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.

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.

A Partial Safety Factor Method for System Reliability Prediction With Outsourced Components

2018 ◽  
Author(s):  
Zhengwei Hu ◽  
Xiaoping Du
Keyword(s):  
System Reliability ◽  
Joint Probability ◽  
System Level ◽  
Reliability Prediction ◽  
Safety Factors ◽  
Component Reliability ◽  
Reliability Method ◽  
Component Supplier ◽  
Partial Safety Factors ◽  
Joint Probability Density

System reliability is usually predicted with the assumption that all component states are independent. This assumption is particularly useful for systems with outsourced components. The assumption, however, may produce large errors in the system reliability prediction since many component states are strongly dependent. The purpose of this study is to develop an accurate system reliability method that can produce complete joint probability density function (PDF) of all the component states, thereby leading to accurate system reliability predictions. The proposed method works for systems whose failures are caused by excessive loading. In addition to the component reliability, system designers also ask for partial safety factors for shared loadings from component suppliers. The information is then sufficient for building a system-level joint PDF. Algorithms are designed for a component supplier to generate partial safety factors, which enables accurate system reliability predictions without requiring proprietary information from component suppliers.

A Partial Safety Factor Method for System Reliability Prediction With Outsourced Components

2019 ◽  
Vol 5 (2) ◽  
Author(s):  
Zhengwei Hu ◽  
Xiaoping Du
Keyword(s):  
System Reliability ◽  
Joint Probability ◽  
System Level ◽  
Safety Factors ◽  
Component Reliability ◽  
Reliability Method ◽  
Component Supplier ◽  
Partial Safety Factors ◽  
Joint Probability Density ◽  
Probability Density Function Pdf

System reliability is usually predicted with the assumption that all component states are independent. This assumption may not accurate for systems with outsourced components since their states are strongly dependent and component details may be unknown. The purpose of this study is to develop an accurate system reliability method that can produce complete joint probability density function (PDF) of all the component states, thereby leading to accurate system reliability predictions. The proposed method works for systems whose failures are caused by excessive loading. In addition to the component reliability, system designers also ask for partial safety factors for shared loadings from component suppliers. The information is then sufficient for building a system-level joint PDF. Algorithms are designed for a component supplier to generate partial safety factors. The method enables accurate system reliability predictions without requiring proprietary information from component suppliers.

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 Time-Variant Reliability Analysis Method Based on Stochastic Process Discretization

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
C. Jiang ◽  
X. P. Huang ◽  
X. Han ◽  
D. Q. Zhang
Keyword(s):  
Stochastic Process ◽  
Reliability Analysis ◽  
System Reliability ◽  
Limit State ◽  
Complex Structure ◽  
Random Variable ◽  
State Function ◽  
Analysis Method ◽  
Reliability Problem ◽  
Reliability Method

Time-variant reliability problems caused by deterioration in material properties, dynamic load uncertainty, and other causes are widespread among practical engineering applications. This study proposes a novel time-variant reliability analysis method based on stochastic process discretization (TRPD), which provides an effective analytical tool for assessing design reliability over the whole lifecycle of a complex structure. Using time discretization, a stochastic process can be converted into random variables, thereby transforming a time-variant reliability problem into a conventional time-invariant system reliability problem. By linearizing the limit-state function with the first-order reliability method (FORM) and furthermore, introducing a new random variable, the converted system reliability problem can be efficiently solved. The TRPD avoids the calculation of outcrossing rates, which simplifies the process of solving time-variant reliability problems and produces high computational efficiency. Finally, three numerical examples are used to verify the effectiveness of this approach.

Recovering Missing Component Dependence for System Reliability Prediction via Synergy between Physics and Data

2021 ◽  
pp. 1-39
Author(s):  
Huiru Li ◽  
Xiaoping Du
Keyword(s):  
System Reliability ◽  
Traditional Method ◽  
Joint Probability ◽  
Systems Design ◽  
Physical Models ◽  
Design System ◽  
Model Parameters ◽  
Component Reliability ◽  
Reliability Method ◽  
Series Systems

Abstract Predicting system reliability is often a core task in systems design. System reliability depends on component reliability and dependence of components. Component reliability can be predicted with a physics-based approach if the associated physical models are available. If the models do not exist, component reliability may be estimated from data. When both types of components coexist, their dependence is often unknown, and the component states are therefore assumed independent by the traditional method, which can result in a large error. This work proposes a new system reliability method to recover the missing component dependence, thereby leading to a more accurate estimate of the joint probability density (PDF) of all the component states. The method works for series systems whose load is shared by its components that may fail due to excessive loading. For components without physical models available, the load data are recorded upon failure, and equivalent physical models are created; the model parameters are estimated by the proposed Bayesian approach. Then models of all component states become available, and the dependence of component states, as well as their joint PDF, can be estimated. Four examples are used to evaluate the proposed method, and the results indicate that the method can produce more accurate predictions of system reliability than the traditional method that assumes independent component states.

Time-Dependent Reliability Analysis by a Sampling Approach to Extreme Values of Stochastic Processes

2012 ◽  
Author(s):  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Stochastic Processes ◽  
Reliability Analysis ◽  
Extreme Values ◽  
Limit State ◽  
Time Dependent ◽  
State Function ◽  
Limit State Function ◽  
Reliability Method ◽  
Time Invariant ◽  
State Functions

Maintaining high accuracy and efficiency is a challenging issue in time-dependent reliability analysis. In this work, an accurate and efficient method is proposed for limit-state functions with the following features: The limit-state function is implicit with respect to time, and its input contains stochastic processes; the stochastic processes include only general strength and stress variables, or the limit-state function is monotonic to these stochastic processes. The new method employs random sampling approaches to estimate the distributions of the extreme values of the stochastic processes. The extreme values are then used to replace the corresponding stochastic processes, and consequently the time-dependent reliability analysis is converted into its time-invariant counterpart. The commonly used time-invariant reliability method, the First Order Reliability Method, is then applied for the time-variant reliability analysis. The results show that the proposed method significantly improves the accuracy and efficiency of time-dependent reliability analysis.

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.

The SVC Based AFOSM Method for the Structure Reliability Sensitivity Analysis

2013 ◽  
Vol 477-478 ◽  
pp. 146-149
Author(s):  
Wei Dong Chen ◽  
Ping Jia ◽  
Xian De Wu ◽  
Yan Chun Yu ◽  
Feng Chao Zhang ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Support Vector ◽  
State Function ◽  
Structure Reliability ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Reliability Method ◽  
First Order Second Moment

The limit state function (LSF) is implicit to many structure reliability analysis problems, which may make some classical reliability method complicated to be applied. One of the surrogate methods-support vector classification (SVC) was applied in the structural reliability analysis herein which has not been applied to structure reliability analysis until recent years. Then the advanced first order second moment method (AFOSM) can be applied. The expressions of structure system reliability sensitivity to basic variable were deduced. The flow of how to call the SVC program was presented. An example was shown to compare the SVC based method with some other classical reliability analysis methods. The results are accurately accepted and the advantages of SVC are analyzed.

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