A single-loop Kriging surrogate model method by considering the first failure instant for time-dependent reliability analysis and safety lifetime analysis

2020 ◽  
Vol 145 ◽  
pp. 106963
Author(s):  
Yingshi Hu ◽  
Zhenzhou Lu ◽  
Ning Wei ◽  
Changcong Zhou
Keyword(s):  
Reliability Analysis ◽  
Surrogate Model ◽  
Time Dependent ◽  
Kriging Surrogate Model ◽  
Single Loop ◽  
Model Method ◽  
Lifetime Analysis

scholarly journals A Single-Loop Kriging Surrogate Modeling for Time-Dependent Reliability Analysis

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Reliability Analysis ◽  
Surrogate Model ◽  
Surrogate Modeling ◽  
Computational Effort ◽  
Time Dependent ◽  
Convergence Criterion ◽  
Double Loop ◽  
Single Loop ◽  
Loop Procedure ◽  
Optimization Loop

Current surrogate modeling methods for time-dependent reliability analysis implement a double-loop procedure, with the computation of extreme value response in the outer loop and optimization in the inner loop. The computational effort of the double-loop procedure is quite high even though improvements have been made to improve the efficiency of the inner loop. This paper proposes a single-loop Kriging (SILK) surrogate modeling method for time-dependent reliability analysis. The optimization loop used in current methods is completely removed in the proposed method. A single surrogate model is built for the purpose of time-dependent reliability assessment. Training points of random variables and over time are generated at the same level instead of at two separate levels. The surrogate model is refined adaptively based on a learning function modified from time-independent reliability analysis and a newly developed convergence criterion. Strategies for building the surrogate model are investigated for problems with and without stochastic processes. Results of three numerical examples show that the proposed single-loop procedure significantly increases the efficiency of time-dependent reliability analysis without sacrificing the accuracy.

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.

Mixed Efficient Global Optimization for Time-Dependent Reliability Analysis

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Global Optimization ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Extreme Value ◽  
Time Dependent ◽  
Efficient Global Optimization ◽  
Highly Nonlinear ◽  
Adaptive Kriging

Time-dependent reliability analysis requires the use of the extreme value of a response. The extreme value function is usually highly nonlinear, and traditional reliability methods, such as the first order reliability method (FORM), may produce large errors. The solution to this problem is using a surrogate model of the extreme response. The objective of this work is to improve the efficiency of building such a surrogate model. A mixed efficient global optimization (m-EGO) method is proposed. Different from the current EGO method, which draws samples of random variables and time independently, the m-EGO method draws samples for the two types of samples simultaneously. The m-EGO method employs the adaptive Kriging–Monte Carlo simulation (AK–MCS) so that high accuracy is also achieved. Then, Monte Carlo simulation (MCS) is applied to calculate the time-dependent reliability based on the surrogate model. Good accuracy and efficiency of the m-EGO method are demonstrated by three examples.

scholarly journals An Efficient Entropy-Based Method for Reliability Assessment by Combining Kriging Meta-Models

2019 ◽  
Author(s):  
Jafar Vahedi ◽  
Mohammad Reza Ghasemi ◽  
Mahmoud Miri
Keyword(s):  
Reliability Analysis ◽  
Surrogate Model ◽  
Numerical Models ◽  
Reliability Assessment ◽  
Simulation Method ◽  
Adaptive Method ◽  
Kriging Surrogate Model ◽  
Constant Regression ◽  
Training Samples ◽  
Mcs Method

Meta-models or surrogate models are convenient tools for reliability assessment of problems with time-consuming numerical models. Recently, an adaptive method called AK-MCS has been widely used for reliability analysis by combining Mont-Carlo simulation method and Kriging surrogate model. The AK-MCS method usually uses constant regression as a Kriging trend. However, other regression trends may have better performance for some problems. So, a method is proposed by combining multiple Kriging meta-models with various trends. The proposed method is based on the maximum entropy of predictions to select training samples. Using multiple Kriging models can reduce the sensitivity to the regression trend. So, the propped method can have better performance for different problems. The proposed method is applied to some examples to show its efficiency.

Uncertainty Quantification in Time-Dependent Reliability Analysis

2015 ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan ◽  
Xiaoping Du
Keyword(s):  
Uncertainty Quantification ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Reliability Index ◽  
Epistemic Uncertainty ◽  
Random Variables ◽  
Time Dependent ◽  
State Function ◽  
Uncertainty Sources ◽  
Stochastic Load

One of the essential steps in time-dependent reliability analysis is the characterization of stochastic load processes and system random variables based on experimental or historical data. Limited data results in uncertainty in the modeling of random variables and stochastic loadings. The uncertainty in random variable and stochastic load models later causes uncertainty in the results of reliability analysis. An uncertainty quantification framework is developed in this paper for time-dependent reliability analysis. The effects of two kinds of uncertainty sources, namely data uncertainty and model uncertainty on the results of time-dependent reliability analysis are investigated. The Bayesian approach is employed to model the epistemic uncertainty sources in random variables and stochastic processes. A straightforward formulation of uncertainty quantification in time-dependent reliability analysis results in a double-loop implementation, which is computationally expensive. Therefore, this paper builds a surrogate model for the conditional reliability index in terms of variables with imprecise parameters. Since the conditional reliability index is independent of the epistemic uncertainty, the surrogate model is applicable for any realizations of the epistemic uncertainty. Based on the surrogate model, the uncertainty in time-dependent reliability analysis is quantified without evaluating the original limit-state function, which increases the efficiency of uncertainty quantification. The effectiveness of the proposed method is demonstrated using a mathematical example and an engineering application example.

Advanced time-dependent reliability analysis based on adaptive sampling region with Kriging model

2020 ◽  
Vol 234 (4) ◽  
pp. 588-600
Author(s):  
Yan Shi ◽  
Zhenzhou Lu ◽  
Ruyang He
Keyword(s):  
Reliability Analysis ◽  
Failure Probability ◽  
Surrogate Model ◽  
Adaptive Sampling ◽  
Computational Cost ◽  
Kriging Model ◽  
Time Dependent ◽  
Computational Time ◽  
Optimization Strategy ◽  
Dependent Failure

Aiming at accurately and efficiently estimating the time-dependent failure probability, a novel time-dependent reliability analysis method based on active learning Kriging model is proposed. Although active surrogate model methods have been used to estimate the time-dependent failure probability, efficiently estimating the time-dependent failure probability by a fewer computational time remains an issue because screening all the candidate samples iteratively by the active surrogate model is time-consuming. This article is intended to address this issue by establishing an optimization strategy to search the new training samples for updating the surrogate model. The optimization strategy is performed in the adaptive sampling region which is first proposed. The adaptive sampling region is adjustable by the current surrogate model in order to provide a proper candidate samples region of the input variables. The proposed method employs the optimization strategy to select the optimal sample to be the new training sample point in each iteration, and it does not need to predict the values of all the candidate samples at every time instant in each iterative step. Several examples are introduced to illustrate the accuracy and efficiency of the proposed method for estimating the time-dependent failure probability by simultaneously considering the computational cost and precision.

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