SYSTEM RELIABILITY-BASED DESIGN OPTIMIZATION WITH ASSOCIATED CONFIDENCE LEVELS UNDER INPUT AND MODEL UNCERTAINTIES Dr. K.K. Choi Roy J. Carver Professor in Mechanical Engineering Department of Mechanical and Industrial Engineering College of Engineering, The University of Iowa ABSTRACT An increasingly competitive global market demands product designs that can be uniformly relied on to demonstrate consistently high levels of performance under a wide range of operational conditions without being subject to unanticipated failure and with substantially reduced maintenance requirements. Thus, simulationbased design engineers are facing the formidable tasks of obtaining optimum designs under a variety of input uncertainties in material properties, geometrical dimensions, and operational conditions; as well as statistical uncertainties due to limited test data and lack of information. In addition, what confidence level can the design engineer predict for the simulation-based optimum design in light of simplifying model assumptions, inaccurate boundary conditions, unknown effects of other variables, etc.? New technology and numerical methods are being developed for system-level reliability-based design optimization (RBDO) with the associated target confidence level under these input and simulation model uncertainties. Accordingly, four technical developments are being pursued. First, for accurate inverse reliability analysis, the correct input joint CDF types need to be identified and accurately quantified, which is quite challenging when input variables are correlated with joint non-Gaussian CDFs. Moreover, in broad industrial applications, usually only the marginal CDFs and paired samples are available from limited test data. The copula, which has been used extensively in economics and biostatistics to model the uncertainty, offers an excellent method for modeling the input uncertainty in RBDO. However, to offset the inexact quantification of the input uncertainties due to limited test data, a method to assess the confidence level of the input model will be developed. Second, to assess the confidence level of the simulation model for RBDO, a design-driven validation & verification (V&V) method needs to be developed using a Gaussian stochastic process to estimate the measurement error and construct the prediction of the simulation model. The challenge is to develop and integrate the design-driven V&V method with the RBDO process to obtain a reliable design with the associated target confidence level. Third, when input variables are correlated or the performances are nonlinear functions of multi-variables, the error associated with the first-order reliability method (FORM) is unacceptable. The most probable point (MPP)-based dimension reduction method (DRM) provides an accurate inverse reliability analysis without requiring second-order sensitivities like the second-order reliability method (SORM). Being a higher-order reliability analysis method, the MPP-based DRM is an ideal method for solving the system-level RBDO, by integrating it with the Ditlevsen’s second-order upper bound. Finally, a unique feature of the research is the integration of these three technical developments to develop a simulation-based design tool for system-level RBDO with the associated target confidence level and parallelization of the integrated software system on the U.S. Army TARDEC High Performance Computing (HPC) to demonstrate feasibility of practical applications to large-scale ground vehicles. LECTURE SERIES Lecture 1. Introduction to System Reliability-Based Design Optimization with Associated Confidence Levels under Input and Simulation Model Uncertainties (14 charts) - 20 min. Lecture 2. Basics of Reliability-Based Design Optimization & Performance Measure Approach (38 charts) - 75 min. Lecture 3. A Design Optimization Formulation for Problems with Random and Fuzzy Input Variables Using Performance Measure Approach (44 charts) - 85 min. Lecture 4. Component and System RBDO Using Dimension Reduction Method (DRM) (32 charts) - 65 min. Lecture 5. Modeling of Input Uncertainty Using Copula and DRM-Based RBDO (42 charts) - 90 min. Lecture 6. Reliability-Based Design Optimization with Confidence Level under Input Model Uncertainty (22 charts) - 35 min. Lecture 7. Comparison Study between Probabilistic and Possibilistic Approach for Problems with Lack of Input Statistical Information (17 charts) - 30 min.
BIOGRAPHICAL SKETCH KYUNG K. CHOI, Roy J. Carver Professor in Mechanical Engineering Department of Mechanical and Industrial Engineering and Center for Computer-Aided Design The University of Iowa, Iowa City, IA 52242 Tel: (319) 335-5684; Fax (319) 335-5669; E-mail:
[email protected]
A. Professional Preparation Yonsei Univ., Seoul, Korea The University of Iowa The University of Iowa
Physics Mechanical Engineering Applied Mathematics
B.S. (1970) M.S. (1977) Ph.D. (1980)
B. Appointments Roy J. Carver Professor in Mechanical Engineering, University of Iowa, 2003-present Adjunct Professor, K-JIST, Korea, 1999-present Director (CCAD), University of Iowa, 1996-2003 Associate/Deputy Director (CCAD), University of Iowa, 1990-1995 Professor, University of Iowa, 1990-2003 Visiting Professor, U.S. Army Tank-Automotive Command, MI, Jun-Aug 1987 Senior Research Scientist, Scientific Research Lab., Ford, MI, May-Sep 1989 Associate Professor, University of Iowa, 1986-1990 Assistant Professor, University of Iowa, 1984-1986 Adjunct Assistant Professor, University of Iowa, 1981-1983
C. Publications (5 books; 118 journal papers; 156 conference papers or book chapters; 69 reports) C.1 Five Publications Closely Related to Proposed Project: 1. Noh, Y., Choi, K.K., and Du, L., “Reliability Based Design Optimization of Problems with Correlated Input Variables Using Copulas,” Structural and Multidisciplinary Optimization, to appear, 2008. 2. Lee, I., Choi, K.K., Du, L., and Gorsich, D., “Dimension Reduction Method-Based MPP for Reliability-Based Design Optimization of Highly Nonlinear Multi-Dimensional Systems,” Special Issue of Computer Methods in Applied Mechanics and Engineering: Computational Methods in Optimization Considering Uncertainties, to appear, 2008. 3. Youn, B.D., Choi, K.K., and Yi, K., “Performance Moment Integration (PMI) Method for Quality Assessment in ReliabilityBased Robust Optimization,” Mechanics Based Design of Structures and Machines, Vol. 33, No. 2, 2005, pp. 185-213. 4. Youn, B.D., Choi, K.K., and Du, L., “Enriched Performance Measure Approach for Reliability-Based Design Optimization,” AIAA Journal, Vol. 43, No. 4, 2005, pp. 874-884. 5. Youn, B.D., Choi, K.K., and Park, Y.H., “Hybrid Analysis Method for Reliability-Based Design Optimization,” ASME Journal of Mechanical Design, Vol. 125, No. 2, 2003, pp. 221-232. C.2 Five Other Significant Publications for Proposed Project: 1. Lee, I., Choi, K.K., Du, L., and Gorsich, D. “Dimension Reduction Method (DRM) Based RBDO for Highly Nonlinear Systems” 7th World Congress on Structural and Multidisciplinary Optimization, May 21-25, 2007, Seoul, Korea, Received the ISSMO-Springer Prize 2007. 2. Noh, Y., Choi, K.K., and Du, L., “New Transformation of Dependent Input Variables Using Copula for RBDO,” 7th World Congress on Structural and Multidisciplinary Optimization, May 21-25, 2007, Seoul, Korea, Runner-up paper of the ISSMO-Springer Prize 2007. 3. Youn, B.D., Choi, K.K., and Yang, R.J., “Efficient Evaluation Approaches for Probabilistic Constraints in ReliabilityBased Design Optimization,” 5th World Congress of Structural and Multidisciplinary Optimization, May 19-23, 2003, Lido di Jesolo-Venice, Italy. Received the ISSMO-Springer Prize 2003. 4. Choi, K.K. and Youn, B.D., “Hybrid Analysis Method for Reliability-Based Design Optimization,” 27th ASME Design Automation Conference, September 9-12, 2001, Pittsburgh, PA. Received the 2001 ASME Black and Decker Best Paper Award. 5. Tu, J. and Choi, K.K., “A New Study on Reliability Based Design Optimization,” ASME Journal of Mechanical Design, Vol. 121, No. 4, 1999, pp. 557-564. Cited 175 times in literatures.
D. Synergistic Activities Associate Editor, Mechanics of Structures and Machines, 1990-present Associate Editor, Journal of Optimization Theory and Applications, 1993-present
Associate Editor, ASME Journal of Mechanical Engineering, 2003-2006 Member of Editorial Board, Journal of Structural Optimization, 1995-present Editorial Board Member, International Journal of Reliability and Safety (IJRS), 2004- present Editorial Board Member, The Open Acoustics Journal, 2007-present Reviewer, NSF & Other Proposals (50), Journals & Conf. Publications (384), and Books (1)
E. Collaborators & Other Affiliations E.1 Collaborators and Co-Authors: Prof. Christophe Pierre (McGill University), Prof. Nick Vlahopoulos (Michigan), Prof. Weimin Han (Iowa), Prof. Sharif Rahman (Iowa), and Prof. J.S. Chen (UCLA), Prof. Nam Ho Kim (Florida), Prof. Byeng Dong Youn (Maryland) E.2 Graduate and Postdoctoral Advisors: (i) Graduate Advisors Prof. George M. Lance and Prof. Edward J. Haug; (ii) Postdoctoral Advisors Prof. Edward J. Haug (Iowa) E.3 Thesis Advisor and Postgraduate-Scholar Sponsor: (i) 31 Ph.D. Students: Ikjin Lee (2008), Liu Du (2006), Tao Zhang (2006), Ki-young Yi (2005), Chwail Kim (2004), Jun Dong (2004), Yiming Yuan (2002), Byeng-Dong Youn (2001), Jian Tu (1999), Iulian Grindeanu (1999), Nam Ho Kim (1999), Brian Seung Choi (1998), Seonho Cho (1998), Wei Duan (1996), Xiaoming Yu (1996), Hsiu-Ying Hwang (1995), Youngho Park (1994), Ching-Jen Chen (1994), Inbo Shim (1993), Semyung Wang (1991), Mohan M. Godse (1991), Kuang-H Chang (1990), Sung-Ling Twu (1990), Jaehwan Lee (1989), Jong-Sang Park (1989), Jose L.T. Santos (1987), Tse-Min Yao (1986), Bernhard Dopker (1986), Hwal G. Seong (1985), Hee G. Lee (1984), Ren-Jye Yang (1984); (ii) 3 M.S. Students: Jian Tu (1997), Iulian Grindeanu (1996), Marge Frederick (1984); (iii) 11 Postgraduate Scholar Sponsor: Liu Du (2007-08), Chwail Kim (2006-07), Byeng-Dong Youn (2002-05), Nam Ho Kim (1999-01), Young Ho Park (1996-00), Kuang-Hua Chang (1990-94), Semyung Wang (1991-95), Sung-Ling Twu (1990-91), Yul-W. Hyun (1990-91), Jaehwan Lee (1989-90), J.L.T. Santos (1987-89)
F. Others Fellow, American Society of Mechanical Engineers. Associate Fellow, American Institute of Aeronautics and Astronautics. Executive Committee Member, Int. Soc. for Structural and Multidisciplinary Optimization (ISSMO) 2003-present. Faculty Scholar Award (The University of Iowa), September 1987-August 1990. College of Engineering Faculty Excellence Award for Service (The Univ. of Iowa), 1996. Best Paper Award in the ASME Design Automation Conf, September 11, 2001. 2002 Maurice Simpson Technical Editors Award in Design, Test, and Evaluation from the Institute of Environmental Sciences and Technology, April 30, 2002. College of Engineering Faculty Excellence Award for Research (The Univ. of Iowa), 2003. Iowa Board of Regents Award for Faculty Excellence (State of Iowa), 2003. Best Paper Award in the ASME Design Automation Conference, September 4, 2003. ASME Design Automation Award, 2006. President Elect, International Society for Structural and Multidisciplinary Optimization (ISSMO), 2007-2011.
