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International Journal for Uncertainty Quantification
Habib N. Najm (open in a new tab) Sandia National Laboratories, P.O. Box 969, MS 9051, Livermore, CA 94551, USA
Dongbin Xiu (open in a new tab) Department of Mathematics, The Ohio State University, Columbus, 43210 Ohio, USA
Tao Zhou (open in a new tab) LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Nicholas Zabaras (open in a new tab) Department of Mechanical and Aerospace Engineering, Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA; University of Warwick, Coventry CV4 7AL, UK
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ERROR AND UNCERTAINTY QUANTIFICATION AND SENSITIVITY ANALYSIS IN MECHANICS COMPUTATIONAL MODELS

pages 147-161
DOI: 10.1615/Int.J.UncertaintyQuantification.v1.i2.30
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RÉSUMÉ

Multiple sources of errors and uncertainty arise in mechanics computational models and contribute to the uncertainty in the final model prediction. This paper develops a systematic error quantification methodology for computational models. Some types of errors are deterministic, and some are stochastic. Appropriate procedures are developed to either correct the model prediction for deterministic errors or to account for the stochastic errors through sampling. First, input error, discretization error in finite element analysis (FEA), surrogate model error, and output measurement error are considered. Next, uncertainty quantification error, which arises due to the use of sampling-based methods, is also investigated. Model form error is estimated based on the comparison of corrected model prediction against physical observations and after accounting for solution approximation errors, uncertainty quantification errors, and experimental errors (input and output). Both local and global sensitivity measures are investigated to estimate and rank the contribution of each source of error to the uncertainty in the final result. Two numerical examples are used to demonstrate the proposed methodology by considering mechanical stress analysis and fatigue crack growth analysis.

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