Fuzzy Structural Reliability Analysis using the Dynamic Directional Stability Transformation Method
Authors
Abstract
In this paper, a new method is proposed for fuzzy structural reliability analysis; it considers epistemic uncertainty arising from the statistical ambiguity of random variables. The proposed method, namely, fuzzy dynamic-directional stability transformation method, includes two iterative loops. An internal algorithm performs the reliability analysis using the dynamic-directional stability transformation method and an external algorithm performs the fuzzy analysis by applying the alpha-cut level optimization method based on the genetic algorithm. Implementation of the proposed method, which solves some nonlinear performance functions, indicates the efficiency and robustness of the dynamic-directional stability transformation method, as compared to other first order reliability methods.
Keywords
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2. Yang, D., “Chaos Control for Numerical Instability of First Order Reliability Method”, Communications in Nonlinear Science and Numerical Simulation, Vol. 15, pp. 3131-3141, 2010.
3. Armen, D. K., and Taleen, D., “Multiple Design Points in First and Second-order Reliability”, Structural Safety, Vol. 20, pp. 37-49, 1998.
4. Papadopoulos, V., Giovanis, D. G., Lagaros, N. D., and Papadrakakis, M., “Accelerated Subset Simulation with Neural Networks for Reliability Analysis”, Computer Methods in Applied Mechanics and Engineering, Vol. 223, 70-80, 2012.
5. Guo, H., and Zhang, L., “A Weighted Balance Evidence Theory for Structural Multiple Damage Localization”, Computer Methods in Applied Mechanics and Engineering, Vol. 195, No. 15, pp. 6225-6238, 2006.
6. Angelikopoulos, P., Papadimitriou, C., and Koumoutsakos, P., “X-TMCMC: Adaptive Kriging for Baysian Inverse Moeling”, Computer Methods in Applied Mechanics and Engineering, Vol. 289, pp. 409-428, 2015.
7. Wang, M., and Huang, Q., “A New Hybrid Uncertain Analysis Method for Structural-acoustic Systems with Random and Interval Parameters”, Computers & Structures, Vol. 175, pp. 15-28, 2016.
8. Möller, B., and Beer, M., Fuzzy Randomness: Uncertainty in Civil Engineering and Computational Mechanics, Springer Science & Business Media, 2013.
9. Möller, B., Graf, W., and Beer, M., “Fuzzy Structural Analysis using α-level Optimization”, Computational Mechanics, Vol. 26, pp. 547-565, 2000.
10. Zadeh, L. A., “Fuzzy Sets”, Information and Control, Vol. 8, pp. 338-353, 1965.
11. Kwakernaak, H., “Fuzzy Random Variables-I. Definitions and Theorems”, Information Sciences, Vol. 15, pp. 1-29, 1978.
12. Möller, B., Graf, W., and Beer, M., “Safety Assessment of Structures in View of Fuzzy Randomness”, Computers & Structures, Vol. 81, pp. 1567-1582, 2003.
13. Hurtado, J. E., Alvarez, D. A., and RamíRez, J., “Fuzzy Structural Analysis Based on Fundamental Reliability Concepts”, Computers & Structures, Vol. 112, pp. 183-192, 2012.
14. Giuseppe, M., and Giuseppe, Q., “A New Possibilistic Reliability Index Definition”, Acta Mechanics, Vol. 210, pp. 291-303, 2010.
15. Cremona, C., and Gao, Y., “The Possibilistic Reliability Theory: Theoretical Aspects and Applications”, Structural Safety, Vol. 19, No. 2, pp. 173-201, 1997.
16. Isbendiyar, M. A., and Kara, Z., “Fuzzy System Reliability Analysis using Time Dependent Fuzzy Set”, Control and Cybernetics, Vol. 33, No. 4, 2004.
17. Zhang, M. Q., Beer, M., Quek, S. T., and Choo, Y. S., “Comparison of Uncertainty Models in Reliability Analysis of Offshore Structures Under Marine Corrosion”, Structural Safety, Vol. 32, pp. 425-432, 2010.
18. Möller, B., Beer, M., Graf, W., and Sickert, J. U., “Time-dependent Reliability of Textile-strengthened RC Structures Under Consideration of Fuzzy Randomness”, Computers and Structures, Vol. 84, pp. 585-603, 2006.
19. Achintya, H., and Mahadevan, S., Probability, Reliability, and Statistical Methods in Engineering Design, John Wiley & Sons, 2000.
20. Liu, P -L, and Der Kiureghian, A. “Optimization Algorithms for Structural Reliability”, Structural Safety, Vol. 9, pp. 161-77, 1991.
21. Yang, D., “Chaos Control for Numerical Instability of First Order Reliability Method”, Communications in Nonlinear Science and Numerical Simulation, Vol. 15, pp. 3131-3141, 2010.
22. Keshtegar, B., “Limited Conjugate Gradient Method for Structural Reliability Analysis”, Engineering with Computers, pp. 1-9, 2016.
23. Keshtegar, B., “A Hybrid Conjugate Finite-step Length Method for Robust and Efficient Reliability Analysis”, Applied Mathematical Modelling, Vol. 45, pp. 226-237, 2017.
24. Meng, Z., Li, G., Yang, D., and Zhan, L., “A New Directional Stability Transformation Method of Chaos Control for First Order Reliability Analysis”, Structural and Multidisciplinary Optimization, pp. 1-12, 2016.
25. Keshtegar, B., “Chaotic Conjugate Stability Transformation Method for Structural Reliability Analysis” Computer Methods in Applied Mechanics and Engineering, Vol. 310, pp. 866-85, 2016.
26. B. Keshtegar, B., and Meng, Z., “A Hybrid Relaxed First-order Reliability Method for Efficient Structural Reliability Analysis”, Structural Safety, Vol. 66, pp. 84-93, 2017.
27. Keshtegar B, and Meng, Z., “Conjugate and Directional Chaos Control Methods for Reliability Analysis of CNT–reinforced Nanocomposite Beams under Buckling Forces; a Comparative Study”, Journal of Applied and Computational Mechanics, Vol. 2, pp. 144-151, 2016.
28. Zhang, B. T., and Kim, J. J., “Comparison of Selection Methods for Evolutionary Optimization”, Evolutionary Optimization, Vol. 2, pp. 55-70, 2000.
29. باقری، م.، میری، م.، و شابختی، ن.، "محاسبه شاخص قابلیت اعتماد فازی سازهها با استفاده از تکنیک بهینهسازی آلفا برشها"، مجله مهندسی عمران و محیط زیست دانشگاه تبریز سال 34، دوره 4، شماره 73، ص ص 12-1، 1392.
30. Pandian, M. V., Handbook of Research on Novel Soft Computing Intelligent Algorithms: Theory and Practical Applications, 1nd Ed, IGI Global, 2013.
31. Bagheri, M., Miri, M., and 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.
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