Markov Description of Corrosion Defects Growth and Its Application to Reliability Based Inspection and Maintenance of Pipelines

2008 ◽  
Author(s):  
S. A. Timashev ◽  
M. G. Malyukova ◽  
L. V. Poluian ◽  
A. V. Bushinskaya
Keyword(s):  
Markov Model ◽  
Conditional Probability ◽  
Limit State ◽  
Simulation Method ◽  
Probability Of Failure ◽  
State Function ◽  
Main Concern ◽  
Defect Parameter ◽  
Pipeline Failure ◽  
Pressurized Pipelines

The paper describes a Markov model of corrosion growth of pipe wall defects and its implementation for assessing the conditional probability of pipeline failure and optimizing pipeline repair and maintenance. This pure growth Markov model is of the continuous time, discrete states type. This model is used in conjunction with the geometrical limit state function (LSF) to assess the conditional probability of failure of pressurized pipelines when the main concern is loss of containment. It is shown how to build an empirical Markov model for the length, depth and width of defects, using field data gathered by In-line inspection (ILI) or direct assessment (DA) or by using a combination of a differential equation (DE) that describes defect parameter growth with the Monte Carlo simulation method. As a result of implementation of this approach the probability for the defect parameters being in a given state (analog of a histogram) and the transition intensities (from state to state) are easily derived for any given moment of time. This approach automatically gives an assessment of the probability of failure of a pipeline segment, as it is derived using the data from a specific pipeline length. This model also allows accounting for the pipeline failure pressure LSF. On the basis of this model an algorithm is constructed for optimizing the time of the next inspection/repair. This methodology is implemented to a specific operating pipeline which was several times inspected by a MFL inspection tool. The expected number and volume of repairs depend on the value of the ultimate permissible pipeline failure probability. Sensitivity of pipeline conditional failure rate and optimal repair time to actual growth rate is investigated. A brief description of the software that implements the described above technology is given.

Probabilistic Risk Analysis of a LNG Carrier Loading Pipeline

2012 ◽  
Author(s):  
Gilberto Francisco Martha de Souza ◽  
Erick Miguel Portugal Hidalgo ◽  
Dennis Wilfredo Roldán Silva ◽  
Marcelo Ramos Martins
Keyword(s):  
Brittle Fracture ◽  
Structural Reliability ◽  
Limit State ◽  
Simulation Method ◽  
Crack Size ◽  
Probability Of Failure ◽  
State Function ◽  
Loading And Unloading ◽  
Material Fracture ◽  
Accident Scenarios

The loading and unloading operation of a LNG carrier is dependent on the perfect performance of the loading/unloading equipment, such as valves, tanks and pipes. The rupture of a ship pipeline (part of the manifold or other secondary pipes) used for LNG loading or unloading can cause the leakage of the fluid causing not only the complete stop of the loading or unloading operation but also exposing the ship and other terminal facilities to a risk associated with LNG leakage. The paper applies structural reliability concepts to evaluate the probability of failure of a pipeline due to the presence of a crack in the pipe wall. The analysis considers the probability of occurrence of brittle fracture associated with a through thickness crack propagation. The limit state function as for brittle fracture analysis is presented and as for reliability analysis three random variables are considered: material fracture toughness, crack size and pipe thickness. The Monte Carlo simulation method is used to calculate the probability of failure. Based on those results, the paper proposes the use of the cause-consequence diagram to evaluate the accident scenarios associated with the pipe rupture, which failure probability was previously calculated. The events that appear in the diagram are associated with alarm and control systems that are used as monitoring system for loading and unloading operations. Those failure probabilities can be calculated using reliability database. The consequences of each scenario can be defined based on literature review. The main analysis result will be the risk profile associated with a pipe brittle fracture. The method is used for the analysis of a LNG carrier operating in a Brazilian harbor.

scholarly journals Semi-Supervised Deep Learning for High-Dimensional Uncertainty Quantification

2020 ◽  
Author(s):  
Zequn Wang ◽  
Mingyang Li
Keyword(s):  
Uncertainty Quantification ◽  
Reliability Analysis ◽  
Supervised Learning ◽  
Dimensional Space ◽  
Limit State ◽  
Failure Surface ◽  
Simulation Method ◽  
High Dimensional ◽  
State Function ◽  
Latent Space

Abstract Conventional uncertainty quantification methods usually lacks the capability of dealing with high-dimensional problems due to the curse of dimensionality. This paper presents a semi-supervised learning framework for dimension reduction and reliability analysis. An autoencoder is first adopted for mapping the high-dimensional space into a low-dimensional latent space, which contains a distinguishable failure surface. Then a deep feedforward neural network (DFN) is utilized to learn the mapping relationship and reconstruct the latent space, while the Gaussian process (GP) modeling technique is used to build the surrogate model of the transformed limit state function. During the training process of the DFN, the discrepancy between the actual and reconstructed latent space is minimized through semi-supervised learning for ensuring the accuracy. Both labeled and unlabeled samples are utilized for defining the loss function of the DFN. Evolutionary algorithm is adopted to train the DFN, then the Monte Carlo simulation method is used for uncertainty quantification and reliability analysis based on the proposed framework. The effectiveness is demonstrated through a mathematical example.

Reliability-Based Optimal Design and Tolerancing for Multibody Systems Using Explicit Design Space Decomposition

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Henry Arenbeck ◽  
Samy Missoum ◽  
Anirban Basudhar ◽  
Parviz Nikravesh
Keyword(s):  
Multibody Systems ◽  
Adaptive Sampling ◽  
Design Space ◽  
Limit State ◽  
Uniform Design ◽  
Probability Of Failure ◽  
Support Vector ◽  
State Function ◽  
Nominal System ◽  
Truncated Normal

This paper introduces a new approach for the optimal geometric design and tolerancing of multibody systems. The approach optimizes both the nominal system dimensions and the associated tolerances by solving a reliability-based design optimization (RDBO) problem under the assumption of truncated normal distributions of the geometric properties. The solution is obtained by first constructing the explicit boundaries of the failure regions (limit state function) using a support vector machine, combined with adaptive sampling and uniform design of experiments. The use of explicit boundaries enables the treatment of systems with discontinuous or binary behaviors. The explicit boundaries also allow for an efficient calculation of the probability of failure using importance sampling. The probability of failure is subsequently approximated over the whole design space (the nominal system dimensions and the associated tolerances), thus making the solution of the RBDO problem straightforward. The proposed approach is applied to the optimization of a web cutter mechanism.

Reliability-Based Topology Optimization Using Mean-Value Second-Order Saddlepoint Approximation

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Dimitrios I. Papadimitriou ◽  
Zissimos P. Mourelatos
Keyword(s):  
Topology Optimization ◽  
Limit State ◽  
Random Variables ◽  
Saddlepoint Approximation ◽  
Probability Of Failure ◽  
Mean Value ◽  
Second Order ◽  
State Function ◽  
Sensitivity Derivatives ◽  
Reliability Method

A reliability-based topology optimization (RBTO) approach is presented using a new mean-value second-order saddlepoint approximation (MVSOSA) method to calculate the probability of failure. The topology optimizer uses a discrete adjoint formulation. MVSOSA is based on a second-order Taylor expansion of the limit state function at the mean values of the random variables. The first- and second-order sensitivity derivatives of the limit state cumulant generating function (CGF), with respect to the random variables in MVSOSA, are computed using direct-differentiation of the structural equations. Third-order sensitivity derivatives, including the sensitivities of the saddlepoint, are calculated using the adjoint approach. The accuracy of the proposed MVSOSA reliability method is demonstrated using a nonlinear mathematical example. Comparison with Monte Carlo simulation (MCS) shows that MVSOSA is more accurate than mean-value first-order saddlepoint approximation (MVFOSA) and more accurate than mean-value second-order second-moment (MVSOSM) method. Finally, the proposed RBTO-MVSOSA method for minimizing a compliance-based probability of failure is demonstrated using two two-dimensional beam structures under random loading. The density-based topology optimization based on the solid isotropic material with penalization (SIMP) method is utilized.

Failure Assessment and Reliability Analysis of CFRP Composite Pressure Vessel

2007 ◽  
Vol 348-349 ◽  
pp. 225-228
Author(s):  
Jun Shen ◽  
M.L. Zhang ◽  
D.Y. Hou
Keyword(s):  
Reliability Analysis ◽  
Pressure Vessel ◽  
Progressive Failure ◽  
Limit State ◽  
Probability Of Failure ◽  
Fiber Direction ◽  
State Function ◽  
Design Variables ◽  
Composite Pressure Vessel ◽  
Cfrp Composite

A new approach for progressive failure and reliability analysis of carbon fiber reinforced polymeric (CFRP) composite pressure vessel with many base random variables is developed in the paper. The elastic constants of CFRP lamina and geometric parameters of the vessel are selected as the base design variables. CFRP lamina specimen and pressure vessel were manufactured and tested in order to obtain statistics of design variables. The limit state function for progressive failure analysis was set up. Then the progressive failure and reliability analysis of the vessel were performed according to the stiffness degradation model based on Monte Carlo simulation procedure using MATLAB. The distributions of failure loads and the probability of failure of the vessel were obtained. The feasibility and accuracy of the proposed method is validated by good agreement between the simulation and experimental results. Further analysis indicates that the lamina tensile strength in the fiber direction and hoop layer thickness of the vessel have significant influence on the probability of failure of composite pressure vessel.

Safety and Reliability Analysis of Composites Under Low Velocity Impact

2016 ◽  
Author(s):  
Shivdayal Patel ◽  
Suhail Ahmad ◽  
Manander Singh
Keyword(s):  
Material Properties ◽  
Limit State ◽  
Composite Plates ◽  
Probability Of Failure ◽  
Matrix Cracking ◽  
Low Velocity Impact ◽  
State Function ◽  
Random Parameters ◽  
Low Velocity ◽  
Velocity Impact

Low velocity impact on composite plates is studied taking material properties and initial velocity as random parameters. Graphite fiber reinforced composite plates are susceptible to damage due to impact by foreign objects and in plane loading. In order to assess the safe load carrying capacity and the probability of failure under impact, dynamic analysis of composite plate subjected to low velocity impact is carried out. Finite element method is used to study impact. During impact, the in-plane damage modes such as matrix cracking, fiber failure and shear cracking are modeled using a failure criterion. The out of plane de-lamination is modeled using cohesive surfaces. The uncertainties associated with the system properties due to the inherent scatter in the geometric and material properties and input loads are modeled in a probabilistic fashion. Random parameters represent various characteristics appearing in the limit state function. The probabilistic analysis and reliability prediction of the system is carried out using Gaussian response surface method and validity of method for the present problem is establish using Monte Carlo simulation (MCS) procedure. Sensitivity analysis of the probability of failure with respect to random parameters considered is an important study for design optimization. The safety level qualification is achieved in terms of reliability level targeted. The mean and standard deviations of random variables show an appreciable influence on the probabilistic failure. Systematic changes in the input parameters are governed by the probabilistic sensitivity tools to achieve target reliability.

Application of Partial Safety Factors for Fitness-for-Service Assessment of Pressure Equipment With Local Metal Loss

2017 ◽  
Author(s):  
Takuyo Kaida ◽  
Shinsuke Sakai
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Probability Of Failure ◽  
Pressure Vessels ◽  
Metal Loss ◽  
State Function ◽  
Safety Factors ◽  
Loss Assessment ◽  
Reliability Method ◽  
Partial Safety Factors

Reliability analysis considering data uncertainties can be used to make a rational decision as to whether to run or repair a pressure equipment that contains a flaw. Especially, partial safety factors (PSF) method is one of the most useful reliability analysis procedure and considered in a Level 3 assessment of a crack-like flaw in API 579-1/ASME FFS-1:2016. High Pressure Institute of Japan (HPI) formed a committee to develop a HPI FFS standard including PSF method. To apply the PSF method effectively, the safety factors for each dominant variable should be prepared before the assessment. In this paper, PSF for metal loss assessment of typical pressure vessels are derived based on first order reliability method (FORM). First, a limit state function and stochastic properties of random variables are defined. The properties of a typical pressure vessel are based on actual data of towers in petroleum and petrochemical plants. Second, probability of failure in several cases are studied by Hasofer-Lind method. Finally, PSF’s in each target probability of failure are proposed. HPI published a new technical report, HPIS Z 109 TR:2016, that provide metal loss assessment procedures based on FORM and the proposed PSF’s described in this paper.

Reliability Analysis of Marine Platforms Subject to Fatigue Damage for Risk Based Inspection Planning

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Ernesto Heredia-Zavoni ◽  
Francisco Silva-González ◽  
Roberto Montes-Iturrizaga
Keyword(s):  
Fatigue Damage ◽  
Wave Height ◽  
Limit State ◽  
Probability Of Failure ◽  
Shear Capacity ◽  
State Function ◽  
Strength Ratio ◽  
Inspection Planning ◽  
Reserve Strength ◽  
State Functions

The probability of failure of steel jacket platforms subjected to fatigue damage is computed by means of Monte Carlo simulations using limit state functions in which wave, wind, and deck loadings are expressed in terms of empirical functions of uncertain maximum wave height. Limit state functions associated with the base shear capacity of the jacket and the shear capacity of the deck legs were used. The sensitivity of the probability of failure to the coefficient of variation of resistance, of wave height, of resistance and loading biases, and to parameters in empirical loading functions, as well as the influence of the reserve strength ratio is analyzed using a simplified limit state function. Results from simulations are compared to those obtained with a formulation that relates the reserve strength ratio to the reliability index. An application to risk based inspection planning for extension of the service life of a platform is given.

Local Monte Carlo Simulation for the Reliability Sensitivity Analysis

2011 ◽  
Vol 291-294 ◽  
pp. 2183-2188 ◽  
Author(s):  
Da Wei Li ◽  
Zhen Zhou Lu ◽  
Zhang Chun Tang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Numerical Technique ◽  
Limit State ◽  
Computational Cost ◽  
Simulation Method ◽  
State Function ◽  
Local Domain ◽  
Monte Carlo Simulation Method ◽  
Reliability Sensitivity

An efficient numerical technique, namely the Local Monte Carlo Simulation method, is presented to assess the reliability sensitivity in this paper. Firstly some samples are obtained by the random sampling, then the local domain with a constant probability content corresponding to each sample point can be defined, finally the conditional reliability and reliability sensitivity corresponding to every local region can be calculated by using linear approximation of the limit state function. The reliability and reliability sensitivity can be estimated by the expectation of all the conditional reliability and reliability sensitivity. Three examples testify the applicability, validity and accuracy of the proposed method. The results computed by the Local Monte Carlo Simulation method and the Monte Carlo method are compared, which demonstrates that, without losing precision, the computational cost by the former method is much less than the later.

scholarly journals Copula-Based Slope Reliability Analysis Using the Failure Domain Defined by theg-Line

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaoliang Xu ◽  
Jianlin Li ◽  
Jiawei Gong ◽  
Huafeng Deng ◽  
Liangpeng Wan
Keyword(s):  
Shear Strength ◽  
Reliability Analysis ◽  
Slope Failure ◽  
Limit State ◽  
Probability Of Failure ◽  
Function Approach ◽  
State Function ◽  
Shear Strength Parameters ◽  
Strength Parameters ◽  
Reliability Method

The estimation of the cross-correlation of shear strength parameters (i.e., cohesion and internal friction angle) and the subsequent determination of the probability of failure have long been challenges in slope reliability analysis. Here, a copula-based approach is proposed to calculate the probability of failure by integrating the copula-based joint probability density function (PDF) on the slope failure domain delimited with theg-line. Here, copulas are used to construct the joint PDF of shear strength parameters with specific marginal distributions and correlation structure. In the paper a failure (limit state) function approach is applied to investigate a system characterized by a homogeneous slope. The results show that the values obtained by using the failure function approach are similar to those calculated by means of conventional methods, such as the first-order reliability method (FORM) and Monte Carlo simulations (MC). In addition, an entropy weight (EW) copula is proposed to address the discrepancies of the results calculated by different copulas to avoid over- or underestimating the slope reliability.

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