Non-Probabilistic Reliability Indexes Based on the Generalized Super Ellipsoid Model

QIAO Xinzhou; ZHAO Yuetong; FANG Xiurong; LIU Peng

doi:10.21656/1000-0887.440061

Volume 45 Issue 4

Apr. 2024

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(4): 458-469

QIAO Xinzhou, ZHAO Yuetong, FANG Xiurong, LIU Peng. Non-Probabilistic Reliability Indexes Based on the Generalized Super Ellipsoid Model[J]. Applied Mathematics and Mechanics, 2024, 45(4): 458-469. doi: 10.21656/1000-0887.440061

Citation:

PDF( 2683 KB)

Non-Probabilistic Reliability Indexes Based on the Generalized Super Ellipsoid Model

doi: 10.21656/1000-0887.440061

College of Mechanical Engineering, Xi'an University of Science and Technology, Xi'an 710054, P.R.China

Received Date: 2023-03-07
Rev Recd Date: 2023-09-17
Publish Date: 2024-04-01

Abstract

Abstract

The non-probabilistic convex model only requires the bounds or domains of structural uncertain parameters to measure structural reliability, and therefore is more appropriate for engineering structures with limited experimental data. The problem of non-probabilistic reliability measurement of the generalized super ellipsoid model was studied. A simple non-probabilistic reliability index was first proposed to evaluate the safety degree of a structure, which was defined as the ratio of the mean value of the performance function to its deviation. The inconsistency problem in the simple non-probabilistic reliability index was further discussed. To overcome the above inconsistency problem, a ratio factor reliability index was then presented, which was defined as the minimum ratio factor at which the failure surface is in contact with the uncertainty domain contracting inward or expanding outward. Three numerical examples demonstrate the validity and feasibility of the proposed non-probabilistic reliability indexes.

FullText(HTML)

References(21)

References

[1]	YAN Y H, WANG X J, LI Y L. Structural reliability with credibility based on the non-probabilistic set-theoretic analysis[J]. Aerospace Science and Technology, 2022, 127: 107730. doi: 10.1016/j.ast.2022.107730
[2]	CHANG Q, ZHOU C C, WEI P F, et al. A new non-probabilistic time-dependent reliability model for mechanisms with interval uncertainties[J]. Reliability Engineering & System Safety, 2021, 215: 107771.
[3]	FANG P Y, LI S H, GUO X L, et al. Response surface method based on uniform design and weighted least squares for non-probabilistic reliability analysis[J]. International Journal for Numerical Methods in Engineering, 2020, 121(18): 4050-4069. doi: 10.1002/nme.6426
[4]	郭书祥, 吕震宙, 冯元生. 基于区间分析的结构非概率可靠性模型[J]. 计算力学学报, 2001, 18(1): 56-60. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG200101009.htm GUO Shuxiang, LÜ Zhenzhou, FENG Yuansheng. A non-probabilistic model of structural reliability based on interval analysis[J]. Chinese Journal of Computational Mechanics, 2001, 18(1): 56-60. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG200101009.htm
[5]	曹鸿钧, 段宝岩. 基于凸集合模型的非概率可靠性研究[J]. 计算力学学报, 2005, 22(5): 546-549. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG200505007.htm CAO Hongjun, DUAN Baoyan. An approach on the non-probabilistic reliability of structures based on uncertainty convex models[J]. Chinese Journal of Computational Mechanics, 2005, 22(5): 546-549. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG200505007.htm
[6]	JIANG C, ZHANG Q F, HAN X, et al. A non-probabilistic structural reliability analysis method based on a multidimensional parallelepiped convex model[J]. Acta Mechanica, 2013, 225(2): 383-395.
[7]	MENG Z, HU H, ZHOU H L. Super parametric convex model and its application for non-probabilistic reliability-based design optimization[J]. Applied Mathematical Modelling, 2018, 55(5): 354-370.
[8]	QIAO X Z, SONG L F, LIU P, et al. Invariance problem in structural non-probabilistic reliability index[J]. Journal of Mechanical Science and Technology, 2021, 35(11): 4953-4961. doi: 10.1007/s12206-021-1014-1
[9]	WANG L, WANG X J, CHEN X, et al. Time-variant reliability model and its measure index of structures based on a non-probabilistic interval process[J]. Acta Mechanica, 2015, 226: 3221-3241. doi: 10.1007/s00707-015-1379-2
[10]	ZHAN J J, LUO Y J, ZHANG X P, et al. A general assessment index for non-probabilistic reliability of structures with bounded field and parametric uncertainties[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 366(12): 113046.
[11]	WANG X J, QIU Z P, ELISHAKOFF I. Non-probabilistic set-theoretic model for structural safety measure[J]. Acta Mechanica, 2008, 198: 51-64. doi: 10.1007/s00707-007-0518-9
[12]	JIANG C, BI R G, LU G Y, et al. Structural reliability analysis using non-probabilistic convex model[J]. Computer Methods in Applied Mechanics and Engineering, 2013, 254: 83-98. doi: 10.1016/j.cma.2012.10.020
[13]	HONG L X, LI H C, FU J F, et al. Hybrid active learning method for non-probabilistic reliability analysis with multi super ellipsoidal model[J]. Reliability Engineering & System Safety, 2022, 222: 108414.
[14]	JIANG C, NI B Y, HAN X, et al. Non-probabilistic convex model process: a new method of time-variant uncertainty analysis and its application to structural dynamic reliability problems[J]. Computer Methods in Applied Mechanics & Engineering, 2014, 268: 656-676.
[15]	QIAO X Z, WANG B, FANG X R, et al. Non-probabilistic reliability bounds for series structural systems[J]. International Journal of Computational Methods, 2021, 18(9): 2150038. doi: 10.1142/S0219876221500389
[16]	CAO L X, LIU J, XIE L, et al. Non-probabilistic polygonal convex set model for structural uncertainty quantification[J]. Applied Mathematical Modelling, 2021, 89(1): 504-518.
[17]	NI B Y, ELISHAKOFF I, JIANG C, et al. Generalization of the super ellipsoid concept and its application in mechanics[J]. Applied Mathematical Modelling, 2016, 40(21/22): 9427-9444.
[18]	AYYASAMY S, RAMU P, ELISHAKOFF I. Chebyshev inequality-based inflated convex hull for uncertainty quantification and optimization with scarce samples[J]. Structural and Multidisciplinary Optimization, 2021, 64(4): 2267-2285. doi: 10.1007/s00158-021-02981-5
[19]	ELISHAKOFF I, FANG T, SARLIN N, et al. Uncertainty quantification and propagation based on hybrid experimental, theoretical, and computational treatment[J]. Mechanical Systems and Signal Processing, 2021, 147(1): 107058.
[20]	刘成立, 吕震宙, 罗志清, 等. 一种通用的稳健可靠性指标[J]. 机械工程学报, 2011, 47(10): 192-198. https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201110032.htm LIU Chengli, LÜ Zhenzhou, LUO Zhiqing, et al. A general robust reliability index[J]. Journal of Mechanical Engineering, 2011, 47(10): 192-198. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201110032.htm
[21]	矿用高强度圆环链: GB/T 12718—2009[S]. 北京: 中国标准出版社, 2009. High-tensile steel chains (round link) for mining: GB/T 12718—2009[S]. Beijing: Standards Press of China, 2009. (in Chinese)