RESEARCH PAPER
Structural reliability analysis based on fuzzy random uncertainty
1
School of Reliability and Systems Engineering Beihang University XueYuan Road No.37,HaiDian District, BeiJing, China
Publication date: 2019-12-31
Eksploatacja i Niezawodność – Maintenance and Reliability 2019;21(4):599-609
KEYWORDS
ABSTRACT
To address the fuzzy random uncertainty in structural reliability analysis, a novel method for obtaining the membership function of
fuzzy reliability is proposed on the two orders four central moments (TOFM) method based on envelope distribution. At each cut
level, the envelope distribution is first constructed, which is a new expression to describe the bound of the fuzzy random variable
distribution. The central moments of the bound distribution are determined by generating samples from the envelope distribution,
and they are used to calculate the central moments of the limit state function based on the first two orders of the Taylor expansion.
Thereafter, the modern approximation method is used to approximate the polynomial expression for the limit state function probability density function (PDF) by considering the central moments as constraint conditions. Thus, the reliability boundaries can
be calculated under the considered cut level, and the membership function of the fuzzy reliability is subsequently obtained. Three
examples are evaluated to demonstrate the efficiency and accuracy of the proposed method. Moreover, a comparison is made between the proposed method, Monte Carlo simulation (MCS) method, and fuzzy first-order reliability method (FFORM). The results
show the superiority of the proposed method, which is feasible for the analysis of structural reliability with fuzzy randomness.
REFERENCES (41)
1.
Dempster A P. Upper and lower probabilities induced by a multivalued mapping. The Annals of Mathematical Statistics 1967; 38(2): 325-339, https://doi.org/10.1214/aoms/1....
2.
Dhande S G, Chakraborty J. Analysis and synthesis of mechanical error in linkages-a stochastic approach. Journal of Engineering for Industry 1973; 95: 672-676, https://doi.org/10.1115/1.3438....
4.
Gil M Á, Miguel L D, Ralescu D A. Overview on the development of fuzzy random variables. Fuzzy Sets and Systems 2006;157(19): 2546-2557, https://doi.org/10.1016/j.fss.....
5.
Grandhi R V, Wang L. Higher-order failure probability calculation using nonlinear approximations. Computer Methods in Applied Mechanics & Engineering 2013; 168(1-4): 185-206, https://doi.org/10.1016/S0045-....
6.
Hryniewicz O. Bayes statistical decisions with random fuzzy data-an application in reliability. Reliability Engineering & System Safety 2016; 151: 20-33, https://doi.org/10.1016/j.ress....
7.
Huang H Z. Structural reliability analysis using fuzzy sets theory. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2012; 14: 284-294.
8.
Jahani E, Muhanna R L, Shayanfar M A, Barkhordari M A. Reliability Assessment with Fuzzy Random Variables Using Interval Monte Carlo Simulation. Computer-Aided Civil and Infrastructure Engineering 2014; 29(3): 208-220, https://doi.org/10.1111/mice.1....
9.
Jiang C, Zhang Q F, Han X, Qian Y H. A non-probabilistic structural reliability analysis method based on a multidimensional parallelepiped convex model. Acta Mechanica 2014; 225(2): 383-395, https://doi.org/10.1007/s00707....
10.
Kato M, Ono T, Zhao Y G. Second-Order third-moment reliability method. Journal of Structural Engineering 2002;128(8):1087-1090, https://doi.org/10.1061/(ASCE)...).
11.
Kiureghian A D, Ditlevsen O. Aleatory or epistemic? Does it matter? Structural Safety 2009; 31(2): 105-112, https://doi.org/10.1016/j.stru....
12.
Koç M L, Balas C E. Reliability analysis of a rubble mound breakwater using the theory of fuzzy random variables. Applied Ocean Research 2013; 39: 83-88, https://doi.org/10.1016/j.apor....
13.
Körner R. On the variance of fuzzy random variables. Fuzzy Sets and Systems 1997; 92(1): 83-93, https://doi.org/10.1016/S0165-....
14.
Kwakernaak H. Fuzzy random variables - I. Definitions and theorems. Information Sciences 1978; 15(1): 1-29, https://doi.org/10.1016/0020-0....
15.
Laulin L, Kieffer M, Didrit O, Walter E. Applied interval analysis. Berlin: Springer, 2001, https://doi.org/10.1007/978-1-....
16.
Li D Q, Chen Y F, Lu W B. Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables. Computers and Geotechnics 2011; 38(1): 58-68, https://doi.org/10.1016/j.comp....
17.
Li D Q, Jiang S H, Cao Z J, Zhou W, Zhou C B, Zhang L M. A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties. Engineering Geology 2015; 187: 60-72, https://doi.org/10.1016/j.engg....
18.
Li H Z, Chen F, Yang Z J, Wang L D, Kan Y N. Failure mode analysis on machining center based on possibility theory. 5th International Conference on Electrical Engineering and Automatic Control. Weihai. 2016: 627-636, https://doi.org/10.1007/978-3-....
19.
Li H B, Nie X. Structural reliability analysis with fuzzy random variables using error principle. Engineering Applications of Artificial Intelligence 2018; 67: 91-99, https://doi.org/10.1016/j.enga....
21.
Liu Y B, Zhong Q, Wang G Y. Fuzzy random reliability of structures based on fuzzy random variables. Fuzzy Sets and Systems. 1997; 86(3):345-355, https://doi.org/10.1016/S0165-....
22.
Lutterkort D, Peters J, Reif U. Polynomial degree reduction in the L2-norm equals best Euclidean approximation of Bézier coefficients. Computer Aided Geometric Design 1998;16(7): 607-612, https://doi.org/10.1016/S0167-....
23.
Möller B, Beer M. Engineering computation under uncertainty - Capabilities of non-traditional models. Computers & Structures 2008; 86(10): 1024-1041, https://doi.org/10.1016/j.comp....
24.
Möller B, Graf W, Beer M. Safety assessment of structures in view of fuzzy randomness. Computers & Structures 2003; 81(15): 1567-1582, https://doi.org/10.1016/S0045-....
25.
Möller B, Reuter U. Prediction of uncertain structural responses using fuzzy time series. Computers & Structures 2008; 86(10): 1123-1139, https://doi.org/10.1016/j.comp....
26.
Möller B, Reuter U. Uncertainty forecasting in engineering. Berlin: Springer, 2007.
27.
Neumaier A. Interval methods for systems of equations. Cambridge: Cambridge University Press, 1990.
28.
Penmetsa R C, Grandhi R V. Uncertainty propagation using possibility theory and function approximations. Mechanics Based Design of Structures & Machines 2003; 31(2): 257-279, https://doi.org/10.1081/SME-12....
29.
Shapiro, Arnold F. Modeling future lifetime as a fuzzy random variable. Insurance: Mathematics and Economics 2013; 53(3): 864-870, https://doi.org/10.1016/j.insm....
30.
Shi Z X, Yang X Q, Yang W, Cheng Q. Robust synthesis of path generating linkages. Mechanism and Machine Theory 2005;40(1):45-54. https://doi.org/10.1016/j.mech....
31.
Smith S A, Krishnamurthy T, Mason B H. Optimized vertex method and hybrid reliability. 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver. 2002: 1465, https://doi.org/10.2514/6.2002....
32.
Song J, Lu Z Z. Moment method for general failure probability with fuzzy failure state and fuzzy safety state. Engineering Mechanics 2008; 25(2): 71-77.
33.
Terán P. Probabilistic foundations for measurement modelling with fuzzy random variables. Fuzzy Sets & Systems 2007; 158(9): 973-986, https://doi.org/10.1016/j.fss.....
34.
Willner K, Möller B, Beer M. Fuzzy Randomness. Uncertainty in civil engineering and computational mechanics. Computational Mechanics 2005; 36(1): 83-83, https://doi.org/10.1007/s00466....
35.
Wang Z L, Huang H Z. An approach to system reliability analysis with fuzzy random variables. Mechanism and Machine Theory 2012; 52: 35-46, https://doi.org/10.1016/j.mech....
36.
Xu W L, Zhang Q X. Probabilistic analysis and Monte Carlo Simulation of the kinematic error in a spatial linkage. Mechanism and Machine Theory 1989; 24(1): 19-27, https://doi.org/10.1016/0094-1....
37.
Zavadskas E K, Vaidogas E R. Multiattribute selection from alternative designs of infrastructure components for accidental situations. Computer‐aided Civil & Infrastructure Engineering 2010; 24(5): 346-358, https://doi.org/10.1111/j.1467....
38.
Zhang L, Sheng D, Dong Z X. Application of direct integration method in breakwater reliability analysis. Ocean Engineering 2011; 29(4): 103-107.
39.
Zhao G T, Dong Y G, Song Z Y. Random reliability analysis based on the fuzzy theory. Journal of Hefei University of Technology 2010; 33(2): 249-253.
40.
Zhao Y G, Ono T. A general procedure for first/second-order reliability method (FORM/SORM). Journal of Structural Engineering 1999; 21(2): 95-112, https://doi.org/10.1016/S0167-....
41.
Zheng J M, Wang G Z. Perturbing Bézier coefficients for best constrained degree reduction in the L 2 -norm. Graphical Models 2003; 65(6):351-368, https://doi.org/10.1016/j.gmod....
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| eISSN: | 2956-3860 |
| ISSN: | 1507-2711 |
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