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.

Structural Reliability Analysis Using Fourier Orthogonal Neural Network Method

2013 ◽  
Vol 838-841 ◽  
pp. 360-363 ◽  
Author(s):  
Li Rong Sha ◽  
Yue Yang
Keyword(s):  
Neural Network ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
Structural Reliability ◽  
Random Variables ◽  
Structural Reliability Analysis ◽  
Surface Method ◽  
Structural Responses

In order to predict the failure probability of a complicated structure, the structural responses usually need to be predicted by a numerical procedure, such as FEM method. The response surface method could be used to reduce the computational effort required for reliability analysis. However the conventional response surface method is still time consuming when the number of random variables is large. In this paper, a Fourier orthogonal neural network (FONN)-based response surface method is proposed. In this method, the relationship between the random variables and structural responses is established using FONN models. Then the FONN model is connected to the first order and second moment method (FORM) to predict the failure probability. Numerical example result shows that the proposed approach is efficient and accurate, and is applicable to 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.

scholarly journals Structural Reliability Analysis of Ship Hulls Accounting for Collision or Grounding Damage

2020 ◽  
Author(s):  
Branka Bužančić Primorac ◽  
Joško Parunov ◽  
C. Guedes Soares
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
Bending Moment ◽  
State Equation ◽  
Limit States ◽  
Moment Capacity ◽  
Ship Hulls ◽  
Structural Reliability Analysis

AbstractClassical structural reliability analysis of intact ship hulls is extended to the case of ships with collision or grounding damages. Still water load distribution and residual bending moment capacity are included as random variables in the limit state equation. The probability density functions of these random variables are defined based on random damage parameters given by the Marine Environment Protection Committee of the International Maritime Organization, while the proposed reliability formulation is consistent with international recommendations and thus may be valuable in the development of rules for accidental limit states. The methodology is applied on an example of an Aframax oil tanker. The proposed approach captures in a rational way complex interaction of different pertinent variables influencing safety of damaged ship structure.

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