Integrated multi-objective robust optimization and sensitivity analysis with irreducible and reducible interval uncertainty

References

• Acar , E. , Haftka , R. T. and Johnson , T. F. 2007 . Tradeoff of uncertainty reduction mechanisms for reducing weight of composite laminates . Journal of Mechanical Design , 129 ( 3 ) : 266 – 274 .
   Google Scholar
• Aughenbaugh , J. M. and Paredis , C. J. 2006 . The value of using imprecise probabilities in engineering design . Journal of Mechanical Design , 128 ( 4 ) : 969 – 979 .
   Web of Science ®Google Scholar
• Avila , S. L. 2006 . Sensitivity analysis applied to decision making in multiobjective evolutionary optimization . IEEE Transactions on Magnetics , 42 ( 4 ) : 1103 – 1106 .
   Web of Science ®Google Scholar
• Chen , W. , Jin , R. and Sudjianto , A. 2005 . Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty . Journal of Mechanical Design , 127 ( 5 ) : 875 – 886 .
   Web of Science ®Google Scholar
• Deb , K. 2001 . Multiobjective optimization using evolutionary algorithms , New York, NY : John Wiley & Sons .
   Google Scholar
• Du , L. and Choi , K. K. An inverse analysis method for design optimization with both statistical and fuzzy uncertainties . Proceedings of ASME IDETC/CIE2006 . September 10–13 , Philadelphia, Pennsylvania. New York : ASME .
   Google Scholar
• Du , L. , Choi , K. K. and Lee , I. Robust design concept in possibility theory and optimization for system with both random and fuzzy input variables . Proceedings of ASME IDETC/ CIE2007 . September 4–7 , Las Vegas, Nevada. New York : ASME .
   Google Scholar
• Du , X. Interval reliability analysis . Proceedings of ASME IDETC/CIE 2007 . September 4–7 , Las Vegas, Nevada. New York : ASME .
   Google Scholar
• Frey , H. C. and Patil , S. R. 2002 . Identification and review of sensitivity analysis methods . Risk Analysis , 22 ( 3 ) : 553 – 578 .
   PubMed Web of Science ®Google Scholar
• Gunawan , S. and Azarm , S. 2005 . Multi-objective robust optimization using a sensitivity region concept . Structural and Multidisciplinary Optimization , 29 ( 1 ) : 50 – 60 .
   Web of Science ®Google Scholar
• Gunawan , S. and Papalambros , P. 2007 . Reliability optimization with mixed continuous-discrete random variables and parameters . Journal of Mechanical Design , 129 ( 2 ) : 158 – 165 .
   Web of Science ®Google Scholar
• Guo , J. and Du , X. 2007 . Sensitivity analysis with the mixture of epistemic and aleatory uncertainties . AIAA Journal , 45 ( 9 ) : 2337 – 2349 .
   Web of Science ®Google Scholar
• Hamby , D. M. 1994 . Review of techniques for parameter sensitivity analysis of environmental models . Environmental Monitoring and Assessment , 32 ( 2 ) : 135 – 154 .
   PubMed Web of Science ®Google Scholar
• Helton , J. C. and Davis , F. J. 2003 . Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems . Reliability Engineering & Systems Safety , 81 ( 1 ) : 23 – 69 .
   Web of Science ®Google Scholar
• Helton , J. C. , Johnson , J. D. and Oberkampf , W. L. 2004 . An exploration of alternative approaches to the representation of uncertainty in model predictions . Reliability Engineering & System Safety , 85 ( 1/3 ) : 39 – 71 .
   Google Scholar
• Iman , R. L. and Helton , J. C. 1988 . An investigation of uncertainty and sensitivity analysis techniques for computer models . Risk Analysis , 8 ( 1 ) : 71 – 90 .
   Web of Science ®Google Scholar
• Jeankoplis , C. J. 1993 . Transport processes and unit operations , 3 , Englewood Cliffs, NJ : PTR Prentice-Hall .
   Google Scholar
• Jung , D. H. and Lee , B. C. 2002 . Development of a simple and efficient method for robust optimization . International Journal for Numerical Methods in Engineering , 23 : 2201 – 2215 .
   Web of Science ®Google Scholar
• Kale , A. A. and Haftka , R. T. 2008 . Tradeoff of weight and inspection cost in reliability-based structural optimization . Journal of Aircraft , 45 ( 1 ) : 77 – 85 .
   Google Scholar
• Kern , D. , Du , X. and Sudjianto , A. Forecasting manufacturing quality during design using process capability data . Proceedings of the IMECE’ 03, ASME 2003 International Mechanical Engineering Congress and RD&D Expo . November 15–21 , Washington, DC. New York : ASME .
   Google Scholar
• Li , M. 2007 . Robust optimization and sensitivity analysis with multi-objective genetic algorithms: Single- and multi-disciplinary applications , College Park, , Maryland, USA : University of Maryland . Dissertation (PhD)
   Google Scholar
• Li , M. , Azarm , S. and Boyars , A. 2006 . A new deterministic approach using sensitivity region measures for multi-objective and feasibility robust design optimization . Journal of Mechanical Design , 128 ( 4 ) : 874 – 883 .
   Web of Science ®Google Scholar
• Li , M. , Williams , N. and Azarm , S. 2009 . Interval uncertainty reduction and single-disciplinary sensitivity analysis with multi-objective optimization . Journal of Mechanical Design , 131 ( 3 ) 031007/1–031007/11
   Google Scholar
• Li , M. , Hamel , J. and Azarm , S. 2008 . Optimal uncertainty reduction for multi-disciplinary multi-output systems using sensitivity analysis . Structural and Multidisciplinary Optimization , (accepted)
   Google Scholar
• Li , G. 2009 . Improving multi-objective genetic algorithms with adaptive design of experiments and online metamodeling . Structural and Multidisciplinary Optimization , 37 ( 5 ) : 447 – 461 .
   Web of Science ®Google Scholar
• Mourelatos , Z. P. and Zhou , J. 2006 . A design optimization method using evidence theory . Journal of Mechanical Design , 128 ( 4 ) : 901 – 908 .
   Web of Science ®Google Scholar
• Oberkampf , W. L. 2002 . Error and uncertainty in modeling and simulation . Reliability Engineering & System Safety , 75 ( 3 ) : 333 – 357 .
   Web of Science ®Google Scholar
• Oberkampf , W. L. 2004 . Challenge problems: Uncertainty in system response given uncertain parameters . Reliability Engineering & System Safety , 85 ( 1–3 ) : 11 – 19 .
   Web of Science ®Google Scholar
• O'Hagan , A. and Oakley , J. E. 2004 . Probability is perfect, but we can't elicit it perfectly . Reliability Engineering & System Safety , 85 ( 1–3 ) : 239 – 248 .
   Web of Science ®Google Scholar
• Parkinson , A. , Sorensen , C. and Pourhassan , N. A. 1993 . General approach to robust optimal design . Journal of Mechanical Design , 115 ( 1 ) : 74 – 80 .
   Web of Science ®Google Scholar
• Qiu , Y. , Ge , P. and Yim , S. C. 2008 . Risk-based resource allocation for collaborative system design in a distributed environment . Journal of Mechanical Design , 130 ( 6 ) 061403/1–061403/10
   Google Scholar
• Qu , X. , Haftka , R. T. , Venkataraman , S. and Johnson , T. F. 2003 . Deterministic and reliability-based optimization of composite laminates for cryogenic environments . AIAA Journal , 41 ( 10 ) : 2029 – 2036 .
   Web of Science ®Google Scholar
• Saltelli , A. , Chan , K. and Scott , E. M. 2000 . Sensitivity analysis , New York, NY : John Wiley & Sons .
   Google Scholar
• Saltelli , A. 2008 . Global sensitivity analysis: The primer , New York, NY : John Wiley & Sons .
   Google Scholar
• Saltelli , A. , Tarantola , S. and Chan , K. 1999 . A role for sensitivity analysis in presenting the results from MCDA studies to DMs . Journal of Multi-Criteria Decision Analysis , 8 ( 3 ) : 139 – 145 .
   Google Scholar
• Seader , J. D. and Henley , E. J. 2006 . Separation process principles , 2 , New York, NY : John Wiley & Sons .
   Google Scholar
• Sobol , I. M. 1993 . Sensitivity analysis for non-linear mathematical models . Mathematical Modeling and Computational Experiment , 1 : 407 – 414 . (Translation of I.M. Sobol, 1990. Sensitivity estimates for nonlinear mathematical models. Matematicheskoe Modelirovanie, 2, 112–118 (in Russian).)
   Google Scholar
• Sobol , I. M. 2001 . Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates . Mathematics and Computers in Simulation , 55 ( 1–3 ) : 271 – 280 .
   Web of Science ®Google Scholar
• Stump , G. The ARL trade space visualizer – An engineering decision-making tool . 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference . August–September 30–1 , Albany, NY. Reston, VA : AIAA .
   Google Scholar
• Taguchi , G. 1978 . Performance analysis design . International Journal of Production Research , 16 : 521 – 530 .
   Web of Science ®Google Scholar
• Williams , N. , Azarm , S. and Kannan , P. K. 2008 . Engineering product design optimization for retail channel acceptance . Journal of Mechanical Design , 130 ( 6 ) 061402/1–061402/10
   Google Scholar
• Wu , W. D. and Rao , S. S. 2007 . Uncertainty analysis and allocation of joint tolerances in robot manipulators based on interval analysis . Reliability Engineering & System Safety , 92 ( 1 ) : 54 – 64 .
   Web of Science ®Google Scholar
• Youn , B. D. , Choi , K. K. and Park , Y. H. 2003 . Hybrid analysis method for reliability-based design optimization . Journal of Mechanical Design , 125 ( 2 ) : 221 – 232 .
   Web of Science ®Google Scholar
• Yu , J. C. and Ishii , K. 1998 . Design for robustness based on manufacturing variation patterns . Journal of Mechanical Design , 120 ( 2 ) : 196 – 202 .
   Web of Science ®Google Scholar