System Reliability Analysis With Autocorrelated Kriging Predictions

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
Hao Wu ◽  
Zhifu Zhu ◽  
Xiaoping Du
Keyword(s):  
System Reliability ◽  
Limit State ◽  
Surrogate Models ◽  
First Order ◽  
Highly Nonlinear ◽  
Reliability Method ◽  
Reliability Methods ◽  
Computationally Intensive ◽  
Improved Accuracy ◽  
State Functions

Abstract When limit-state functions are highly nonlinear, traditional reliability methods, such as the first-order and second-order reliability methods, are not accurate. Monte Carlo simulation (MCS), on the other hand, is accurate if a sufficient sample size is used but is computationally intensive. This research proposes a new system reliability method that combines MCS and the Kriging method with improved accuracy and efficiency. Accurate surrogate models are created for limit-state functions with minimal variance in the estimate of the system reliability, thereby producing high accuracy for the system reliability prediction. Instead of employing global optimization, this method uses MCS samples from which training points for the surrogate models are selected. By considering the autocorrelation of a surrogate model, this method captures the more accurate contribution of each MCS sample to the uncertainty in the estimate of the serial system reliability and therefore chooses training points efficiently. Good accuracy and efficiency are demonstrated by four examples.

A System Reliability Method With Dependent Kriging Predictions

2016 ◽  
Author(s):  
Zhifu Zhu ◽  
Xiaoping Du
Keyword(s):  
System Reliability ◽  
Limit State ◽  
Surrogate Models ◽  
First Order ◽  
Highly Nonlinear ◽  
Reliability Method ◽  
Reliability Methods ◽  
Computationally Intensive ◽  
Improved Accuracy ◽  
State Functions

When limit-state functions are highly nonlinear, traditional reliability methods, such as the first order and second order reliability methods, are not accurate. Monte Carlo simulation (MCS), on the other hand, is accurate if a sufficient sample size is used, but is computationally intensive. This research proposes a new system reliability method that combines MCS and the Kriging method with improved accuracy and efficiency. Cheaper surrogate models are created for limit-state functions with the minimal variance in the estimate of the system reliability, thereby producing high accuracy for the system reliability prediction. Instead of employing global optimization, this method uses MCS samples from which training points for the surrogate models are selected. By considering the dependence between responses from a surrogate model, this method captures the true contribution of each MCS sample to the uncertainty in the estimate of the system reliability and therefore chooses training points efficiently. Good accuracy and efficiency are demonstrated by three examples.

Reliability Methods for Bimodal Distribution With First-Order Approximation1

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Zhangli Hu ◽  
Xiaoping Du
Keyword(s):  
Probability Density ◽  
Order Approximation ◽  
Limit State ◽  
Random Variables ◽  
Random Variable ◽  
State Function ◽  
First Order ◽  
Reliability Method ◽  
Reliability Methods ◽  
Basic Random Variable

In traditional reliability problems, the distribution of a basic random variable is usually unimodal; in other words, the probability density of the basic random variable has only one peak. In real applications, some basic random variables may follow bimodal distributions with two peaks in their probability density. When binomial variables are involved, traditional reliability methods, such as the first-order second moment (FOSM) method and the first-order reliability method (FORM), will not be accurate. This study investigates the accuracy of using the saddlepoint approximation (SPA) for bimodal variables and then employs SPA-based reliability methods with first-order approximation to predict the reliability. A limit-state function is at first approximated with the first-order Taylor expansion so that it becomes a linear combination of the basic random variables, some of which are bimodally distributed. The SPA is then applied to estimate the reliability. Examples show that the SPA-based reliability methods are more accurate than FOSM and FORM.

Time-Dependent System Reliability Analysis With Second-Order Reliability Method

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Hao Wu ◽  
Zhangli Hu ◽  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Limit State ◽  
Second Order ◽  
Time Dependent ◽  
Component Reliability ◽  
Reliability Method ◽  
Series Systems ◽  
State Functions ◽  
Time Dependent System

Abstract System reliability is quantified by the probability that a system performs its intended function in a period of time without failures. System reliability can be predicted if all the limit-state functions of the components of the system are available, and such a prediction is usually time consuming. This work develops a time-dependent system reliability method that is extended from the component time-dependent reliability method using the envelope method and second-order reliability method. The proposed method is efficient and is intended for series systems with limit-state functions whose input variables include random variables and time. The component reliability is estimated by the second-order component reliability method with an improve envelope approach, which produces a component reliability index. The covariance between component responses is estimated with the first-order approximations, which are available from the second-order approximations of the component reliability analysis. Then, the joint distribution of all the component responses is approximated by a multivariate normal distribution with its mean vector being component reliability indexes and covariance being those between component responses. The proposed method is demonstrated and evaluated by three examples.

Time-Dependent System Reliability Analysis With Second Order Reliability Method

2020 ◽  
Author(s):  
Hao Wu ◽  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Limit State ◽  
Second Order ◽  
Time Dependent ◽  
Component Reliability ◽  
Reliability Method ◽  
Series Systems ◽  
State Functions ◽  
Time Dependent System

Abstract System reliability is quantified by the probability that a system performs its intended function in a period of time without failure. System reliability can be predicted if all the limit-state functions of the components of the system are available, and such a prediction is usually time consuming. This work develops a time-dependent system reliability method that is extended from the component time-dependent reliability method that uses the envelop method and second order reliability method. The proposed method is efficient and is intended for series systems with limit-state functions whose input variables include random variables and time. The component reliability is estimated by the existing second order component reliability method, which produces component reliability indexes. The covariance between components responses are estimated with the first order approximations, which are available from the second order approximations of the component reliability analysis. Then the joint probability of all the component responses is approximated by a multivariate normal distribution with its mean vector being component reliability indexes and covariance being those between component responses. The proposed method is demonstrated and evaluated by three examples.

scholarly journals Integration of Statistics- and Physics-Based Methods—A Feasibility Study on Accurate System Reliability Prediction

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Zhengwei Hu ◽  
Xiaoping Du
Keyword(s):  
System Reliability ◽  
Learning Strategy ◽  
Limit State ◽  
Joint Probability ◽  
Reliability Prediction ◽  
Support Vector ◽  
State Function ◽  
Component Reliability ◽  
Reliability Method ◽  
State Functions

Component reliability can be estimated by either statistics-based methods with data or physics-based methods with models. Both types of methods are usually independently applied, making it difficult to estimate the joint probability density of component states, which is a necessity for an accurate system reliability prediction. The objective of this study is to investigate the feasibility of integrating statistics- and physics-based methods for system reliability analysis. The proposed method employs the first-order reliability method (FORM) directly for a component whose reliability is estimated by a physics-based method. For a component whose reliability is estimated by a statistics-based method, the proposed method applies a supervised learning strategy through support vector machines (SVM) to infer a linear limit-state function that reveals the relationship between component states and basic random variables. With the integration of statistics- and physics-based methods, the limit-state functions of all the components in the system will then be available. As a result, it is possible to predict the system reliability accurately with all the limit-state functions obtained from both statistics- and physics-based reliability methods.

System reliability prediction with shared load and unknown component design details

2017 ◽  
Vol 31 (3) ◽  
pp. 223-234 ◽  
Author(s):  
Zhengwei Hu ◽  
Xiaoping Du
Keyword(s):  
System Reliability ◽  
Limit State ◽  
Common Factor ◽  
Design Stage ◽  
Limited Information ◽  
System Load ◽  
Component Design ◽  
Reliability Method ◽  
Other Information ◽  
State Functions

AbstractIn many system designs, it is a challenging task for system designers to predict the system reliability due to limited information about component designs, which is often proprietary to component suppliers. This research addresses this issue by considering the following situation: all the components share the same system load, and system designers know component reliabilities with respect to the component load, but do not know other information, such as component limit-state functions. The strategy is to reconstruct the equivalent component limit-state functions during the system design stage such that they can accurately reproduce component reliabilities. Because the system load is a common factor shared by all the reconstructed component limit-state functions, the component dependence can be captured implicitly. As a result, more accurate system reliability can be produced compared with traditional methods. An engineering example demonstrates the feasibility of the new system reliability method.

A New Methodology for the Reliability Based Particle Swarm Optimization with Simulated Annealing

2011 ◽  
Vol 274 ◽  
pp. 101-111 ◽  
Author(s):  
Norelislam Elhami ◽  
Rachid Ellaia ◽  
Mhamed Itmi
Keyword(s):  
Particle Swarm Optimization ◽  
Simulated Annealing ◽  
Numerical Models ◽  
Limit State ◽  
Particle Swarm ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Swarm Optimization ◽  
Reliability Methods ◽  
State Functions

This paper presents a new methodology for the Reliability Based Particle Swarm Optimization with Simulated Annealing. The reliability analysis procedure couple traditional and modified first and second order reliability methods, in rectangular plates modelled by an Assumed Modes approach. Both reliability methods are applicable to the implicit limit state functions through numerical models, like those based on the Assumed Mode Method. For traditional reliability approaches, the algorithms FORM and SORM use a Newton-Raphson procedure for estimate design point. In modified approaches, the algorithms are based on heuristic optimization methods such as Particle Swarm Optimization and Simulated Annealing Optimization. Numerical applications in static, dynamic and stability problems are used to illustrate the applicability and effectiveness of proposed methodology. These examples consist in a rectangular plates subjected to in-plane external loads, material and geometrical parameters which are considered as random variables. The results show that the predicted reliability levels are accurate to evaluate simultaneously various implicit limit state functions with respect to static, dynamic and stability criterions.

Second-Order Reliability Method With First-Order Efficiency

2010 ◽  
Author(s):  
Xiaoping Du ◽  
Junfu Zhang
Keyword(s):  
Limit State ◽  
Saddlepoint Approximation ◽  
Quadratic Function ◽  
Second Order ◽  
State Function ◽  
Limit State Function ◽  
First Order ◽  
Reliability Method ◽  
Order Of Magnitude ◽  
Univariate Function

The widely used First Order Reliability Method (FORM) is efficient, but may not be accurate for nonlinear limit-state functions. The Second Order Reliability Method (SORM) is more accurate but less efficient. To maintain both high accuracy and efficiency, we propose a new second order reliability analysis method with first order efficiency. The method first performs the FORM and identifies the Most Probable Point (MPP). Then the associated limit-state function is decomposed into additive univariate functions at the MPP. Each univariate function is further approximated as a quadratic function, which is created with the gradient information at the MPP and one more point near the MPP. The cumulant generating function of the approximated limit-state function is then available so that saddlepoint approximation can be easily applied for computing the probability of failure. The accuracy of the new method is comparable to that of the SORM, and its efficiency is in the same order of magnitude as the FORM.

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