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Structural and Multidisciplinary Optimization

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01-07-2015 | RESEARCH PAPER

An important boundary sampling method for reliability-based design optimization using kriging model

Authors: Zhenzhong Chen, Siping Peng, Xiaoke Li, Haobo Qiu, Huadi Xiong, Liang Gao, Peigen Li

Published in: Structural and Multidisciplinary Optimization | Issue 1/2015

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Abstract

Reliability-based design optimization (RBDO) combined with metamodel is a powerful tool to deal with variation of system output induced by uncertainties during practical engineering design. In this paper, the importance boundary sampling (IBS) method is proposed to enhance the efficiency of Kriging-model-based RBDO. Rather than fitting all the parts of the limit state constraints precisely within the design region, the proposed IBS mainly selects sample points on the critical parts of the limit state constraints. Two importance coefficients are proposed to identify these critical boundary parts: the first importance coefficient is determined by the objective function value; and the second one is calculated using the joint probability density value of the design variables. The sampling and optimization processes are conducted alternately to select the sample points more rationally. The computation capability of the proposed method is demonstrated using several mathematical RBDO problems and a box girder design application. The comparison results show that the proposed IBS method is very efficient.

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Agarwal H, Mozumder CK, Renaud JE, Watson LT (2007) An inverse-measure-based unilevel architecture for reliability-based design optimization. Struct Multidiscip Optim 33(3):217–227. doi:10.1007/s00158-006-0057-3 CrossRef

Aoues Y, Chateauneuf A (2008) Reliability-based optimization of structural systems by adaptive target safety – application to RC frames. Struct Saf 30(2):144–161. doi:10.1016/j.strusafe.2006.10.002 CrossRef

Bect J, Ginsbourger D, Li L, Picheny V, Vazquez E (2012) Sequential design of computer experiments for the estimation of a probability of failure. Stat Comput 22(3):773–793MathSciNetCrossRefMATH

Bichon BJ, Eldred MS, Swiler LP, Mahadevan S, McFarland JM (2008) Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J 46(10):2459–2468. doi:10.2514/1.34321 CrossRef

Chan K-Y, Papalambros PY, Skerlos SJ (2010) A method for reliability-based optimization with multiple non-normal stochastic parameters: a simplified airshed management study. Stoch Env Res Risk A 24(1):101–116. doi:10.1007/s00477-009-0304-4 CrossRef

Chen, Xiaoguan, Hasselman, Timothy K, & Neill, Douglas J. (1997). Reliability based structural design optimization for practical applications. Paper presented at the Proceedings of the 38th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference.

Chen Z, Qiu H, Gao L, Li P (2013a) An optimal shifting vector approach for efficient probabilistic design. Struct Multidiscip Optim 47(6):905–920. doi:10.1007/s00158-012-0873-6 CrossRef

Chen Z, Qiu H, Gao L, Su L, Li P (2013b) An adaptive decoupling approach for reliability-based design optimization. Comput Struct 117:58–66. doi:10.1016/j.compstruc.2012.12.001 CrossRef

Chen Z, Qiu H, Gao L, Li X, Li P (2014) A local adaptive sampling method for reliability-based design optimization using kriging model. Struct Multidiscip Optim 49(3):401–416. doi:10.1007/s00158-013-0988-4 MathSciNetCrossRef

Cheng G, Xu L, Jiang L (2006) A sequential approximate programming strategy for reliability-based structural optimization. Comput Struct 84(21):1353–1367. doi:10.1016/j.compstruc.2006.03.006 CrossRef

Ching J, Hsu W-C (2008) Transforming reliability limit-state constraints into deterministic limit-state constraints. Struct Saf 30(1):11–33. doi:10.1016/j.strusafe.2006.04.002 CrossRef

Cheng J, Li QS (2008) Reliability analysis of structures using artificial neural network based genetic algorithms. Comput Methods Appl Mech Eng 197(45–48):3742–3750

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. doi:10.1016/j.strusafe.2010.05.003 CrossRef

Du X, Chen W (2001) A most probable point-based method for efficient uncertainty analysis. J Des Manuf Autom 4(1):47–66

Du X, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. J Mech Des 126(2):225–233. doi:10.1115/1.1649968 CrossRef

Du X, Sudjianto A, Chen W (2004) An integrated framework for optimization under uncertainty using inverse reliability strategy. J Mech Des 126(4):562. doi:10.1115/1.1759358 CrossRef

Du X, Sudjianto A, Huang B (2005) Reliability-based design with the mixture of random and interval variables. J Mech Des 127(6):1068. doi:10.1115/1.1992510 CrossRef

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. doi:10.1016/j.strusafe.2011.01.002 CrossRef

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

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

Glynn PW, Iglehart DL (1989) Importance sampling for stochastic simulations. Manag Sci 35(11):1367–1392MathSciNetCrossRefMATH

Grandhi RV, Wang L (1998) Reliability-based structural optimization using improved two-point adaptive nonlinear approximations. Finite Elem Anal Des 29(1):35–48. doi:10.1016/s0168-874x(98)00007-9 CrossRefMATH

Hack, Michael, d'Ippolito, Roberto, Donders, Stijn, & Van Der Linden, Geert. (2009). Reliability-Based Fatigue Optimization of an Air Plane Slat Track with Respect to Manufacturing Tolerances. Materials Testing-Materials and Components Technology and Application, 51 (7–8), 437–443

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

Huang Y-C, Chan K-Y (2010) A modified efficient global optimization algorithm for maximal reliability in a probabilistic constrained space. J Mech Des 132(6):061002. doi:10.1115/1.4001532 CrossRef

Jiang C, Li WX, Han X, Liu LX, Le PH (2011) Structural reliability analysis based on random distributions with interval parameters. Comput Struct 89(23–24):2292–2302. doi:10.1016/j.compstruc.2011.08.006 CrossRef

Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13(4):455–492MathSciNetCrossRefMATH

Ju BH, Lee BC (2008) Reliability-based design optimization using a moment method and a kriging metamodel. Eng Optim 40(5):421–438. doi:10.1080/03052150701743795 MathSciNetCrossRef

Kang W-H, Lee Y-J, Song J, Gencturk B (2012) Further development of matrix-based system reliability method and applications to structural systems. Struct Infrastruct Eng 8(5):441–457. doi:10.1080/15732479.2010.539060 CrossRef

Kharmanda G, Mohamed A, Lemaire M (2002) Efficient reliability-based design optimization using a hybrid space with application to finite element analysis. Struct Multidiscip Optim 24(3):233–245. doi:10.1007/s00158-002-0233-z CrossRef

Kim C, Choi KK (2008) Reliability-Based Design Optimization Using Response Surface Method With Prediction Interval Estimation. J Mech Des 130(12):121401–1

Kim B-S, Lee Y-B, Choi D-H (2009a) Comparison study on the accuracy of metamodeling technique for non-convex functions. J Mech Sci Technol 23(4):1175–1181MathSciNetCrossRef

Kim B, Lee Y, Choi D-H (2009b) Construction of the radial basis function based on a sequential sampling approach using cross-validation. J Mech Sci Technol 23(12):3357–3365. doi:10.1007/s12206-009-1014-z CrossRef

Kirjner-Neto C, Polak E, Der Kiureghian A (1998) An outer approximations approach to reliability-based optimal design of structures. J Optim Theory Appl 98(1):1–16. doi:10.1023/a:1022647728419 MathSciNetCrossRefMATH

Kogiso N, Yang Y-S, Kim B-J, Lee J-O (2012) Modified single-loop-single-vector method for efficient reliability-based design optimization. J Adv Mech Des Syst 6(7):1206–1221. doi:10.1299/jamdsm.6.1206

Kuczera, Ramon C, Mourelatos, Zissimos P, & Nikolaidis, Efstratios. (2010). System RBDO with correlated variables using probabilistic re-analysis and local metamodels. Paper presented at the ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.

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. doi:10.1016/j.compstruc.2007.05.023 CrossRef

Lee I, Choi KK, Du L, Gorsich D (2008a) Dimension reduction method for reliability-based robust design optimization. Comput Struct 86(13–14):1550–1562. doi:10.1016/j.compstruc.2007.05.020 CrossRef

Lee I, Choi KK, Du L, Gorsich D (2008b) Inverse analysis method using MPP-based dimension reduction for reliability-based design optimization of nonlinear and multi-dimensional systems. Comput Methods Appl Mech Eng 198(1):14–27. doi:10.1016/j.cma.2008.03.004 CrossRefMATH

Lee, Ikjin, Choi, Kyung K, & Gorsich, David. (2011). Equivalent standard deviation to convert high-reliability model to low-reliability model for efficiency of sampling-based RBDO. Paper presented at the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.

Lee G, Yook S, Kang K, Choi D-H (2012) Reliability-based design optimization using an enhanced dimension reduction method with variable sampling points. Int J Precis Eng Manuf 13(9):1609–1618. doi:10.1007/s12541-012-0211-3 CrossRef

Li F, Wu T, Badiru A, Hu M, Soni S (2013) A single-loop deterministic method for reliability-based design optimization. Eng Optim 45(4):435–458. doi:10.1080/0305215x.2012.685071 MathSciNetCrossRef

Liang J, Mourelatos ZP, Tu J (2008) A single-loop method for reliability-based design optimisation. Int J Prod Dev 5(1):76–92CrossRef

Liu P-L, Der Kiureghian A (1986) Multivariate distribution models with prescribed marginals and covariances. Probabilistic Eng Mech 1(2):105–112CrossRef

Lophaven, Søren N., Nielsen, Hans Bruun, & Søndergaard, Jacob. (2002). A MATLAB Kriging Toolbox: Technical University of Denmark, Kongens Lyngby. Technical Report No. IMM-TR-2002-12.

Matheron G (1963) Principles of geostatistics. Econ Geol 58(8):1246–1266CrossRefMATH

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

Papadopoulos V, Giovanis DG, Lagaros ND, Papadrakakis M (2012) Accelerated subset simulation with neural networks for reliability analysis. Comput Methods Appl Mech Eng 223–224:70–80. doi:10.1016/j.cma.2012.02.013 MathSciNetCrossRef

Papadrakakis M, Lagaros ND (2002) Reliability-based structural optimization using neural networks and monte Carlo simulation. Comput Methods Appl Mech Eng 191(32):3491–3507. doi:10.1016/s0045-7825(02)00287-6 CrossRefMATH

Picheny, Victor, Ginsbourger, David, Roustant, Olivier, Haftka, Raphael T., & Kim, Nam-Ho. (2010). Adaptive Designs of Experiments for Accurate Approximation of a Target Region. Journal of Mechanical Design, 132(7). doi: 10.1115/1.4001873

Rasmussen, Carl Edward. (2004). Gaussian processes in machine learning Advanced Lectures on Machine Learning (pp. 63–71): Springer.

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

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

Royset JO, Kiureghian AD, Polak E (2001) Reliability-based optimal structural design by the decoupling approach. Reliab Eng Syst Saf 73(3):213–221. doi:10.1016/s0951-8320(01)00048-5 CrossRef

Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4(4):409–423MathSciNetCrossRefMATH

Shan S, Wang GG (2008) Reliable design space and complete single-loop reliability-based design optimization. Reliab Eng Syst Saf 93(8):1218–1230. doi:10.1016/j.ress.2007.07.006 CrossRef

Shan, Songqing, & Wang, G Gary. (2009). Development of adaptive rbf-hdmr model for approximating high dimensional problems. Paper presented at the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.

Siegmund D (1976) Importance sampling in the monte Carlo study of sequential tests. Ann Stat 673–684

Sues, R. H., Cesare, M. A., Pageau, S. S., & Wu, J. Y. T. (2001). Reliability-based optimization considering manufacturing and operational uncertainties. Journal of Aerospace Engineering, 14 (4), 166–174. doi: 10.1061/(asce)0893-1321(2001)14:4(166)

Tang Z, Lu Z, Feng J, Wang B (2012) The applications of an importance sampling method to reliability analysis of the inside flap of an aircraft Proceedings of the Institution of Mechanical Engineers, Part G. J Aerosp Eng 227(6):916–932. doi:10.1177/0954410012444185

Tu J, Choi KK, Park YH (1999) A new study on reliability-based design optimization. J Mech Des 121(4):557–564. doi:10.1115/1.2829499 CrossRef

Valdebenito MA, Schuëller GI (2010) A survey on approaches for reliability-based optimization. Struct Multidiscip Optim 42(5):645–663. doi:10.1007/s00158-010-0518-6 MathSciNetCrossRefMATH

Valdebenito MA, Schuëller GI (2011) Efficient strategies for reliability-based optimization involving non-linear, dynamical structures. Comput Struct 89(19–20):1797–1811. doi:10.1016/j.compstruc.2010.10.014 CrossRef

Wang, G Gary, Wang, Liqun, & Shan, Songqing. (2005). Reliability assessment using discriminative sampling and metamodeling. Paper presented at the 2005 SAE World Congress.

Weiji L, Li Y (1994) An effective optimization procedure based on structural reliability. Comput Struct 52(5):1061–1067CrossRefMATH

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. doi:10.1016/j.strusafe.2006.08.003 CrossRef

Youn BD, Choi KK (2004) An investigation of nonlinearity of reliability-based design optimization approaches. J Mech Des 126(3):403. doi:10.1115/1.1701880 CrossRef

Youn BD, Choi KK, Du L (2005a) Enriched performance measure approach for reliability-based design optimization. AIAA J 43(4):874–884. doi:10.2514/1.6648 CrossRef

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

Zhao, Liang, Choi, Kyung K, Lee, Ikjin, & Du, Liu. (2009). Response surface method using sequential sampling for reliability-based design optimization. Paper presented at the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.

Zhuang X, Pan R (2012) A sequential sampling strategy to improve reliability-based design optimization with implicit constraint functions. J Mech Des 134(2):021002. doi:10.1115/1.4005597 CrossRef

Zou T, Mahadevan S (2006) A direct decoupling approach for efficient reliability-based design optimization. Struct Multidiscip Optim 31(3):190–200. doi:10.1007/s00158-005-0572-7 CrossRef

Title: An important boundary sampling method for reliability-based design optimization using kriging model
Authors: Zhenzhong Chen
Siping Peng
Xiaoke Li
Haobo Qiu
Huadi Xiong
Liang Gao
Peigen Li
Publication date: 01-07-2015
Publisher: Springer Berlin Heidelberg
Published in: Structural and Multidisciplinary Optimization / Issue 1/2015
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-014-1173-0

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