A time-variant reliability analysis method for non-linear limit-state functions with the mixture of random and interval variables

2020 ◽  
Vol 213 ◽  
pp. 110588 ◽  
Author(s):  
Fangyi Li ◽  
Jie Liu ◽  
Yufei Yan ◽  
Jianhua Rong ◽  
Jijun Yi ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Analysis Method ◽  
Interval Variables ◽  
Linear Limit ◽  
Non Linear ◽  
State Functions

scholarly journals An Efficient Time-Variant Reliability Analysis Method with Mixed Uncertainties

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 229
Author(s):  
Fangyi Li ◽  
Yufei Yan ◽  
Jianhua Rong ◽  
Houyao Zhu
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Random Variables ◽  
Equivalent Model ◽  
Independent Random Variables ◽  
Problem Analysis ◽  
Analysis Method ◽  
Calculation Algorithm ◽  
Reliability Problem ◽  
Interval Variables

In practical engineering, due to the lack of information, it is impossible to accurately determine the distribution of all variables. Therefore, time-variant reliability problems with both random and interval variables may be encountered. However, this kind of problem usually involves a complex multilevel nested optimization problem, which leads to a substantial computational burden, and it is difficult to meet the requirements of complex engineering problem analysis. This study proposes a decoupling strategy to efficiently analyze the time-variant reliability based on the mixed uncertainty model. The interval variables are treated with independent random variables that are uniformly distributed in their respective intervals. Then the time-variant reliability-equivalent model, containing only random variables, is established, to avoid multi-layer nesting optimization. The stochastic process is first discretized to obtain several static limit state functions at different times. The time-variant reliability problem is changed into the conventional time-invariant system reliability problem. First order reliability analysis method (FORM) is used to analyze the reliability of each time. Thus, an efficient and robust convergence hybrid time-variant reliability calculation algorithm is proposed based on the equivalent model. Finally, numerical examples shows the effectiveness of the proposed method.

Motion Reliability Analysis of a 3-RRR Parallel Manipulator With Random and Interval Variables

2016 ◽  
Author(s):  
Zhenhui Zhan ◽  
Xianmin Zhang
Keyword(s):  
Reliability Analysis ◽  
Parallel Manipulator ◽  
Random Variable ◽  
Parallel Manipulators ◽  
Analysis Method ◽  
Motion Error ◽  
Interval Variables ◽  
First Order Second Moment ◽  
Joint Clearances ◽  
Mcs Method

A general methodology for motion error and motion reliability analysis of planar parallel manipulators (PPMs) with random and interval variables is presented. The inherent uncertainties of the manipulator, including tolerances in manufactures, errors in inputs as well as joint clearances are taken into account. The error model of a 3-RRR parallel manipulator is built and the global sensitivity coefficients of motion errors to variations are defined and obtained. The joint clearances are treated as interval variables while the others are treated as random variables. As a result, the motion error of the manipulator could turn out to be the mixture of a random variable and an interval variable. A new motion reliability analysis method based on the First Order Second Moment (FOSM) method and the Monte Carlo simulation (MCS) method is developed for the manipulator with random and interval variables. This paper provides a new idea to better understand the motion reliability affected by the inherent uncertainties of PPMs.

A Novel Time-Variant Reliability Analysis Method Based on Failure Processes Decomposition for Dynamic Uncertain Structures

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Shui Yu ◽  
Zhonglai Wang
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Dynamic Properties ◽  
Limit State ◽  
Quadratic Function ◽  
State Function ◽  
Analysis Method ◽  
Engineering Structures ◽  
Reliability Problem ◽  
Time Invariant

Abstract Due to the uncertainties and the dynamic parameters from design, manufacturing, and working conditions, many engineering structures usually show uncertain and dynamic properties. This paper proposes a novel time-variant reliability analysis method using failure processes decomposition to transform the time-variant reliability problems to the time-invariant problems for dynamic structures under uncertainties. The transformation is achieved via a two-stage failure processes decomposition. First, the limit state function with high dimensional input variables and high order temporal parameters is transformed to a quadratic function of time based on the optimized time point in the first-stage failure processes decomposition. Second, based on the characteristics of the quadratic function and reliability criterion, the time-variant reliability problem is then transformed to a time-invariant system reliability problem in the second-stage failure processes decomposition. Then, the kernel density estimation (KDE) method is finally employed for the system reliability evaluation. Several examples are used to verify the effectiveness of the proposed method to demonstrate its efficiency and accuracy.

A SEQUENTIAL AUGMENTED METAMODELING METHOD FOR ENGINEERING RELIABILITY ANALYSIS

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Qian Wang ◽  
Jun Ji
Keyword(s):  
Sample Size ◽  
Reliability Analysis ◽  
Limit State ◽  
Engineering Systems ◽  
Analysis Method ◽  
Model Accuracy ◽  
Performance Function ◽  
Analysis And Design ◽  
Optimal Sample ◽  
Practical Engineering

Metamodeling methods provide useful tools to replace expensive numerical simulations in engineering reliability analysis and design optimization. The radial basis functions (RBFs) and augmented RBFs can be used to create accurate metamodels; therefore they can be integrated with a reliability analysis method such as the Monte Carlo simulations (MCS). However the model accuracy of RBFs depends on the sample size, and the accuracy generally increases as the sample size increases. Since the optimal sample size used to create RBF metamodels is not known before the creation of the models, a sequential RBF metamodeling method was studied. In each iteration of reliability analysis, augmented RBFs were used to generate metamodels of a limit state or performance function, and the failure probability was calculated using MCS. Additional samples were generated in subsequent analysis iterations in order to improve the metamodel accuracy. Numerical examples from literature were solved, and the failure probabilities based on the RBF metamodels were found to have a good accuracy. In addition, only small numbers of iterations were required for the reliability analysis to converge. The proposed method based on sequential RBF metamodels is useful for probabilistic analysis of practical engineering systems.

scholarly journals Hybrid Reliability Analysis for Spacecraft Docking Lock with Random and Interval Uncertainty

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jianguo Zhang ◽  
Jiwei Qiu ◽  
Pidong Wang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
Simple Problem ◽  
State Function ◽  
Limit State Function ◽  
Interval Variables ◽  
Reliability Method ◽  
Hybrid Reliability

This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis with hybrid variables, that is, random and interval variables. This method can significantly improve the computational efficiency for the abovementioned hybrid reliability analysis (HRA), while generally providing sufficient precision. In the proposed procedure, the hybrid problem is reduced to standard reliability problem with the polar coordinates, where an n-dimensional limit-state function is defined only in terms of two random variables. Firstly, the linear Taylor series is used to approximate the limit-state function around the design point. Subsequently, with the approximation of the n-dimensional limit-state function, the new bidimensional limit state is established by the polar coordinate transformation. And the probability density functions (PDFs) of the two variables can be obtained by the PDFs of random variables and bounds of interval variables. Then, the interval of failure probability is efficiently calculated by the integral method. At last, one simple problem with explicit expressions and one engineering application of spacecraft docking lock are employed to demonstrate the effectiveness of the proposed methods.

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