[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content

Advertisement

Springer Nature Link
Log in

Benchmark study of numerical methods for reliability-based design optimization

  • Benchmark Case Studies
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

The reliability-based design optimization (RBDO) seeks for the best compromise between cost and safety, by considering system uncertainties. In order to overcome computational difficulties, many formulations have been recently developed, leading to confusion about what method should be selected for a given application, due to the lack of full-scale comparative studies. In this context, the present paper aims at giving an overview of various RBDO approaches which are tested on a benchmark constituted of four examples using mathematical and finite element models, with different levels of difficulties. The study is focused on the three main approaches, namely the two-level approach, the single loop approach and the decoupled approach; for each category, two RBDO formulations are discussed, implemented and tested for numerical examples. The benchmark study allows us to give comprehensive overview of various approaches, to give clear ideas about their capabilities and limitations, and to draw useful conclusions regarding robustness and numerical performance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Chan KY, Skerlos SJ, Papalambros P (2007) An adaptive sequential linear programming algorithm for optimal design problems with probabilistic constraints. J Mech Des 129(2):140–149

    Article  Google Scholar 

  • Chen D, Hasselman TK, Neill DJ (1997) Reliability-based structural design optimization for practical applications. In: Proceedings of the 38th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and material conference, Kissimmee, AIAA-97-1403

  • Cheng G, Xu L, Jiang L (2006) A sequential approximate programming strategy for reliability-based structural optimization. Comput Struct 84(21):1353–1367

    Article  Google Scholar 

  • Ching J, Hsu WC (2008) Transforming reliability limit-state constraints into deterministic limit-state constraints. Struct Saf 30(1):11–33

    Article  Google Scholar 

  • Division of Structural Mechanics and Division of Solid Mechanics (2006) CALFEM: a finite element toolbox to MATLAB, version 3.4

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

    Article  Google Scholar 

  • Enevoldsen I, Sørensen JD (1994) Reliability-based optimization in structural engineering. Struct Saf 15(3):169–196

    Article  Google Scholar 

  • Gasser M, Schueller GI (1997) Reliability-based optimization of structural systems. Math Methods Oper Res 46(3):287–307

    Article  MATH  MathSciNet  Google Scholar 

  • Grandhi RV, Wang L (1998) Reliability-based structural optimization using improved two point adaptive nonlinear approximations. Finite Elem Anal Des 29(1):35–48

    Article  MATH  Google Scholar 

  • Hasofer AM, Lind NC (1974) Exact and invariant second moment code format. J Eng Mech Div 100(1):111–121

    Google Scholar 

  • Kaymaz I, Marti K (2007) Reliability-based design optimization for elastoplastic mechanical structures. Comput Struct 85(10):615–625

    Article  MathSciNet  Google Scholar 

  • Kharmanda G, Mohamed A, Lemaire M (2002) Efficient reliability-based design optimization using a hybrid space with application to finite element analysis. Struct Multidiscipl Optim 24(3):233–245

    Article  Google Scholar 

  • Kirjner-Neto C, Polak E, Der Kiureghian A (1998) An outer approximation approach to reliability-based optimal design of structures. J Optim Theory Appl 98(1):1–16

    Article  MATH  MathSciNet  Google Scholar 

  • Kuschel N, Rackwitz R (1997) Two basic problems in reliability-based structural optimization. Math Methods Oper Res 46(3):309–333

    Article  MATH  MathSciNet  Google Scholar 

  • Kuschel N, Rackwitz R (2000) Optimal design under time-variant reliability constraints. Struct Saf 22(2):113–127

    Article  Google Scholar 

  • Lee JO, Yang YS, Ruy WS (1999) Comparative study on reliability-index and target performance based probabilistic structural design optimization. Comput Struct 80(3–4):257–269

    Google Scholar 

  • Li W, Yang L (1994) An effective optimization procedure based on structural reliability. Comput Struct 52(5):1061–1067

    Article  MATH  Google Scholar 

  • Liang J, Mourelatos ZP, Tu J (2004) A single-loop method for reliability-based design optimization. In: Proceedings of ASME design engineering technical conferences, paper N°DETC2004/DAC-57255

  • Liang J, Mourelatos ZP, Nikolaidis E (2007) A single-loop approach for system reliability-based design optimization. J Mech Des 129(12):1215–1224

    Article  Google Scholar 

  • Liu PL, Der Kiureghian A (1991) Optimization algorithms for structural reliability. Struct Saf 9(3):161–177

    Article  Google Scholar 

  • Madsen HO, Friis Hansen F (1992) A comparison of some algorithms fo reliability-based structural optimization and sensitivity analysis. In: Rackwitz R, Thoft-Christensen P (eds) Proceedings of the 4th IFIP WG 7.5 conference, Munich. Springer-Verlag, Berlin, pp 443–451

    Google Scholar 

  • Mathworks INC. (2007) http://www.mathworks.com. MATLAB

  • Nikolaidis E, Burdisso R (1988) Reliability-based optimization: a safety index approach. Comput Struct 28(6):781–788

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Reddy MV, Grandhi RV, Hopkins DA (1994) Reliability based structural optimization: a simplified safety index approach. Comput Struct 53(6):1407–1418

    Article  MATH  Google Scholar 

  • Royset JO, Der Kiureghian A, Polak E (2001) Reliability-based optimal structural design by the decoupling approach. Reliab Eng Syst Saf 73(3):213–221

    Article  Google Scholar 

  • Shan S, Wang GG (2008) Reliable design space and complete single-loop reliability-based design optimization. Reliab Eng Syst Saf 93(8):1218–1230

    Article  Google Scholar 

  • Torng TY, Yang RJ (1993) An advanced reliability-based optimization method for robust design optimization method. In: Spanos PD, Wu YT (eds) Probabilistic structural mechanics: advances in structural reliability methods. Springer, New-York, pp 534–549

    Google Scholar 

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

    Article  Google Scholar 

  • Wu YT, Wang W (1998) Efficient probabilistic design by converting reliability constraints to approximately equivalent deterministic constraints. J Integr Des Process Sci 2(4):13–21

    Google Scholar 

  • Yang RJ, Gu L (2004) Experience with approximate reliability-based optimization methods. Struct Multidiscipl Optim 26(1–2):152–159

    Article  MathSciNet  Google Scholar 

  • Yi P, Cheng G, Jiang L (2008) A sequential approximate programming strategy for performance-measure-based probabilistic structural design optimization. Struct Saf 30(2):91–109

    Article  Google Scholar 

  • Youn BD, Choi KK (2004) An investigation of nonlinearity of reliability based design optimization approaches. J Mech Des (ASME) 126(3):403–411

    Article  Google Scholar 

  • Youn BD, Choi KK, Liu D (2005) Enriched performance measure approach for reliability-based design optimization. AIAA J 43(4):874–884

    Article  Google Scholar 

  • Zou T, Mahadevan S (2006) A direct decoupling approach for efficient reliability-based design optimization. Struct Multidiscipl Optim 31(3):190–200

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LaMI, Polytech’Clermont-Ferrand, Campus des Cézeaux, BP 206, 63174, Aubière Cedex, France

    Younes Aoues & Alaa Chateauneuf

Authors
  1. Younes Aoues
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alaa Chateauneuf
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alaa Chateauneuf.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aoues, Y., Chateauneuf, A. Benchmark study of numerical methods for reliability-based design optimization. Struct Multidisc Optim 41, 277–294 (2010). https://doi.org/10.1007/s00158-009-0412-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-009-0412-2

Keywords

Search

Navigation