scholarly journals A Comparative Study of First-Order Reliability Method-Based Steepest Descent Search Directions for Reliability Analysis of Steel Structures

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Hamed Makhduomi ◽  
Behrooz Keshtegar ◽  
Mehdi Shahraki
Keyword(s):  
Reliability Index ◽  
Steel Structures ◽  
Steepest Descent ◽  
Building Code ◽  
Step Size ◽  
First Order Reliability Method ◽  
First Order ◽  
Confidence Levels ◽  
Reliability Method ◽  
Bending Capacity

Three algorithms of first-order reliability method (FORM) using steepest descent search direction are compared to evaluate the reliability index of structural steel problems which are designed by the Iranian National Building code. The FORM formula is modified based on a dynamic step size which is computed based on the merit functions named modified Hasofer-Lind and Rackwitz-Fiessler (MHL-RF) method. The efficiency of the gradient, HL-RF, and MHL-RF method was compared for a bar structure under tensile capacity, a multispan beam under bending capacity, a connection under tension load, and a column under axial force. The results illustrated that the MHL-RF method is more efficient than the HL-RF and gradient method. The designed steel components by the Iranian National Building code showed good confidence levels with the reliability index in the range from 2.5 to 3.0.

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.

scholarly journals Hybrid Approach to the First Order Reliability Method in the Reliability Analysis of a Spatial Structure

2021 ◽  
Vol 11 (2) ◽  
pp. 648
Author(s):  
Agnieszka Dudzik ◽  
Beata Potrzeszcz-Sut
Keyword(s):  
Reliability Analysis ◽  
Reliability Index ◽  
Limit State ◽  
Hybrid Approach ◽  
Reference Method ◽  
Transformation Method ◽  
State Function ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method

The objective of the article involves presenting two approaches to the structure reliability analysis. The primary research method was the First Order Reliability Method (FORM). The Hasofer–Lind reliability index β in conjunction with transformation method in the FORM was adopted as the measure of reliability. The first proposal was combining NUMPRESS software with the non-commercial KRATA program. In this case, the implicit form of the random variables function was created. Limit state function was symbolically given in the standard math notation as a function of the basic random and external variables. The second analysis proposed a hybrid approach enabling the introduction of explicit forms of limit state functions to the reliability program. To create the descriptions of this formula, the neural networks were used and our own original FEM module. The combination of conventional and neural computing can be seen as a hybrid system. The explicit functions were implemented into NUMPRESS software. The values of the reliability index for different descriptions of the mathematical model of the structure were determined. The proposed hybrid approach allowed us to obtain similar results to the results from the reference method.

scholarly journals The Impact of Node Location Imperfections on the Reliability of Single-Layer Steel Domes

2019 ◽  
Vol 9 (13) ◽  
pp. 2742 ◽  
Author(s):  
Paweł Zabojszcza ◽  
Urszula Radoń
Keyword(s):  
Reliability Index ◽  
Single Layer ◽  
Random Variable ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method ◽  
Node Location ◽  
Academy Of Sciences ◽  
The Impact ◽  
Layer Steel

This study is an attempt to assess the effect of node location imperfections on the reliability dome. The analysis concerns a single-layer steel lattice dome that is very sensitive to node snap-through. The load-displacement path of the structure was determined using the program, Finite Element Method-Krata. To determine the failure probability, reliability index, and elasticity index, the first-order reliability method approximation method was employed. The reliability analysis was conducted with Numpress Explore software, developed at the Institute of Fundamental Technological Research of the Polish Academy of Sciences, Warsaw. In this paper, it is shown how large differences in the assessment of the safety of a structure can appear when we incorrectly estimate the standard deviation of the random variable responsible for the imperfections of node locations.

An improved first order reliability method based on modified Armijo rule and interpolation-based backtracking scheme

2020 ◽  
pp. 1748006X2095989
Author(s):  
Sheng-Tong Zhou ◽  
Di Wang ◽  
Qian Xiao ◽  
Jian-min Zhou ◽  
Hong-Guang Li ◽  
...  
Keyword(s):  
Structural Reliability ◽  
Limit State ◽  
Initial Step ◽  
State Function ◽  
Computationally Efficient ◽  
Step Size ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method ◽  
Initial Step Size

Hasofer-Lind and Rackwtiz-Fiessler (HLRF) method is an efficient iterative algorithm for locating the most probable failure point and calculating the first order reliability index in structural reliability analysis. However, this method may encounter numerical instability problems for high nonlinear limit state function (LSF). In this paper, an improved HLRF-based first order reliability method is developed based on a modified Armijo line search rule and an interpolation-based step size backtracking scheme to improve the robustness and efficiency of the original HLRF method. Compared with other improved HLRF-based methods, the proposed method can not only guarantee the global convergence but also adaptively estimate some sensitive algorithm parameters, such as initial step size, step-size reduction coefficient, using the current known iterative information. Ten selected examples with high nonlinear LSFs are used to compare the robustness and efficiency of the proposed method with the original HLRF method and the improved HLRF (iHLRF) method. Results indicate that the proposed method is not only more computationally efficient but also less sensitive to the remaining user-defined algorithm parameters than the iHLRF method.

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.

scholarly journals Analysis of reliability of compressed masonry structures

2020 ◽  
Vol 10 (1) ◽  
pp. 462-468
Author(s):  
Joanna Zięba ◽  
Izabela Skrzypczak
Keyword(s):  
Compressive Strength ◽  
Reliability Index ◽  
Masonry Structure ◽  
Masonry Structures ◽  
First Order Reliability Method ◽  
First Order ◽  
Adequate Level ◽  
Reliability Method ◽  
Partial Factor ◽  
The Relationship

AbstractDesigning masonry structures or any other structures involves ensuring an adequate level of safety. This is done by applying the appropriate set of partial factor for strength and partial factors for actions in accordance with the recommendations of the Eurocodes. The paper presents an analysis of the reliability of a compressive masonry structure on the example of a wall fragment made of silicate blocks. The relationship between partial factors applied to actions in various configurations and factors for the compressive strength of masonry was investigated. The analyses consisted in determining the reliability index β using the First Order Reliability Method (FORM). The results are presented in diagrams with reference to different construction classes execution of works, as well as different reliability classes from RC1 to RC3.

Some Important Issues on First-Order Reliability Analysis With Nonprobabilistic Convex Models

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
C. Jiang ◽  
G. Y. Lu ◽  
X. Han ◽  
R. G. Bi
Keyword(s):  
Reliability Analysis ◽  
Reliability Index ◽  
Probability Model ◽  
Mean Value ◽  
Convex Model ◽  
First Order ◽  
Reliability Method ◽  
Complex Engineering ◽  
Mean Value Method ◽  
Form Type

Compared with the probability model, the convex model approach only requires the bound information on the uncertainty, and can make it possible to conduct the reliability analysis for many complex engineering problems with limited samples. Presently, by introducing the well-established techniques in probability-based reliability analysis, some methods have been successfully developed for convex model reliability. This paper aims to reveal some different phenomena and furthermore some severe paradoxes when extending the widely used first-order reliability method (FORM) into the convex model problems, and whereby provide some useful suggestions and guidelines for convex-model-based reliability analysis. Two FORM-type approximations, namely, the mean-value method and the design-point method, are formulated to efficiently compute the nonprobabilistic reliability index. A comparison is then conducted between these two methods, and some important phenomena different from the traditional FORMs are summarized. The nonprobabilistic reliability index is also extended to treat the system reliability, and some unexpected paradoxes are found through two numerical examples.

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