A hybrid relaxed first-order reliability method for efficient structural reliability analysis

2017 ◽  
Vol 66 ◽  
pp. 84-93 ◽  
Author(s):  
Behrooz Keshtegar ◽  
Zeng Meng
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
First Order Reliability Method ◽  
First Order ◽  
Structural Reliability Analysis ◽  
Reliability Method

First-Order Reliability Method for Structural Reliability Analysis in the Presence of Random and Interval Variables

2015 ◽  
Vol 1 (4) ◽  
Author(s):  
Umberto Alibrandi ◽  
C. G. Koh
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Computational Cost ◽  
Computational Effort ◽  
Stochastic Dynamic ◽  
First Order Reliability Method ◽  
First Order ◽  
Structural Reliability Analysis ◽  
Reliability Method

This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis in the presence of random parameters and interval uncertain parameters. In the proposed formulation, the hybrid problem is reduced to standard reliability problems, where the limit state functions are defined only in terms of the random variables. Monte Carlo simulation (MCS) for hybrid reliability analysis (HRA) is presented, and it is shown that it requires a tremendous computational effort; FORM for HRA is more efficient but still demanding. The computational cost is significantly reduced through a simplified procedure, which gives good approximations of the design points, by requiring only three classical FORMs and one interval analysis (IA), developed herein through an optimization procedure. FORM for HRA and its simplified formulation achieve a much improved efficiency than MCS by several orders of magnitude, and it can thus be applied to real-world engineering problems. Representative examples of stochastic dynamic analysis and performance-based engineering are presented.

scholarly journals An Adaptive First-Order Reliability Analysis Method for Nonlinear Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zhiming Wang ◽  
Yafei Zhang ◽  
Yalong Song
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Nonlinear Problems ◽  
Iteration Step ◽  
Step Size ◽  
First Order Reliability Method ◽  
First Order ◽  
Highly Nonlinear ◽  
Reliability Method ◽  
Solution Efficiency

The HL-RF algorithm of the first-order reliability method (FORM) is a widely useful tool in structural reliability analysis. However, the iteration results of HL-RF algorithm may not converge due to periodic cycles for some highly nonlinear reliability problems. In this paper, an adaptive first-order reliability method (AFORM) is proposed to improve solution efficiency for some highly nonlinear reliability problems by introducing an adaptive factor. In AFORM, based on the two-parameter approximate first-order reliability method, the new iteration point and the previous iteration point are used to obtain the corresponding angle, and the result of convergence is judged by angle condition. According to the convergence degree of the results, two iteration parameters of the approximate reliability method are adjusted continuously by adaptive factor. Moreover, iteration step size is adjusted by changing the parameters to improve the efficiency and robustness of FORM. Finally, four numerical examples and one mechanical reliability analysis example are used to verify the proposed method. Compared with the different algorithms, the results show that AFORM has better efficiency and robustness for some highly nonlinear reliability problems.

An accuracy analysis method for first-order reliability method

2018 ◽  
Vol 233 (12) ◽  
pp. 4319-4327 ◽  
Author(s):  
Zhenzhong Chen ◽  
Zihao Wu ◽  
Xiaoke Li ◽  
Ge Chen ◽  
Guangfeng Chen ◽  
...  
Keyword(s):  
Structural Reliability ◽  
Nonlinear Problems ◽  
Accuracy Analysis ◽  
Analysis Method ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Level ◽  
Reliability Method ◽  
Value Range ◽  
Crashworthiness Design

The first-order reliability method is widely used for structural reliability analysis; however, its accuracy would become worse for nonlinear problems. This paper proposes the accuracy analysis method of the first-order reliability method, which considers the worst cases when using the first-order reliability method and gives the possible value range of the probability of safety. The accuracy analysis method can evaluate the reliability level of the first-order reliability method when the failure surfaces are nonlinear. The calculation formula for the possible value range of the probability of safety is proposed, and its trend as the dimensions and reliability rise is also discussed in this paper. A numerical example and a honeycomb crashworthiness design are presented to validate the accuracy of the first-order reliability method, and the results show that they are located within the possible value range proposed in this paper.

Reliability analysis of corroded pipelines: Novel adaptive conjugate first order reliability method

2019 ◽  
Vol 62 ◽  
pp. 103986 ◽  
Author(s):  
Behrooz Keshtegar ◽  
Mohamed El Amine Ben Seghier ◽  
Shun-Peng Zhu ◽  
Rouzbeh Abbassi ◽  
Nguyen-Thoi Trung
Keyword(s):  
Reliability Analysis ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method

scholarly journals A decoupling algorithm with first-order asymptotic integration for reliability-based design optimization

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401879333 ◽  
Author(s):  
Zhiliang Huang ◽  
Tongguang Yang ◽  
Fangyi Li
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Optimization Problems ◽  
Asymptotic Integration ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Based Design ◽  
Reliability Method

Conventional decoupling approaches usually employ first-order reliability method to deal with probabilistic constraints in a reliability-based design optimization problem. In first-order reliability method, constraint functions are transformed into a standard normal space. Extra non-linearity introduced by the non-normal-to-normal transformation may increase the error in reliability analysis and then result in the reliability-based design optimization analysis with insufficient accuracy. In this article, a decoupling approach is proposed to provide an alternative tool for the reliability-based design optimization problems. To improve accuracy, the reliability analysis is performed by first-order asymptotic integration method without any extra non-linearity transformation. To achieve high efficiency, an approximate technique of reliability analysis is given to avoid calculating time-consuming performance function. Two numerical examples and an application of practical laptop structural design are presented to validate the effectiveness of the proposed approach.

scholarly journals An improved approach by introducing copula functions for structural reliability analysis under hybrid uncertainties

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878583 ◽  
Author(s):  
Zheng Liu ◽  
Xin Liu
Keyword(s):  
Probability Theory ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Field Tests ◽  
Copula Function ◽  
Working Environment ◽  
Imprecise Probability ◽  
Copula Functions ◽  
Structural Reliability Analysis ◽  
Reliability Method

The structural composition of the oil platform is very complicated, and its working environment is harsh, thus conducting a large number of reliability tests is not feasible, and the field tests are also hard to accomplish. So the reliability of the oil platform cannot be analyzed and calculated by the traditional reliability method which needs a lot of test data, and new methods should be studied. In recent years, imprecise probability theory has attracted more and more attention because when unified, it can quantify hybrid uncertainty. Structural reliability analysis on the basis of imprecise probability theory has made remarkable achievements in theoretical aspects, but it is scarcely used in practical engineering domains due to the complexity in the developed methods and the unavailability of suitable or specific modeling steps for applications. In this regard, we propose a unified quantification method for statistical data, fuzzy data, incomplete information, and the like, which can handle the issue of hybrid uncertainties, and then, we construct an improved imprecise structural reliability model aiming at the practical problems by introducing copula function. To verify the existing methodology, we also consider a cantilever beam widely applied in the oil platform here for the structural reliability analysis.

Neural network approach to model the limit state surface for reliability analysis

2003 ◽  
Vol 40 (6) ◽  
pp. 1235-1244 ◽  
Author(s):  
Anthony TC Goh ◽  
Fred H Kulhawy
Keyword(s):  
Neural Network ◽  
Reliability Index ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
First Order Reliability Method ◽  
First Order ◽  
The Neural Network ◽  
Reliability Method ◽  
Geotechnical Structures

Structural reliability methods are often used to evaluate the failure performance of geotechnical structures. A common approach is to use the first-order reliability method. Its popularity results from the mathematical simplicity of the method, since only second moment information (mean and coefficient of variation) on the random variables is required. The probability of failure is then assessed by an index known commonly as the reliability index. One critical aspect in determining the reliability index is the explicit definition of the limit state surface of the system. In a problem involving multi-dimensional random variables, the limit state surface is the boundary separating the safe domain from the "failure" (or lack of serviceability) domain. In many complicated and nonlinear problems where the analyses involve the use of numerical procedures such as the finite element method, this surface may be difficult to determine explicitly in terms of the random variables, and therefore the limit state can only be expressed implicitly rather than in a closed-form solution. It is proposed in this paper to use an artificial intelligence technique known as the back-propagation neural network algorithm to model the limit state surface. First, the failure domain is found through repeated point-by-point numerical analyses with different input values. The neural network is then trained on this set of data. Using the optimal weights of the neural network connections, it is possible to develop a mathematical expression relating the input and output variables that approximates the limit state surface. Some examples are given to illustrate the application and accuracy of the proposed approach.Key words: first-order reliability method, geotechnical structures, limit state surface, neural networks, reliability.

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