A Structural Reliability Approach to Management of Defective Spiral Welding in a ‘Legacy’ Pipeline

2010 ◽  
Author(s):  
Michael Gardiner ◽  
Ross Michie ◽  
Gerardo Douce
Keyword(s):  
Structural Reliability ◽  
Buenos Aires ◽  
Limit State ◽  
State Function ◽  
Operating Pressure ◽  
Limit State Function ◽  
Line Pipe ◽  
Failure Frequency ◽  
Failure Point ◽  
Weld Root

Metrogas SA operates a natural gas distribution concession within the Greater Buenos Aires region of Argentina. In August 2007 a failure occurred on a section of the 22-bar system that dates from the early 1960s and, as such, was ‘inherited’ by Metrogas at privatization. The line pipe in this part of the system is spirally welded and at the failure point the spiral weld root was found to have been incomplete. Subsequent investigations showed that incomplete spiral welds were also present at other locations in the same section of the system. This paper describes some of the steps taken to investigate the incident of 2007 and to manage the threat from other defective spiral welds in the same pipeline section. We present a limit state model for through-wall failure of such features and show how this was used to help understand the incident. We also discuss modeling of uncertainties in parameters of the model and look at results from a probabilistic structural reliability implementation of the limit state function, which allowed the failure frequency of other defective spiral welds in this section to be predicted for various reductions of the operating pressure. Metrogas was then able to use these quantified reliability data to make a responsible, informed decision to keep the affected section in downrated service.

An Efficient Response Surface Method Using Givens Transformation for Structural Reliability Analysis

2012 ◽  
Vol 532-533 ◽  
pp. 408-411
Author(s):  
Wei Tao Zhao ◽  
Yi Yang ◽  
Tian Jun Yu
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Mathematical Techniques ◽  
Input Variables ◽  
Improved Accuracy

The response surface method was proposed as a collection of statistical and mathematical techniques that are useful for modeling and analyzing a system which is influenced by several input variables. This method gives an explicit approximation of the implicit limit state function of the structure through a number of deterministic structural analyses. However, the position of the experimental points is very important to improve the accuracy of the evaluation of failure probability. In the paper, the experimental points are obtained by using Givens transformation in such way these experimental points nearly close to limit state function. A Numerical example is presented to demonstrate the improved accuracy and computational efficiency of the proposed method compared to the classical response surface method. As seen from the result of the example, the proposed method leads to a better approximation of the limit state function over a large region of the design space, and the number of experimental points using the proposed method is less than that of classical response surface method.

An Upheaval Buckling Limit State Function for Onshore Natural Gas Pipelines

2008 ◽  
Author(s):  
Ian Matheson ◽  
Wenxing Zhou ◽  
Joe Zhou ◽  
Rick Gailing
Keyword(s):  
Natural Gas ◽  
Elevated Temperatures ◽  
Limit State ◽  
State Function ◽  
Operating Pressure ◽  
Limit State Function ◽  
Gas Pipelines ◽  
Upheaval Buckling ◽  
Natural Gas Pipelines ◽  
Axial Forces

The reliability-based design and assessment (RBDA) methodology has gained increasing acceptance in the pipeline industry, largely due to a multi-year PRCI program aimed at establishing RBDA as a viable alternative for the design and assessment of onshore natural gas pipelines. A key limit state of buried pipelines that operate at elevated temperatures is upheaval buckling. The elevated temperatures generate large compressive axial forces that can cause Euler buckling susceptibility. The tendency to buckle is increased at vertical imperfections (i.e. a series of cold formed bends) that primarily occur due to topography. Upheaval buckling in itself is not an ultimate limit state but can lead to high strains, local buckling, high cycle fatigue, expensive remediation measures, and even loss of pressure integrity. The critical forces at which upheaval buckling occurs for typical hill-crest type imperfections present in onshore pipelines cannot be readily predicted using analytical methods. A parametric study is therefore undertaken using non-linear finite element analyses to generate a matrix of upheaval buckling responses. The critical force for the onset of upheaval buckling is then developed using a series of empirical relationships to capture the influences of all key parameters. An upheaval buckling limit state function is subsequently developed by comparing the critical buckling force with applied compressive force, which is a function of operating pressure and temperature differential between the operating and tie-in conditions. The limit state function can be readily implemented in a reliability analysis framework to calculate the pipeline failure probability due to upheaval buckling.

LIMIT AND SHAKEDOWN ANALYSIS UNDER UNCERTAINTY

2014 ◽  
Vol 11 (03) ◽  
pp. 1343008 ◽  
Author(s):  
MANFRED STAAT
Keyword(s):  
Structural Reliability ◽  
High Reliability ◽  
Limit State ◽  
Mathematical Optimization ◽  
Element Model ◽  
General Purpose ◽  
State Function ◽  
Limit State Function ◽  
Shakedown Analysis ◽  
Definition Of

Structural reliability analysis is based on the concept of a limit state function separating failure from safe states of a structure. Upper and lower bound theorems of limit and shakedown analysis are used for a direct definition of the limit state function for failure by plastic collapse or by inadaptation. Shakedown describes an asymptotic and therefore time invariant structural behavior under time variant loading. The limit state function and its gradient are obtained from a mathematical optimization problem. The method is implemented into a general purpose finite element model (FEM) code. Combined with first-order methods/second-order methods (FORM/SORM) robust and precise analyses can be performed for structures with high reliability. This approach is particularly effective because the sensitivities which are needed by FORM/SORM are derived from the solution of the deterministic problem.

scholarly journals Hybrid Reliability Analysis for Spacecraft Docking Lock with Random and Interval Uncertainty

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jianguo Zhang ◽  
Jiwei Qiu ◽  
Pidong Wang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
Simple Problem ◽  
State Function ◽  
Limit State Function ◽  
Interval Variables ◽  
Reliability Method ◽  
Hybrid Reliability

This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis with hybrid variables, that is, random and interval variables. This method can significantly improve the computational efficiency for the abovementioned hybrid reliability analysis (HRA), while generally providing sufficient precision. In the proposed procedure, the hybrid problem is reduced to standard reliability problem with the polar coordinates, where an n-dimensional limit-state function is defined only in terms of two random variables. Firstly, the linear Taylor series is used to approximate the limit-state function around the design point. Subsequently, with the approximation of the n-dimensional limit-state function, the new bidimensional limit state is established by the polar coordinate transformation. And the probability density functions (PDFs) of the two variables can be obtained by the PDFs of random variables and bounds of interval variables. Then, the interval of failure probability is efficiently calculated by the integral method. At last, one simple problem with explicit expressions and one engineering application of spacecraft docking lock are employed to demonstrate the effectiveness of the proposed methods.

scholarly journals A New SORM Method for Structural Reliability with Hybrid Uncertain Variables

2020 ◽  
Vol 11 (1) ◽  
pp. 346
Author(s):  
Pidong Wang ◽  
Lechang Yang ◽  
Ning Zhao ◽  
Lefei Li ◽  
Dan Wang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
State Function ◽  
Strong Nonlinearity ◽  
Limit State Function ◽  
Practical Applications ◽  
Uncertain Variables ◽  
Practical Engineering

(1) Background: in practical applications, probabilistic and non-probabilistic information often simultaneously exit. For a complex system with a nonlinear limit-state function, the analysis and evaluation of the reliability are imperative yet challenging tasks. (2) Methods: an improved second-order method is proposed for reliability analysis in the presence of both random and interval variables, where a novel polar transformation is employed. This method enables a unified reliability analysis taking both random variables and bounded intervals into account, simplifying the calculation by transforming a high-dimension limit-state function into a bivariate state function. The obtained nonlinear probability density functions of two variables in the function inherit the statistic characteristics of interval and random variables. The proposed method does not require any strong assumptions and so it can be used in various practical engineering applications. (3) Results: the proposed method is validated via two numerical examples. A comparative study towards a contemporary algorithm in state-of-the-art literature is carried out to demonstrate the benefits of our method. (4) Conclusions: the proposed method outperforms existing methods both in efficiency and accuracy, especially for cases with strong nonlinearity.

Seismic Reliability Analysis of Complex Structure

2012 ◽  
Vol 446-449 ◽  
pp. 2321-2325
Author(s):  
Zhi Yong Zhang ◽  
Wen Bo Huang ◽  
Yue Fa Zhou ◽  
Tian Shu Song
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Complex Structure ◽  
State Function ◽  
Limit State Function ◽  
Seismic Reliability ◽  
Element Method

The seismic reliability analysis of complex structure is carried out based on the response surface method and finite element method. Firstly, the appropriate design points are selected based on the mean values and standard deviations of the basic random variables. Secondly, the finite element method is employed to obtain the values of the limit state function of the complex structure. Thirdly, with selected design points and the obtained values of the limit state function of the complex structure, a polynomial function is constructed to approximate the original implicit limit state function. Then, with the established explicit polynomial limit state function and available methods of structural reliability analysis, the seismic reliability of the complex structure is estimated. Numerical analyses show that the established method is simple to use for the evaluation of the reliability analysis of complex structure.

Influence Research of Correlation of Random Variables on Structural Reliability

2011 ◽  
Vol 243-249 ◽  
pp. 245-250
Author(s):  
Yan Feng Fang ◽  
Li Yan Chen ◽  
Hua Xi Gao
Keyword(s):  
Monte Carlo ◽  
Correlation Coefficient ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
State Equation ◽  
Maximum Intensity ◽  
State Function ◽  
Sampling Techniques ◽  
Limit State Function

In this paper, the influence of correlation of variables on structural reliability is discussed. Using importance, condition and duality sampling techniques of Monte Carlo method, accepted accuracy can be obtained. For the limit state function, the correlation of random variables will influence structural reliability, and the influence can be described. For the case of positive correlation, reliability will increase as the the correlation coefficient raise. For the case of negative correlation, reliability will drop as the correlation coefficient raise. The level of influence depends on the slope of limit state equation in standardized coordinate. When k=1, the influence attains maximum intensity for both cases.

scholarly journals An Energy-Based Limit State Function for Estimation of Structural Reliability in Shock Environments

2013 ◽  
Vol 20 (5) ◽  
pp. 933-950 ◽  
Author(s):  
Michael A. Guthrie
Keyword(s):  
Reliability Index ◽  
Structural Reliability ◽  
Limit State ◽  
Element Model ◽  
Monte Carlo Analysis ◽  
State Function ◽  
Limit State Function ◽  
Qualitative Comparison ◽  
Structural Capacity ◽  
Mass Spring

limit state function is developed for the estimation of structural reliability in shock environments. This limit state function uses peak modal strain energies to characterize environmental severity and modal strain energies at failure to characterize the structural capacity. The Hasofer-Lind reliability index is briefly reviewed and its computation for the energy-based limit state function is discussed. Applications to two degree of freedom mass-spring systems and to a simple finite element model are considered. For these examples, computation of the reliability index requires little effort beyond a modal analysis, but still accounts for relevant uncertainties in both the structure and environment. For both examples, the reliability index is observed to agree well with the results of Monte Carlo analysis. In situations where fast, qualitative comparison of several candidate designs is required, the reliability index based on the proposed limit state function provides an attractive metric which can be used to compare and control reliability.

scholarly journals Structural Reliability Algorithms of Kriging Model Based on Improved Learning Strategy

2020 ◽  
Vol 38 (2) ◽  
pp. 412-419
Author(s):  
Linxiong Hong ◽  
Huacong Li ◽  
Kai Peng ◽  
Hongliang Xiao
Keyword(s):  
Active Learning ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Learning Strategy ◽  
Limit State ◽  
Surface Region ◽  
Kriging Model ◽  
State Function ◽  
Limit State Function ◽  
Highly Nonlinear

Aiming at the problems of implicit and highly nonlinear limit state function in the process of reliability analysis of mechanical products, a reliability analysis method of mechanical structures based on Kriging model and improved EGO active learning strategy is proposed. For the problem that the traditional EGO method cannot effectively select points in the limit state surface region, an improved EGO method is proposed. By dealing with the predicted values of sample point model with absolute values and assume that the distribution state of response values remains the same, the work focus of active learning selection points is moved to the vicinity, where the points are with larger prediction variance or close to the limit state surface. Three examples show that, compared with the classical active learning method, the proposed method has good global and local search ability, and can estimate the exact failure probability value under the condition of less calculation of the limit state function.

scholarly journals An Improved Structural Reliability Analysis Method Based on Local Approximation and Parallelization

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 209
Author(s):  
Bolin Liu ◽  
Liyang Xie
Keyword(s):  
Reliability Analysis ◽  
Failure Probability ◽  
Structural Reliability ◽  
Limit State ◽  
Local Approximation ◽  
State Function ◽  
Limit State Function ◽  
Enrichment Technique ◽  
Reliability Method ◽  
Multiple Sample

The Kriging-based reliability method with a sequential design of experiments (DoE) has been developed in recent years for implicit limit state functions. Such methods include the efficient global reliability analysis, the active learning reliability method combining Kriging and MCS Simulations. In this research, a novel local approximation method based on the most probable failure point (MPFP) is proposed to improve such methods. In this method, the MPFP calculated in the last iteration is the center of the next sampling region. The size of the local region depends on the reliability index obtained by the First Order Reliability Method (FORM) and the deviation distance of the standard deviation. The proposed algorithm, which approximates the limit state function accurately near MPFP rather than in the whole design space, can avoid selecting samples in regions that have negligible effects on the reliability analysis results. In addition, a multi-point enrichment technique is also introduced to select multiple sample points in each iteration. After the high-quality approximation of limit state function is obtained, the failure probability is calculated by the Monte Carlo method. Four numerical examples are used to validate the accuracy and efficiency of the proposed method. Results show that the proposed method is very effective for an accurate evaluation of the failure probability.

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