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.

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.

Partial Safety Factors Assessment of Pipes With a Circumferential Surface Flaw

2010 ◽  
Author(s):  
Hideo Machida ◽  
Hiromasa Chitose ◽  
Manabu Arakawa
Keyword(s):  
Fracture Resistance ◽  
Design Method ◽  
Limit State ◽  
Surface Flaw ◽  
Flaw Size ◽  
Material Strength ◽  
State Function ◽  
Safety Factors ◽  
Related Parameter ◽  
Partial Safety Factors

This paper describes the evaluation of partial safety factors (PSF’s) for parameters related to flaw evaluation of pipes which have a circumferential surface flaw, and proposes the important matter which should be pay attention in the setup of the safety factors used in flaw evaluation. PSF’s were evaluated considering randomness of flaw size, a fracture resistance curve (J-R curve) and applied loads using load and resistance factor design method (LRFD). The limit state function is expressed by fracture resistance (resistance-related parameter) and applied J integral (load-related parameter). The measure parameters in the reliability assessment are the flaw size and the J-R curve, and PSF’s of them are larger than those of applied loads. Since the material properties used in the flaw evaluation are generally set to the engineering lower limit of their variation (e.g., 95% lower confidence limit), variation of the flaw size is considered to have important role on flaw evaluation. Therefore, when setting up the safely factors used in Rules on Fitness-for-Service (FFS), it is necessary to take into consideration not only the influence of variation of loads or material strength but the influence of variation of flaw size.

Analysis of the Partial Safety Factor Method Using Probabilistic Techniques

2010 ◽  
Author(s):  
B. A. Lindley ◽  
P. M. James
Keyword(s):  
Probabilistic Method ◽  
Probability Of Failure ◽  
Safety Factors ◽  
First Order Reliability Method ◽  
First Order ◽  
Target Probability ◽  
Reliability Method ◽  
Input Parameters ◽  
Partial Safety Factors ◽  
Hand Calculation

Partial Safety Factors (PSFs) are scaling factors which are used to modify the input parameters to a deterministic fracture mechanics assessment in order to consider the effects of variability or uncertainty in the values of the input parameters. BS7910 and SINTAP have adopted the technique, both of which use the First Order Reliability Method (FORM) to derive values for PSFs. The PSFs are tabulated, varying with the target probability of failure, p(F), and the Coefficient of Variance (COV) of the variable. An accurate assessment of p(F) requires a probabilistic method with enough simulations. This has previously been found to be time consuming, due to the large number of simulations required. The PSF method has been seen as a quick way of calculating an approximate, conservative value of p(F). This paper contains a review of the PSF method, conducted using an efficient probabilistic method called the Hybrid probabilistic method. The Hybrid probabilistic method is used to find p(F) at a large number of assessment points, for a range of different PSFs. These p(F) values are compared to those obtained using the PSF method. It is found that the PSF method was usually, and often extremely, conservative. However there are also cases where the PSF method was non-conservative. This result is verified by a hand calculation. Modifications to the PSF method are suggested, including the establishment of a minimum PSF on each variable to reduce non-conservatisms. In light of the existence of efficient probabilistic techniques, the non-conservatisms that have been found in the PSF method, coupled with the impracticality of completely removing these non-conservatisms, it is recommended that a full probabilistic assessment should generally be performed.

Fatigue Design Margin Evaluation for Carbon and Low-Alloy Steels by Reliability-Based Load and Resistance Factor Method

2011 ◽  
Author(s):  
Masahiro Takanashi ◽  
Makoto Higuchi ◽  
Junki Maeda ◽  
Shinsuke Sakai
Keyword(s):  
Applied Stress ◽  
Limit State ◽  
State Function ◽  
Low Alloy Steels ◽  
Limit State Function ◽  
Safety Factors ◽  
Fatigue Data ◽  
Alloy Steels ◽  
Partial Safety Factors ◽  
Two Parameters

This paper discusses the margins of the design fatigue curve in the ASME Boiler and Pressure Vessel Codes Section III from a reliability analysis point of view. It is reported that these margins were developed so as to cover uncertainties of fatigue data scatter, size effect, and surface condition[1], but the reasons for them remain unclear. In order to investigate the physical implications of the design margin, a probabilistic approach is taken for the collected fatigue data of carbon and low-alloy steels. In this approach, these three parameters are treated as random variables, and an applied stress is also taken into consideration as a random variable. For the analysis, to begin with, a limit state function for fatigue is proposed. Next, reliability index contours of the design fatigue curves for carbon and low-alloy steels are obtained based on the proposed limit state function. The contours indicate that the margins 2 on stress and 20 on life do not provide equal reliability. The margin 20 on life is more conservative and the margin became a minimum near intersections of the design curves with margins 2 on stress and 20 on life. For practical applications, the partial safety factors (PSF) for the target reliability are computed for all materials and several levels of coefficients of variation (COV) of the applied stress. A sensitivity analysis of the PSFs clarifies that only two parameters, the strength (or the life) and the applied stress, are predominant. Thus, the partial safety factors for these two parameters are proposed in a tabular form.

Fatigue Safety Factors for Flexible Risers Based on Case Specific Reliability Analysis

2005 ◽  
Author(s):  
Bernt J. Leira ◽  
Ragnar T. Igland ◽  
Gro S. Baarholm ◽  
Knut A. Farnes ◽  
Dick Percy
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
State Function ◽  
Safety Factors ◽  
Fatigue Lifetime ◽  
Statistical Variation ◽  
Parametric Studies ◽  
Flexible Risers ◽  
Corrosive Environments ◽  
Wave Induced

In the present paper, fatigue safety factors for flexible risers are assessed. A procedure for reliability analysis of wave-induced fatigue is first described. The procedure is based on performing a number of parametric studies with respect to variables that influence the fatigue lifetime. The results of these parametric studies are subsequently combined with models describing the statistical scatter of the same parameters. By application of this procedure, the safety factors which are required in order to reach specific target reliability levels can be computed. Such safety factors are computed for three specific flexible riser configurations. Different SN -curves which correspond to different corrosive environments are considered. The percentwise contribution from each parameter to the total statistical variation of the limit state function is also quantified.

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.

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.

Partial Safety Factors for Vertical Bending Loads on Containerships

1992 ◽  
Vol 114 (2) ◽  
pp. 129-136 ◽  
Author(s):  
C. O¨stergaard
Keyword(s):  
Probability Density ◽  
Reliability Analysis ◽  
Limit State ◽  
Bending Moment ◽  
Bending Moments ◽  
Wave Loads ◽  
Safety Factors ◽  
The North ◽  
Design Values ◽  
Partial Safety Factors

International design codes for seagoing steel ships of today are in the process of testing a new safety format with load factors separately multiplied with nominal (code) values of still water and wave loads. This leads to two design values of these loads, the sum of which must not exceed a design value of the strength of the ship structure, which is again a nominal (code) value of strength, this time divided by a strength factor. Such load and strength factors are generally termed partial safety factors. In the paper, vertical still water and wave bending moments of containerships are considered as loads. The partial safety factors are determined on the basis of reliability analysis, i.e., the sum of the design values of the loads will not exceed a design serviceability limit state of the ship’s structure with given probability. To enable reliability analysis, distribution density of the ship’s strength to resist bending moments is based on a stochastic interpretation of nominal (code) values used in the conventional safety format. The probability density of the still water bending moment is obtained from recently published statistical data. The probability density of the wave bending moment is calculated using advanced hydrodynamic and spectral analysis, including long-term statistics of the (North Atlantic) seaway. Reliability and related design values are estimated using the FORM algorithm with due consideration of the different repetition numbers for which the stochastic models of the two bending moments are valid. The results are presented as nonlinear regression formulas and as diagrams that specify partial safety factors related to length and beam of containerships. The nominal values of bending moments to be used with these partial safety factors are given as functions of length, beam, and block coefficient of those ships.

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.

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