Sensitivity Analysis of Fuzzy Structural Reliability Using Adaptive Stability Transformation Method

Document Type : پژوهشی

Authors

• Behrooz Keshtegar ¹
• Mansuor Bagheri ²

¹ University of Zabol

² Birjand University of Technology

10.22067/civil.v32i1.63984

Abstract

In this paper epistemic uncertainty of random variables in the reliability analysis of Adjusted Stability Transformation Method has been modeled and fuzzy structural reliability index has been determined using GA. In the reliability analysis process, a dynamic adaptive approach based on stability transformation method has been applied which the control coefficient is self-adapted at each iteration. Moreover in order to investigate the importance of epistemic uncertainty in the fuzzy structural reliability index, sensitivity analysis using Entropy-Shannon has been done. Survey results of three structural examples indicate that the proposed reliability method provides stable results with suitable computational efficiency. The sensitivity of failure probability to epistemic uncertainty has shown a considerable effect on the structural reliability in some problems.    

Keywords

• fuzzy reliability analysis
• Entropy-Shannon sensitivity analysis
• adaptive stability transformation method

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References

1. Nowak, A. S., Collins, K. R., "Reliability of Structures", McGraw-Hill, (2000).

2. William, M. Bulleit, M., "Uncertainty in Structural Engineering", Journal of Practice Periodical on Structural Design and Construction, Vol. 13, Issue. 1, Pp. 24-30, (2008).

3. Grooteman, F., "Adaptive Radial-based Importance Sampling Method for Structural Reliability", Structural Safety, Vol. 30, Pp. 533-542, (2008).

4. Chakraborty, S., Chowdhury, R., "A Semi-analytical Framework for Structural Reliability Analysis", Computer Methods in Applied Mechanics and Engineering, Vol. 289, Pp. 475-497, (2015).

5. Keshtegar, B., "A Hybrid Conjugate Finite-step Length Method for Robust and Efficient Reliability Analysis", Applied Mathematical Modelling, Vol. 45, Pp. 226–237, (2017).

6. Bagheri, M., Miri, M., Shabakhty, N., "Fuzzy Reliability Analysis Using a New Alpha Level Set Optimization Approach Based on Particle Swarm Optimization", Journal of Intelligent & Fuzzy Systems, Vol. 30, Pp. 235-244, (2015).

7. باقری، منصور، میری، محمود، شابختی، ناصر، «محاسبۀ شاخص قابلیت اعتماد فازی سازه‌ها بااستفاده از تکنیک بهینه‏سازی آلفا برش‌ها»، مجلۀ مهندسی عمران و محیط زیست دانشگاه تبریز، دورۀ 43، 44، ش. 73، صص. 12-1، (1392).

8. Zadeh Lotfi, A., "Fuzzy Sets", Journal of Information Control, Vol. 8, Issue. 3, Pp.338-553, (1965).

 

9. Hurtado, J. E, Alvarez, D. A, Ramirez, J., "Fuzzy Structural Analysis Based on Fundamental Reliability Concepts", Journal of Computers and Structures, Vol. 112-113, Pp. 183-192, (2012).

10. Dong, W, Shah, H., "Vertex Method for Computing Functions on Fuzzy Variables", Journal of Fuzzy Sets and Systems, Vol. 24, Issue. 1, Pp. 65-78, (1987).

11. Möller, B., Graf, W., Beer, M., "Fuzzy Structural Analysis Using α-level Optimization", Computational Mechanics, Vol. 26, Pp. 547-565, (2000).

12. Bagheri, M., Miri, M., Shabakhty, N., "Modeling of Epistemic Uncertainty in Reliability Analysis of Structures Using a Robust Genetic Algorithm", Iranian Journal of Fuzzy Systems, Vol. 12, Pp. 23-40, (2015).

13. Farkas, L., Moens, D., Vandepitte, D., Desmet, D., "Fuzzy Finite Element Analysis Based on Reanalysis Technique", Structural Safety, Vol. 32, No. 6, Pp. 442-448, (2010).

14. Serafinska, A., Kaliske, M., Zopf, C., Graf, M., "A Multi-objective Optimization Approach with Consideration of Fuzzy Variables Applied to Structural Tire Design", Computers and Structures, Vol. 116, Pp. 9-17, (2013).

15. Zhang, M. Q., Beer, M., Quek, S. T., Choo, Y. S., "Comparison of Uncertainty Models in Reliability Analysis of Offshore Structures under Marine Corrosion", Structural Safety, Vol. 32, Pp. 425-432, (2010).

16.Yang, D., "Chaos Control for Numerical Instability of First Order Reliability Method", Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 10, Pp. 3131-3141, (2010).

17. 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).

18. کشته‌گر، بهروز، «تحلیل قابلیت اعتماد مرتبه اول سازه‌ها به‌کمک روش بهینه‌سازی بهبود یافته جستجوی هارمونی»، مدل‌سازی در مهندسی، 15(51)، 12-1، doi: 10.22075/jme.2017.2687، (1396).

19.کشته‌گر، بهروز، «نقش طول گام بر همگرایی روش مرتبه اول قابلیت اعتماد سازه‌ها»، نشریۀ مهندسی عمران و محیط زیست دانشگاه تبریز، 45،3(80)، صص. 107-116، (1394).

20. Keshtegar, B., "A Hybrid Conjugate Finite-step Length Method for Robust and Efficient Reliability Analysis", Applied Mathematical Modelling, Vol. 45, Pp. 226-237, (2017).

21. Keshtegar, B., Meng, Z., "A Hybrid Relaxed First-order Reliability Method for Efficient Structural Reliability Analysis", Structural Safety, Vol. 66, Pp. 84-93, (2017).

22. کشته‌گر، بهروز، «بهبود روش انتقال پایدار جهت تحلیل قابلیت اعتماد مرتبه اول»، علوم کاربردی و محاسباتی در مکانیک، 28(2)، (1395).

23. کشته‌گر، بهروز، میری، محمود، شابختی، ناصر، «ارائۀ الگوریتمی اصلاحی برای روش‌های گرادیان مزدوج غیرخطی به‌منظور محاسبۀ شاخص قابلیت اعتماد سازه‌ها»، فصلنامۀ مهندسی عمران فردوسی، 24(2)، 14، (1392).

24. Timothy J. Ross.," Fuzzy Logic with Engineering Applications", Third Edition Publisher: Wiley, 3th edition, (2010).

25. Möller, B., Beer, M., "Fuzzy Randomness- uncertainty in Civil Engineering and Computational Mechanics", Springer Verlag, Berlin, (2004).

26. Dubois, D., Prade, H., "Operations on Fuzzy Numbers", International Journal of Systems Science, Vol. 9, No. 6, Pp. 613-626, (1978).

27. Keshtegar, B., Meng, Z., "A Hybrid Relaxed First-order Reliability Method for Efficient Structural Reliability Analysis", Structural Safety, Vol. 66, Pp. 84-93, (2017).

28. Keshtegar, B., "Chaotic Conjugate Stability tTransformation Method for Structural Reliability Analysis", Computer Methods in Applied Mechanics and Engineering, Vol. 310, Pp. 866-885, (2016).

29. Keshtegar, B., "Limited Conjugate Gradient Method for Structural Reliability Analysis", Engineering with Computers, Vol. 1-9, (2016).

30. Schmelcher, P., Diakonos, F. K., "Detecting Unstable Periodic Orbits of Chaotic Dynamical Systems", Physical Review Letters, Vol. 78, No. 25, Pp. 4733–4736, (1997).

31. Li, G., Meng, Z., Hu, H., "An Adaptive Hybrid Approach for Reliability-based Design Optimization", Structural and Multidisciplinary Optimization, Vol. 51, No. 5, Pp.1051-1065, (2015).

32. Meng, Z., Li, G., Wang, BP., Hao, P., "A Hybrid Chaos Control Approach of the Performance Measure Functions for Reliability-based Design Optimization", Computers & Structures, Vol. 146, Pp. 32-43, (2015).

33. Keshtegar, B., Hao, P., Meng, Z., "A Self-adaptive Modified Chaos Control mMethod for Reliability-Based Design Optimization", Structural and Multidisciplinary Optimization, Vol. 55, No. 51, Pp. 63-75, (2017).

34. Hao, P., Wang, Y., Liu, C., Wang, B., Wu, H., "A Novel Non-probabilistic Reliability-based Design Optimization Aalgorithm Using Enhanced Chaos Control Method", Computer Methods in Applied Mechanics and Engineering, Vol. 318, Pp. 572-593, (2017).

35. Keshtegar, B., "A Modified Mean Value of Performance Measure Approach for Reliability-based Design Optimization", Arabian Journal for Science and Engineering, Vol. 42, Pp. 1093–1101, (2017).