008). https://doi.org/10.1007/s00158-007-0121-7

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  • DOI: https://doi.org/10.1007/s00158-007-0121-7

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