Reliability analysis of brittle systems considering several random variables

1989 ◽  
Vol 33 (1) ◽  
pp. 37-44
Author(s):  
T.Y. Kam ◽  
C.D. Lu
Keyword(s):  
Reliability Analysis ◽  
Random Variables

scholarly journals An Efficient Time-Variant Reliability Analysis Method with Mixed Uncertainties

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 229
Author(s):  
Fangyi Li ◽  
Yufei Yan ◽  
Jianhua Rong ◽  
Houyao Zhu
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Random Variables ◽  
Equivalent Model ◽  
Independent Random Variables ◽  
Problem Analysis ◽  
Analysis Method ◽  
Calculation Algorithm ◽  
Reliability Problem ◽  
Interval Variables

In practical engineering, due to the lack of information, it is impossible to accurately determine the distribution of all variables. Therefore, time-variant reliability problems with both random and interval variables may be encountered. However, this kind of problem usually involves a complex multilevel nested optimization problem, which leads to a substantial computational burden, and it is difficult to meet the requirements of complex engineering problem analysis. This study proposes a decoupling strategy to efficiently analyze the time-variant reliability based on the mixed uncertainty model. The interval variables are treated with independent random variables that are uniformly distributed in their respective intervals. Then the time-variant reliability-equivalent model, containing only random variables, is established, to avoid multi-layer nesting optimization. The stochastic process is first discretized to obtain several static limit state functions at different times. The time-variant reliability problem is changed into the conventional time-invariant system reliability problem. First order reliability analysis method (FORM) is used to analyze the reliability of each time. Thus, an efficient and robust convergence hybrid time-variant reliability calculation algorithm is proposed based on the equivalent model. Finally, numerical examples shows the effectiveness of the proposed method.

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 Reliability analysis for high-lift device based on Copula function and Bayesian updating

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401881929 ◽  
Author(s):  
Jiazhen Feng ◽  
Jianguo Zhang ◽  
Jiwei Qiu
Keyword(s):  
Reliability Analysis ◽  
Joint Distribution ◽  
Likelihood Function ◽  
Random Variables ◽  
Bayesian Updating ◽  
Copula Function ◽  
High Lift ◽  
Independence Assumption ◽  
Analytic Expressions ◽  
Probability Information

In order to improve the reliability analysis accuracy of the aircraft high-lift, an approach based on the Copula function theory and Bayesian updating is proposed. Considering the influence of the random variables’ correlation in the process of updating, choosing the reasonable prior joint distribution and likelihood function is crucial. Under the condition of the incomplete probability information, the analytic expressions of the prior joint distribution and likelihood function of the correlated random variables are derived through the Copula function. Then, the posterior joint distribution is obtained by Bayesian updating. The reliability of the lifting device is calculated based on the posterior distribution. The case analysis shows that the reliability results based on the proposed approach are more accurate and more coincident with the factual situation than the reliability analysis results based on the independence assumption of random variables.

Uncertainty Quantification of Time-Dependent Reliability Analysis in the Presence of Parametric Uncertainty

2016 ◽  
Vol 2 (3) ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan ◽  
Xiaoping Du
Keyword(s):  
Uncertainty Quantification ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Reliability Index ◽  
Integration Method ◽  
Epistemic Uncertainty ◽  
Random Variables ◽  
Time Dependent ◽  
Data Uncertainty ◽  
State Function

Limited data of stochastic load processes and system random variables result in uncertainty in the results of time-dependent reliability analysis. An uncertainty quantification (UQ) framework is developed in this paper for time-dependent reliability analysis in the presence of data uncertainty. The Bayesian approach is employed to model the epistemic uncertainty sources in random variables and stochastic processes. A straightforward formulation of UQ in time-dependent reliability analysis results in a double-loop implementation procedure, which is computationally expensive. This paper proposes an efficient method for the UQ of time-dependent reliability analysis by integrating the fast integration method and surrogate model method with time-dependent reliability analysis. A surrogate model is built first for the time-instantaneous conditional reliability index as a function of variables with imprecise parameters. For different realizations of the epistemic uncertainty, the associated time-instantaneous most probable points (MPPs) are then identified using the fast integration method based on the conditional reliability index surrogate without evaluating the original limit-state function. With the obtained time-instantaneous MPPs, uncertainty in the time-dependent reliability analysis is quantified. The effectiveness of the proposed method is demonstrated using a mathematical example and an engineering application example.

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 Reliability Analysis Approach For Intersection Sight Distance Of A Symmetrical Single-Lane Roundabout

2021 ◽  
Author(s):  
Paria Sarshar
Keyword(s):  
Reliability Analysis ◽  
Safety Margin ◽  
Random Variables ◽  
Analysis Approach ◽  
Deterministic Models ◽  
Second Moment ◽  
First Order ◽  
Sight Distance ◽  
Design Variables ◽  
First Order Second Moment

The current intersection sight distance values on a roundabout provided by ASSHTO and other worldwide guidelines are based on deterministic methods considering only single variables as the design inputs. However, most of the input design variables such as entering speed and the deceleration rate are random variables which are stochastic in nature. Therefore, this study proposes a reliability analysis approach to add uncertainty to the current deterministic models. Two different reliability approaches; the first order second moment and advanced first order second moment are presented in this paper. These approaches rely on the normal distribution of the random variables using the mean, variance and the covariance of the probability distribution of each variable rather than the single deterministic values. Results show that the AFOSM reliability methodology provides a more conservative outcome which ensures a greater safety margin comparing to FOSM which appears to be a more efficient and robust methodology.

Reliability Analysis of Nonlinear Vibratory Systems Under Non-Gaussian Loads Using a Sensitivity-Based Propagation of Moments

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Dimitrios Papadimitriou ◽  
Zissimos P. Mourelatos ◽  
Santosh Patil ◽  
Zhen Hu ◽  
Vasiliki Tsianika ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Autocorrelation Function ◽  
Computational Cost ◽  
Random Variables ◽  
Random Coefficients ◽  
Time Dependent ◽  
Vibratory System ◽  
First Order ◽  
Non Gaussian ◽  
First Four Moments

Abstract The paper proposes a new methodology for time-dependent reliability analysis of vibratory systems using a combination of a first-order, four-moment (FOFM) method and a non-Gaussian Karhunen–Loeve (NG-KL) expansion. The approach can also be used for random vibrations studies. The vibratory system is nonlinear and is excited by stationary non-Gaussian input random processes which are characterized by their first four marginal moments and autocorrelation function. The NG-KL expansion expresses each input non-Gaussian process as a linear combination of uncorrelated, non-Gaussian random variables and computes their first four moments. The FOFM method then uses the moments of the NG-KL variables to calculate the moments and autocorrelation function of the output processes based on a first-order Taylor expansion (linearization) of the system equations of motion. Using the output moments and autocorrelation function, another NG-KL expansion expresses the output processes in terms of uncorrelated non-Gaussian variables in the time domain, allowing the generation of output trajectories. The latter are used to estimate the time-dependent probability of failure using Monte Carlo simulation (MCS). The computational cost of the proposed approach is proportional to the number of NG-KL random variables and is significantly lower than that of other recently developed methodologies which are based on sampling. The accuracy and efficiency of the proposed methodology is demonstrated using a two-degree-of-freedom nonlinear vibratory system with random coefficients excited by a stationary non-Gaussian random process.

Reliability Analysis and Random Vibration of Nonlinear Systems Using the Adjoint Method and Projected Differentiation

2020 ◽  
Vol 143 (6) ◽  
Author(s):  
Dimitrios Papadimitriou ◽  
Zissimos P. Mourelatos ◽  
Zhen Hu
Keyword(s):  
Reliability Analysis ◽  
Equations Of Motion ◽  
Random Variables ◽  
Random Processes ◽  
Time Dependent ◽  
Vibratory System ◽  
Standard Normal ◽  
Non Gaussian ◽  
Nonlinear Equations Of Motion ◽  
Adjoint Approach

Abstract This paper proposes a new methodology for time-dependent reliability and random vibrations of nonlinear vibratory systems using a combination of a time-dependent adjoint variable (AV) method and a projected differentiation (PD) method. The proposed approach is called AV-PD. The vibratory system is excited by stationary Gaussian or non-Gaussian input random processes. A Karhunen–Loeve (KL) expansion expresses each input random process in terms of standard normal random variables. The nonlinear equations of motion (EOM) are linearized using a Taylor expansion using the first-order derivatives of the output with respect to the input KL random variables. An adjoint approach obtains the output derivatives accurately and efficiently requiring the solution of as many sets of EOM as the number of outputs of interest, independently of the number of KL random variables. The proposed PD method then computes the autocorrelation function of each output process at an additional cost of solving as many sets of EOM as the number of outputs of interest, independently of the time horizon (simulation time). A time-dependent reliability analysis is finally performed using a KL expansion of the output processes and Monte Carlo simulation (MCS). The number of solutions of the EOM scales only with the number of output random processes which is commonly much smaller than the number of input KL random variables. The efficiency and accuracy of the proposed approach is demonstrated using a four degree-of-freedom (DOF) half-car vibratory problem.

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