ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Non-probabilistic reliability analysis with fuzzy failure and safe states
Received date: 2023-12-15
Revised date: 2024-01-02
Accepted date: 2024-01-25
Online published: 2024-02-02
Supported by
National Science and Technology Major Project(J2019-V-0016-0111)
In practical engineering， it is sometimes difficult to clearly determine the output state of a structure. The non-probabilistic reliability analysis with the binary state ignores the fuzzy output state， which is too ideal. To solve this problem， we conduct the non-probabilistic reliability analysis with fuzzy failure and safe states by introducing the fuzzy state assumption， with the input uncertainties quantified by the ellipsoidal model. According to the fuzzy state assumption， the states of structures are described by fuzziness， and then combined with the principle of indifference. The non-probabilistic fuzzy reliability degree is developed as a measure of the non-probabilistic reliability of the structure， followed by the corresponding Monte Carlo simulation method for the non-probabilistic fuzzy reliability. To overcome the inefficiency associated with the Monte Carlo simulation method， a novel active learning Kriging method is proposed. Finally， an efficient non-probabilistic reliability analysis method with fuzzy states is established. Examples are used to illustrate the engineering practicality of the proposed non-probabilistic reliability analysis method.
Feng JIANG , Huacong LI , Jiangfeng FU , Xianwei LIU . Non-probabilistic reliability analysis with fuzzy failure and safe states[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2024 , 45(20) : 229989 -229989 . DOI: 10.7527/S1000-6893.2024.29989
| 1 | WEI Z Z， JIN H， PEI X J， et al. A simplified approach to estimate the fatigue life of full-scale welded cast steel thin-walled tubular structures［J］. Thin-Walled Structures， 2021， 160： 107348. |
| 2 | SONG K L， ZHANG Y G， YU X S， et al. A new sequential surrogate method for reliability analysis and its applications in engineering［J］. IEEE Access， 2019， 7： 60555-60571. |
| 3 | DANG C， VALDEBENITO M A， SONG J W， et al. Estimation of small failure probabilities by partially Bayesian active learning line sampling： Theory and algorithm［J］. Computer Methods in Applied Mechanics and Engineering， 2023， 412： 116068. |
| 4 | KIM M， JUNG Y， LEE M Y， et al. An expected uncertainty reduction of reliability： Adaptive sampling convergence criterion for Kriging-based reliability analysis［J］. Structural and Multidisciplinary Optimization， 2022， 65（7）： 206. |
| 5 | ZHONG C T， WANG M F， DANG C， et al. First-order reliability method based on Harris Hawks Optimization for high-dimensional reliability analysis［J］. Structural and Multidisciplinary Optimization， 2020， 62（4）： 1951-1968. |
| 6 | WANG C， MATTHIES H G. Epistemic uncertainty-based reliability analysis for engineering system with hybrid evidence and fuzzy variables［J］. Computer Methods in Applied Mechanics and Engineering， 2019， 355： 438-455. |
| 7 | 檀中强， 潘骏， 胡明， 等. 基于椭球模型的机构非精确概率可靠性分析方法［J］. 机械工程学报， 2019， 55（2）： 168-176. |
| TAN Z Q， PAN J， HU M， et al. Imprecise probabilistic reliability analysis method for MechanismBased on ellipsoid model［J］. Journal of Mechanical Engineering， 2019， 55（2）： 168-176 （in Chinese）. | |
| 8 | BEN-HAIM Y. A non-probabilistic concept of reliability［J］. Structural Safety， 1994， 14（4）： 227-245. |
| 9 | ELISHAKOFF Y B H A I. Convex models of uncertainty in applied mechanics［M］. Amsterdam： Elsevier， 1990. |
| 10 | JIANG C， HAN X， LU G Y， et al. Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique［J］. Computer Methods in Applied Mechanics and Engineering， 2011， 200（33-36）： 2528-2546. |
| 11 | 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， 578. |
| CAO H J， DUAN B Y. 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， 578 （in Chinese）. | |
| 12 | 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. |
| 13 | HONG L X， LI H C， GAO N， et al. Random and multi-super-ellipsoidal variables hybrid reliability analysis based on a novel active learning Kriging model［J］. Computer Methods in Applied Mechanics and Engineering， 2021， 373： 113555. |
| 14 | 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. |
| 15 | 郭书祥，吕震宙. 结构体系的非概率可靠性分析方法［J］. 计算力学学报， 2002， 19 （3）： 332-335. |
| GUO S， LU Z Z. A procedure of the analysis of non-probabilistic reliability of structural systems［J］. Chinese Journal of Computational Mechanics， 2002， 19（3）： 332-335 （in Chinese）. | |
| 16 | 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： 354-370. |
| 17 | WANG X J， WANG L， ELISHAKOFF I， et al. Probability and convexity concepts are not antagonistic［J］. Acta Mechanica， 2011， 219（1）： 45-64. |
| 18 | JIANG C， LU G Y， HAN X， et al. Some important issues on first-order reliability analysis with nonprobabilistic convex models［J］. Journal of Mechanical Design， 2014， 136（3）： 034501. |
| 19 | 路国营. 基于非概率凸模型的可靠性分析及应用［D］. 长沙： 湖南大学， 2012. |
| LU G Y. The reliability analysis and it’s application based on the non-probabilistic convex model［D］.Changsha： Hunan University， 2012 （in Chinese）. | |
| 20 | 毕仁贵. 考虑相关性的不确定凸集模型与非概率可靠性分析方法［D］. 长沙： 湖南大学， 2015. |
| BI R G. Non-probabilistic uncertainty convex model and reliability analysis method incorporating correlation［D］.Changsha： Hunan University， 2015 （in Chinese）. | |
| 21 | MENG Z， WAN H P， SHENG Z L， et al. A novel study of structural reliability analysis and optimization for super parametric convex model［J］. International Journal for Numerical Methods in Engineering， 2020， 121（18）： 4208-4229. |
| 22 | 黄晓宇， 王攀， 李海和， 等. 具有模糊失效状态的涡轮盘疲劳可靠性及灵敏度分析［J］. 西北工业大学学报， 2021， 39（6）： 1312-1319. |
| HUANG X Y， WANG P， LI H H， et al. Fatigue reliability and sensitivity analysis of turbine disk with fuzzy failure status［J］. Journal of Northwestern Polytechnical University， 2021， 39（6）： 1312-1319 （in Chinese）. | |
| 23 | 张萌. 统一模糊可靠性模型理论研究及叶片抗振模糊可靠性评估建模［D］. 西安： 西北工业大学， 2015. |
| ZHANG M. Theoretical study on the unified fuzzy reliability model and reliability assessment modeling of blades to avoid resonance［D］. Xi’an： Northwestern Polytechnical University， 2015 （in Chinese）. | |
| 24 | FENG K X， LU Z Z， YUN W Y. Aircraft icing severity analysis considering three uncertainty types［J］. AIAA Journal， 2019， 57（4）： 1514-1522. |
| 25 | FENG K X， LU Z Z， PANG C， et al. Efficient numerical algorithm of profust reliability analysis： An application to wing box structure［J］. Aerospace Science and Technology， 2018， 80： 203-211. |
| 26 | PANDEY D， TYAGI S K. Profust reliability of a gracefully degradable system［J］. Fuzzy Sets and Systems， 2007， 158（7）： 794-803. |
| 27 | CAI K Y. System failure engineering and fuzzy methodolog： An introductory overview［J］. Fuzzy Sets and Systems， 1996， 83（2）： 113-133. |
| 28 | CAI K Y， WEN C Y， ZHANG M L. Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context［J］. Fuzzy Sets and Systems， 1991， 42（2）： 145-172. |
| 29 | CAI K Y， WEN C Y， ZHANG M L. Fuzzy reliability modeling of gracefully degradable computing systems［J］. Reliability Engineering & System Safety， 1991， 33（1）： 141-157. |
| 30 | WANG J Q， LU Z Z， SHI Y. Aircraft icing safety analysis method in presence of fuzzy inputs and fuzzy state［J］. Aerospace Science and Technology， 2018， 82-83： 172-184. |
| 31 | LING C Y， LU Z Z， SUN B， et al. An efficient method combining active learning Kriging and Monte Carlo simulation for profust failure probability［J］. Fuzzy Sets and Systems， 2020， 387： 89-107. |
| 32 | YUN W Y， LU Z Z， FENG K X， et al. A novel step-wise AK-MCS method for efficient estimation of fuzzy failure probability under probability inputs and fuzzy state assumption［J］. Engineering Structures， 2019， 183： 340-350. |
| 33 | KEYNES J M. A Treatise on probability［M］. London： Macmillan & Co.， Ltd.， 1921. |
| 34 | ZADEH L A. Probability measures of fuzzy events［J］. Journal of Mathematical Analysis and Applications， 1968， 23（2）： 421-427. |
| 35 | FORRESTER A I J， SóBESTER A， KEANE A J. Engineering design via surrogate modelling： A practical guide［M］. Chichester： Wiley， 2008. |
| 36 | DANG C， WEI P F， FAES M G R， et al. Interval uncertainty propagation by a parallel Bayesian global optimization method［J］. Applied Mathematical Modelling， 2022， 108： 220-235. |
| 37 | ECHARD B， GAYTON N， LEMAIRE M. AK-MCS： An active learning reliability method combining Kriging and Monte Carlo Simulation［J］. Structural Safety， 2011， 33（2）： 145-154. |
| 38 | ZHANG Y S， LIU Y S， YANG X F， et al. An efficient Kriging method for global sensitivity of structural reliability analysis with non-probabilistic convex model［J］. Proceedings of the Institution of Mechanical Engineers， Part O： Journal of Risk and Reliability， 2015， 229（5）： 442-455. |
| 39 | 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. |
| 40 | SONG J W， WEI P F， VALDEBENITO M A， et al. Data-driven and active learning of variance-based sensitivity indices with Bayesian probabilistic integration［J］. Mechanical Systems and Signal Processing， 2022， 163： 108106. |
/
| 〈 |
|
〉 |
CJA