A Rosenblatt Transformation Method Based on Copula Function for Solving Structural Reliability

2019 ◽  
Author(s):  
Juan Du ◽  
Hai-bin Li
Keyword(s):  
Structural Reliability ◽  
Copula Function ◽  
Transformation Method ◽  
Rosenblatt Transformation

scholarly journals Hermite polynomial normal transformation for structural reliability analysis

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jinsheng Wang ◽  
Muhannad Aldosary ◽  
Song Cen ◽  
Chenfeng Li
Keyword(s):  
Reliability Analysis ◽  
Hermite Polynomial ◽  
Structural Reliability ◽  
Hermite Polynomials ◽  
Random Variables ◽  
Transformation Method ◽  
Statistical Moments ◽  
Content Type ◽  
Structural Reliability Analysis ◽  
Normal Transformation

Purpose Normal transformation is often required in structural reliability analysis to convert the non-normal random variables into independent standard normal variables. The existing normal transformation techniques, for example, Rosenblatt transformation and Nataf transformation, usually require the joint probability density function (PDF) and/or marginal PDFs of non-normal random variables. In practical problems, however, the joint PDF and marginal PDFs are often unknown due to the lack of data while the statistical information is much easier to be expressed in terms of statistical moments and correlation coefficients. This study aims to address this issue, by presenting an alternative normal transformation method that does not require PDFs of the input random variables. Design/methodology/approach The new approach, namely, the Hermite polynomial normal transformation, expresses the normal transformation function in terms of Hermite polynomials and it works with both uncorrelated and correlated random variables. Its application in structural reliability analysis using different methods is thoroughly investigated via a number of carefully designed comparison studies. Findings Comprehensive comparisons are conducted to examine the performance of the proposed Hermite polynomial normal transformation scheme. The results show that the presented approach has comparable accuracy to previous methods and can be obtained in closed-form. Moreover, the new scheme only requires the first four statistical moments and/or the correlation coefficients between random variables, which greatly widen the applicability of normal transformations in practical problems. Originality/value This study interprets the classical polynomial normal transformation method in terms of Hermite polynomials, namely, Hermite polynomial normal transformation, to convert uncorrelated/correlated random variables into standard normal random variables. The new scheme only requires the first four statistical moments to operate, making it particularly suitable for problems that are constraint by limited data. Besides, the extension to correlated cases can easily be achieved with the introducing of the Hermite polynomials. Compared to existing methods, the new scheme is cheap to compute and delivers comparable accuracy.

scholarly journals An improved approach by introducing copula functions for structural reliability analysis under hybrid uncertainties

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878583 ◽  
Author(s):  
Zheng Liu ◽  
Xin Liu
Keyword(s):  
Probability Theory ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Field Tests ◽  
Copula Function ◽  
Working Environment ◽  
Imprecise Probability ◽  
Copula Functions ◽  
Structural Reliability Analysis ◽  
Reliability Method

The structural composition of the oil platform is very complicated, and its working environment is harsh, thus conducting a large number of reliability tests is not feasible, and the field tests are also hard to accomplish. So the reliability of the oil platform cannot be analyzed and calculated by the traditional reliability method which needs a lot of test data, and new methods should be studied. In recent years, imprecise probability theory has attracted more and more attention because when unified, it can quantify hybrid uncertainty. Structural reliability analysis on the basis of imprecise probability theory has made remarkable achievements in theoretical aspects, but it is scarcely used in practical engineering domains due to the complexity in the developed methods and the unavailability of suitable or specific modeling steps for applications. In this regard, we propose a unified quantification method for statistical data, fuzzy data, incomplete information, and the like, which can handle the issue of hybrid uncertainties, and then, we construct an improved imprecise structural reliability model aiming at the practical problems by introducing copula function. To verify the existing methodology, we also consider a cantilever beam widely applied in the oil platform here for the structural reliability analysis.

scholarly journals The structural reliability analysis using explicit neural state functions

2019 ◽  
Vol 262 ◽  
pp. 10002 ◽  
Author(s):  
Agnieszka Dudzik ◽  
Beata Potrzeszcz-Sut
Keyword(s):  
Reliability Analysis ◽  
Reliability Index ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
Transformation Method ◽  
Stability Loss ◽  
Cross Sectional ◽  
Component Reliability ◽  
State Functions

The present study considers the problems of stability and reliability of spatial truss susceptible to stability loss from the condition of node snapping. In the reliability analysis of structure, uncertain parameters, such us load magnitudes, cross-sectional area, modulus of elasticity are represented by random variables. Random variables are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier. In the performed analyses explicit form of the random variables function were used. To formulate explicit limit state functions the neural networks is used. In the paper only the time independent component reliability analysis problems are considered. The NUMPRESS software, created at the IFTR PAS, was used in the reliability analysis. The Hasofer-Lind index in conjunction with transformation method in the FORM was used as a reliability measure. The primary research method is the FORM method. In order to verify the correctness of the calculation SORM and Monte Carlo methods are used. The values of reliability index for different descriptions of mathematical model of the structure were determined. The sensitivity of reliability index to the random variables is defined.

Functional and operational risk as a criterion for assessing the durability of an autonomous energy system

2019 ◽  
Vol 12 (1) ◽  
pp. 56-62 ◽  
Author(s):  
A. O. Nedosekin ◽  
A. V. Smirnov ◽  
D. P. Makarenko ◽  
Z. I. Abdoulaeva
Keyword(s):  
Service Life ◽  
Structural Reliability ◽  
Residual Life ◽  
Fuzzy Random Variable ◽  
Operational Risk ◽  
Energy System ◽  
Technical System ◽  
Residual Service Life ◽  
Technological Parameters ◽  
Residual Service

The article presents new models and methods for estimating the residual service life of an autonomous energy system, using the functional operational risk criterion (FOR). The purpose of the article is to demonstrate a new method of durability evaluation using the fuzzy logic and soft computing framework. Durability in the article is understood as a complex property directly adjacent to the complex property of system resilience, as understood in the Western practice of assessing and ensuring the reliability of technical systems. Due to the lack of reliable homogeneous statistics on system equipment failures and recoveries, triangular fuzzy estimates of failure and recovery intensities are used as fuzzy functions of time based on incomplete data and expert estimates. The FOR in the model is the possibility for the system availability ratio to be below the standard level. An example of the evaluation of the FOR and the residual service life of a redundant cold supply system of a special facility is considered. The transition from the paradigm of structural reliability to the paradigm of functional reliability based on the continuous degradation of the technological parameters of an autonomous energy system is considered. In this case, the FOR can no longer be evaluated by the criterion of a sudden failure, nor is it possible to build a Markov’s chain on discrete states of the technical system. Assuming this, it is appropriate to predict the defi ning functional parameters of a technical system as fuzzy functions of a general form and to estimate the residual service life of the technical system as a fuzzy random variable. Then the FOR is estimated as the possibility for the residual life of the technical system to be below its warranty period, as determined by the supplier of the equipment.

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