The inverse transformation of the explicit fourth-moment standardization for structural reliability

2017 ◽  
Vol 21 (5) ◽  
pp. 769-782 ◽  
Author(s):  
Xuan-Yi Zhang ◽  
Yan-Gang Zhao ◽  
Zhao-Hui Lu
Keyword(s):  
Structural Reliability ◽  
Probability Distributions ◽  
Reliability Assessment ◽  
Random Variables ◽  
Inverse Transformation ◽  
Fourth Moment ◽  
Unknown Probability ◽  
Practical Engineering ◽  
Definition Of ◽  
Skewness And Kurtosis

In practical engineering, the probability distributions of some random variables are often unknown, and the only available information about these may be their statistical moments. To conduct structural reliability assessment without the exclusion of random variables with unknown probability distributions, an explicit fourth-moment standardization function has been proposed, and a single expression of its inverse transformation, that is, normal transformation, with limitations of inputting sets of the third and fourth moments (skewness and kurtosis) of random variables was derived. However, the clear definition of the complete expressions of the inverse transformation of fourth-moment standardization function under different combinations of skewness and kurtosis of random variables has not been provided yet. It is in this regard that four criteria are proposed to derive the complete inverse transformation of fourth-moment standardization function, and then the complete expressions of the inverse transformation are formulated. Through the numerical examples presented, the proposed complete expressions are found to be quite efficient for normal transformations and to be sufficiently accurate to include random variables with unknown probability distributions in structural reliability assessment.

Simplified Strength Reliability and Integrity Analysis of TTRs

2014 ◽  
Author(s):  
Mir Emad Mousavi ◽  
Sanjeev Upadhye ◽  
Kevin Haverty
Keyword(s):  
Extreme Events ◽  
Structural Reliability ◽  
Probability Distributions ◽  
Probabilistic Approach ◽  
Reliability Assessment ◽  
Cost Effective ◽  
Probability Of Failure ◽  
Annual Probability ◽  
Reliability Methods ◽  
Integrity Analysis

The design of riser systems can be improved if structural reliability methods are used to assess their safety and integrity and confirm that such design meets a target annual probability of failure. TTRs are typically multi–bore assemblies involving several sub-assemblies. The failure of any of the components of a TTR under extreme or service environmental conditions can lead to an immediate failure of the entire assembly and impose a direct risk of damaging the wellheads, conductors, casing and tubing hangers, or other subsea equipment, because they are installed directly on top of the wellhead. However, the actual strength safety of the TTR cannot be examined unless after it is installed and examined under extreme events. Because of the numerous uncertainties associated with the design of TTRs, a probabilistic approach based on structural reliability methods can account for many of those uncertainties and serve as a basis for their reliable and cost-effective design. In turn, a comprehensive reliability assessment of a TTR requires extensive analysis that is considerably more complex and time consuming compared to a conventional deterministic-based analysis. This paper presents a probabilistic-based simplified methodology for the strength reliability assessment of TTR systems. In this method, marginal values on some uncertain model inputs are considered similar to the conventional analysis methods but, some key random variables related to environmental demands and component capacities are considered with their associated probability distributions. As a result, this method can be used to estimate the minimum level of safety of the TTR under extreme events. Additionally, results of the proposed method are discussed for integrity analysis and integrity-based optimal design of the TTR system, which compare the safety of the TTR components and estimate the component Optimality Factors for improving the design integrity and meeting a target minimum annual probability of failure.

Iteration Algorithm for Propagation of Mixed Uncertainties in Reliability Analysis

2011 ◽  
Vol 199-200 ◽  
pp. 569-574
Author(s):  
Chang Cong Zhou ◽  
Zhen Zhou Lu ◽  
Qi Wang
Keyword(s):  
Structural Reliability ◽  
Random Variables ◽  
Point Estimate ◽  
Iteration Algorithm ◽  
Fourth Moment ◽  
Performance Function ◽  
Fuzzy Variables ◽  
Point Estimate Method ◽  
Interval Variables ◽  
Reliability Method

For structural reliability problems simultaneously involving random variables, interval variables and fuzzy variables, an iteration algorithm is proposed to deal with the propagation of uncertainties. Corresponding to assumed membership value in the membership level interval [0,1], the membership interval of fuzzy variables can be obtained. After the fuzzy variables and the interval variables’ effects on the extreme value of performance function are alternately and iteratively analyzed with the random variables’ effects on statistical properties of the performance function, converged design point can be calculated, and the reliability can be as well calculated by the fourth moment algorithm based on the point estimate method. Finally the membership function of the reliability can be solved. Owing to the faster convergence of the iteration algorithm, the efficiency of the proposed algorithm is highly improved compared to the conventional numerical simulation method. And the adoption of fourth moment method proves much better in accuracy than only applying first order reliability method in the iteration algorithm. After the basic concept and process of the proposed algorithm is detailed, several numerical and engineering examples are studied to demonstrate its advantage both in efficiency and accuracy.

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.

Reliability and Uncertainty Evaluation for Longitudinal Bending of Hull Girders of Surface Ships

1997 ◽  
Vol 41 (01) ◽  
pp. 57-68
Author(s):  
Ru-Jen Chao ◽  
Bilal M. Ayyub
Keyword(s):  
Closed Form ◽  
Ultimate Strength ◽  
Structural Reliability ◽  
Variance Reduction ◽  
Reliability Assessment ◽  
Random Variables ◽  
Closed Form Expression ◽  
Performance Function ◽  
Strength Assessment ◽  
Hull Girder

Structural reliability and uncertainty assessment of hull-girder bending of surface ships requires the consideration of the following three aspects:structural strength,loads, andmethods of reliability analysis. A methodology was developed to assess the reliability of hull girders subjected to extreme bending moments. The methodology is based on ultimate strength assessment of hull-girder bending using an incremental strain compatibility method. Two reliability assessment methods—(1) advanced second moment (ASM) method, and (2) Monte Carlo simulation (MCS) method with variance reduction techniques—were employed for structural reliability assessment of hull-girder bending of surface ships. This study demonstrates the structural reliability evaluation of hull-girder bending of ships (1) by considering its strength parameters as random variables, and (2) by considering a non-closed performance function using both reliability methods. This technique can also be applied to a closed-form expression of the performance function. Utilizing such a methodology, ultimate strength and loads for hull-girder bending can be developed individually as modules, and then combined into a non-closed form in a performance function. Simulation methods are also used to assess the uncertainty in hull girder strength due to uncertainties in basic random variables. Examples using the ASM and MCS methods for reliability assessment are also presented.

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