Structural reliability analysis with fuzzy random variables using error principle

Abstract In structural reliability calculation, there are fuzzy uncertainties in the distribution parameters of random variables, which bring the problem of large computation and poor precision. In order to improve the accuracy and efficiency of structural reliability, a novel structural reliability calculation method with fuzzy random variables is proposed from the perspective of error propagation. Firstly, fuzzy variables are transformed into uncertain interval variables according to the fuzzy decomposition theorem. Secondly, by using the error transfer principle, the s i g k . function is introduced into the reliability function to approximate the step function, and a structural reliability error analysis model based on the direct integration method is established. On this basis, the equivalent error of the fuzzy variable is determined by traversing the interval value of the membership function at [0, 1] level cut set, and then the structural reliability interval values corresponding to each cut set are obtained. The examples are investigated to demonstrate the efficiency and accuracy of the proposed method, which provides a feasible way to analyze and calculate the structural reliability with uncertain variables such as fuzzy random variables, random variables and fuzzy variables.

[1]  Dian-Qing Li,et al.  Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables , 2011 .

[2]  Song Zhi-yan.  Random reliability analysis based on the fuzzy theory , 2010 .

[3]  Yan-Gang Zhao,et al.  A general procedure for first/second-order reliabilitymethod (FORM/SORM) , 1999 .

[4]  Yan-Gang Zhao,et al.  Third-Moment Standardization for Structural Reliability Analysis , 2000 .

[5]  Song Jun.  MOMENT METHOD FOR GENERAL FAILURE PROBABILITY WITH FUZZY FAILURE STATE AND FUZZY SAFETY STATE , 2008 .

[6]  Guo Shu,et al.  A non-probabilistic model of structural reliability based on interval analysis , 2001 .

[7]  Huibert Kwakernaak,et al.  Fuzzy random variables - I. definitions and theorems , 1978, Inf. Sci..

[8]  BI Wei-hua.  Fuzzy random finite element reliability analysis of slope stability , 2009 .

[9]  Yan-Gang Zhao,et al.  Second-Order Third-Moment Reliability Method , 2002 .

[10]  Dian-Qing Li,et al.  A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties , 2015 .

[11]  Xu Han,et al.  A novel evidence-theory-based reliability analysis method for structures with epistemic uncertainty , 2013 .

[12]  Rafi L. Muhanna,et al.  Reliability Assessment with Fuzzy Random Variables Using Interval Monte Carlo Simulation , 2014, Comput. Aided Civ. Infrastructure Eng..

[13]  Unyime O. Akpan,et al.  Practical fuzzy finite element analysis of structures , 2001 .

[14]  R. Rackwitz.  Reliability analysis—a review and some perspectives , 2001 .

[15]  Fei Chen,et al.  Failure Mode Analysis on Machining Center Based on Possibility Theory , 2016 .

[16]  Cui Li.  RELIABILITY MEASURE AND ITS SOLUTION BASED ON RANDOM AND FUZZY DISTRIBUTION PARAMETERS , 2011 .

[17]  Luuk Franssen,et al.  Reliability of the compensation comparison method for measuring retinal stray light studied using Monte-Carlo simulations. , 2006, Journal of biomedical optics.

[18]  Qiu Zhiping,et al.  Reliability analysis of structures with fuzzy and non-probabilistic hybrid variables , 2014 .

[19]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[20]  Chao Jiang,et al.  A non-probabilistic structural reliability analysis method based on a multidimensional parallelepiped convex model , 2014 .

[21]  Zhang Xiang-dong.  Application of direct integration method in breakwater reliability analysis , 2011 .

[22]  Hong-Zhong Huang,et al.  An approach to system reliability analysis with fuzzy random variables , 2012 .

[23]  Qiu Zhiping.  NON-PROBABILITY RELIABILITY OPTIMIZATION DESIGN FOR STRUCTURES WITH FUZZY AND INTERVAL VARIABLES , 2013 .