Research article Special Issues

Generalized first-order second-moment method for uncertain random structures

  • Received: 10 February 2023 Revised: 20 March 2023 Accepted: 23 March 2023 Published: 06 April 2023
  • MSC : 62N05, 68M15

  • In this paper, a new reliability assessing method for structures influenced by both aleatory and epistemic uncertainty simultaneously is developed. To handle hybrid types of uncertainties, chance theory is introduced to define a new hybrid reliability index. By mathematical derivation and theorems proofs, the new index is showed to be effective and compatible with hybrid types of uncertainties. Correspondingly, a generalized first-order second-moment (GFOSM) algorithm is established for practical reliability assessment of structures with hybrid uncertainties. Based on the first two moments of basic variables, the GFOSM method can perform fast and effective reliability assessment without large-scale integration operations and can be considered as an extension and expansion of the traditional FOSM method. Two numerical cases further illustrate the effectiveness and practicability of the proposed method from different perspectives.

    Citation: Yubing Chen, Meilin Wen, Qingyuan Zhang, Yu Zhou, Rui Kang. Generalized first-order second-moment method for uncertain random structures[J]. AIMS Mathematics, 2023, 8(6): 13454-13472. doi: 10.3934/math.2023682

    Related Papers:

  • In this paper, a new reliability assessing method for structures influenced by both aleatory and epistemic uncertainty simultaneously is developed. To handle hybrid types of uncertainties, chance theory is introduced to define a new hybrid reliability index. By mathematical derivation and theorems proofs, the new index is showed to be effective and compatible with hybrid types of uncertainties. Correspondingly, a generalized first-order second-moment (GFOSM) algorithm is established for practical reliability assessment of structures with hybrid uncertainties. Based on the first two moments of basic variables, the GFOSM method can perform fast and effective reliability assessment without large-scale integration operations and can be considered as an extension and expansion of the traditional FOSM method. Two numerical cases further illustrate the effectiveness and practicability of the proposed method from different perspectives.



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    [1] G. Narayanan, Probabilistic fatigue model for cast alloys of aero engine applications, Int. J. Struct. Integr., 12 (2021), 454–469.
    [2] Y. Yang, G. Wang, Q. Zhong, H. Zhang, J. He, H. Chen, Reliability analysis of gas pipeline with corrosion defect based on finite element method, Int. J. Struct. Integr., 12 (2021), 854–863.
    [3] D. Meng, S. Yang, T. Lin, J. Wang, RBMDO using gaussian mixture model-based second-order mean-value saddlepoint approximation, Comput. Model. Eng. Sci., 132 (2022), 553–568.
    [4] D. Meng, S. Yang, C. He, H. Wang, Z. Lv, Y. Guo, et al., Multidisciplinary design optimization of engineering systems under uncertainty: a review, Int. J. Struct. Integr., 13 (2022), 565–593.
    [5] D. Meng, S. Yang, A. de Jesus, S. P. Zhu, A novel Kriging-model-assisted reliability-based multidisciplinary design optimization strategy and its application in the offshore wind turbine tower, Renew. Energy, 203 (2023), 407–420. https://doi.org/10.1016/j.renene.2022.12.062 doi: 10.1016/j.renene.2022.12.062
    [6] A. Kiureghian, O. Ditlevsen, Aleatory or epistemic? Does it matter, Struct. Saf., 31 (2009), 105–112. https://doi.org/10.1016/j.strusafe.2008.06.020 doi: 10.1016/j.strusafe.2008.06.020
    [7] R. Kang, Q. Zhang, Z. Zeng, Z. Enrico, X. Li, Measuring reliability under epistemic uncertainty: review on non-probabilistic reliability metrics, Chinese J. Aeronaut., 29 (2016), 571–579. https://doi.org/10.1016/j.cja.2016.04.004 doi: 10.1016/j.cja.2016.04.004
    [8] R. E. Melchers, A. T. Beck, Structural reliability analysis and prediction, 3 Eds., John Wiley & Sons Ltd, 2018.
    [9] W. C. Broding, F. W. Diederich, P. S. Parker, Structural optimization and design based on a reliability design criterion, J. Spacecraft Rockets, 1 (1964), 56–61. https://doi.org/10.2514/3.27592 doi: 10.2514/3.27592
    [10] C. A. Cornell, A probability-based structural code, ACI-Abst. Search, 12 (1969), 974–985.
    [11] A. M. Hasofer, N. C. Lind, Exact and invariant second-moment code format, J. Eng. Mech., 100 (1974), 111–121. https://doi.org/10.1061/JMCEA3.0001848 doi: 10.1061/JMCEA3.0001848
    [12] R. Rackwitz, B. Fiessler, Structural reliability under combined random load sequences, Comput. Struct., 9 (1978), 489–494. https://doi.org/10.1016/0045-7949(78)90046-9 doi: 10.1016/0045-7949(78)90046-9
    [13] S. Chen, C. Duffield, S. Miramini, B. N. K. Raja, L. Zhang, Life-cycle modelling of concrete cracking and reinforcement corrosion in concrete bridges: a case study, Eng. Struct., 237 (2021), 112143. https://doi.org/10.1016/j.engstruct.2021.112143 doi: 10.1016/j.engstruct.2021.112143
    [14] M. Ricker, T. Feiri, K. Nille-Hauf, V. Adam, J. Hegger, Enhanced reliability assessment of punching shear resistance models for flat slabs without shear reinforcement, Eng. Struct., 226 (2021), 111319. https://doi.org/10.1016/j.engstruct.2020.111319 doi: 10.1016/j.engstruct.2020.111319
    [15] M. Nahal, R. Khelif, A finite element model for estimating time-dependent reliability of a corroded pipeline elbow, Int. J. Struct. Integr., 12 (2021), 306–321.
    [16] L. Hu, R. Kang, X. Pan, D. Zuo, Uncertainty expression and propagation in the risk assessment of uncertain random system, IEEE Syst. J., 15 (2021), 1604–1615. https://doi.org/10.1109/JSYST.2020.2990679 doi: 10.1109/JSYST.2020.2990679
    [17] C. Cremona, Y. Gao, The possibilistic reliability theory: theoretical aspects and applications, Struct. Saf., 19 (1997), 173–201. https://doi.org/10.1016/S0167-4730(97)00093-3 doi: 10.1016/S0167-4730(97)00093-3
    [18] Y. Ben-Haim, I. Elishakoff, Convex, models of uncertainty in applied mechanics, Elsevier, 1990.
    [19] H. R. Bae, R. V. Grandhi, R. A. Canfield, An approximation approach for uncertainty quantification using evidence theory, Reliab. Eng. Syst. Safe., 86 (2004), 215–225. https://doi.org/10.1016/j.ress.2004.01.011 doi: 10.1016/j.ress.2004.01.011
    [20] Z. Zeng, M. Wen, R. Kang, Belief reliability: a new metrics for products' reliability, Fuzzy Optim. Decis. Making, 12 (2013), 15–27. https://doi.org/10.1007/s10700-012-9138-5 doi: 10.1007/s10700-012-9138-5
    [21] P. Wang, J. Zhang, H. Zhai, J. Qiu, A new structural reliability index based on uncertainty theory, Chinese J. Aeronaut., 30 (2017), 1451–1458. https://doi.org/10.1016/j.cja.2017.04.008 doi: 10.1016/j.cja.2017.04.008
    [22] Y. Liu, Uncertain random variables: a mixture of uncertainty and randomness, Soft Comput., 4 (2013), 625–634. https://doi.org/10.1007/s00500-012-0935-0 doi: 10.1007/s00500-012-0935-0
    [23] Z. He, H. Ahmadzade, K. Rezaei, H. Rezaei, H. Naderi, Tsallis entropy of uncertain random variables and its application, Soft Comput., 25 (2021), 11735–11743. https://doi.org/10.1007/s00500-021-06070-z doi: 10.1007/s00500-021-06070-z
    [24] Q. Zhang, R. Kang, M. Wen, Belief reliability for uncertain random systems, IEEE Trans. Fuzzy Syst., 26 (2018), 3605–3614. https://doi.org/10.1109/TFUZZ.2018.2838560 doi: 10.1109/TFUZZ.2018.2838560
    [25] Y. Tan, X. Ji, S. Yan, New models of supply chain network design by different decision criteria under hybrid uncertainties, J. Ambient. Intell. Human. Comput., 10 (2019), 2843–2853. https://doi.org/10.1007/s12652-018-1001-2 doi: 10.1007/s12652-018-1001-2
    [26] L. Zhang, J. Zhang, L. You, S. Zhou, Reliability analysis of structures based on a probability-uncertainty hybrid model, Qual. Reliab. Eng. Int., 35 (2019), 263–279. https://doi.org/10.1002/qre.2396 doi: 10.1002/qre.2396
    [27] B. Liu, Uncertainty theory, Berlin: Springer-Verlag, 2007.
    [28] X. Chen, W. Dai, Maximum entropy principle for uncertain variables, Int. J. Fuzzy Syst., 13 (2011), 232–236.
    [29] T. Zu, R. Kang, M. Wen, Graduation formula: a new method to construct belief reliability distribution under epistemic uncertainty, J. Syst. Eng. Electron., 31 (2020), 626–633. https://doi.org/10.23919/JSEE.2020.000038 doi: 10.23919/JSEE.2020.000038
    [30] Q. Zhang, Belief reliability metric and analysis methods of uncertain random systems, Beijing: Beihang University, M1-Doctor, 2020.
    [31] B. Liu, Some research problems in uncertainty theory, J. Uncertain Syst., 3 (2009), 3–10.
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