Time-dependent mechanism reliability analysis based on envelope function and vine-copula function

2019 ◽  
Vol 134 ◽  
pp. 667-684 ◽  
Author(s):  
Zhihua Wang ◽  
Zhonglai Wang ◽  
Shui Yu ◽  
Kewang Zhang
Keyword(s):  
Reliability Analysis ◽  
Copula Function ◽  
Envelope Function ◽  
Time Dependent ◽  
Vine Copula ◽  
Dependent Mechanism

An Envelope Approach to Time-Dependent Reliability Analysis for Mechanisms

2013 ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
Envelope Function ◽  
Time Dependent ◽  
Normal Distribution Function ◽  
Maximum Probability ◽  
Accuracy Improvement ◽  
Motion Error ◽  
Time Period ◽  
Time Dependent Problem ◽  
Dependent Mechanism

This work is concerned with the time-dependent mechanism reliability defined over a period of time where a certain motion output is required. An envelope approach is proposed to improve the accuracy of the time-dependent mechanism reliability analysis. The envelope function of the motion error over the time period is created. Since the envelope function is not explicitly related to time, the time-dependent problem is converted into a time-independent problem. Then the envelope function is approximated by piecewise hyper-planes. To find the expansion points of the hyper-planes, the approach linearizes the motion error at the means of random dimension variables, and this approximation is accurate because the tolerances or the variances of the dimension variables are small. Then the expansion points are found with the maximum probability density at the failure threshold. The time-dependent mechanism reliability is then estimated by a multivariable normal distribution function at the expansion points. As an example, analytical equations are derived for a four-bar function generating mechanism. The numerical example shows the significant accuracy improvement.

Time-Dependent Reliability Analysis Using a Vine-ARMA Load Model

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Stochastic Processes ◽  
Reliability Analysis ◽  
Arma Model ◽  
Tail Dependence ◽  
Time Dependent ◽  
Arma Models ◽  
Non Gaussian ◽  
Vine Copula ◽  
Stochastic Loads ◽  
Gaussian Stochastic Processes

A common strategy for the modeling of stochastic loads in time-dependent reliability analysis is to describe the loads as independent Gaussian stochastic processes. This assumption does not hold for many engineering applications. This paper proposes a Vine-autoregressive-moving average (Vine-ARMA) load model for time-dependent reliability analysis, in problems with a vector of correlated non-Gaussian stochastic loads. The marginal stochastic processes are modeled as univariate ARMA models. The correlations among different univariate ARMA models are captured using the Vine copula. The ARMA model maintains the correlation over time. The Vine copula represents not only the correlation among different ARMA models but also the tail dependence of different ARMA models. Therefore, the developed Vine-ARMA model can flexibly model a vector of high-dimensional correlated non-Gaussian stochastic processes with the consideration of tail dependence. Due to the complicated structure of the Vine-ARMA model, new challenges are introduced in time-dependent reliability analysis. In order to overcome these challenges, the Vine-ARMA model is integrated with a single-loop Kriging (SILK) surrogate modeling method. A hydrokinetic turbine blade subjected to a vector of correlated river flow loads is used to demonstrate the effectiveness of the proposed method.

Time-Dependent Reliability Analysis Using a New Multivariate Stochastic Load Model

2016 ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Stochastic Processes ◽  
Reliability Analysis ◽  
Arma Model ◽  
Tail Dependence ◽  
Time Dependent ◽  
Arma Models ◽  
Non Gaussian ◽  
Vine Copula ◽  
Stochastic Loads ◽  
Gaussian Stochastic Processes

A common strategy for the modeling of stochastic loads in time-dependent reliability analysis is to describe the loads as independent Gaussian stochastic processes. This assumption does not hold for many engineering applications. This paper proposes a Vine-autoregressive-moving average (Vine-ARMA) load model for time-dependent reliability analysis, in problems with a vector of correlated non-Gaussian stochastic loads. The marginal stochastic processes are modeled as univariate ARMA models. The correlations between different univariate ARMA models are captured using the Vine-copula. The ARMA model maintains the correlation over time. The Vine-copula represents not only the correlation between different ARMA models, but also the tail dependence of different ARMA models. The developed Vine-ARMA model therefore can flexibly model a vector of high-dimensional correlated non-Gaussian stochastic processes with the consideration of tail dependence. Due to the complicated structure of the Vine-ARMA model, new challenges are introduced in time-dependent reliability analysis. In order to overcome these challenges, the Vine-ARMA model is integrated with a recently developed single-loop Kriging (SILK) surrogate modeling method. A hydrokinetic turbine blade subjected to a vector of correlated river flow loads is used to demonstrate the effectiveness of the proposed method.

Time-Dependent Mechanism Reliability Analysis With Envelope Functions and First-Order Approximation

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Order Approximation ◽  
Envelope Function ◽  
Time Dependent ◽  
Maximum Probability ◽  
Accuracy Improvement ◽  
Motion Error ◽  
First Order ◽  
First Order Approximation ◽  
Dependent Mechanism ◽  
Envelope Functions

This work develops an envelope approach to time-dependent mechanism reliability defined in a period of time where a certain motion output is required. Since the envelope function of the motion error is not explicitly related to time, the time-dependent problem can be converted into a time-independent problem. The envelope function is approximated by piecewise hyperplanes. To find the expansion points for the hyperplanes, the approach linearizes the motion error at the means of random dimension variables, and this approximation is accurate because the tolerances of the dimension variables are small. The expansion points are found with the maximum probability density at the failure threshold. The time-dependent mechanism reliability is then estimated by a multivariable normal distribution at the expansion points. As an example, analytical equations are derived for a four-bar function generating mechanism. The numerical example shows the significant accuracy improvement.

scholarly journals Time-Dependent Reliability Analysis of Reinforced Concrete Beams Subjected to Uniform and Pitting Corrosion and Brittle Fracture

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1820
Author(s):  
Mohamed El Amine Ben Seghier ◽  
Behrooz Keshtegar ◽  
Hussam Mahmoud
Keyword(s):  
Reinforced Concrete ◽  
Brittle Fracture ◽  
Reliability Analysis ◽  
Pitting Corrosion ◽  
Structural Reliability ◽  
Time Dependent ◽  
State Function ◽  
Rc Beams ◽  
Highly Nonlinear ◽  
Reliability Method

Reinforced concrete (RC) beams are basic elements used in the construction of various structures and infrastructural systems. When exposed to harsh environmental conditions, the integrity of RC beams could be compromised as a result of various deterioration mechanisms. One of the most common deterioration mechanisms is the formation of different types of corrosion in the steel reinforcements of the beams, which could impact the overall reliability of the beam. Existing classical reliability analysis methods have shown unstable results when used for the assessment of highly nonlinear problems, such as corroded RC beams. To that end, the main purpose of this paper is to explore the use of a structural reliability method for the multi-state assessment of corroded RC beams. To do so, an improved reliability method, namely the three-term conjugate map (TCM) based on the first order reliability method (FORM), is used. The application of the TCM method to identify the multi-state failure of RC beams is validated against various well-known structural reliability-based FORM formulations. The limit state function (LSF) for corroded RC beams is formulated in accordance with two corrosion types, namely uniform and pitting corrosion, and with consideration of brittle fracture due to the pit-to-crack transition probability. The time-dependent reliability analyses conducted in this study are also used to assess the influence of various parameters on the resulting failure probability of the corroded beams. The results show that the nominal bar diameter, corrosion initiation rate, and the external loads have an important influence on the safety of these structures. In addition, the proposed method is shown to outperform other reliability-based FORM formulations in predicting the level of reliability in RC beams.

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