A Most Probable Point-Based Method for Efficient Uncertainty Analysis

REFERENCES

• De Neufville , S. 1990 . Applied Systems Analysis , Singapore : McGraw-Hill, Inc. .
   Google Scholar
• Hazelrigg , G. A. 1996 . Systems Engineering: An Approach to Information-Based Design , New Jersey : Prentice Hall .
   Google Scholar
• Hazelrigg , G. A. 1998 . A Framework for Decision-Based Engineering Design . ASME J. Mech. Design , Vol. 120 ( 4 ) : 653 – 658 .
   Web of Science ®Google Scholar
• Hazelrigg , G. A. 1999 . An Axiomatic Framework for Engineering Framework for Engineering Design . ASME J. Mech. Design , Vol. 121 ( 3 ) : 342 – 347 .
   Web of Science ®Google Scholar
• Pinto , J. C. 1998 . On the Costs of Parameter Uncertainties. Effects of Parameter uncertainties During Optimization and Design of Experiments, . Chem. Eng. Sci. , 53 ( 11 ) : 2029 – 2040 .
   Web of Science ®Google Scholar
• DeLaurentis , D. and Marvris , D. 2000 . “ Uncertainty Modeling and Management in Multidisciplinary Analysis and Synthesis ” . In The 38^th AIAA Aerospace Sciences Meeting Reno, NV Paper No. AIAA 2000-0422, January 10-13,2000
   Google Scholar
• Manners , W. 1990 . “ Classification and Analysis of Uncertainty in Structural System ” . In Proceedings of the 3rdIFIP WG 7.5 Conference on Reliability and Optimization of Structural Systems 251 – 260 . Berkeley, California March
   Google Scholar
• Laskey , K. B. 1996 . Model Uncertainty: Theory and Practical Implications, IEEE Transactions on System . Man, and Cybernetics - Part A: System and Human , Vol. 26 : 340 – 348 . No. 3
   Web of Science ®Google Scholar
• Ayyub , B. M. and Chao , R. U. 1997 . “ Uncertainty Modeling in Civil Engineering with Structural and Reliability Applications ” . In Uncertainty Modeling and Analysis in Civil Engineering, B.M. , 1 – 8 . CRC Press .
   Google Scholar
• Du , X. and Chen , W. 2000 . An Integrated Methodology for Uncertainity Propagation and Management in Simulation-Based Systems Design, . AIAA J. , 38 ( 8 ) : 1471 – 1478 .
   Google Scholar
• Eggert , R. J. 1991 . Quantifying Design Feasibility Using Probabilistic Feasibility Analysis, 1991 . ASME Advances in Design Automation , DE-Vol. 32-1 : 235 – 240 . Paper No
   Google Scholar
• Parkinson , A. , Sorensen , C. and Pourhassan , N. 1993 . A General Approach for Robust Optimal Design . Trans. ASME , Vol. 115 : 74 – 80 .
   Google Scholar
• Du , X. and Chen , W. 2000 . Towards a Better Understanding of Modeling Feasibility Robustness Engineering, J. . Mech. Design , 122 ( 4 ) : 357 – 583 .
   Web of Science ®Google Scholar
• Du , X. and Chen , W. 2000 . “ An Efficient Approach To Probabilistic Uncertainty Analysis In Simulation-Based Multidisciplinary Design ” . In The 38^th AIAA Aerospace Sciences Meeting Reno, NV Paper No. AIAA 2000-0423, January 10-13, 2000
   Google Scholar
• Kahn , H. 1956 . “ Use of Different Monte Carlo Sampling Techniques ” . In Proc. Symp. on Monte Carlo Methods , Edited by: Meyer , H. A. 149 – 190 . New York : John Wiley & Sons .
   Google Scholar
• Rubinstein , R. Y. 1981 . Simulation and Monte Carlo Method , New York : John Wiley & Sons .
   Google Scholar
• Walker , J. R. 1986 . Practical Application Of Variance Reduction Techniques In Probabilistic Assessments . the Second International Conference on Radioactive Waste Management. 1986 . pp. 517 – 521 . Winnipeg, Manitoba, Canada
   Google Scholar
• Brown , S. A. and Sepulveda , A. E. 1997 . Approximation of System Reliability Using a Shooting Monte Carlo Approach, . AIAA J. , 35 ( 6 ) : 1064 – 1071 .
   Google Scholar
• Ditlevsen , O. , Olesen , R. and Mohr , G. 1987 . Solution of A Class of Load Combination Problems by Directional Simulation . Structural Safety , : 95 – 109 . No. 4
   Web of Science ®Google Scholar
• Chen , W. , Allen , J. K. , Mistree , F. and Tsui , K.-L. 1996 . A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors . ASMEJ. Mech. Design , Vol. 118 : 478 – 485 .
   Web of Science ®Google Scholar
• Sues , R. H. , Oakley , D. R. and Rhodes , G. S. 1995 . Multidisciplinary Stochastic Optimization . Proceedings of the 1 0th Conference on Engineering Mechanics . May 1995 , Boulder, CO. Part 2 Vol. 2
   Google Scholar
• Kowal , M. and Mahadevan , S. 1998 . “ Uncertainty-Based Multidisciplinary Design Optimization, 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary ” . In Analysis and Optimization St. Louis, MO
   Google Scholar
• Koch , P. N. , Simpson , T. W. , Allen , J. K. and Mistree , F. 1999 . Statistical Approximations for Multidisciplinary Design Optimization: The Problem of Size, . J. Aircraft , 36 ( 1 ) : 275 – 286 .
   Web of Science ®Google Scholar
• Isukapalli , S. S. and Georgopoulos , P. G. 1998 . Stochastic Response Surface Methods (SRSMs) for Uncertainty Propagation: Application to Environmental and Biological Systems . Risk Anal. , Vol. 18 : 351 – 363 .
   Web of Science ®Google Scholar
• Wang , C. 1999 . Parametric Uncertainty Analysis for Complex Engineering Systems , MIT . June Ph.D. thesis
   Google Scholar
• Wu , Y.-T. 1998 . Methods for Efficient Probabilistic Analysis of System with Large Numbers of Random Variables, 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis Optimization, September 15-18, 1998 98 – 4908 . St. Louis, MO Paper No. AIAA
   Google Scholar
• Mitteau , J.-C. 1999 . Error Evaluations for the Computation of Failure Probability in Static Structural Reliability Problems . Probabilistic Engineering Mechanics , Vol. 14 : 119 – 135 . No. 1/2
   Web of Science ®Google Scholar
• Melchers , R. E. 1999 . Structural Reliability Analysis and Prediction , Chichester, , England : John Wiley & Sons .
   Google Scholar
• Niederreiter , H. 1992 . Random Ñumber Generation and Quasi-Monte Carlo Methods , Philadelphia : Society for Industrial and Applied Mathematics .
   Google Scholar
• Hasofer , A. M. and Lind , N. C. 1974 . Exact and Invariant Second-Moment Code Format . J. Eng. Mech. Div., ASCE , Vol. 100 : 111 – 121 .
   Web of Science ®Google Scholar
• Rosenblatt , M. 1952 . Remarks on a Multivariate Transformation . Annu. Math. Stat. , Vol. 23 : 470 – 472 .
   Google Scholar
• Wu , Y.-T. , Millwater , H. R. and Cruse , T. A. 1990 . An Advance Probabilistic Analysis Method for Implicit Performance Function . AIAA J. , Vol. 28 : 1663 – 1669 .
   Google Scholar
• Breitung , K. 1984 . Asymptotic Approximation for multinormal Integrals . ASCE J. Eng. Mech. , Vol. 110 : 357 – 366 .
   Web of Science ®Google Scholar
• Tichy , M. 1993 . Applied Methods of Structural Reliability , Kluwer Academic .
   Google Scholar
• Ang , A. H.-S. and Tang , W. H. 1984 . Probabilistic Concepts in Engineering Planning and Decision , Vol. II , New York : John Wiley and Sons .
   Google Scholar
• Varadarajan , S. , Chen , W. and Pelka , C. 2000 . The Robust Concept Exploration Method with Enhanced Model Approximation Capabilities . J. Eng. Optimiz. , Vol. 32 No. 3
   Web of Science ®Google Scholar
• Fiessler , B. , Neuman , H-J. and Rackwitz , R. 1979 . Quadratic Limit States in Structural Reliability . J. Eng. Mech., ASCE , Vol. 105 : 661 – 676 . No. 4
   Web of Science ®Google Scholar
• Hohenbichler , M. , Gollwitzer , S. , Kruse , W. and Rackwitz , R. 1987 . New Light on First - and Second- Order Reliability Methods . Struct. Saf. , : 267 – 284 . No. 4
   Web of Science ®Google Scholar
• Kiureghian , A. D. , Lin , H.-Z. and Hwang , S.-J. 1987 . Second-order Reliability Approximations, . J. Eng. Mech. , 113 ( 8 ) : 1208 – 1225 .
   Web of Science ®Google Scholar
• Box , G. E. P. , Hunter , W. G. and Hunter , J. S. 1978 . Statistics for Experiments , New York : John Wiley & Sons .
   Google Scholar