High-dimensional model representation for structural reliability analysis

This paper presents a new computational tool for predicting failure probability of structural/mechanical systems subject to random loads, material properties, and geometry. The method involves high‐dimensional model representation (HDMR) that facilitates lower‐dimensional approximation of the origin...

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Published in:	Communications in numerical methods in engineering Vol. 25; no. 4; pp. 301 - 337
Main Authors:	Chowdhury, Rajib, Rao, B. N., Prasad, A. Meher
Format:	Journal Article
Language:	English
Published:	Chichester, UK John Wiley & Sons, Ltd 01.04.2009 Wiley
Subjects:	Computational techniques Exact sciences and technology failure probability Fracture mechanics (crack, fatigue, damage...) Fundamental areas of phenomenology (including applications) high-dimensional model representation Mathematical methods in physics moving least squares Physics response surface Solid mechanics Structural and continuum mechanics structural reliability Monte Carlo method Statistical analysis Probabilistic approach Rupture moving least squares Structural reliability Modeling high-dimensional model representation System with n degrees of freedom Least squares method Mechanical system Random load Response surface Implicit function theorem failure probability Non linear effect Random medium Quantitative analysis Structural analysis Input output model
ISSN:	1069-8299, 1099-0887
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Abstract	This paper presents a new computational tool for predicting failure probability of structural/mechanical systems subject to random loads, material properties, and geometry. The method involves high‐dimensional model representation (HDMR) that facilitates lower‐dimensional approximation of the original high‐dimensional implicit limit state/performance function, response surface generation of HDMR component functions, and Monte Carlo simulation. HDMR is a general set of quantitative model assessment and analysis tools for capturing the high‐dimensional relationships between sets of input and output model variables. It is a very efficient formulation of the system response, if higher‐order variable correlations are weak, allowing the physical model to be captured by the first few lower‐order terms. Once the approximate form of the original implicit limit state/performance function is defined, the failure probability can be obtained by statistical simulation. Results of nine numerical examples involving mathematical functions and structural mechanics problems indicate that the proposed method provides accurate and computationally efficient estimates of the probability of failure. Copyright © 2008 John Wiley & Sons, Ltd.
AbstractList	This paper presents a new computational tool for predicting failure probability of structural/mechanical systems subject to random loads, material properties, and geometry. The method involves high‐dimensional model representation (HDMR) that facilitates lower‐dimensional approximation of the original high‐dimensional implicit limit state/performance function, response surface generation of HDMR component functions, and Monte Carlo simulation. HDMR is a general set of quantitative model assessment and analysis tools for capturing the high‐dimensional relationships between sets of input and output model variables. It is a very efficient formulation of the system response, if higher‐order variable correlations are weak, allowing the physical model to be captured by the first few lower‐order terms. Once the approximate form of the original implicit limit state/performance function is defined, the failure probability can be obtained by statistical simulation. Results of nine numerical examples involving mathematical functions and structural mechanics problems indicate that the proposed method provides accurate and computationally efficient estimates of the probability of failure. Copyright © 2008 John Wiley & Sons, Ltd. This paper presents a new computational tool for predicting failure probability of structural/mechanical systems subject to random loads, material properties, and geometry. The method involves high-dimensional model representation (HDMR) that facilitates lower-dimensional approximation of the original high-dimensional implicit limit state/performance function, response surface generation of HDMR component functions, and Monte Carlo simulation. HDMR is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. It is a very efficient formulation of the system response, if higher-order variable correlations are weak, allowing the physical model to be captured by the first few lower-order terms. Once the approximate form of the original implicit limit state/performance function is defined, the failure probability can be obtained by statistical simulation. Results of nine numerical examples involving mathematical functions and structural mechanics problems indicate that the proposed method provides accurate and computationally efficient estimates of the probability of failure.
Author	Prasad, A. Meher Chowdhury, Rajib Rao, B. N.
Author_xml	– sequence: 1 givenname: Rajib surname: Chowdhury fullname: Chowdhury, Rajib organization: Structural Engineering Division, Department of Civil Engineering, Indian Institute of Technology Madras, Chennai 600 036, India – sequence: 2 givenname: B. N. surname: Rao fullname: Rao, B. N. email: bnrao@iitm.ac.in organization: Structural Engineering Division, Department of Civil Engineering, Indian Institute of Technology Madras, Chennai 600 036, India – sequence: 3 givenname: A. Meher surname: Prasad fullname: Prasad, A. Meher organization: Structural Engineering Division, Department of Civil Engineering, Indian Institute of Technology Madras, Chennai 600 036, India
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Keywords	Monte Carlo method Statistical analysis Probabilistic approach Rupture moving least squares Structural reliability Modeling high-dimensional model representation System with n degrees of freedom Least squares method Mechanical system Random load Response surface Implicit function theorem failure probability Non linear effect Random medium Quantitative analysis Structural analysis Input output model
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References_xml	– reference: Rabitz H, Alis OF, Shorter J, Shim K. Efficient input-output model representations. Computer Physics Communications 1999; 117(1-2):11-20. – reference: Au SK, Beck JL. Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Engineering Mechanics 2001; 16(4):263-277. – reference: Alis OF, Rabitz H. Efficient implementation of high dimensional model representations. Journal of Mathematical Chemistry 2001; 29(2):127-142. – reference: Ditlevsen O, Madsen HO. Structural Reliability Methods. Wiley: Chichester, 1996. – reference: Penmetsa RC, Grandhi RV. Efficient estimation of structural reliability for problems with uncertain intervals. Computers and Structures 2002; 80:1103-1112. – reference: Lancaster P, Salkauskas K. Curve and Surface Fitting: An Introduction. Academic Press: London, 1986. – reference: Guan XL, Melchers RE. Effect of response surface parameter variation on structural reliability estimates. Structural Safety 2001; 23(4):429-444. – reference: Sobol IM. Theorems and examples on high dimensional model representations. Reliability Engineering and System Safety 2003; 79(2):187-193. – reference: Rao BN, Rahman S. An efficient meshless method for fracture analysis of cracks. Computational Mechanics 2000; 26:398-408. – reference: Der Kiureghian A, Dakessian T. Multiple design points in first and second-order reliability. Structural Safety 1998; 20(1):37-49. – reference: Ditlevsen O. Uncertainty Modeling. McGraw-Hill: New York, NY, 1981. – reference: Bjerager P. Probability integration by directional simulation. Journal of Engineering Mechanics (ASCE) 1988; 114(8):285-1302. – reference: Schuëller GI, Pradlwarter HW, Koutsourelakis PS. A critical appraisal of reliability estimation procedures for high dimensions. Probabilistic Engineering Mechanics 2004; 19(4):463-474. – reference: Singh IV. A numerical solution of composite heat transfer problems using meshless method. 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Snippet	This paper presents a new computational tool for predicting failure probability of structural/mechanical systems subject to random loads, material properties,...
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SubjectTerms	Computational techniques Exact sciences and technology failure probability Fracture mechanics (crack, fatigue, damage...) Fundamental areas of phenomenology (including applications) high-dimensional model representation Mathematical methods in physics moving least squares Physics response surface Solid mechanics Structural and continuum mechanics structural reliability
Title	High-dimensional model representation for structural reliability analysis
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