Failure probability of corroded pipeline considering the correlation of random variables

Based on the entropy of the uncertain variable, a novel importance measure is proposed to identify the effect of the uncertain variables on the system, which is subjected to the combination of random variables and fuzzy variables. For the system with the mixture of random variables and fuzzy variables, the membership function of the failure probability can be obtained by the uncertainty propagation theory first. And then the effect of each input variable on the output response of the system can be evaluated by measuring the shift between entropies of two membership functions of the failure probability, obtained before and after the uncertainty elimination of the input variable. The intersecting effect of the multiple input variables can be calculated by the similar measure. The mathematical properties of the proposed global sensitivity indicators are investigated and proved in detail. A simple example is first employed to demonstrate the procedure of solving the proposed global sensitivity indicators and then the influential variables of four practical applications are identified by the proposed global sensitivity indicators.

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The Influence of Flow Strength and Fracture Toughness on the Computed Reliability of Thermally Aged Grade CF-8M Cast Austenitic Stainless Steel Piping

Volume 1: Codes and Standards ◽

10.1115/pvp2014-28089 ◽

2014 ◽

Author(s):

Timothy J. Griesbach ◽

Dilip Dedhia ◽

David O. Harris ◽

Nathaniel G. Cofie ◽

Kyle Amberge ◽

...

Keyword(s):

Fracture Toughness ◽

Stainless Steel ◽

Austenitic Stainless Steel ◽

Fracture Mechanics ◽

Failure Probability ◽

Crack Depth ◽

Random Variables ◽

Low Flow ◽

Flow Strength ◽

Distribution Type

Thermal aging of cast austenitic stainless steel (CASS) piping is a concern for long-term operation of nuclear power plants. Traditional conservative deterministic fracture mechanics analyses lead to tolerable crack sizes well below the sizes that are readily detectable in these large-grained materials. This is largely due to the conservative treatment of the scatter in material properties and the imposition of multipliers (structural factors) on the applied loads. In order to account for the scatter in the tensile and fracture toughness properties that enter into the analysis, a probabilistic approach is taken. Application of the probabilistic fracture mechanics (PFM) model to representative problems has led to questions regarding the dominant random variables and the influence of the tails of their distributions on computed failure probability. The purpose of this paper is to report the results of a study to identify the important random variables in the PFM model and to investigate the influence of the distribution type on the computed failure probability. Application of the PFM model to a representative piping problem to compute the depth of a part-through part-circumferential crack that will fail with a defined probability (10−6 for example) revealed that the fracture toughness was not a dominant variable and the distribution of the toughness did not strongly affect the results. In contrast to this, the flow strength (which enters into the calculation of the applied crack driving force — J) was important in that low flow strength was controlling the low probability failures in the Monte Carlo simulation. Hence, the low-end tail of the flow strength distribution was influential. Various types of distribution of flow strength consistent with the available data were considered. It was found that the distribution type has a marked, but not overwhelming, effect on the crack depth that would fail with a given probability. From this it is concluded that the PFM model is quite robust, in that it is not highly sensitive to uncertainties in the dominant input distributions.

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Structural Reliability Analysis Using Fourier Orthogonal Neural Network Method

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.838-841.360 ◽

2013 ◽

Vol 838-841 ◽

pp. 360-363 ◽

Cited By ~ 1

Author(s):

Li Rong Sha ◽

Yue Yang

Keyword(s):

Neural Network ◽

Reliability Analysis ◽

Response Surface ◽

Response Surface Method ◽

Failure Probability ◽

Structural Reliability ◽

Random Variables ◽

Structural Reliability Analysis ◽

Surface Method ◽

Structural Responses

In order to predict the failure probability of a complicated structure, the structural responses usually need to be predicted by a numerical procedure, such as FEM method. The response surface method could be used to reduce the computational effort required for reliability analysis. However the conventional response surface method is still time consuming when the number of random variables is large. In this paper, a Fourier orthogonal neural network (FONN)-based response surface method is proposed. In this method, the relationship between the random variables and structural responses is established using FONN models. Then the FONN model is connected to the first order and second moment method (FORM) to predict the failure probability. Numerical example result shows that the proposed approach is efficient and accurate, and is applicable to structural reliability analysis.

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Study on System Reliability Updating through Inspection Information for Existing Cable-Stayed Bridges

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.250-253.2011 ◽

2011 ◽

Vol 250-253 ◽

pp. 2011-2015 ◽

Cited By ~ 2

Author(s):

Jin Song Zhu ◽

Jian Hui Wu

Keyword(s):

Service Life ◽

Failure Probability ◽

System Reliability ◽

Reliability Index ◽

Bayesian Method ◽

Residual Life ◽

Random Variables ◽

Modified Model ◽

Cable Stayed Bridge ◽

Cable Stayed Bridges

In order to accurately evaluate the reliability of the existing cable-stayed bridge, a method based on inspection information is proposed to update the system reliability. Using Bayesian method and inspection information, the modified model of cable-stayed bridge random variables is established, and then the failure probability of cable-stayed bridge components is updated. Theβ-Tcurves of changing rules of inspection information on system reliability index and service life are obtained. The method has been applied to a cable-stayed bridge, the results show that the proposed method is effective to update the system reliability and can predict the residual life of the existing cable-stayed bridges.

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Reliability and Reliability-based Sensitivity Analyses of Steel Moment-Resisting Frame Structure subjected to Extreme Actions

Frattura ed Integrità Strutturale ◽

10.3221/igf-esis.57.12 ◽

2021 ◽

Vol 15 (57) ◽

pp. 138-159

Author(s):

Abbasali Sadeghi ◽

Hamid Kazemi ◽

Maysam Samadi

Keyword(s):

Failure Probability ◽

Fragility Curves ◽

Random Variables ◽

Frame Structure ◽

Sensitivity Analyses ◽

Effective Parameters ◽

Sample Number ◽

Moment Resisting Frame ◽

Moment Resisting ◽

Steel Moment Resisting Frame

The ground external columns of buildings are vulnerable to the extreme actions such as a vehicle collision. This event is a common scenario of buildings' damages. In this study, a nonlinear model of 2-story steel moment-resisting frame (SMRF) is made in OpenSees software. This paper aims investigating the reliability analysis of aforementioned structure under heavy vehicle impact loadings by Monte Carlo Simulation (MCS) in MATLAB software. To reduce computational costs, meta-model techniques such as Kriging, Polynomial Response Surface Methodology (PRSM) and Artificial Neural Network (ANN) are applied and their efficiency is assessed. At first, the random variables are defined. Then, the sensitivity analyses are performed using MCS and Sobol's methods. Finally, the failure probabilities and reliability indices of studied frame are presented under impact loadings with various collision velocities at different performance levels and thus, the behavior of selected SMRF is compared by using fragility curves. The results showed that the random variables such as mass and velocity of vehicle and yield strength of used materials were the most effective parameters in the failure probability computation. Among the meta-models, Kriging can estimate the failure probability with the least error, sample number with minimum computer processing time, in comparison with MCS.

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Effect of Shock Wave on Reliability of Buried Pipelines

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.297-300.1888 ◽

2005 ◽

Vol 297-300 ◽

pp. 1888-1894

Author(s):

Ouk Sub Lee ◽

Dong Hyeok Kim

Keyword(s):

Shock Wave ◽

Wave Velocity ◽

Failure Probability ◽

Lognormal Distribution ◽

Random Variables ◽

P Wave ◽

Buried Pipeline ◽

S Wave ◽

Reliability Method ◽

Distribution Type

The effects of varying distribution type of random variables and environmental, operational, and design random variables influenced by a shock wave caused from various origins on the failure probability are systematically investigated using the first order reliability method (FORM) for buried pipeline. It is found that the failure probability of the buried pipeline increases with faster P-wave velocity and slower S-wave velocity. The failure probability is estimated to be the largest for the Weibull distribution and the smallest for the lognormal distribution. A set of similar values of the failure probability for the normal distribution and lognormal distribution are noted. The normalized margin is defined and estimated. Furthermore, the normalized margin is used to predict the failure probability simply by using the fitting lines between the failure probability and the normalized margin.

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Reliability Analysis for Stiffened Plate on the Maximum Entropy Method

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.525-526.361 ◽

2012 ◽

Vol 525-526 ◽

pp. 361-364

Author(s):

Jian He ◽

Xiao Yan Chen

Keyword(s):

Probability Density Function ◽

Probability Density ◽

Maximum Entropy ◽

Density Function ◽

Failure Probability ◽

Maximum Entropy Method ◽

Random Variables ◽

Entropy Method ◽

Stiffened Plate ◽

Performance Function

Stiffened plate is widely used in vessel structure because of its high bearing capacity and low weight so the research of failure probability for stiffened plate under explosion load has important engineering meaning. Stiffened plate under near-field explosion is taken as research subject, dynamite density and yield stress of plate are selected as random variables, the original values of one hundred groups of random variables are gotten through the random number generation program, and the moments of random variables are obtained. Based on failure criterion of displacement ductility, the performance function of structure is established, probability density function of performance function is fitted using maximum entropy method then the failure probability of stiffened plate structure is obtained. So as to solve the problem of calculate failure probability when the sample size is small and the probability density function is unknown.

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Reliability sensitivity analysis using axis orthogonal importance Latin hypercube sampling method

Advances in Mechanical Engineering ◽

10.1177/1687814019826414 ◽

2019 ◽

Vol 11 (3) ◽

pp. 168781401982641 ◽

Cited By ~ 1

Author(s):

Wei Zhao ◽

YangYang Chen ◽

Jike Liu

Keyword(s):

Sensitivity Analysis ◽

Importance Sampling ◽

Failure Probability ◽

Random Variables ◽

Latin Hypercube Sampling ◽

Sampling Point ◽

Latin Hypercube ◽

Sensitivity Estimation ◽

Reliability Sensitivity ◽

Reliability Sensitivity Analysis

In this article, a combined use of Latin hypercube sampling and axis orthogonal importance sampling, as an efficient and applicable tool for reliability analysis with limited number of samples, is explored for sensitivity estimation of the failure probability with respect to the distribution parameters of basic random variables, which is equivalently solved by reliability sensitivity analysis of a series of hyperplanes through each sampling point parallel to the tangent hyperplane of limit state surface around the design point. The analytical expressions of these hyperplanes are given, and the formulas for reliability sensitivity estimators and variances with the samples are derived according to the first-order reliability theory and difference method when non-normal random variables are involved and not involved, respectively. A procedure is established for the reliability sensitivity analysis with two versions: (1) axis orthogonal Latin hypercube importance sampling and (2) axis orthogonal quasi-random importance sampling with the Halton sequence. Four numerical examples are presented. The results are discussed and demonstrate that the proposed procedure is more efficient than the one based on the Latin hypercube sampling and the direct Monte Carlo technique with an acceptable accuracy in sensitivity estimation of the failure probability.

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Effects of Various Types of Distribution on Probabilistic Method and FAD

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.353-358.2561 ◽

2007 ◽

Vol 353-358 ◽

pp. 2561-2564

Author(s):

Ouk Sub Lee ◽

Dong Hyeok Kim

Keyword(s):

Failure Probability ◽

Probabilistic Method ◽

Limit State ◽

Random Variables ◽

Reliability Estimation ◽

Probabilistic Methods ◽

State Function ◽

Operating Pressure ◽

Lognormal Distributions ◽

Reliability Method

The reliability estimation of pipeline is performed in accordance with the probabilistic methods such as the FORM (first order reliability method) and the SORM (second order reliability method). A limit state function has been formulated with help of the FAD (failure assessment diagram). Various types of distribution of random variables are assumed to investigate its effect on the failure probability. It is noted that the failure probability increases with the increase of the dent depth, the operating pressure and the outside radius, and the decrease of the wall thickness. Furthermore it is found that the failure probability for the random variables having the Weibull distribution is larger than those of the normal and the lognormal distributions.

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Global sensitivity analysis of failure probability caused by fatigue crack propagation

The proceedings of the 13th international conference "Modern Building Materials, Structures and Techniques" (MBMST 2019) ◽

10.3846/mbmst.2019.054 ◽

2019 ◽

Author(s):

Zdeněk Kala

Keyword(s):

Sensitivity Analysis ◽

Failure Probability ◽

Structural Reliability ◽

Global Sensitivity Analysis ◽

Limit State ◽

Random Variables ◽

Probability Of Failure ◽

Global Sensitivity ◽

Sensitivity Indices ◽

Stress Changes

The probability of failure of a load bearing steel member is investigated using a new type of global sensitivity analysis subordinated to contrasts. The main objective of the probability-oriented sensitivity analysis is structural reliability. The structural reliability methodology uses random variables as inputs. The subject of interest is the identification of those random variables that are most important when the limit state of a steel bridge member is reached. The limit state is defined by the occurrence of brittle fracture, which results from stress changes caused by multiple repeated loads. The propagation of a single-edge crack from initial to critical size is analysed using linear fracture mechanics. The failure probability and sensitivity indices are calculated using sampling-based methods. The sensitivity indices are estimated using double-nested-loop simulation of the Latin Hypercube Sampling method. New findings indicate that interaction effects among input variables strongly influence the probability of failure especially at the beginning of the operating period.

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