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A local adaptive sampling method for reliability-based design optimization using Kriging model

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Abstract

Reliability-based design optimization (RBDO) in practical applications is hindered by its huge computational cost during structure reliability evaluating process. Kriging-model-based RBDO is an effective method to overcome this difficulty. However, the accuracy of Kriging model depends directly on how to select the sample points. In this paper, the local adaptive sampling (LAS) is proposed to enhance the efficiency of constructing Kriging models for RBDO problems. In LAS, after initialization, new samples for probabilistic constraints are mainly selected within the local region around the current design point from each optimization iteration, and in the local sampling region, sample points are first considered to be located on the limit state constraint boundaries. The size of the LAS region is adaptively defined according to the nonlinearity of the performance functions. The computation capability of the proposed method is demonstrated using three mathematical RBDO problems and a honeycomb crash-worthiness design application. The comparison results show that the proposed method is very efficient.

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References

  • Agarwal H, Mozumder CK, Renaud JE, Watson LT (2007) An inverse-measure-based unilevel architecture for reliability-based design optimization. Struct Multidisc Optim 33(2):217–227

    Article  Google Scholar 

  • Aoues Y, Chateauneuf A (2010) Benchmark study of numerical methods for reliability-based design optimization. Struct Multidisc Optim 41(2):277–294

    Article  MATH  MathSciNet  Google Scholar 

  • Basudhar A, Missoum S (2008) Adaptive explicit decision functions for probabilistic design and optimization using support vector machines. Comput Struct 86(19–20):1904–1917

    Article  Google Scholar 

  • Bichon BJ, Eldred MS, Swiler LP, Mahadevan S, McFarland JM (2008) Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J 46(9):2459–2468

    Article  Google Scholar 

  • Chen X, Hasselman TK, Neill DJ (1997) Reliability based structural design optimization for practical applications. In: 38th AIAA SDM conference, AIAA-97-1403

  • Chen ZZ, Qiu HB, Gao L, Li PG (2013a) An optimal shifting vector approach for efficient probabilistic design. Struct Multidisc Optim 47(5):905–920

    Article  Google Scholar 

  • Chen ZZ, Qiu HB, Gao L, Su L, Li PG (2013b) An adaptive decoupling approach for reliability-based design optimization. Comput Struct 117:58–66

    Article  Google Scholar 

  • 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 

  • Cho TM, Lee BC (2011) Reliability-based design optimization using convex linearization and sequential optimization and reliability assessment method. Struct Saf 33(1):42–50

    Article  Google Scholar 

  • Choi KK, Youn BD, Yang RJ (2001) Moving least square method for reliability-based design optimization. In: The 4th world congress of structural and multidisciplinary optimization. Dalian

  • Dersjö T, Olsson M (2011) Reliability based design optimization using a single constraint approximation point. J Mech Des 133(2):031006

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Du XP, Sudjianto A, Chen W (2004) An integrated framework for optimization under uncertainty using inverse reliability strategy. J Mech Des 126(3):562–571

    Article  Google Scholar 

  • Echard B, Gayton N, Lemaire M (2011) AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation. Struct Saf 33(2):145–154

    Article  Google Scholar 

  • Enevoldsen I, Sørensen JD (1994) Reliability-based optimization in structural engineering. Struct Saf 15(2):169–196

    Article  Google Scholar 

  • Gasser M, Schuëller GI (1997) Reliability-based optimization of structural systems. Math Methods Oper Res 46(2):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 

  • Huang Y, Chan K (2010) A modified efficient global optimization algorithm for maximal reliability in a probabilistic constrained space. J Mech Des 134(5):061002

    Article  Google Scholar 

  • Ju BH, Lee B (2008) Reliability-based design optimization using a moment method and a Kriging metamodel. Eng Optimiz 40(4):411–438

    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 Multidisc Optim 24(2):233–245

    Article  Google Scholar 

  • Kim C, Choi KK (2008) Reliability-based design optimization using response surface method with prediction interval estimation. J Mech Des 130(11):121401

    Article  MathSciNet  Google Scholar 

  • Kim BS, Lee YB, Choi DH (2009a) Comparison study on the accuracy of metamodeling technique for non-convex functions. J Mech Sci Tech 23(3):1175–1181

    Article  Google Scholar 

  • Kim BS, Lee YB, Choi DH (2009b) Construction of the radial basis function based on a sequential sampling approach using cross-validation. J Mech Sci Tech 23(11):3357–3365

    Article  Google Scholar 

  • Kirjner-Neto C, Polak EA, Kiureghian D (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 

  • Kiureghian A, Stefano M (1991) Efficient algorithm for second-order reliability analysis. J Eng Mech 117(11):2904–2923

    Article  Google Scholar 

  • Kuczera RC, Mourelatos ZP, Nikolaidis E (2010) System RBDO with correlated variables using probabilistic re-analysis and local metamodels. ASME, Montereal, Quebec

  • Lee TH, Jung JJ (2008) A sampling technique enhancing accuracy and efficiency of metamodel-based RBDO: constraint boundary sampling. Comput Struct 86(13–14):1463–1476

    Article  Google Scholar 

  • Lee J, Song C (2011) Role of conservative moving least squares methods in reliability based design optimization: a mathematical foundation. J Mech Des 133(11):121005

    Article  Google Scholar 

  • Lee I, Choi KK, Du L, Gorsich D (2008) Dimension reduction method for reliability-based robust design optimization. Comput Struct 86(13–14):1550–1562

    Article  Google Scholar 

  • Lee I, Choi KK, Gorsich D (2011a) Equivalent standard deviation to convert high-reliability model to low-reliability model for efficiency of sampling-based RBDO. ASME, Washington, DC

  • Lee I, Choi KK, Zhao L (2011b) Sampling-based RBDO using the stochastic sensitivity analysis and dynamic Kriging method. Struct Multidisc Optim 44(2):299–317

    Article  MATH  MathSciNet  Google Scholar 

  • Lee G, Yook S, Kang K, Choi DH (2012) Reliability-based design optimization using an enhanced dimension reduction method with variable sampling points. Int J Precis Eng Manuf 13(8):1609–1618

    Article  Google Scholar 

  • Li F, Wu T, Hu M (2010) An accurate penalty-based approach for reliability-based design optimization. Res Eng Des 21(2):87–98

    Article  MathSciNet  Google Scholar 

  • Liang J, Mourelatos ZP, Tu J (2008) A single-loop method for reliability-based design optimization. Int J Product Dev 5(1–2):76–92

    Article  Google Scholar 

  • Lin PT, Gea HC, Jaluria Y (2011) A modified reliability index approach for reliability-based design optimization. J Mech Des 133(3):044501

    Google Scholar 

  • Lophaven S, Nielsen H, Sondergaard J (2002) A MATLAB Kriging toolbox. Technical University of Denmark, Kongens Lyngby. Technical Report No. IMM-TR-2002-12

  • Lu ZZ, Song SF, Li HS, Yuan XK (2009) The structural reliability analysis and reliability sensitivity analysis. Science Press, Beijing

    Google Scholar 

  • Mourelatos ZP (2005) Design of crankshaft main bearings under uncertainty. In: ANSA & META international congress, Athos Kassndra, Halkidiki

  • Nikolaidis E, Burdisso R (1988) Reliability-based optimization: a safety index approach. Comput Struct 28(5):781–788

    Article  MATH  Google Scholar 

  • Picheny V, Ginsbourger D, Roustant O, Haftka RT, Kim NH (2010) Adaptive designs of experiments for accurate approximation of a target region. J Mech Des (ASME) 132:071008

    Article  Google Scholar 

  • Pretorius CA, Craig KJ, Haarhoff LJ (2004) Kriging response surface as an alternative implementation of RBDO in continuous casting design optimization. In: 10th AIAA/ISSMO multidisciplinary analysis and optimization conference. Albany

  • Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. MIT Press, Cambridge, Massachusetts

    MATH  Google Scholar 

  • Reddy MV, Grandhi RV, Hopkins DA (1994) Reliability based structural optimization: a simplified safety index approach. Comput Struct 53(5):1407–1418

    Article  MATH  Google Scholar 

  • Royset JO, Kiureghian AD, Polak E (2001) Reliability-based optimal structural design by the decoupling approach. Reliab Eng Syst Saf 73(2):213–221

    Article  Google Scholar 

  • Sacks J, Welch W, Mitchell T, Wynn H (1989) Design and analysis of computer experiments. Stat Sci 4(3):409–423

    Article  MATH  MathSciNet  Google Scholar 

  • Shan S, Wang GG (2008) Reliable design space and complete single loop reliability-based design optimization. Reliab Eng Syst Saf 93(7):1218–1230

    Article  Google Scholar 

  • Song SF, Lu ZZ, Qiao H (2009) Subset simulation for structural reliability sensitivity analysis. Reliab Eng Syst Saf 94(2):658–665

    Article  Google Scholar 

  • Sun GY, Li GY, Stone M, Li Q (2010) A two-stage multi-fidelity optimization procedure for honeycomb-type cellular materials. Comput Material Sci 49(2):500–511

    Article  Google Scholar 

  • Tu J, Choi KK (1999) A new study on reliability-based design optimization. J Mech Des 121(3):557–564

    Article  Google Scholar 

  • Valdebenito MA, Schuëller GI (2010) A survey on approaches for reliability-based optimization. Struct Multidisc Optim 42(4):645–663

    Article  MATH  Google Scholar 

  • Valdebenito MA, Schuëller GI (2011) Efficient strategies for reliability-based optimization involving non-linear, dynamical structures. Comput Struct 89(19–20):1797–1811

    Article  Google Scholar 

  • Wu YT, Millwater HR, Cruse TA (1990) An advance probabilistic analysis method for implicit performance function. AIAA J 28(8):1663–1669

    Article  Google Scholar 

  • Wu YT, Shin Y, Sues R, Cesare M (2001) Safety-factor based approach for probabilistic-based design optimization. In: 42nd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference and exhibit. AIAA 2001-1522, Seattle

  • 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) A new response surface methodology for reliability-based design optimization. Comput Struct 82(2–3):241–256

    Article  Google Scholar 

  • Youn BD, Choi KK, Du L (2005a) Enriched performance measure approach for reliability-based design optimization. AIAA J 43(3):874–884

    Article  Google Scholar 

  • Youn BD, Choi KK, Du L (2005b) Adaptive probability analysis using an enhanced hybrid mean value method. Struct Multidisc Optim 29(2):134–148

    Article  Google Scholar 

  • Zhao L, Choi KK, Lee I (2009) Response surface method using sequential sampling for reliability-based design optimization. In: 35th design automation conference, simulation-based design under uncertainty, pp 1171–1181

  • Zhao L, Choi KK, Lee I (2011) Metamodeling method using dynamic Kriging for design optimization. AIAA J 49(8):2034–2046

    Article  Google Scholar 

  • Zhuang XT, Pan R (2012) A sequential sampling strategy to improve reliability-based design optimization with implicit constraint functions. J Mech Des 134(2):021002-1–021002-10

    Article  Google Scholar 

  • Zou T, Mahadevan S (2006) A direct decoupling approach for efficient reliability-based design optimization. Struct Multidisc Optim 31(2):190–200

    Article  Google Scholar 

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Acknowledgments

Financial support from the National Natural Science Foundation of China under Grant No. 51175199; National Natural Science Foundation of China under Grant No. 51121002 and National technology major projects under Grant No. 2011ZX04002-091 are gratefully acknowledged.

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Authors and Affiliations

  1. The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, 1037 Luoyu Road, 430074, Wuhan, People’s Republic of China

    Zhenzhong Chen, Haobo Qiu, Liang Gao, Xiaoke Li & Peigen Li

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  1. Zhenzhong Chen
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  2. Haobo Qiu
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  4. Xiaoke Li
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Correspondence to Haobo Qiu.

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Chen, Z., Qiu, H., Gao, L. et al. A local adaptive sampling method for reliability-based design optimization using Kriging model. Struct Multidisc Optim 49, 401–416 (2014). https://doi.org/10.1007/s00158-013-0988-4

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  • DOI: https://doi.org/10.1007/s00158-013-0988-4

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