Non-probabilistic uncertainty quantification and response analysis of structures with a bounded field model

A general framework for quantifying bounded field uncertainties in loading conditions, material properties and geometrical dimensions is developed in this study. By using a non-probabilistic series expansion (NPSE) method similar as the Expansion Optimal Linear Estimator (EOLE), the bounded field un...

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Vydáno v:	Computer methods in applied mechanics and engineering Ročník 347; s. 663 - 678
Hlavní autoři:	Luo, Yangjun, Zhan, Junjie, Xing, Jian, Kang, Zhan
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 15.04.2019 Elsevier BV
Témata:	Algorithms Bounded field model Lower bounds Material properties Mathematical models Mathematical programming Non-probabilistic uncertainty Probabilistic methods Sensitivity Sensitivity analysis Series expansion Uncertainty Uncertainty quantification Uncertainty quantification Non-probabilistic uncertainty Bounded field model Sensitivity
ISSN:	0045-7825, 1879-2138
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Abstract	A general framework for quantifying bounded field uncertainties in loading conditions, material properties and geometrical dimensions is developed in this study. By using a non-probabilistic series expansion (NPSE) method similar as the Expansion Optimal Linear Estimator (EOLE), the bounded field uncertainties with certain spatial correlation characteristic are modeled with a reduced set of uncertain-but-bounded coefficients. Further, it is shown that these coefficients are bounded by a multi-ellipsoid convex model. The gradient-based mathematical programming algorithm combined with an efficient adjoint variable sensitivity scheme is then employed to evaluate the upper and lower bounds of structural performance. The proposed method allows spatially varying uncertainties as well as their dependencies to be described in a non-probabilistic framework, which ensures the objectivity and accuracy of representations of bounded field uncertainties. Moreover, it provides an efficient way to evaluate the variation range of structural performance with a significant reduction of computational cost compared to direct treatments. Numerical examples regarding the performance bound evaluation of structures with bounded field uncertainties are presented to illustrate the validity and applicability of this method. •This study presents a new non-probabilistic framework for quantifying bounded field uncertainties in loading conditions, material properties and geometrical dimensions.•The bounded field uncertainties with certain spatial correlation characteristic are modeled with a reduced set of non-probabilistic series expansion (NPSE) coefficients.•It is shown that NPSE coefficients are bounded by a multi-ellipsoid convex model.•The upper and lower bounds of structural performance are obtained by the gradient-based algorithm combined with an efficient adjoint variable sensitivity scheme.
AbstractList	A general framework for quantifying bounded field uncertainties in loading conditions, material properties and geometrical dimensions is developed in this study. By using a non-probabilistic series expansion (NPSE) method similar as the Expansion Optimal Linear Estimator (EOLE), the bounded field uncertainties with certain spatial correlation characteristic are modeled with a reduced set of uncertain-but-bounded coefficients. Further, it is shown that these coefficients are bounded by a multi-ellipsoid convex model. The gradient-based mathematical programming algorithm combined with an efficient adjoint variable sensitivity scheme is then employed to evaluate the upper and lower bounds of structural performance. The proposed method allows spatially varying uncertainties as well as their dependencies to be described in a non-probabilistic framework, which ensures the objectivity and accuracy of representations of bounded field uncertainties. Moreover, it provides an efficient way to evaluate the variation range of structural performance with a significant reduction of computational cost compared to direct treatments. Numerical examples regarding the performance bound evaluation of structures with bounded field uncertainties are presented to illustrate the validity and applicability of this method. A general framework for quantifying bounded field uncertainties in loading conditions, material properties and geometrical dimensions is developed in this study. By using a non-probabilistic series expansion (NPSE) method similar as the Expansion Optimal Linear Estimator (EOLE), the bounded field uncertainties with certain spatial correlation characteristic are modeled with a reduced set of uncertain-but-bounded coefficients. Further, it is shown that these coefficients are bounded by a multi-ellipsoid convex model. The gradient-based mathematical programming algorithm combined with an efficient adjoint variable sensitivity scheme is then employed to evaluate the upper and lower bounds of structural performance. The proposed method allows spatially varying uncertainties as well as their dependencies to be described in a non-probabilistic framework, which ensures the objectivity and accuracy of representations of bounded field uncertainties. Moreover, it provides an efficient way to evaluate the variation range of structural performance with a significant reduction of computational cost compared to direct treatments. Numerical examples regarding the performance bound evaluation of structures with bounded field uncertainties are presented to illustrate the validity and applicability of this method. •This study presents a new non-probabilistic framework for quantifying bounded field uncertainties in loading conditions, material properties and geometrical dimensions.•The bounded field uncertainties with certain spatial correlation characteristic are modeled with a reduced set of non-probabilistic series expansion (NPSE) coefficients.•It is shown that NPSE coefficients are bounded by a multi-ellipsoid convex model.•The upper and lower bounds of structural performance are obtained by the gradient-based algorithm combined with an efficient adjoint variable sensitivity scheme.
Author	Kang, Zhan Luo, Yangjun Xing, Jian Zhan, Junjie
Author_xml	– sequence: 1 givenname: Yangjun surname: Luo fullname: Luo, Yangjun email: yangjunluo@dlut.edu.cn organization: State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China – sequence: 2 givenname: Junjie surname: Zhan fullname: Zhan, Junjie organization: State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China – sequence: 3 givenname: Jian orcidid: 0000-0003-2577-3192 surname: Xing fullname: Xing, Jian organization: State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China – sequence: 4 givenname: Zhan orcidid: 0000-0001-6652-7831 surname: Kang fullname: Kang, Zhan email: zhankang@dlut.edu.cn organization: Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China
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Snippet	A general framework for quantifying bounded field uncertainties in loading conditions, material properties and geometrical dimensions is developed in this...
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SubjectTerms	Algorithms Bounded field model Lower bounds Material properties Mathematical models Mathematical programming Non-probabilistic uncertainty Probabilistic methods Sensitivity Sensitivity analysis Series expansion Uncertainty Uncertainty quantification
Title	Non-probabilistic uncertainty quantification and response analysis of structures with a bounded field model
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