Interval Reliability Analysis

2007 ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
Performance Characteristic ◽  
Extreme Values ◽  
Probability Distributions ◽  
Probability Of Failure ◽  
Interval Reliability ◽  
Interval Variables ◽  
Inverse Reliability Analysis ◽  
Reliability Method ◽  
A Performance

Traditional reliability analysis uses probability distributions to calculate reliability. In many engineering applications, some nondeterministic variables are known within intervals. When both random variables and interval variables are present, a single probability measure, namely, the probability of failure or reliability, is not available in general; but its lower and upper bounds exist. The mixture of distributions and intervals makes reliability analysis more difficult. Our goal is to investigate computational tools to quantify the effects of random and interval inputs on reliability associated with performance characteristics. The proposed reliability analysis framework consists of two components — direct reliability analysis and inverse reliability analysis. The algorithms are based on the First Order Reliability Method and many existing reliability analysis methods. The efficient and robust improved HL-RF method is further developed to accommodate interval variables. To deal with interval variables for black-box functions, nonlinear optimization is used to identify the extreme values of a performance characteristic. The direct reliability analysis provides bounds of a probability of failure; the inverse reliability analysis computes the bounds of the percentile value of a performance characteristic given reliability. One engineering example is provided.

A New Inverse Reliability Analysis Method Using MPP-Based Dimension Reduction Method (DRM)

2007 ◽  
Author(s):  
Ikjin Lee ◽  
Kyung K. Choi ◽  
Liu Du ◽  
David Gorsich
Keyword(s):  
Dimension Reduction ◽  
Reliability Analysis ◽  
Reduction Method ◽  
Probability Of Failure ◽  
Second Order ◽  
Dimension Reduction Method ◽  
Inverse Reliability Analysis ◽  
Highly Nonlinear ◽  
Reliability Method ◽  
Nonlinear Performance

There are two commonly used reliability analysis methods of analytical methods: linear approximation - First Order Reliability Method (FORM), and quadratic approximation - Second Order Reliability Method (SORM), of the performance functions. The reliability analysis using FORM could be acceptable for mildly nonlinear performance functions, whereas the reliability analysis using SORM is usually necessary for highly nonlinear performance functions of multi-variables. Even though the reliability analysis using SORM may be accurate, it is not desirable to use SORM for probability of failure calculation since SORM requires the second-order sensitivities. Moreover, the SORM-based inverse reliability analysis is very difficult to develop. This paper proposes a method that can be used for multi-dimensional highly nonlinear systems to yield very accurate probability of failure calculation without requiring the second order sensitivities. For this purpose, the univariate dimension reduction method (DRM) is used. A three-step computational process is proposed to carry out the inverse reliability analysis: constraint shift, reliability index (β) update, and the most probable point (MPP) approximation method. Using the three steps, a new DRM-based MPP is obtained, which computes the probability of failure of the performance function more accurately than FORM and more efficiently than SORM.

A Novel Second-Order Reliability Method (SORM) Using Non-Central or Generalized Chi-Squared Distributions

2012 ◽  
Author(s):  
Ikjin Lee ◽  
David Yoo ◽  
Yoojeong Noh
Keyword(s):  
Reliability Analysis ◽  
Linear Combination ◽  
Quadratic Function ◽  
Failure Surface ◽  
Probability Of Failure ◽  
Second Order ◽  
Cumulative Distribution ◽  
State Function ◽  
Reliability Method ◽  
Chi Squared

This paper proposes a novel second-order reliability method (SORM) using non-central or general chi-squared distribution to improve the accuracy of reliability analysis in existing SORM. Conventional SORM contains three types of errors: (1) error due to approximating a general nonlinear limit state function by a quadratic function at most probable point (MPP) in the standard normal U-space, (2) error due to approximating the quadratic function in U-space by a hyperbolic surface, and (3) error due to calculation of the probability of failure after making the previous two approximations. The proposed method contains the first type of error only which is essential to SORM and thus cannot be improved. However, the proposed method avoids the other two errors by describing the quadratic failure surface with the linear combination of non-central chi-square variables and using the linear combination for the probability of failure estimation. Two approaches for the proposed SORM are suggested in the paper. The first approach directly calculates the probability of failure using numerical integration of the joint probability density function (PDF) over the linear failure surface and the second approach uses the cumulative distribution function (CDF) of the linear failure surface for the calculation of the probability of failure. The proposed method is compared with first-order reliability method (FORM), conventional SORM, and Monte Carlo simulation (MCS) results in terms of accuracy. Since it contains fewer approximations, the proposed method shows more accurate reliability analysis results than existing SORM without sacrificing efficiency.

On the Use of Surrogate Models in Reliability-Based Analysis of Dented Pipes

2016 ◽  
Author(s):  
Sherif Hassanien ◽  
Muntaseer Kainat ◽  
Samer Adeeb ◽  
Doug Langer
Keyword(s):  
Finite Element ◽  
Reliability Analysis ◽  
Random Systems ◽  
Probability Of Failure ◽  
Surrogate Models ◽  
Operating Conditions ◽  
Additional Stress ◽  
Internal Stresses ◽  
Stress Risers ◽  
Reliability Method

Pipeline dents lead to changes in the stress/strain state of the pipe body, making it more susceptible to integrity concerns. This susceptibility is especially prevalent in cases where additional stress risers such as crack and/or corrosion features interact with the dented region. While some guidance is available in codes, regulations, and industry best practices, there is substantial room for innovation and improvement to ensure pipeline safety. Existing explicit models are primarily based on experimental correlations and historical findings using simple parameters such as dent depth and location on the pipeline. Moreover, these models are subjected to a substantial uncertainty in both accuracy and precision. This paper presents a state-of-the-art methodology for analyzing dents and dents associated with stress risers through the use of finite element method (FEM) as a mechanical model and reliability analysis to address uncertainties associated with input variables. FEM is used to model the full geometry of dents and any interacting stress risers reported by inline inspection (ILI) to be incorporated into calculations of the internal stresses/strains within the feature. Theoretically, FEM and reliability analysis can be integrated through reliability-based stochastic finite element methodologies due to the absence of closed form mechanical models of dented pipes. However, these methodologies are computationally prohibitive and not suited/designed for frequent integrity analysis. This study aims at further advancing such integration by combining FEM with reliability science to account for pipe properties and measurement uncertainties in order to determine the probability of failure under different operating conditions using surrogate models. This provides the opportunity to more accurately assess the risk posed by ILI reported dent features. Herein, surrogate models refer to the response surface method (RSM) which is considered as a valuable tool for obtaining insight into the behavior of structural random systems at low computational costs. The proposed approach was applied focusing on a plain dent, a dent interacting with a corrosion feature, and a dent interacting with a crack feature. First Order Reliability Method (FORM) is used to evaluate the probability of failure/reliability using the resulting RSM non-linear limit states for each dent feature.

Time-Dependent System Reliability Analysis Using Random Field Discretization

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Random Field ◽  
Reliability Analysis ◽  
System Reliability ◽  
Probability Of Failure ◽  
Two Dimensions ◽  
Time Dependent ◽  
Time Interval ◽  
System Reliability Analysis ◽  
Reliability Method ◽  
Time Dependent System

This paper proposes a novel and efficient methodology for time-dependent system reliability analysis of systems with multiple limit-state functions of random variables, stochastic processes, and time. Since there are correlations and variations between components and over time, the overall system is formulated as a random field with two dimensions: component index and time. To overcome the difficulties in modeling the two-dimensional random field, an equivalent Gaussian random field is constructed based on the probability equivalency between the two random fields. The first-order reliability method (FORM) is employed to obtain important features of the equivalent random field. By generating samples from the equivalent random field, the time-dependent system reliability is estimated from Boolean functions defined according to the system topology. Using one system reliability analysis, the proposed method can get not only the entire time-dependent system probability of failure curve up to a time interval of interest but also two other important outputs, namely, the time-dependent probability of failure of individual components and dominant failure sequences. Three examples featuring series, parallel, and combined systems are used to demonstrate the effectiveness of the proposed method.

AN ITERATIVE HDMR APPROACH FOR ENGINEERING RELIABILITY ANALYSIS

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Qian Wang
Keyword(s):  
Reliability Analysis ◽  
Probabilistic Analysis ◽  
Surrogate Models ◽  
Second Order ◽  
High Dimensional Model Representation ◽  
Performance Function ◽  
Reliability Indices ◽  
Reliability Method ◽  
Sample Points ◽  
A Performance

Engineering reliability analysis has long been an active research area. Surrogate models, or metamodels, are approximate models that can be created to replace implicit performance functions in the probabilistic analysis of engineering systems. Traditional 1st-order or second-order high dimensional model representation (HDMR) methods are shown to construct accurate surrogate models of response functions in an engineering reliability analysis. Although very efficient and easy to implement, 1st-order HDMR models may not be accurate, since the cross-effects of variables are neglected. Second-order HDMR models are more accurate; however they are more complicated to implement. Moreover, they require much more sample points, i.e., finite element (FE) simulations, if FE analyses are employed to compute values of a performance function. In this work, a new probabilistic analysis approach combining iterative HDMR and a first-order reliability method (FORM) is investigated. Once a performance function is replaced by a 1st-order HDMR model, an alternate FORM is applied. In order to include higher-order contributions, additional sample points are generated and HDMR models are updated, before FORM is reapplied. The analysis iteration continues until the reliability index converges. The novelty of the proposed iterative strategy is that it greatly improves the efficiency of the numerical algorithm. As numerical examples, two engineering problems are studied and reliability analyses are performed. Reliability indices are obtained within a few iterations, and they are found to have a good accuracy. The proposed method using iterative HDMR and FORM provides a useful tool for practical engineering applications.

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.

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.

A Random Field Approach to Reliability Analysis With Random and Interval Variables

2015 ◽  
Vol 1 (4) ◽  
Author(s):  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Random Field ◽  
Reliability Analysis ◽  
Extreme Values ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Response Variable ◽  
Field Approach ◽  
Reliability Bounds ◽  
Interval Variables

Interval variables are commonly encountered in design, especially in the early design stages when data are limited. Thus, reliability analysis (RA) should deal with both interval and random variables and then predict the lower and upper bounds of reliability. The analysis is computationally intensive, because the global extreme values of a limit-state function with respect to interval variables must be obtained during the RA. In this work, a random field approach is proposed to reduce the computational cost with two major developments. The first development is the treatment of a response variable as a random field, which is spatially correlated at different locations of the interval variables. Equivalent reliability bounds are defined from a random field perspective. The definitions can avoid the direct use of the extreme values of the response. The second development is the employment of the first-order reliability method (FORM) to verify the feasibility of the random field modeling. This development results in a new random field method based on FORM. The new method converts a general response variable into a Gaussian field at its limit state and then builds surrogate models for the autocorrelation function and reliability index function with respect to interval variables. Then, Monte Carlo simulation is employed to estimate the reliability bounds without calling the original limit-state function. Good efficiency and accuracy are demonstrated through three examples.

Sign in / Sign up

Export Citation Format

Share Document