Structural reliability analysis based on random distributions with interval parameters

Jiang, Chao; Li, W. X.; Han, Xu; Liu, L. X.; Lé, Pierre

doi:10.1016/j.compstruc.2011.08.006

Cited by 161 publications

(63 citation statements)

References 29 publications

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“…Notably, the distributions of random variables are varied and include the uniform, Weibull, and normal distributions. The normal distribution is among the most widely used ones, and other distributions can be converted into it using a certain approach [25,26]. The most commonly used transformation is given by Rosenblatt [27] as…”

Section: Newmentioning

confidence: 99%

A New Sampling Approach for Response Surface Method Based Reliability Analysis and Its Application

Meng

Jing

Zhang

et al. 2014

Advances in Mechanical Engineering

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A response surface method based on the all sample point interpolation approach (ASPIA) is proposed to improve the efficiency of reliability computation. ASPIA obtains new sample points through linear interpolation. These new sample points are occasionally extremely dense, thus easily generating an ill-conditioned problem for approximation functions. A mobile most probable failure point strategy is used to solve this problem. The advantage of the proposed method is proven by two numerical examples. With the ASPIA, the approximated process can rapidly approach the actual limit equation with accuracy. Additionally, there are no difficulties in applying the proposed ASPIA to the response surface model with or without cross terms. Solution results for the numerical examples indicate that the use of the response surface function with cross terms increases time cost, but result accuracy cannot be improved significantly. Finally, the proposed method is successfully used to analyze the reliability of the hydraulic cylinder of a forging hydraulic press by combining MATLAB and ANSYS software. The engineering example confirms the practicality of this method.

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Section: Newmentioning

confidence: 99%

A New Sampling Approach for Response Surface Method Based Reliability Analysis and Its Application

Meng

Jing

Zhang

et al. 2014

Advances in Mechanical Engineering

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“…If there is to be any negative value, it can be amended by the methods in Zhang et al 30,31 With respect to a complicated structure with both random and interval variables, according to the monotony of the function, 32 the upper limits and the lower limits of the cumulative distribution function F(g) and the probability density function f (g) may be expressed as follows…”

Section: Edgeworth Seriesmentioning

confidence: 99%

Hybrid reliability analysis of structural fatigue life: Based on Taylor expansion method

Meng

Feng

Zhou

et al. 2016

Advances in Mechanical Engineering

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A new method for computing the failure probability of the fatigue life is proposed, dealing with uncertain problems with both random and interval variables. Using a Taylor expansion and the concept of statistical moment, the first four central moments of the structural fatigue life performance function are obtained. Then, using a second Taylor expansion, the first four central moments are expanded at the midpoint of the interval variable, and the intervals of the statistical moments of the performance function are calculated. The obtained moment information is applied into an Edgeworth series expansion expression, giving the cumulative distribution function of the structural fatigue life performance function and getting its interval of the failure probability. Two numerical examples of growing complexity are employed to demonstrate the feasibility of the proposed approach.

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“…Nowadays, interval reliability-based design optimization has become a research hotspot of structural optimization (Wang et al, 2008;Du, 2012;Elishakoff et al, 2013;Jiang et al, 2013). For example, Jiang et al (2011) developed a new reliability analysis technique for uncertain structures based on random distributions with interval parameters. Guo et al (2001; presented a non-probabilistic model of structural reliability based on interval analysis and described the procedures for computing the interval reliability index.…”

Section: Introductionmentioning

confidence: 99%

Direct reliability-based design optimization of uncertain structures with interval parameters

Cheng

Tang

Liu

et al. 2016

J. Zhejiang Univ. Sci. A

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Abstract:In order to enhance the reliability of an uncertain structure with interval parameters and reduce its chance of function failure under potentially critical conditions, an interval reliability-based design optimization model is constructed. With the introduction of a unified formula for efficiently computing interval reliability, a new concept of the degree of interval reliability violation (DIRV) and the DIRV-based preferential guidelines are put forward for the direct ranking of various design vectors. A direct interval optimization algorithm integrating a nested genetic algorithm (GA) and the Kriging technique is proposed for solving the interval reliability-based design model, which avoids the complicated model transformation process in indirect ones and yields an interval solution that provides more insights into the optimization problem. The effectiveness of the proposed algorithm is demonstrated by a numeric example. Finally, the proposed direct reliability-based design optimization method is applied to the optimization of a press upper beam with interval uncertain parameters, the results of which demonstrate its feasibility and effectiveness in engineering.

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Structural reliability analysis based on random distributions with interval parameters

Cited by 161 publications

References 29 publications

A New Sampling Approach for Response Surface Method Based Reliability Analysis and Its Application

A New Sampling Approach for Response Surface Method Based Reliability Analysis and Its Application

Hybrid reliability analysis of structural fatigue life: Based on Taylor expansion method

Direct reliability-based design optimization of uncertain structures with interval parameters

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