Refined second-order reliability analysis

Cai, Guorong; Elishakoff, Isaac

doi:10.1016/0167-4730(94)90015-9

Cited by 133 publications

(50 citation statements)

References 8 publications

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“…Tvedt [18] proposed a three-term approximation in which the last two terms can be interpreted as correctors to Breitung's form. More accurate closed form formulas were derived using Maclaurin series expansion and Taylor series expansion [19] [20]. These formulas generally work well in the case of a large curvature radius and a small number of random variables.…”

Section: Second-order Reliability Methods (Sorm)mentioning

confidence: 99%

Overview of Structural Reliability Analysis Methods — Part I : Local Reliability Methods

Huang¹,

Hami²,

Radi³

2017

IncertFia

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ABSTRACT. Our work presents an overview of structural reliability analysis, which plays important roles in structural design. In Part I of the overview, the so-called local reliability methods are summarized. The term "local reliability methods" refers to reliability analysis methods that use the local approximate of actual limit state function in calculation of failure probability. From this perspective of view, the mean value first-order second moment (MVFOSM) method, design pointbased methods (FORM/SORM and RSM) are included in local reliability methods. Local reliability methods are basic approaches for reliability analysis and commonly used in research and applications.

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Section: Second-order Reliability Methods (Sorm)mentioning

confidence: 99%

Overview of Structural Reliability Analysis Methods — Part I : Local Reliability Methods

Huang¹,

Hami²,

Radi³

2017

IncertFia

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“…To alleviate this problem, many recent researches were aimed at using more accurate approximations and efficient search methods. These techniques cover Monte Carlo Method based on first-and second-order approximations to the failure region (Sweeting and Finn 1992), refined second-order reliability analysis (Cai and Elishakoff 1994), first-order third-moment reliability method (Tichy 1994), SOP~M (second-order reliability method) integrals based on new and simple closed form approximations (Koyluoglu and Nielsen 1994), physical and normal spaces (Lin and Khalessi 1993), the simplified safety index algorithm (l~eddy et al 1994), the advanced mean value (AMV) procedure (Wu et al 1990), etc. Earlier developed a safety index algorithm utilizing the nonlinear approximation of the performance function (g-function) in original space (X-space) of random variables.…”

Section: Introductionmentioning

confidence: 99%

Intervening variables and constraint approximations in safety index and failure probability calculations

Wang

Grandhi

1995

Structural Optimization

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The emphasis of this paper is on developing suitable intervening variables and constraint approximations for structural reliability analysis. Traditionally, these procedures are used in structural optimization, whereas this research work adopts these concepts to safety index and failure probability computations. The use of these concepts enables the development of an efficient and stable iteration algorithm for identifying the most probable failure points (MPPs) of the limit state functions. An approximate second-order failure probability is calculated at this MPP with no extra computations of the limit state function and gradients. The efficiency and accuracy of the proposed algorithm are demonstrated by several examples with highly nonlinear, complex, explicit/implicit performance functions.

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“…In addition, ( 1,2) i i D are independent random variables with Beta distribution, of which the probability density function is written as The failure probability of the random beam is computed by four methods, i.e., FORM, SORM, OSFEM-P, DMC. the results of failure probability calculated by these four methods are listed in Table 1.…”

Section: Figure 1 Random Continuous Beammentioning

confidence: 99%

“…Since multiple probability factors existed in the safety analysis of structural component or system, a multi-fold integral needs to be calculated to obtain the failure probability of the structure. However, even if the performance function is explicit, the nonlinearity of the function and the non-Gaussian distribution of random variables always make it impossible to obtain the exact solution of this multi-fold integral [1], [2]. Various methods have been used to analyze the failure probability of structures subjected to random material parameters, such as the first-and second-order reliability methods (FORM/SORM) [3], [4], the simulation methods [5]- [7], the traditional perturbation stochastic finite element methods (PSFEM) [8], [9], the response surface method [10], [11], and so on.…”

Section: Introductionmentioning

confidence: 99%

Structural Reliability Analysis Using Orthogonalizable Power Polynomial Basis Vector

Huang

2017

MATEC Web Conf.

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Abstract.A new method for structural reliability analysis using orthogonalizable power polynomial basis vector is presented. Firstly, a power polynomial basis vector is adopted to express the initial series solution of structural response, which is determined by a series of deterministic recursive equation based on perturbation technique, and then transferred to be a set of orthogonalizable power polynomial basis vector using the orthogonalization technique. By conducting Garlekin projection, an accelerating factor vector of the orthogonalizable power polynomial expansion is determined by solving small scale algebraic equations. Numerical results of a continuous bridge structure on reliability analysis shows that the proposed method can achieve the accuracy of the Direct Monte Carlo method and can save a lot of computation time at the same time, it is both accurate and efficient, and is very competitive to be used in structural reliability analysis.

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Refined second-order reliability analysis

Cited by 133 publications

References 8 publications

Overview of Structural Reliability Analysis Methods — Part I : Local Reliability Methods

Overview of Structural Reliability Analysis Methods — Part I : Local Reliability Methods

Intervening variables and constraint approximations in safety index and failure probability calculations

Structural Reliability Analysis Using Orthogonalizable Power Polynomial Basis Vector

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