Sampling-based RBDO using the Dynamic Kriging (D-Kriging) method and stochastic sensitivity analysis

13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 2010

Volumn , Issue , 2010, Pages

  Lee, Ikjin ^a   Choi, K K ^a   Zhao, Liang ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DESIGN VARIABLES; EFFICIENT STRATEGY; MONTE-CARLO SIMULATIONS; NUMERICAL EXAMPLE; OPTIMUM DESIGNS; PERFORMANCE FUNCTIONS; PROBABILISTIC CONSTRAINTS; STOCHASTIC SENSITIVITY ANALYSIS;

COMPUTER SIMULATION; FUEL ADDITIVES; MONTE CARLO METHODS; OPTIMIZATION; SENSITIVITY ANALYSIS; STOCHASTIC SYSTEMS;

INTERPOLATION;

EID: 84880770110     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2010-9036     Document Type: Conference Paper

References (41)

1. Yi, K., Choi, K.K., Kim, N.H., and Botkin, M.E., "Design Sensitivity Analysis and Optimization for Minimizing Springback of Sheet-Formed Part, " Int. J. of Numerical Methods in Engineering, Vol. 71, 2007, pp. 1483-1511.
2. Youn, B.D., Choi, K.K., and Yi, K., "Performance Moment Integration (PMI) Method for Quality Assessment in Reliability-Based Robust Optimization, " Mechanics Based Design of Structures and Machines, Vol. 33, No. 2, 2005, pp. 185-213.
3. Youn, B.D., Choi, K.K., Yang, R-J, Gu, L., "Reliability-Based Design Optimization for Crashworthiness of Vehicle Side Impact, " Structural and Multidisciplinary Optimization, Vol. 26, No. 3-4, 2004, pp. 272-283.
4. Youn, B.D., Choi, K.K., and Tang, J., "Structural Durability Design Optimization and Its Reliability Assessment, " International Journal of Product Development, Vol. 1, Nos. 3/4, 2005, pp. 383-401.
5. Dong, J., Choi, K.K., Wang, A., Zhang, W., and Vlahopoulos, N., "Parametric Design Sensitivity Analysis of High Frequency Structural-Acoustic Problems Using Energy Finite Element Method, " Int. J. of Numerical Methods in Engineering, Vol. 62, 2005, pp. 83-121.
6. Dong, J., Choi, K.K., Vlahopoulos, N., Wang, A., and Zhang, W., "Design Sensitivity Analysis and Optimization of High Frequency Radiation Problems Using Energy Finite Element and Energy Boundary Element Methods, " AIAA Journal, Vol. 45, No. 6, 2007, pp. 1187-1198.
7. Haldar, A., and Mahadevan, S., Probability, Reliability and Statistical Methods in Engineering Design, John Wiley & Sons, New York, NY, 2000.
8. Madsen, H. O., Krenk, S., and Lind, N. C., Methods of Structural Safety, Prentice-Hall Inc., Englewood Cliffs, NJ, 1986.
9. Hasofer, A. M. and Lind, N. C., "An Exact and Invariant First Order Reliability Format, " ASCE Journal of the Engineering Mechanics Division, Vol. 100, No. 1, 1974, pp. 111-121.
10. Ditlevsen, O., and Madsen, H.O., Structural Reliability Methods, John Wiley & Sons Ltd., Chichester, 1996.
11. Hohenbichler, M., and Rackwitz, R., "Improvement of Second-Order Reliability Estimates by Importance Sampling, " ASCE Journal of Engineering Mechanics, Vol. 114, No. 12, 1988, pp. 2195-2199.
12. Breitung, K., "Asymptotic Approximations for Multinormal Integrals, " ASCE Journal of Engineering Mechanics, Vol. 110, No. 3, 1984, pp. 357-366.
13. Rahman, S., and Wei, D., "A Univariate Approximation at Most Probable Point for Higer-Order Reliability Analysis, " International Journal of Solids and Structures, Vol. 43, 2006, pp. 2820-2839.
14. Wei, D., "A Univariate Decomposition Method for Higher-Order Reliability Analysis and Design Optimization, " Ph. D. Thesis, The University of Iowa, 2006.
15. Lee, I., Choi, K.K., Du, L., and Gorsich, D., "Inverse Analysis Method Using MPP-Based Dimension Reduction for Reliability-Based Design Optimization of Nonlinear and Multi-Dimensional Systems, " Computer Methods in Applied Mechanics and Engineering, Vol. 198, No. 1, 2008, pp. 14-27.
16. Youn, B.D. and Choi, K.K., "A New Response Surface Methodology for Reliability-Based Design Optimization, " Computers and Structures, Vol. 82, Nos. 2-3, 2004, pp. 241-256.
17. Zhang, T., Choi, K.K., Rahman, S., Cho, K., Perry, B., and Shakil, M., and Heitka, D., "A Response Surface and Pattern Search Based Hybrid Optimization Method and Application to Microelectronics, " Structural and Multidisciplinary Optimization, Vol. 32, No. 4, 2006, pp. 327-345.
18. Kim, C. and Choi, K.K., "Reliability-Based Design Optimization Using Response Surface Method with Prediction Interval Estimation, " ASME Journal of Mechanical Design, Vol. 130, No. 12, 2008, pp. 1-12.
19. Rubinstein, R. Y., Simulation and Monte Carlo Method, John Wiley & Sons, New York, 1981.
20. Lee, I., Choi, K.K., Noh, Y. and Zhao, L., "Sampling-Based Stochastic Sensitivity Analysis Using Score Functions for RBDO Problems with Correlated Random Variables, " Submitted to ASME Journal of Mechanical Design, 2010.
21. Zhao, L., Choi, K.K., Lee, I., "A Metamodel Method using Dynamic Kriging and Sequential Sampling, " Submitted to AIAA Journal, 2010.
22. Noh, Y., Choi, K.K., and Du, L., "Reliability Based Design Optimization of Problems with Correlated Input Variables Using Copulas, " Structural and Multidisciplinary Optimization, Vol. 38, No. 1, 2009, pp. 1-16.
23. Noh, Y., Choi, K.K., and Lee, I., "Reduction of Transformation Ordering Effect in RBDO Using MPP-Based Dimension Reduction Method, " AIAA Journal, Vol. 47, No. 4, 2009, pp. 994-1004.
24. Noh, Y., Choi, K.K., and Lee, I., "Identification of Marginal and Joint CDFs Using the Bayesian Method for RBDO, " Structural and Multidisciplinary Optimization, Vol. 40, No. 1, 2010, pp. 35-51.
25. Rahman, S., "Stochastic Sensitivity Analysis by Dimensional Decomposition and Score Functions, " Probabilistic Engineering Mechanics, Vol. 24, 2009, pp. 278-287.
26. McDonald, M., and Mahadevan, S., "Design Optimization with System-Level Reliability Constraints, " Journal of Mechanical Design, Vol. 130, No. 2, 2008, paper# 21403.
27. Lee, I., Choi, K.K., and Gorsich, D., "System Reliability-Based Design Optimization Using the MPP-Based Dimension Reduction Method, " Journal of Structural and Multidisciplinary Optimization, Vol. 41, No. 6, 2010, pp. 823-839.
28. Chiles, J.P., and Delfiner, P., Geostatistics:-Modeling Spatial Uncertainty, Wiley, New York, 1999.
29. Martin, J.D. and Simpson, T.W., "Use of Kriging Models to Approximate Deterministic Computer Models, " AIAA Journal, Vol. 43, No. 4, 2005, pp.853-863.
30. Lewis, R.M., and Torczon, V., "Pattern Search Algorithms for Bound Constrained Minimization, " SIAM Journal on Optimization, Vol. 9, No. 4, 1999, pp. 1082-1099.
31. Browder, A., Mathematical Analysis: An Introduction, Springer-Verlag, New York, 1996.
32. Hijab, O., Introduction to Calculus and Classical Analysis, Springer-Verlag, New York, 1997.
33. Haldar, A., and Mahadevan, S., Probability, Reliability and Statistical Methods in Engineering Design, John Wiley & Sons, New York, NY, 2000.
34. Burkardt, J., Gunzburger, M., Peterson, J., and Brannon, R., "User Manual and Supporting Information for Library of Codes for Centroidal Voronoi Placement and Associated Zeroth, First, and Second Moment Determination, " Sandia National Laboratories Technical Report, vSAND2002-0099, Feb. 2002.
35. Jin, R., Chen, W., and Simpson, T.W., "Comparative Studies of metamodelling Techniques under Multiple Modelling Criteria, " Structural and Multidisciplinary Optimization, Vol. 23, No. 1, 2001, pp.1-13.
36. Youn, B. D., Choi, K.K., and Du, L., "Enriched Performance Measure Approach (PMA+) for Reliability-Based Design Optimization, " AIAA Journal, Vol. 43, No. 4, 2005, pp. 874-884.
37. Swanson Analysis System Inc., ANSYS Engineering Analysis System User's Manual, Vol. I, II, Houston, PA, 1989.
38. Center for Computer-Aided Design, College of Engineering, DRAW Concept Manual, The University of Iowa, Iowa City, IA, 1999.
39. Center for Computer-Aided Design, College of Engineering, DRAW User Reference, The University of Iowa, Iowa City, IA, 1999.
40. Meggiolaro, M.A., and Castro, J.T.P., "Statistical Evaluation of Strain-Life Fatigue Crack Initiation Predictions, " International Journal of Fatigue, Vol. 26, No. 5, 2004, pp.463-476.
41. Annis, C., "Probabilistic Life Prediction Isn't as Easy as It Looks, " Journal of ASTM International, Vol. 1, No. 2, pp. 3-14, 2004.