Development of an Efficient Optimization Technique for Robust Design by Approximating Probability Constratints

확률조건의 근사화를 통한 효율적인 강건 최적설계 기법의 개발

  • Published : 2000.12.01


Alternative formulation is presented for robust optimization problems and an efficient computational scheme for reliability estimation is proposed. Both design variables and design parameters considered as random variables about their nominal values. To ensure the robustness of objective performance a new cost function bounding the performance and a new constraint limiting the performance variation are introduced. The constraint variations are regulated by considering the probability of feasibility. Each probability constraint is transformed into a sub-optimization problem and then is resolved with the modified advanced first order second moment(AFOSM) method for computational efficiency. The proposed robust optimization method has advantages that the mean value and the variation of the performance function are controlled simultaneously and the second order sensitivity information is not required even in case of gradient based optimization. The suggested method is examined by solving three examples and the results are compared with those for deterministic case and those available in literature.


Robut Design;Uncertainty;Approximation


  1. 정도현, 이병채, 2000, '기계구조의 강건 설계를 위한 최적화 기법의 개발,' 대한기계학회논문집, 제24권, 제1호, pp. 215-224
  2. Liu, P.L. and Kiureghian, A.D., 1991, 'Optimization Algorithms for Structural Reliability,' Structural Safety, Vol. 9, pp. 161-177
  3. Kwak, B. M. and Lee, T. W., 1987, 'Sensitivity Analysis for Reliability-Based Optimization Using an AFOSM Method,' Computers & Structures, Vol. 27, pp. 399-406
  4. Sepulveda, A. E. and Jensen, H., 1996, 'Comparison of Local and Global Approximations for Reliability Estimation,' AIAA, Vol. 34, No. 10, pp. 2162-2170
  5. Grandhi, R. V. and Wang, L., 1998, 'Reliability-Based Structural Optimization Using Improved Two-Point Adaptive Nonlinear Approximations,' Finite Elements in Analysis and Design, Vol. 29, pp. 35-48
  6. Rao, S. S., 1996, Engineering Optimization, John Wiley & Sons, New York
  7. Swan, D. A. and Savage, G. J., 1998, 'Continuous Taguchi - A Model Based Approach to Taguchi's 'Quality by Design' with Arbitrary Distributions,' Qualty and Reliability Engineering International, Vol. 14, pp. 29-41<29::AID-QRE144>3.0.CO;2-A
  8. Ramakrishnan, B. and Rao, S. S., 1996, 'A General Loss Function Based Optimization Procedure for Robust Design,' Engineering Optimization, Vol. 25, pp. 255-276
  9. Melchers, R. E., 1987, Structural Reliability Analysis and Prediction, Ellis Horwood Limited
  10. Phadke, M. S., 1989, Quality Engineering Using Robust Design, Prentice Hall, Englewood Cliffs, New Jersey
  11. 한형석, 박태원, 1996, '반응표면 분석법을 이용한 기구의 강건설계,' 한국정밀공학회지, 제 13권, 제 10호, pp. 56-61
  12. 이권희, 박경진, 1997, '설계변수의 공차를 고려한 구조물의 강건 최적설계,' 대한기계학회논문집, 제 21권, 제 1호, pp. 112-123