Gradient-Enhanced Universal Kriging for Uncertainty Propagation

REFERENCES

• F. D’AURIA, N. DEBRECIN, and G. GALASSI, “Outline of the Uncertainty Methodology Based on Accuracy Extrapolation,” Nucl. Technol., 109, 21 (1995).
   Web of Science ®Google Scholar
• X. DU and W. CHEN, “Efficient Uncertainty Analysis Methods for Multidisciplinary Robust Design,” AIAA J., 40, 3, 545 (2002).
   Google Scholar
• W. OBERKAMPF, J. HELTON, C. JOSLYN, S. WOJTKIEWICZ, and S. FERSON, “Challenge Problems: Uncertainty in System Response Given Uncertain Parameters,” Reliab. Eng. Syst. Safe., 85, 1–3, 11 (2004).
   Web of Science ®Google Scholar
• S. ISUKAPALLI, A. ROY, and P. GEORGOPOULOS, “Stochastic Response Surface Methods (SRSMs) for Uncertainty Propagation: Application to Environmental and Biological Systems,” Risk Anal., 18, 3, 351 (1998).
   PubMed Web of Science ®Google Scholar
• O. LE MAĪTRE, O. KNIO, H. NAJM, and R. GHANEM, “Uncertainty Propagation Using Wiener-Haar Expansions,” J. Computat. Phys., 197, 1, 28 (2004).
   Google Scholar
• J. JOUHAUD, P. SAGAUT, M. MONTAGNAC, and J. LAURENCEAU, “A Surrogate-Model Based Multidisciplinary Shape Optimization Method with Application to a 2D Subsonic Airfoil,” Comput. Fluids, 36, 3, 520 (2007).
   Web of Science ®Google Scholar
• O. RODERICK, M. ANITESCU, and P. FISCHER, “Polynomial Regression Approaches Using Derivative Information for Uncertainty Quantification,” Nucl. Sci. Eng., 164, 2, 122 (2010).
   Web of Science ®Google Scholar
• O. RODERICK, M. ANITESCU, P. FISCHER, and W.-S. YANG, “Stochastic Finite-Element Approach in Nuclear Reactor Uncertainty Quantification,” Trans. Am. Nucl. Soc., 100, 317 (2009).
   Google Scholar
• A. GRIEWANK, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia (2000).
   Google Scholar
• S. ISUKAPALLI, A. ROY, and P. GEORGOPOULOS, “Efficient Sensitivity/Uncertainty Analysis Using the Combined Stochastic Response Surface Method and Automated Differentiation: Application to Environmental and Biological Systems,” Risk Analy., 20, 5, 591 (2000).
   Web of Science ®Google Scholar
• N. KIM, H. WANG, and N. QUEIPO, “Adaptive Reduction of Random Variables Using Global Sensitivity in Reliability-Based Optimisation,” Int. J. Reliab. Safe., 1, 1, 102 (2006).
   Google Scholar
• D. CACUCI and M. IONESCU-BUJOR, “Best-Estimate Model Calibration and Prediction Through Experimental Data Assimilation—I: Mathematical Framework,” Nucl. Sci. Eng., 165, 18 (2010).
   Web of Science ®Google Scholar
• D. CACUCI and M. IONESCU-BUJOR, “On the Evaluation of Discrepant Scientific Data with Unrecognized Errors,” Nucl. Sci. Eng., 165, 1 (2010).
   Web of Science ®Google Scholar
• D. CACUCI, M. IONESCU-BUJOR, and I. NAVON, Sensitivity and Uncertainty Analysis: Applications to Large-Scale Systems, Vol. 2, CRC (2005).
   Google Scholar
• A. PETRUZZI, D. CACUCI, and F. D’AURIA, “Best-Estimate Model Calibration and Prediction Through Experimental Data Assimilation—II: Application to a Blowdown Benchmark Experiment,” Nucl. Sci. Eng., 165, 45 (2010).
   Web of Science ®Google Scholar
• C. RASMUSSEN and C. WILLIAMS, Gaussian Processes for Machine Learning, MIT Press, Cambridge, Massachusetts (2006).
   Google Scholar
• M. STEIN, Interpolation of Spatial Data: Some Theory for Kriging, Springer-Verlag, Berlin (1999).
   Google Scholar
• T. HASTIE, R. TIBSHIRANI, and J. FRIEDMAN, The Elements of Statistical Learning, Springer-Verlag, Berlin (2001).
   Google Scholar
• A. JOURNEL and M. ROSSI, “When Do We Need a Trend Model in Kriging?” Math. Geol., 21, 715 (1989).
   Google Scholar
• M. KENNEDY and A. O’HAGAN, “Bayesian Calibration of Computer Models,” J. Roy. Stat. Soc. B Meth., 63, 3, 425 (2001).
   Web of Science ®Google Scholar
• J. SACKS, W. WELCH, T. MITCHELL, and H. WYNN, “Design and Analysis of Computer Experiments,” Stat. Sci., 4, 4, 409 (1989).
   Google Scholar
• A. PETRUZZI and F. D’AURIA, “Thermal-Hydraulic System Codes in Nuclear Reactor Safety and Qualification Procedures,” Sci. Technol. Nucl. Installations (2008), doi: 10.1155/2008/460795.
   Google Scholar
• D. HIGDON, M. KENNEDY, J. C. CAVENDISH, J. A. CAFEO, and R. D. RYNE, “Combining Field Data and Computer Simulations for Calibration and Prediction,” SIAM J. Sci. Comput., 26, 2, 448 (2004).
   Web of Science ®Google Scholar
• M. GOLDSTEIN and J. ROUGIER, “Probabilistic Formulations for Transferring Inferences from Mathematical Models to Physical Systems,” SIAM J. Sci. Comput., 26, 2, 467 (2004).
   Web of Science ®Google Scholar
• D. HIGDON, J. GATTIKER, B. WILLIAMS, and M. RIGHTLEY, “Computer Model Calibration Using High-Dimensional Output,” J. Am. Stat. Assoc., 103, 482, 570 (2008).
   Web of Science ®Google Scholar
• M. BAYARRI, J. BERGER, R. PAULO, J. SACKS, J. CAFEO, J. CAVENDISH, C. LIN, and J. TU, “A Framework for Validation of Computer Models,” Technometrics, 49, 2, 138 (2007).
   Web of Science ®Google Scholar
• E. SOLAK, R. MURRAY-SMITH, W. LEITHEAD, D. LEITH, and C. RASMUSSEN, “Derivative Observations in Gaussian Process Models of Dynamical Systems,” Advances in Neural Information Processing Systems, pp. 1057–1064 (2003).
   Google Scholar
• M. D. MORRIS, T. J. MITCHELL, and D. YLVISAKER, “Bayesian Design and Analysis of Computer Experiments: Use of Derivatives in Surface Prediction,” Technometrics, 35, 3, 243 (1993).
   Web of Science ®Google Scholar
• S. G. Z.-H. HAN and R. ZIMMERMANN, “On Improving Efficiency and Accuracy of Variable-Fidelity Surrogate Modeling in Aero-Data for Loads Context,” CEAS 2009 European Air and Space Conf., Manchester, United Kingdom, October 2009.
   Google Scholar
• Y. LI, M. ANITESCU, O. RODERICK, and F. HICKERNELL, “Orthogonal Bases for Polynomial Regression with Derivative Information in Uncertainty Quantification,” Int. J. Uncertain. Quant. (to be published).
   Web of Science ®Google Scholar
• R. GHANEM and P. SPANOS, Stochastic Finite Elements: A Spectral Approach, Dover Publications (2003).
   Google Scholar
• K. BURNHAM and D. ANDERSON, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, Springer-Verlag, New York (2002).
   Google Scholar
• J. NOCEDAL and S. J. WRIGHT, Numerical Optimization, Springer Series in Operations Research (1999).
   Google Scholar
• D. ZIMMERMAN, C. PAVLIK, A. RUGGLES, and M. ARMSTRONG, “An Experimental Comparison of Ordinary and Universal Kriging and Inverse Distance Weighting,” Math. Geol., 31, 375 (1999).
   Google Scholar
• W. Y. M. RUMPFKEIL and D. MAVRIPLIS, “A Dynamic Sampling Method for Kriging and Cokriging Surrogate Models,” 49th Aerospace Sciences Mtg., Orlando, Florida, January 4–7, 2011, paper 2011-883, AIAA (2011).
   Google Scholar
• E. E. MORRIS, “Uncertainty in Unprotected Loss-of-Heat-Sink, Loss-of-Flow, and Transient-Overpower Accidents,” ANL-AFCI-205, Argonne National Laboratory (2007).
   Google Scholar
• M. ALEXE, O. RODERICK, M. ANITESCU, J. UTKE, T. FANNING, and P. HOVLAND, “Using Automatic Differentiation in Sensitivity Analysis of Nuclear Simulation Models,” Trans. Am. Nucl. Soc., 102, 235 (2010).
   Google Scholar
• J. UTKE, U. NAUMANN, M. FAGAN, N. TALLENT, M. STROUT, P. HEIMBACH, C. HILL, and C. WUNSCH, “OpenAD/F: Aspects Modular Open-Source Tool for Automatic Differentiation of Fortran Codes,” ACM Trans. Math. Software, 34, 4, 1 (2008).
   Web of Science ®Google Scholar
• D. A. VENDITTI and D. L. DARMOFAL, “Anisotropic Grid Adaption for Functional Outputs: Application to Two-Dimensional Inviscid Flows,” J. Computat. Phys., 176, 1, 40 (Feb. 2002).
   Google Scholar
• R. HARTMANN, J. HELD, and T. LEICHT, “Adjoint-Based Error Estimation and Adaptive Mesh Refinement for the RANS and k-ω Turbulence Model Equations,” J. Computat. Phys., 230, 11, 4268 (2011).
   Google Scholar
• “Guidelines for Evaluating Fatigue Analyses Incorporating the Life Reduction of Metal Components Due to the Effects of the Light-Water Reactor Environment for New Reactors,” Regulatory Guide 1.207, U.S. Nuclear Regulatory Commission (Mar. 2007).
   Google Scholar
• A. DASGUPTA, Asymptotic Theory of Statistics and Probability, Springer-Verlag, New York (2008).
   Google Scholar