Advertisement

Journal of Global Optimization

, Volume 37, Issue 1, pp 47–62 | Cite as

An Inverse Reliability-based Approach for Designing under Uncertainty with Application to Robust Piston Design

  • Hanif D. Sherali
  • Vikram Ganesan
Original Paper

Abstract

In this work, we propose an optimization framework for designing under uncertainty that considers both robustness and reliability issues. This approach is generic enough to be applicable to engineering design problems involving nonconvex objective and constraint functions defined in terms of random variables that follow any distribution. The problem formulation employs an Inverse Reliability Strategy that uses percentile performance to address both robustness objectives and reliability constraints. Robustness is achieved through a design objective that evaluates performance variation as a percentile difference between the right and left trails of the specified goals. Reliability requirements are formulated as Inverse Reliability constraints that are based on equivalent percentile performance levels. The general proposed approach first approximates the formulated problem via a Gaussian Kriging model. This is then used to evaluate the percentile performance characteristics of the different measures inherent in the problem formulation for various design variable settings via a Most Probable Point of Inverse Reliability search algorithm. By using these percentile evaluations in concert with the response surface methodology, a polynomial programming approximation is generated. The resulting problem formulation is finally solved to global optimality using the Reformulation–Linearization Technique (RLT) approach. We demonstrate this overall proposed approach by applying it to solve the problem of reducing piston slap, an undesirable engine noise due to the secondary motion of a piston within a cylinder.

Keywords

Global optimization Designing under uncertainty Inverse Reliability Reformulation–Linearization Technique Robust piston design 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barton, R.R.: Metamodels for simulation input-output relations. In: Swain, J.J., Goldsman, D., Crain, R.C., Wilson, J.R. (eds.) Proceedings of the 1992 Winter Simulation Conference. Institute of Electrical and Electronics Engineers, pp. 289–299. Arlington, VA (1992)Google Scholar
  2. Bazaraa M.S., Sherali H.D., Shetty C.M. (1993). Nonlinear Programming: Theory and Algorithms, Second edition. John Wiley & Sons, Inc., New YorkGoogle Scholar
  3. Booker, A.J.: Design and analysis of computer experiments. Proceedings of the 7th AIAA/ USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, vol. 1, pp. 118–128 AIAA, Reston VA (1998)Google Scholar
  4. Brown S.A., Sepulveda A.E. (1997). Approximation of system reliability using a shooting Monte Carlo approach. AIAA J. 35(6):1064–1071Google Scholar
  5. Cressie N.A.C. (1993). Statistics for Spatial Data. John Wiley & Sons, New YorkGoogle Scholar
  6. Ditlevsen O., Madsen H.O. (1996). Structural Reliability Methods. John Wiley & Sons, Baffins, Lane EnglandGoogle Scholar
  7. Ditlevsen O., Olsen R., Mohr G. (1987). Solution of a class of load combination problems by directional simulation. Struct. Safety 4:95–109CrossRefGoogle Scholar
  8. Du X., Chen W. (2000). Towards a better understanding of modeling feasibility robustness in engineering. ASME J. Mech. Design 122(4):357–583CrossRefGoogle Scholar
  9. Du X., Chen W. (2002). Efficient uncertainty analysis methods for multidisciplinary robust design. AIAA J. 4(3):545–552Google Scholar
  10. Du X., Chen W. (2001). A most probable point based method for uncertainty analysis. J. Design Manufact. Automat. 4:47–66Google Scholar
  11. Du X., Sudjianto A., Chen W. (2004). An integrated framework for optimization under uncertainty using inverse reliability strategy. ASME J. Mech. Design 126(4):561–764CrossRefGoogle Scholar
  12. Eggert R.J. (1991). Quantifying design feasibility using probabilistic feasibility analysis. ASME Adv. Design Autom. 32(1):235–240Google Scholar
  13. General Algebraic Modeling System: http://www.gams.com, GAMS Development Corporation, Washington, DCGoogle Scholar
  14. Hicks C.R. (1973). Fundamental Concepts in the Design of Experiments. Holt, Rinehart and Winston, New YorkGoogle Scholar
  15. Hines W.W., Montgomery D. (1972). Probability and Statistics in Engineering and Management Science. The Ronald Press Company, New YorkGoogle Scholar
  16. Koch P.N., Simpson T.W., Allen J.K., Mistree F. (1999). Statistical approximations for multidisciplinary optimization: The problem ofsize. J. Aircraft (Special Multidisciplinary Design Optimization Issue). 36(1):275–286Google Scholar
  17. Kocis G.R., Grossmann I.E. (1989). Computational experience with DICOPT: Solving MINLP problems in process systems engineering. Comput. Chem. Enging. 13:307–315CrossRefGoogle Scholar
  18. Melchers R.E. (1999). Structural Reliability Analysis and Prediction. John Wiley & Sons, ChichesterGoogle Scholar
  19. Montes P. (1994). Smoothing noisy data by kriging with nugget effects. In: Laurent P.J. et al (eds) Wavelets, Images, and Surface Fitting. A.K. Peters, Wellesley, MA, pp. 371–378Google Scholar
  20. Myers R.H. (1995). Response Surface Methodology: Process and Product Optimization Using Designed Experiments. John Wiley & Sons Inc., New YorkGoogle Scholar
  21. Osio I.G., Amon C.H. (1996). An engineering design methodology with multistage bayesian surrogates and optimal sampling. Res. Engg. Design 8(4):189–206CrossRefGoogle Scholar
  22. Parkinson A., Sorensen C., Pourhassan N. (1993). A general approach for robust optimal design. Trans. ASME 155:74–80CrossRefGoogle Scholar
  23. Sahinidis N.V. (1996). BARON: A general purpose global optimization software package. J. Global Optimiz. 8(2):201–205CrossRefGoogle Scholar
  24. Sherali H.D., Ganesan V. (2003). A pseudo-global optimization approach with application to the design of containerships. J. Global Optimiz. 26(4):335–360CrossRefGoogle Scholar
  25. Sherali H.D., Tuncbilek C.H. (1992). A Global Optimization Algorithm for polynomial programming problems using a reformulation–linearization technique. J. Global Optimiz. 2:101–112CrossRefGoogle Scholar
  26. Simpson T.W., Mauery T.M., Krote J.J., Mistree F. (2001). Kriging models for global optimization in simulation-based multidisciplinary design optimization. AIAA J 39(12):2233–2241CrossRefGoogle Scholar
  27. Viswanathan J., Grossmann I.E. (1990). A combined penalty function and outer approximation method for MINLP optimization. Comput. Chemi. Engng. 14:769–782CrossRefGoogle Scholar
  28. Youn B.D., Choi K.K., Park Y.H. (2003). Hybrid analysis method for reliability-based design optimization. ASME J. Mech. Design. 125(2):221–232CrossRefGoogle Scholar
  29. Walker, J.R.: Practical application of variance reduction techniques in probabilistic assessments. In: The Second International Conference on Radioactive Waste Management. pp. 517–521, Winnipeg, Manitoba (1996)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Grado Department of Industrial and Systems EngineeringVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.Global Powertrain Engineering and IT Solutions DepartmentFord Motor CompanyDearbornUSA

Personalised recommendations