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

Yubing Chen; Meilin Wen; Qingyuan Zhang; Yu Zhou; Rui Kang; Yubing Chen; Meilin Wen; Qingyuan Zhang; Yu Zhou; Rui Kang

doi:10.3934/math.2023682

AIMS Mathematics

2023, Volume 8, Issue 6: 13454-13472. doi: 10.3934/math.2023682

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

1.
School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
2.
The Key Laboratory on Reliability and Environmental Engineering Technology, Beijing 100191, China
3.
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China
4.
Yunnan Design Institute Group Co., LTD, Kunming 650103, China

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.
- structural reliability,
- reliability assessment,
- aleatory uncertainty,
- epistemic uncertainty,
- uncertainty theory,
- uncertain system
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

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Abstract

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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