Reliability-based design optimization under dependent random variables by a generalized polynomial chaos expansion
This article brings forward a new computational method for reliability-based design optimization (RBDO) of complex mechanical systems subject to input random variables following arbitrary, dependent probability distributions. It involves a generalized polynomial chaos expansion (GPCE) for reliabilit...
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| Published in | Structural and multidisciplinary optimization Vol. 65; no. 1 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.01.2022
Springer Nature B.V |
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| Online Access | Get full text |
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| Abstract | This article brings forward a new computational method for reliability-based design optimization (RBDO) of complex mechanical systems subject to input random variables following arbitrary, dependent probability distributions. It involves a generalized polynomial chaos expansion (GPCE) for reliability analysis subject to dependent input random variables, a novel fusion of the GPCE approximation and score functions for estimating the sensitivities of the failure probability with respect to design variables, and standard gradient-based optimization algorithms, resulting in a multi-point single-step design process. The method, designated as the multi-point single-step GPCE method or simply the MPSS-GPCE method, yields analytical formulae for computing the failure probability and its design sensitivities concurrently from a single stochastic simulation or analysis. For this reason, the MPSS-GPCE method affords the ability to solve industrial-scale problems with large design spaces. Numerical results stemming from mathematical functions or elementary engineering problems indicate that the new method provides more accurate or computationally efficient design solutions than existing methods or reference solutions. Furthermore, the shape design optimization of a jet engine compressor blade root was successfully conducted, demonstrating the power of the new method in confronting practical RBDO problems. |
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| AbstractList | This article brings forward a new computational method for reliability-based design optimization (RBDO) of complex mechanical systems subject to input random variables following arbitrary, dependent probability distributions. It involves a generalized polynomial chaos expansion (GPCE) for reliability analysis subject to dependent input random variables, a novel fusion of the GPCE approximation and score functions for estimating the sensitivities of the failure probability with respect to design variables, and standard gradient-based optimization algorithms, resulting in a multi-point single-step design process. The method, designated as the multi-point single-step GPCE method or simply the MPSS-GPCE method, yields analytical formulae for computing the failure probability and its design sensitivities concurrently from a single stochastic simulation or analysis. For this reason, the MPSS-GPCE method affords the ability to solve industrial-scale problems with large design spaces. Numerical results stemming from mathematical functions or elementary engineering problems indicate that the new method provides more accurate or computationally efficient design solutions than existing methods or reference solutions. Furthermore, the shape design optimization of a jet engine compressor blade root was successfully conducted, demonstrating the power of the new method in confronting practical RBDO problems. |
| ArticleNumber | 21 |
| Author | Lee, Dongjin Rahman, Sharif |
| Author_xml | – sequence: 1 givenname: Dongjin orcidid: 0000-0003-3346-8059 surname: Lee fullname: Lee, Dongjin email: dongjin-lee@uiowa.edu organization: Department of Mechanical Engineering, The University of Iowa – sequence: 2 givenname: Sharif surname: Rahman fullname: Rahman, Sharif organization: Department of Mechanical Engineering, The University of Iowa |
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| Keywords | Design sensitivity analysis Reliability analysis GPCE Stochastic optimization RBDO Score functions |
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The MathWorks Inc., Natick, Massachusetts SuryawanshiAGhoshDReliability based optimization in aeroelastic stability problems using polynomial chaos based metamodelsStruct Multidiscip Optim2016535106910803490932 HassanRCrossleyWSpacecraft reliability-based design optimization under uncertainty including discrete variablesJ Spacecraft Rockets2008452394405 RahmanSWeiDDesign sensitivity and reliability-based structural optimization by univariate decompositionStruct Multidiscip Optim2008353245261 HadigolMDoostanALeast squares polynomial chaos expansion: a review of sampling strategiesComput Methods Appl Mech Eng201833238240737644331440.65007 das Neves CarneiroGAntonioCCDimensional reduction applied to the reliability-based robust design optimization of composite structuresCompos Struct2021255112937 RahmanSA polynomial chaos expansion in dependent random variablesJ Math Anal Appl2018464174977537941141397.60069 ToropovVFilatovAPolynkinAMultiparameter structural optimization using FEM and multipoint explicit approximationsStruct Multidiscip Optim199361714 CREO (2016) version 4.0. 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| References_xml | – reference: TuJChoiKKParkYHA new study on reliability-based design optimizationJ Mech Des19991214557564 – reference: ZhaoLChoiKLeeIMetamodeling method using dynamic kriging for design optimizationAIAA J201149920342046 – reference: RosenblattMRemarks on a multivariate transformationAnn Math Stat195223470472495250047.13104 – reference: LeeDRahmanSRobust design optimization under dependent random variables by a generalized polynomial chaos expansionStruct Multidiscip Optim2021635242524574244965 – reference: RahmanSA polynomial chaos expansion in dependent random variablesJ Math Anal Appl2018464174977537941141397.60069 – reference: DuXChenWSequential optimization and reliability assessment method for efficient probabilistic designJ Mech Des20041262225233 – reference: das Neves CarneiroGAntónioCCSobol’ indices as dimension reduction technique in evolutionary-based reliability assessmentEng Comput2020371368398 – reference: LuthenNMarelliSSudretBSparse polynomial chaos expansions: literature survey and benchmarkSIAM/ASA J Uncertain Quant20219259364942578791464.65008 – reference: XiuDKarniadakisGEThe Wiener–Askey polynomial chaos for stochastic differential equationsSIAM J Sci Comput20022461964419510581014.65004 – reference: RahmanSWeiDDesign sensitivity and reliability-based structural optimization by univariate decompositionStruct Multidiscip Optim2008353245261 – reference: MATLAB (2019) version 9.7.0 (R2019b). The MathWorks Inc., Natick, Massachusetts – reference: RahmanSUncertainty quantification under dependent random variables by a generalized polynomial dimensional decompositionComput Methods Appl Mech Eng201934491093738806471440.60044 – reference: das Neves CarneiroGAntonioCCDimensional reduction applied to the reliability-based robust design optimization of composite structuresCompos Struct2021255112937 – reference: GuXLuJWangHReliability-based design optimization for vehicle occupant protection system based on ensemble of metamodelsStruct Multidiscip Optim2015512533546 – reference: KuschelNRackwitzRTwo basic problems in reliability-based structural optimizationMath Methods Oper Res199746330933316030710896.90106 – reference: FernandesADAtchleyWRGaussian quadrature formulae for arbitrary positive measuresEvol Bioinform200610.1177/117693430600200010 – reference: HadigolMDoostanALeast squares polynomial chaos expansion: a review of sampling strategiesComput Methods Appl Mech Eng201833238240737644331440.65007 – reference: LeeDRahmanSPractical uncertainty quantification analysis involving statistically dependent random variablesAppl Math Model202084324356409121007203996 – reference: YounBDChoiKKA new response surface methodology for reliability-based design optimizationComput Struct2004822–3241256 – reference: YounBDChoiKYangRJGuLReliability-based design optimization for crashworthiness of vehicle side impactStruct Multidiscip Optim2004263272283 – reference: ChiralaksanakulAMahadevanSFirst-order approximation methods in reliability-based design optimizationJ Mech Des20041275851857 – reference: RahmanSStochastic sensitivity analysis by dimensional decomposition and score functionsProbab Eng Mech2009243278287 – reference: StieltjesTJQuelques recherches sur la théorie des quadratures dites mécaniquesAnn Sci l’Écol Norm Supér1884140942616.0242.02 – reference: AgarwalHRenaudJENew decoupled framework for reliability-based design optimizationAIAA J200644715241531 – reference: StephensRFatemiAStephensRRFuchsHMetal fatigue in engineering2000New YorkWiley-Interscience – reference: LeeIChoiKKNohYZhaoLGorsichDSampling-based stochastic sensitivity analysis using score functions for rbdo problems with correlated random variablesJ Mech Des2011101115/14003186 – reference: NohYChoiKDuLReliability-based design optimization of problems with correlated input variables using a Gaussian CopulaStruct Multidiscip Optim2009381116 – reference: NannapaneniSMahadevanSProbability-space surrogate modeling for fast multidisciplinary optimization under uncertaintyReliab Eng Syst Saf2020198106896 – reference: KangBChoiKKimDHAn efficient serial-loop strategy for reliability-based robust optimization of electromagnetic design problemsIEEE Trans Magn201754314 – reference: LeeIChoiKDuLGorsichDDimension reduction method for reliability-based robust design optimizationComput Struct20088613–14155015621194.74250 – reference: LiLWanHGaoWTongFLiHReliability based multidisciplinary design optimization of cooling turbine blade considering uncertainty data statisticsStruct Multidiscip Optim2019592659673 – reference: ToropovVFilatovAPolynkinAMultiparameter structural optimization using FEM and multipoint explicit approximationsStruct Multidiscip Optim199361714 – reference: ABAQUS (2019) version 2019. 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| SubjectTerms | Algorithms Compressor blades Computational Mathematics and Numerical Analysis Dependent variables Design optimization Design standards Engineering Engineering Design Jet engines Mathematical functions Mechanical systems Polynomials Random variables Reliability analysis Research Paper Theoretical and Applied Mechanics |
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| Title | Reliability-based design optimization under dependent random variables by a generalized polynomial chaos expansion |
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