Fuzzy Reliability Analysis Using Genetic Optimization Algorithm Combined with Adaptive Descent Chaos Control
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 6, Issue 2
Abstract
The robust result of analytical fuzzy reliability analysis (FRA) represents the main effort at evaluating the fuzzy reliability index. In this study, a bioloop-based hybrid method is proposed for structural FRA. The genetic operator as optimization solver combined with adaptive descent chaos control (ADCC) as a probabilistic solver called GA-ADCC is applied to evaluate the fuzzy reliability index. The ADCC-based reliability method is formulated based on a dynamical chaos control factor that is computed using an adaptive descent approach from the new and previous results. In GA-ADCC, an outer loop–based genetic optimizer constructs the membership reliability index using an alpha level set. To compute the membership functions of the reliability index, three structural problems are used to show the capability of the proposed method. Results demonstrate that the proposed GA-ADCC method can be used to evaluate reasonable uncertainty bounds in FRA, and it provides the accurate member shape functions for reliability index.
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Data Availability Statement
All codes, including the reliability and fuzzy analysis, generated or used during the study are available from the corresponding author by request.
Acknowledgments
The financial support of the National Natural Science Foundation of China (11672070 and 11972110), Sichuan Provincial Key Research and Development Program (2019YFG0348), the Science and Technology Program of Guangzhou, China (201904010463), and Fundamental Research Funds for the Central Universities (ZYGX2019J040) and the University of Zabol (IR-UOZ-9618-1) are acknowledged.
References
Attarzadeh, M., D. K. Chua, M. Beer, and E. L. Abbott. 2017. “Fuzzy randomness simulation of long-term infrastructure projects.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 3 (3): 04017002. https://doi.org/10.1061/AJRUA6.0000902.
Bagheri, M., M. Miri, and N. Shabakhty. 2015. “Modeling of epistemic uncertainty in reliability analysis of structures using a robust genetic algorithm.” Iran. J. Fuzzy Syst. 12 (2): 23–40. https://doi.org/10.22111/ijfs.2015.1980.
Bagheri, M., M. Miri, and N. Shabakhty. 2016. “Fuzzy reliability analysis using a new alpha level set optimization approach based on particle swarm optimization.” J. Intell. Fuzzy Syst. 30 (1): 235–244. https://doi.org/10.3233/IFS-151749.
Bagheri, M., M. Miri, and N. Shabakhty. 2017. “Fuzzy time dependent structural reliability analysis using alpha level set optimization method based on genetic algorithm.” J. Intell. Fuzzy Syst. 32 (6): 4173–4182. https://doi.org/10.3233/JIFS-161320.
Büche, D., S. Klostermann, and M. Schmelzer. 2019. Uncertainties identification and quantification, in uncertainty management for robust industrial design in aeronautics. Cham, Switzerland: Springer.
Cong, S., and L. Hong. 2001. “Incremental learning for robust visual tracking.” Int. J. Comput. Vision 34 (5): 593–602. https://doi.org/10.1007/s11263-007-0075-7.
Doble, C., J. Matayoshi, E. Cosyn, H. Uzun, and A. Karami. 2019. “A data-based simulation study of reliability for an adaptive assessment based on knowledge space theory.” Int. J. Artif. Intell. Educ. 29 (2): 258–282. https://doi.org/10.1007/s40593-019-00176-0.
Giachetti, R. E., and R. E. Young. 1997. “A parametric representation of fuzzy numbers and their arithmetic operators.” Fuzzy Sets Syst. 91 (2): 185–202. https://doi.org/10.1016/S0165-0114(97)00140-1.
Hao, P., B. Wang, G. Li, Z. Meng, and L. Wang. 2015. “Hybrid framework for reliability-based design optimization of imperfect stiffened shells.” AIAA J. 53 (10): 2878–2889. https://doi.org/10.2514/1.J053816.
Ji, J., C. Zhang, Y. Gao, and J. Kodikara. 2018. “Effect of 2D spatial variability on slope reliability: A simplified FORM analysis.” Geosci. Front. 9 (6): 1631–1638. https://doi.org/10.1016/j.gsf.2017.08.004.
Keshtegar, B. 2016. “Chaotic conjugate stability transformation method for structural reliability analysis.” Comput. Methods Appl. Mech. Eng. 310 (Oct): 866–885. https://doi.org/10.1016/j.cma.2016.07.046.
Keshtegar, B., and M. Bagheri. 2018. “Fuzzy relaxed-finite step size method to enhance the instability of the fuzzy first-order reliability method using conjugate discrete map.” Nonlinear Dyn. 91 (3): 1443–1459. https://doi.org/10.1007/s11071-017-3957-4.
Keshtegar, B., and S. Chakraborty. 2018. “Dynamical accelerated performance measure approach for efficient reliability-based design optimization with highly nonlinear probabilistic constraints.” Reliab. Eng. Syst. Saf. 178 (Oct): 69–83. https://doi.org/10.1016/j.ress.2018.05.015.
Keshtegar, B., P. Hao, and Z. Meng. 2017. “A self-adaptive modified chaos control method for reliability-based design optimization.” Struct. Multidiscip. Optim. 55 (1): 63–75. https://doi.org/10.1007/s00158-016-1471-9.
Keshtegar, B., and O. Kisi. 2017. “M5 model tree and Monte Carlo simulation for efficient structural reliability analysis.” Appl. Math. Modell. 48 (Aug): 899–910. https://doi.org/10.1016/j.apm.2017.02.047.
Keshtegar, B., and S. P. Zhu. 2019. “Three-term conjugate approach for structural reliability analysis.” Appl. Math. Modell. 76 (Dec): 428–442. https://doi.org/10.1016/j.apm.2019.06.022.
Kwakernaak, H. 1978. “Fuzzy random variables—I. Definitions and theorems.” Inf. Sci. 15 (1): 1–29. https://doi.org/10.1016/0020-0255(78)90019-1.
Li, G., Z. Meng, and H. Hu. 2015. “An adaptive decoupling approach for reliability-based design optimization.” Struct. Multidiscip. Optim. 51 (5): 1051–1065. https://doi.org/10.1007/s00158-014-1195-7.
Li, H., and X. Nie. 2018. “Structural reliability analysis with fuzzy random variables using error principle.” Eng. Appl. Artif. Intell. 67 (Jan): 91–99. https://doi.org/10.1016/j.engappai.2017.08.015.
Liu, X., Y. Xu, R. Montes, R. X. Ding, and F. Herrera. 2018. “Alternative ranking-based index-based consensus reaching process for hesitant fuzzy large scclustering and reliability iale group decision making.” IEEE Trans. Fuzzy Syst. 27 (1): 159–171. https://doi.org/10.1109/TFUZZ.2018.2876655.
Meng, D., Y. F. Li, H. Z. Huang, Z. Wang, and Y. Liu. 2015a. “Reliability-based multidisciplinary design optimization using subset simulation analysis and its application in the hydraulic transmission mechanism design.” J. Mech. Des. Trans. ASME 137 (5): 051402. https://doi.org/10.1115/1.4029756.
Meng, D., S. Yang, Y. Zhang, and S. P. Zhu. 2019. “Structural reliability analysis and uncertainties-based collaborative design and optimization of turbine blades using surrogate model.” Fatigue Fract. Eng. Mater. Struct. 42 (6): 1219–1227. https://doi.org/10.1111/ffe.12906.
Meng, Z., and B. Keshtegar. 2019. “Adaptive conjugate single-loop method for efficient reliability-based design and topology optimization.” Comput. Methods Appl. Mech. Eng. 344 (Feb): 95–119. https://doi.org/10.1016/j.cma.2018.10.009.
Meng, Z., G. Li, B. P. Wang, and P. Hao. 2015b. “A hybrid chaos control approach of the performance measure functions for reliability-based design optimization.” Comput. Struct. 146 (Jan): 32–43. https://doi.org/10.1016/j.compstruc.2014.08.011.
Meng, Z., G. Li, D. Yang, and L. Zhan. 2017. “A new directional stability transformation method of chaos control for first order reliability analysis.” Struct. Multidiscip. Optim. 55 (2): 601–612. https://doi.org/10.1007/s00158-016-1525-z.
Meng, Z., Y. Pu, and H. Zhou. 2018. “Adaptive stability transformation method of chaos control for first order reliability method.” Eng. Comput. 34 (4): 671–683. https://doi.org/10.1007/s00366-017-0566-2.
Möller, B., W. Graf, and M. Beer. 2003. “Safety assessment of structures in view of fuzzy randomness.” Comput. Struct. 81 (15): 1567–1582. https://doi.org/10.1016/S0045-7949(03)00147-0.
Möller, B., and B. Michael. 2003. Fuzzy randomness: Uncertainty in civil engineering and computational mechanics. Berlin: Springer Science & Business Media. https://doi.org/10.1103/PhysRevB.89.165407.
Nowak, A. S., and K. R. Collins. 2012. Reliability of structures. London: CRC Press. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:6(743).
Pan, Q., and D. Dias. 2017. “An efficient reliability method combining adaptive Support Vector Machine and Monte Carlo Simulation.” Struct. Saf. 67 (Jul): 85–95. https://doi.org/10.1016/j.strusafe.2017.04.006.
Sundar, V. S., and M. D. Shields. 2019. “Reliability analysis using adaptive kriging surrogates with multimodel inference.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 5 (2): 04019004. https://doi.org/10.1061/AJRUA6.0001005.
Wang, C., H. G. Matthies, M. Xu, and Y. Li. 2018. “Hybrid reliability analysis and optimization for spacecraft structural system with random and fuzzy parameters.” Aerosp. Sci. Technol. 77 (Jun): 353–361. https://doi.org/10.1016/j.ast.2018.03.014.
Wang, R., and Y. Luo. 2019. “Efficient strategy for reliability-based optimization design of multidisciplinary coupled system with interval parameters.” Appl. Math. Modell. 75 (Nov): 349–370. https://doi.org/10.1016/j.apm.2019.05.030.
Yang, D. 2010. “Chaos control for numerical instability of first order reliability method.” Commun. Nonlinear Sci. Numer. Simul. 15 (10): 3131–3141. https://doi.org/10.1016/j.cnsns.2009.10.018.
Zeng, P., T. Li, R. Jimenez, X. Feng, and Y. Chen. 2018. “Extension of quasi-Newton approximation-based SORM for series system reliability analysis of geotechnical problems.” Eng. Comput. 34 (2): 215–224. https://doi.org/10.1007/s00366-017-0536-8.
Zheng, J., Z. Luo, C. Jiang, B. Ni, and J. Wu. 2018. “Non-probabilistic reliability-based topology optimization with multidimensional parallelepiped convex model.” Struct. Multidiscip. Optim. 57 (6): 2205–2221. https://doi.org/10.1007/s00158-017-1851-9.
Zhu, S. P., H. Z. Huang, Y. Li, Y. Liu, and Y. Yang. 2015. “Probabilistic modeling of damage accumulation for time-dependent fatigue reliability analysis of railway axle steels.” Proc. Inst. Mech. Eng. Part F: J. Rail Rapid Transit, 29 (1): 23–33. https://doi.org/10.1177/0954409713496772.
Zhu, S. P., H. Z. Huang, W. Peng, H. K. Wang, and S. Mahadevan. 2016. “Probabilistic physics of failure-based framework for fatigue life prediction of aircraft gas turbine discs under uncertainty.” Reliab. Eng. Syst. Saf. 146 (Feb): 1–12. https://doi.org/10.1016/j.ress.2015.10.002.
Zhu, S. P., H. Z. Huang, and Z. L. Wang. 2011. “Fatigue life estimation considering damaging and strengthening of low amplitude loads under different load sequences using fuzzy sets approach.” Int. J. Damage Mech. 20 (6): 876–899. https://doi.org/10.1177/1056789510397077.
Zhu, S. P., Q. Liu, Q. Lei, and Q. Wang. 2018a. “Probabilistic fatigue life prediction and reliability assessment of a high pressure turbine disc considering load variations.” Int. J. Damage Mech. 27 (10): 1569–1588. https://doi.org/10.1177/1056789517737132.
Zhu, S. P., Q. Liu, W. Peng, and X. C. Zhang. 2018b. “Computational-experimental approaches for fatigue reliability assessment of turbine bladed disks.” Int. J. Mech. Sci. 142–143 (Jul): 502–517. https://doi.org/10.1016/j.ijmecsci.2018.04.050.
Zhu, S. P., Q. Liu, J. Zhou, and Z. Y. Yu. 2018c. “Fatigue reliability assessment of turbine discs under multi-source uncertainties.” Fatigue Fract. Eng. Mater. Struct. 41 (6): 1291–1305. https://doi.org/10.1111/ffe.12772.
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Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 6 • Issue 2 • June 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Sep 24, 2019
Accepted: Dec 17, 2019
Published online: Apr 8, 2020
Published in print: Jun 1, 2020
Discussion open until: Sep 8, 2020
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