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.

Narrower System Reliability Bounds With Incomplete Component Information and Stochastic Process Loading

2017 ◽  
Vol 17 (4) ◽  
Author(s):  
Yao Cheng ◽  
Daniel C. Conrad ◽  
Xiaoping Du
Keyword(s):  
System Reliability ◽  
Operating Conditions ◽  
Reliability Estimation ◽  
Design Stage ◽  
Shared Environment ◽  
Limited Information ◽  
Reliability Bounds ◽  
Component Design ◽  
Wide Range ◽  
Stochastic Load

Incomplete component information may lead to wide bounds for system reliability prediction, making decisions difficult in the system design stage. The missing information is often the component dependence, which is a crucial source for the exact system reliability estimation. Component dependence exists due to the shared environment and operating conditions. But it is difficult for system designers to model component dependence because they may have limited information about component design details if outside suppliers designed and manufactured the components. This research intends to produce narrow system reliability bounds with a new way for system designers to consider the component dependence implicitly and automatically without knowing component design details. The proposed method is applicable for a wide range of applications where the time-dependent system stochastic load is shared by components of the system. Simulation is used to obtain the extreme value of the system load for a given period of time, and optimization is employed to estimate the system reliability bounds, which are narrower than those from the traditional method with independent component assumption and completely dependent component assumption. Examples are provided to demonstrate the proposed method.

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.

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 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.

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.

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.

Mechanical Component’s Dimension Design With Required Reliability by the Monte Carlo Method

2020 ◽  
Author(s):  
Xiaobin Le
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Failure Mode ◽  
Failure Modes ◽  
Limit State ◽  
Design Parameters ◽  
Mechanical Component ◽  
Component Design ◽  
The Monte Carlo Method ◽  
State Functions

Abstract Since the main design parameters in a mechanical component design have some uncertainties and should be treated as random variables, the reliability of a component is a better measurement of the safe status of a component. A component will not be reliable unless it is designed with specified reliability. Therefore, the mechanical component design should be a dimension design with the required reliability. The fundamental concept of the Monte Carlo method is to plug-in randomly generated numerical values into the governing equation of a design problem to get a trial result. The Monte Carlo method has become so powerful numerical simulation approach in almost every field such as optimization, numerical integration, and reliability calculation. But for reliability engineering, most of the literature shows how to use the Monte Carlo method to calculate the reliability of a component. This paper will propose the modified Monte Carlo method to determine a component dimension with required reliability. This paper first discusses and establishes typical limit state functions of a component under static loads. These limit state functions cover two failure modes including the failure mode due to strength and the failure mode due to excessive deformation. Then, the procedure and the flowchart of the modified Monte Carlo method will be explained in detail. The provided procedure and the flowchart are easy to be followed for compiling a MATLAB program to conduct a dimension design with required reliability. Two examples will show how to implement the proposed new method for conducting a dimension design with required reliability.

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.

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