The Comparison of Methods of Assessing the Reliability of the Steel Frame

2015 ◽  
Vol 797 ◽  
pp. 11-18
Author(s):  
Agnieszka Dudzik ◽  
Urszula Radoń
Keyword(s):  
Reliability Index ◽  
Limit State ◽  
Probabilistic Approach ◽  
Random Variables ◽  
Random Variable ◽  
Design Parameters ◽  
Variable Sensitivity ◽  
Index Sensitivity ◽  
The Impact ◽  
The Mathematical Model

The study presents a probabilistic approach to the problems of static analysis of a steel building. Structural design parameters were defined as deterministic values and random variables. The latter were not correlated. The criterion of structural failure is expressed by limit functions related to the ultimate and serviceability limit state. The description of limit functions by the Mathematica program was generated. The Hasofer-Lind index was used as a reliability measure. In the description of random variables were used the normal distribution and, for comparison, different types of probability distribution appropriate to the nature of the variable. Sensitivity of reliability index to the random variables was defined. If the reliability index sensitivity due to the random variable Xi is low when compared with other variables, it can be stated that the impact of this variable on failure probability is small. Therefore, in successive computations it can be treated as a deterministic parameter. Sensitivity analysis leads to simplify the description of the mathematical model, determine the new limit functions and values of the Hasofer-Lind reliability index. The primary research method is the FORM method. In order to verify the correctness of the calculation SORM, Monte Carlo and Importance Sampling methods were used. In the examples of reliability analysis the STAND program was used.

scholarly journals The Evaluation Of Algorithms For Determination Of The Reliability Index

2015 ◽  
Vol 61 (3) ◽  
pp. 133-147 ◽  
Author(s):  
A. Dudzik ◽  
U. Radoń
Keyword(s):  
Reliability Index ◽  
Limit State ◽  
Probabilistic Approach ◽  
Random Variables ◽  
Numerical Procedure ◽  
Vertical Displacement ◽  
Design Parameters ◽  
State Function ◽  
Structural Failure

AbstractThe study deals with stability and dynamic problems in bar structures using a probabilistic approach. Structural design parameters are defined as deterministic values and also as random variables, which are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier and condition of non-exceeding the admissible vertical displacement. The Hasofer-Lind index was used as a reliability measure. The primary research tool is the FORM method. In order to verify the correctness of the calculations Monte Carlo and Importance Sampling methods were used. The sensitivity of the reliability index to the random variables was defined. The limit state function is not an explicit function of random variables. This dependence was determined using a numerical procedure, e.g. the finite element methods. The paper aims to present the communication between the STAND reliability analysis program and the KRATA and MES3D external FE programs.

scholarly journals The proposal of explicit account of the random character of design process parameters

2013 ◽  
Vol 12 (1) ◽  
pp. 219-226
Author(s):  
Agnieszka Dudzik ◽  
Urszula Radoń
Keyword(s):  
Structural Design ◽  
Reliability Index ◽  
Research Method ◽  
Sampling Methods ◽  
Limit State ◽  
Random Variables ◽  
Design Parameters ◽  
Structural Failure ◽  
Primary Research ◽  
Random Character

The study concerns the static analysis of rods structures in terms of probabilism. Structural design parameters are defined as the deterministic values and random variables. Random variables are not correlated. The criterion for structural failure is expressed the limits of functions referring to the ultimate and serviceability limit state. The Cornell and Hasofer-Lind index is used as a reliability measure. The primary research method is the FORM method. In order to verify the correctness of the calculation SORM, Monte Carlo and Importance Sampling methods are used. The sensitivity of reliability index to the random variables is defined. The STAND program is used to present the examples of reliability analysis.

Reliability Methods for Bimodal Distribution With First-Order Approximation1

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Zhangli Hu ◽  
Xiaoping Du
Keyword(s):  
Probability Density ◽  
Order Approximation ◽  
Limit State ◽  
Random Variables ◽  
Random Variable ◽  
State Function ◽  
First Order ◽  
Reliability Method ◽  
Reliability Methods ◽  
Basic Random Variable

In traditional reliability problems, the distribution of a basic random variable is usually unimodal; in other words, the probability density of the basic random variable has only one peak. In real applications, some basic random variables may follow bimodal distributions with two peaks in their probability density. When binomial variables are involved, traditional reliability methods, such as the first-order second moment (FOSM) method and the first-order reliability method (FORM), will not be accurate. This study investigates the accuracy of using the saddlepoint approximation (SPA) for bimodal variables and then employs SPA-based reliability methods with first-order approximation to predict the reliability. A limit-state function is at first approximated with the first-order Taylor expansion so that it becomes a linear combination of the basic random variables, some of which are bimodally distributed. The SPA is then applied to estimate the reliability. Examples show that the SPA-based reliability methods are more accurate than FOSM and FORM.

scholarly journals Simulation Technique of Kinematic Processes in the Vehicle Steering Linkage

2018 ◽  
Vol 7 (4.3) ◽  
pp. 120 ◽  
Author(s):  
Sergii Chernenko ◽  
Eduard Klimov ◽  
Andrii Chernish ◽  
Olexandr Pavlenko ◽  
Volodymyr Kukhar
Keyword(s):  
Three Dimensional ◽  
Simulation Technique ◽  
Design Parameters ◽  
Three Dimensional Model ◽  
Design Data ◽  
Power Characteristics ◽  
Left And Right ◽  
Turning Radius ◽  
The Impact ◽  
The Mathematical Model

The results of the investigation of the turning kinematics of the steerable wheels of the KrAZ-7634NE off-road vehicle with a wheel formula 8x8 and two front steer axles are given. The theoretical relations between the steer angles of the steerable wheels on the basis of the scheme of double-axle steering turning of the vehicle are shown. The mathematical model of flat four-bar vehicle steering linkage is developed, it determines the relation between the steering linkage left and right steering arms turning angles at any turning radius of the vehicle. KrAZ-7634HE steering three-dimensional model was created and simulation technique of its work was carried out using Creo software. It has been shown that the flat steering linkage model provides sufficient accuracy of calculations in analysis of turning kinematics. The design data can be used for any vehicles that have a similar steering linkage, they allow to analyze the impact of the vehicle design parameters on the turning kinematics and optimize them. Further study of the impact of the kingpin inclinations on the steering linkage kinematic and power characteristics are required.  

scholarly journals Analysis of Basic Failure Scenarios of a Truss Tower in a Probabilistic Approach

2019 ◽  
Vol 9 (13) ◽  
pp. 2662 ◽  
Author(s):  
Wojciech Mochocki ◽  
Urszula Radoń
Keyword(s):  
Standard Deviation ◽  
Reliability Analysis ◽  
System Reliability ◽  
Probabilistic Approach ◽  
Random Variable ◽  
Structure Reliability ◽  
System Reliability Analysis ◽  
Steel Truss ◽  
Buckling Coefficient ◽  
The Impact

This paper concerns the system reliability analysis of steel truss towers. Due to failures of towers, the assessment of their reliability seems to be a very important problem. In the analysis, two cases are examined: when the buckling coefficient is a deterministic value and when it is a random variable. The impact of failures of single elements on the structure reliability was investigated. Calculations of the standard deviation of the capacity and reliability indexes were made using author-developed programs in the Mathematica environment.

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.

A Probabilistic Approach for Determining the Component’s Dimension Under Fatigue Loadings

2009 ◽  
Author(s):  
Xiaobin Le ◽  
Jahan Rasty
Keyword(s):  
Fatigue Test ◽  
Test Data ◽  
Probabilistic Approach ◽  
Random Variables ◽  
Random Variable ◽  
Design Equation ◽  
Probabilistic Design ◽  
Material Fatigue ◽  
Stress Levels ◽  
Design Scenario

Due to inherent scatters in fatigue test data, the P-S-N curves are normally used to describe material fatigue behaviors. For probabilistic component’s design under fatigue loadings, the component’s dimension should be treated as a random variable because every dimension is certainly with a dimension tolerance. In this design scenario, it is difficult to determine the component’s dimension under fatigue loadings by using the P-S-N curves because stress levels are unknown and random variables. In this paper, a probabilistic approach is presented to build a generic probabilistic design equation which is governed by random variables related to material fatigue behaviors, component conditions and fatigue loadings. The generic probabilistic design equation can be used to determine component’s dimension with a given reliability. One example is presented for explaining the approach in details.

Matrix Algorithm for Reliability of Structure in Generalized Random Space

2012 ◽  
Vol 166-169 ◽  
pp. 1913-1916
Author(s):  
Xiao Jie Liu ◽  
Xiao Jing Li ◽  
Wei Hua Shi ◽  
Ya Chuan Kuang
Keyword(s):  
Reliability Index ◽  
Limit State ◽  
Random Variable ◽  
State Equation ◽  
Matrix Algorithm ◽  
Covariance Propagation ◽  
The Given

In this paper variance of preformance function is calculated according to law of covariance propagation and matrix algorithm is used to calculate reliability index of structures in generalized random space, which is applicable to independent and correlative random variable, linear or nonlinear limit state equation. The given example has shown that the proposed method is very simple and convenient.

Reliability Analyses of Clay-Embedded Offshore Pipelines Under Vertical Buckling Considering Lower-Bound Pipe-Soil Capacity

2012 ◽  
Author(s):  
Celestino Valle-Molina ◽  
Jorge Alamilla-López ◽  
Shadi S. Najjar ◽  
Francisco Silva-González
Keyword(s):  
Lower Bound ◽  
Reliability Index ◽  
Clayey Soil ◽  
Limit State ◽  
State Function ◽  
Soil System ◽  
Upheaval Buckling ◽  
Vertical Loading ◽  
Reliability Assessments ◽  
The Impact

This paper presents the reliability formulation and analyses for studying and quantifying probabilistically the impact of the main parameters involved in the upheaval buckling of offshore buried pipes due to high pressure high temperature conditions (HPHT) on the reliability of the pipeline. Pipelines are considered installed in a clayey trench and naturally covered. The limit state function is established in terms of the vertical pipe-soil capacity and vertical loading. A lower-bound capacity of the pipe-clayey soil system is included in the reliability analysis in order to represent more realistic conditions with regards to the uncertainty in the capacity. The lower-bound capacity is the smallest possible physical limit of the pipe-soil capacity. Reliability assessments using the main parameters that control the vertical buckling in terms of loading and capacity were performed. Consequently, the variations of the reliability index (β) with the vertical imperfection (δ) and the ratio of the cover height (depth of pipe embedment) to the pipe diameter (H/D) were quantified. The reliability index was evaluated by means of Monte Carlo simulations. The inclusion of the lower-bound capacity by means of a left-censored lognormal distribution was found to increase in some cases the values of β.

Inversion analysis to determine design parameters for reliability assessment in pavement structures

2014 ◽  
Vol 41 (10) ◽  
pp. 845-855 ◽  
Author(s):  
Sungho Mun
Keyword(s):  
Reliability Index ◽  
Limit State ◽  
Reliability Assessment ◽  
Pavement Performance ◽  
Design Parameters ◽  
State Function ◽  
Limit State Function ◽  
Performance Function ◽  
Pavement Structures ◽  
Inversion Analysis

Reliability assessment has been used to evaluate the performance of pavement structures. However, probabilistic inversion analysis of pavement structure design has not yet been tested to determine the design parameters of the pavement performance function, given a specified reliability index. In this study, a limit state function numerical calculation and the inversion technique of the Nelder–Mead simplex algorithm were used to determine the design parameters for the pavement performance function. The method of moments was used to develop the forward limit state function, which was then compared to Monte Carlo simulations; the comparison indicated good agreement between the two methods. Additionally, several cases were studied to determine the design parameters of the pavement performance function for the reliability index specified in this study. The case studies indicated that the structure number significantly affected the pavement performance function.

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