Skip to main content
Erschienen in: Structural and Multidisciplinary Optimization 1/2015

01.07.2015 | RESEARCH PAPER

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

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

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 1/2015

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat 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, 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.
Zurück zum Zitat 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 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
Zurück zum Zitat 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 (2001) A most probable point-based method for efficient uncertainty analysis. J Des Manuf Autom 4(1):47–66
Zurück zum Zitat 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, 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
Zurück zum Zitat Enevoldsen I, Sørensen JD (1994) Reliability-based optimization in structural engineering. Struct Saf 15(3):169–196CrossRef Enevoldsen I, Sørensen JD (1994) Reliability-based optimization in structural engineering. Struct Saf 15(3):169–196CrossRef
Zurück zum Zitat Gasser M, Schuëller GI (1997) Reliability-based optimization of structural systems. Math Meth Oper Res 46(3):287–307CrossRefMATH Gasser M, Schuëller GI (1997) Reliability-based optimization of structural systems. Math Meth Oper Res 46(3):287–307CrossRefMATH
Zurück zum Zitat 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 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
Zurück zum Zitat Hasofer AM, Lind NC (1974) Exact and invariant second-moment code format. J Eng Mech Div 100(1):111–121 Hasofer AM, Lind NC (1974) Exact and invariant second-moment code format. J Eng Mech Div 100(1):111–121
Zurück zum Zitat 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 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
Zurück zum Zitat Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13(4):455–492MathSciNetCrossRefMATH Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13(4):455–492MathSciNetCrossRefMATH
Zurück zum Zitat 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 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
Zurück zum Zitat 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 C, Choi KK (2008) Reliability-Based Design Optimization Using Response Surface Method With Prediction Interval Estimation. J Mech Des 130(12):121401–1
Zurück zum Zitat 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-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
Zurück zum Zitat 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 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
Zurück zum Zitat 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 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
Zurück zum Zitat 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. 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.
Zurück zum Zitat 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 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
Zurück zum Zitat 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, 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.
Zurück zum Zitat 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 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
Zurück zum Zitat Liang J, Mourelatos ZP, Tu J (2008) A single-loop method for reliability-based design optimisation. Int J Prod Dev 5(1):76–92CrossRef Liang J, Mourelatos ZP, Tu J (2008) A single-loop method for reliability-based design optimisation. Int J Prod Dev 5(1):76–92CrossRef
Zurück zum Zitat Liu P-L, Der Kiureghian A (1986) Multivariate distribution models with prescribed marginals and covariances. Probabilistic Eng Mech 1(2):105–112CrossRef Liu P-L, Der Kiureghian A (1986) Multivariate distribution models with prescribed marginals and covariances. Probabilistic Eng Mech 1(2):105–112CrossRef
Zurück zum Zitat 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. 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.
Zurück zum Zitat Nikolaidis E, Burdisso R (1988) Reliability based optimization: a safety index approach. Comput Struct 28(6):781–788CrossRefMATH Nikolaidis E, Burdisso R (1988) Reliability based optimization: a safety index approach. Comput Struct 28(6):781–788CrossRefMATH
Zurück zum Zitat 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 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
Zurück zum Zitat Rasmussen, Carl Edward. (2004). Gaussian processes in machine learning Advanced Lectures on Machine Learning (pp. 63–71): Springer. Rasmussen, Carl Edward. (2004). Gaussian processes in machine learning Advanced Lectures on Machine Learning (pp. 63–71): Springer.
Zurück zum Zitat Reddy MV, Grandhi RV, Hopkins DA (1994) Reliability based structural optimization: a simplified safety index approach. Comput Struct 53(6):1407–1418CrossRefMATH Reddy MV, Grandhi RV, Hopkins DA (1994) Reliability based structural optimization: a simplified safety index approach. Comput Struct 53(6):1407–1418CrossRefMATH
Zurück zum Zitat 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. 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.
Zurück zum Zitat Siegmund D (1976) Importance sampling in the monte Carlo study of sequential tests. Ann Stat 673–684 Siegmund D (1976) Importance sampling in the monte Carlo study of sequential tests. Ann Stat 673–684
Zurück zum Zitat 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) 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)
Zurück zum Zitat 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 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​
Zurück zum Zitat Wang, G Gary, Wang, Liqun, & Shan, Songqing. (2005). Reliability assessment using discriminative sampling and metamodeling. Paper presented at the 2005 SAE World Congress. Wang, G Gary, Wang, Liqun, & Shan, Songqing. (2005). Reliability assessment using discriminative sampling and metamodeling. Paper presented at the 2005 SAE World Congress.
Zurück zum Zitat Weiji L, Li Y (1994) An effective optimization procedure based on structural reliability. Comput Struct 52(5):1061–1067CrossRefMATH Weiji L, Li Y (1994) An effective optimization procedure based on structural reliability. Comput Struct 52(5):1061–1067CrossRefMATH
Zurück zum Zitat Youn BD, Choi KK, Du L (2005b) Adaptive probability analysis using an enhanced hybrid mean value method. Struct Multidiscip Optim 29(2):134–148CrossRef Youn BD, Choi KK, Du L (2005b) Adaptive probability analysis using an enhanced hybrid mean value method. Struct Multidiscip Optim 29(2):134–148CrossRef
Zurück zum Zitat 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. 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.
Zurück zum Zitat 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 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
Metadaten
Titel
An important boundary sampling method for reliability-based design optimization using kriging model
verfasst von
Zhenzhong Chen
Siping Peng
Xiaoke Li
Haobo Qiu
Huadi Xiong
Liang Gao
Peigen Li
Publikationsdatum
01.07.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 1/2015
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-014-1173-0

Weitere Artikel der Ausgabe 1/2015

Structural and Multidisciplinary Optimization 1/2015 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.