Username   Password       Forgot your password?  Forgot your username? 

An Efficient Moving Optimal Radial Sampling Method for Reliability-Based Design Optimization

Volume 13, Number 6, October 2017 - Paper 8  - pp. 864-877
DOI: 10.23940/ijpe.17.06.p8.864877

Xiaoke Lia, Zhenzhong Chenb, Wuyi Minga , Haobo Qiuc,*, Jun Maa,*, Wenbin Hea

aHenan Key Laboratory of Mechanical Equipment Intelligent Manufacturing, School of Mechanical and Electrical Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China
bCollege of Mechanical Engineering, Donghua University, Shanghai 201620, China
cThe State Key Laboratory of Digital Manufacturing Equipment and Technology,Huazhong University of Science & Technology,Wuhan 430074, China

(Submitted on July 25, 2017; Revised on August 30, 2017; Accepted on September 15, 2017)

(This paper was presented at the Third International Symposium on System and Software Reliability.)


Reliability-based design optimization (RBDO) plays an essential role in structure and system design. However, its application in practical engineering is hindered by the huge computational cost in performance function evaluation. In this paper, a moving optimal radial sampling (MORS) method is proposed for RBDO problems to substantially improve the computational efficiency of Monte Carlo simulation (MCS). In MORS, the failure probability and its gradient are calculated using radius based importance sampling (RBIS) method. The initial radius is selected according to the target reliability, which can also be used to check the feasibility of probabilistic constraints afterwards. The arc search scheme in enhanced performance measure approach (PMA+) and linear interpolation scheme are used to calculate the optimal radius of RBIS. After the failure probability and its gradient are calculated, the optimal design is obtained using sequential approximation programming (SAP). The computational capability of the proposed MORS method is demonstrated using a honeycomb crashworthiness design application, a nonlinear mathematical problem and a speed reducer design. The comparison results show that the proposed MORS-SAP method is very efficient and accurate.


References: 32

    1. S. Au and J. L. Beck, "A New Adaptive Importance Sampling Scheme for Reliability Calculations," Structural Safety, vol. 21, no. 2, pp. 135-158, 1999
    2. S. Au and J. L. Beck, "Important Sampling in High Dimensions," Structural Safety, vol. 25, no. 2, pp. 139-163, 2013
    3. T. W. Benanzer, R. V. Grandhi and W. P. Krol, "Reliability-Based Optimization of Design Variance to Identify Critical Tolerances," Advances in Engineering Software, vol. 40, no. 4, pp. 305-311, 2009
    4. X. Chen, T. K. Hasselman and D. J. Neill, "Reliability Based Structural Design Optimization for Practical Applications," in AIAA structures, structural dynamics, and materials conference, pp. 2724-2732, Kissimmee, Florida, USA, 1997
    5. C. K. Choi and H. H. Yoo, "Uncertainty Analysis of Nonlinear Systems Employing the First-Order Reliability Method, " Journal of mechanical science and technology, vol. 26, no. 1, pp. 39-44, 2012
    6. X. P. Du and W. Chen, "Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design," Journal of Mechanical Design, vol. 126, no. 2, pp. 225-233, 2004
    7. F. Grooteman, "Adaptive Radial-Based Importance Sampling Method for Structural Reliability," Structural Safety, vol. 30, no. 6, pp. 533-542, 2008
    8. A. Harbitz, "An Efficient Sampling Method for Probability of Failure Calculation," Structural Safety, vol. 3, no. 2, pp. 109-115, 1986
    9. A. M. Hasofer and N. C. Lind, "Exact and Invariant Second-Moment Code Format", Journal of the Engineering Mechanics Division", vol. 100, no. 1, pp. 111-121, 1974
    10. M. Hohenbichler and R. Rackwitz, "Improvement of Second-Order Reliability Estimates by Importance Sampling," Journal of Engineering Mechanics, vol. 114, no. 12, pp. 2195-2199, 1988
    11. C. Hu and B. D. Youn, "An Asymmetric Dimension-Adaptive Tensor-Product Method for Reliability Analysis," Structural Safety, vol. 33, no. 3, pp. 218-231, 2011
    12. H. Z. Huang, X. Zhang, Y. Liu, D. B. Meng and Z. Wang, "Enhanced Sequential Optimization and Reliability Assessment for Reliability-Based Design Optimization," Journal of Mechanical Science and Technology, vol. 26, no. 7, pp. 2039-2043, 2012
    13. H. Z. Huang, X. Zhang, D. B. Meng, Z. Wang and Y. Liu, "An Efficient Approach to Reliability-Based Design Optimization Within the Enhanced Sequential Optimization and Reliability Assessment Framework," Journal of Mechanical Science and Technology, vol. 27, no. 6, pp. 1781-1789, 2013
    14. I. Lee, K. K. Choi and D. Gorsich, "Equivalent Standard Deviation to Convert High-Reliability Model to Low-Reliability Model for Efficiency of Sampling-Based RBDO," in ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 1127-1138, Washington, DC, USA, 2011
    15. J. O. Lee, Y. S. Yang and W. S. Ruy, "A Comparative Study on Reliability-Index and Target-Performance-Based Probabilistic Structural Design Optimization," Computers & Structures, vol. 80, no. 3, pp. 257-269, 2002
    16. F. Li, T. Wu, A. Badiru, M. Q. Hu and S. Soni, "A Single-Loop Deterministic Method for Reliability-Based Design Optimization," Engineering Optimization, vol. 45, no. 4, pp. 435-458, 2013
    17. F. Li, T. Wu, M. Q. Hu and J. Dong, "An Accurate Penalty-Based Approach for Reliability-Based Design Optimization," Research in Engineering Design, vol. 21, no. 2, pp. 87-98, 2010
    18. X. K. Li, H. B. Qiu, Z. Z. Chen, L. Gao and X. Y. Shao, "A Local Sampling Method with Variable Radius for RBDO Using Kriging," Engineering Computations, vol. 32, no. 7, pp. 1908-1933, 2015
    19. P. L. Liu and A. Der Kiureghian, "Multivariate Distribution Models with Prescribed Marginals and Covariances," Probabilistic Engineering Mechanics, vol. 1, no. 2, pp. 105-112, 1986
    20. M. Rosenblatt, "Remarks on A Multivariate Transformation," The annals of mathematical statistics, vol. 23, pp. 470-472, 1952
    21. S. Santos, L. Matioli and A. Beck, "New Optimization Algorithms for Structural Reliability Analysis," Computer Modeling in Engineering & Sciences, vol. 83, no. 1, pp. 23-55, 2012
    22. S. Shan and G. G. Wang, "Reliable Design Space and Complete Single-Loop Reliability-Based Design Optimization," Reliability Engineering & System Safety, vol. 93, no. 8, pp. 1218-1230, 2008
    23. S. Song, Z. Lu and H. Qiao, "Subset Simulation for Structural Reliability Sensitivity Analysis," Reliability Engineering & System Safety, vol. 94, no. 2, pp. 658-665, 2009
    24. N. Strömberg and M. Tapankov, "Reliability Based Shape Optimization of A Knuckle Component by Using Sequential Linear Programming,", 2011
    25. G. Y. Sun, G. Y. Li, M. Stone and Q. Li, "A Two-Stage Multi-Fidelity Optimization Procedure for Honeycomb-Type Cellular Materials," Computational Materials Science, vol. 49, no. 3, pp. 500-511, 2010
    26. H. Wang, Z. Gong, H. Z. Huang, X. Zhang and Z. Lv, "System Reliability Based Design Optimization with Monte Carlo Simulation," in International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering IEEE, pp. 1143-1147, Chengdu, Sichuan, China, 2012
    27. M. Xiao, L. Gao, X. Y. Shao, H. B. Qiu and P. Jiang, "A Generalised Collaborative Optimisation Method and Its Combination With Kriging Metamodels for Engineering Design," Journal of Engineering Design, vol. 23, no. 5, pp. 379-399, 2012
    28. N. C. Xiao, H. Z. Huang, Z. L. Wang, Y. Pang and L. P. He, "Reliability Sensitivity Analysis for Structural Systems in Interval Probability Form," Structural and Multidisciplinary Optimization, vol. 44, no. 5, pp. 691-705, 2011
    29. P. Yi, G. D. Cheng and L. Jiang, "A Sequential Approximate Programming Strategy for Performance-Measure-Based Probabilistic Structural Design Optimization," Structural Safety, vol. 30, no. 2, pp. 91-109, 2008
    30. B. D. Youn, K. K. Choi and L. Du, "Enriched Performance Measure Approach for Reliability-Based Design Optimization," AIAA Journal, vol. 43, no. 4, pp. 874-884, 2005
    31. B. D. Youn, K. K. Choi and Y. H. Park, "Hybrid Analysis Method for Reliability-Based Design Optimization," Journal of Mechanical Design, vol. 125, no. 2, pp. 221-232, 2003
    32. T. Zou and S. Mahadevan, "A Direct Decoupling Approach for Efficient Reliability-Based Design Optimization," Structural and Multidisciplinary Optimization, vol. 31, no. 3, pp. 190-200, 2006


      Click here to download the paper.

      Please note : You will need Adobe Acrobat viewer to view the full articles.Get Free Adobe Reader

      This site uses encryption for transmitting your passwords.