Improved Stability Transformation Method to Control Convergence of Structural Performance Measure Approach

Document Type : پژوهشی

Author

• Behrooz Keshtegar

University of Zabol

10.22067/civil.v28i2.39323

Abstract

Performance measure approach (PMA) is a method for evaluating the probabilistic constraints in reliability-based design optimization of structures. The advanced mean-value (AMV) method is suitable for PMA, simply and efficiently. The iterative AMV scheme could be yielded to unstable solutions such as periodic-oscillation and chaos for highly nonlinear performance functions. In the present paper, an improved stability transformation method (ISTM) is proposed for appropriate convergence of nonlinear performance functions. This iterative approach has been established based on a suitable stepsize between one and zero that is simply calculated on the basis of the new results of AMV scheme and the previous results of the improved stability transformation iterative formula. The descent condition was applied in the iterative sequences of the ISTM to achieve stable convergence. The results of several nonlinear performance functions in reliability-based design optimization demonstrate that the ISTM is laded to control instability solutions of PMA and also, it is more robust than AMV and more efficient that stability transformation method in structural problems with nonlinear performance functions.

Keywords

• Performance Measure Approach
• Advanced Mean-Value
• Reliability-Based Design Optimization
• Improved Stability Transformation Method

---

References

1. Yang, R.J., Gu, L., "Experience with approximate reliability-based optimization methods", Structural and Multidisciplinary Optimization, Vol, 26, No. 2, pp. 152-159, (2004).

2. Cheng, G.D., Xu, L., Jiang, L., "A sequential approximate programming strategy for reliability-based optimization", Computers and Structures, Vol. 84, No. 21, pp. 1353-1367, (2006).

3. Chiralaksanakul, A., Mahadevan, S., "First-order approximation methods in reliability-based design optimization", ASME Journal of Mechanical Design, Vol. 127, pp. 851-857, (2005).

4. Tu, J., Choi, K.K., Young, H.P., "A new study on reliability-based design optimization", ASME Journal of Mechanical Design, Vol. 121, No. 4, pp. 557-564, (1999).

5. Yang, D., Yi, P., "Chaos control of performance measure approach for evaluation of probabilistic constraints", Structural and Multidisciplinary Optimization, Vol. 38, pp.83-92, (2009).

6. Lee, J.O, Yang, Y.S., Ruy, W.S., "A comparative study on reliability-index and target-performance-based probabilistic structural design optimization", Computers and Structures, Vol. 80, pp. 257-269, (2002).

7. Li, H., Foschi, R.O., "An inverse reliability method and its application", Structural Safety, Vol. 20, pp. 257-270, (1998).

8. Yi, P., Cheng, G.D., Jiang, L., "A sequential approximate programming strategy for performance-measure-based probabilistic structural design optimization", Structural Safety, Vol. 30, No. 2, pp. 91-109, (2008).

9. Youn, B.D., Choi, K.K., "An investigation of nonlinearity of reliability-based design optimization approaches", ASME Journal of Mechanical Design, Vol. 126, No. 5, pp. 403–411, (2004).

10. Youn, B.D., Choi, K.K., Park, Y.H., "Hybrid analysis method for reliability based design optimization", ASME Journal of Mechanical Design, Vol. 125, No. 3, pp. 221–232, (2003).

11. Youn, B.D., Choi, K.K., Du, L., "Adaptive probability analysis using an enhanced hybrid mean value method", Structural and Multidisciplinary Optimization, Vol. 29, pp. 134–148, (2005a).

12. Youn, B.D., Choi, K.K., Du, L., "Enriched performance measure approach for reliability-based design optimization", AIAA Journal, Vol. 43, No.4, pp. 874–884, (2005b).

13. Gong, J.X., Yi, P., "A robust iterative algorithm for structural reliability analysis", Structural and Multidisciplinary Optimization, Vol. 43, No. 4, pp. 519–527, (2011).

14. Keshtegar, B., Miri, M., "An enhanced HL-RF Method for the computation of structural failure probability based on relaxed approach", Civil Engineering Infrastructures, Vol. 1, No. 1, pp. 69-80, (2013).

15. Yang, D., "Chaos control for numerical instability of first order reliability method", Communications in Nonlinear Science and Numerical Simulation, Vol. 5, No. 10, pp. 3131-3141, (2010).

16. Santosh. T. V., Saraf. R.K., Ghosh. A.K., Kushwaha. H.S., "Optimum step length selection rule in modified HL-RF method for structural reliability", International journal of Pressure Vessels Piping, Vol. 83, No. 10, pp. 742–748, (2006).

17. Schmelcher, P., Diakonos, F. K., "General approach to the localization of unstable periodic orbits in chaotic dynamical systems", Physical Review Letters, Vol. 57, No.1, pp. 2739-2754, (1998).

18. Keshtegar, B., Miri, M., "Introducing Conjugate gradient optimization for modified HL-RF method", Engineering Computations, Vol. 31, No. 4, pp. 775-790, )2014(.

19. Narushima,Y., Yabe, H., "Conjugate gradient methods based on secant conditions that generate descent search directions for unconstrained optimization", Journal of Computational and Applied Mathematics, Vol. 236, pp. 4303-4317, (2012).