A Radial-Based Centralized Kriging Method for System Reliability Assessment

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Yao Wang ◽  
Dongpao Hong ◽  
Xiaodong Ma ◽  
Hairui Zhang
Keyword(s):  
System Reliability ◽  
High Efficiency ◽  
Reliability Assessment ◽  
System Failure ◽  
Kriging Method ◽  
Limit States ◽  
Density Region ◽  
High Probability Density ◽  
Failure Region ◽  
Computationally Intensive

System reliability assessment is a challenging task when using computationally intensive models. In this work, a radial-based centralized Kriging method (RCKM) is proposed for achieving high efficiency and accuracy. The method contains two components: Kriging-based system most probable point (MPP) search and radial-based centralized sampling. The former searches for the system MPP by progressively updating Kriging models regardless of the nonlinearity of the performance functions. The latter refines the Kriging models with the training points (TPs) collected from pregenerated samples. It concentrates the sampling in the important high-probability density region. Both components utilize a composite criterion to identify the critical Kriging models for system failure. The final Kriging models are sufficiently accurate only at those sections of the limit states that bound the system failure region. Its efficiency and accuracy are demonstrated via application to three examples.

Reliability Assessment Based on the Concept of Failure Surface Frontier

2005 ◽  
Author(s):  
Songqing Shan ◽  
G. Gary Wang
Keyword(s):  
High Efficiency ◽  
Limit State ◽  
Reliability Assessment ◽  
Failure Surface ◽  
Test Results ◽  
Limit States ◽  
Failure Region ◽  
Novel Concept ◽  
Quadratic Approximations ◽  
State Functions

This work proposes a novel concept of failure surface frontier (FSF), which is a hyper-surface consisting of the set of the non-dominated failure points on the limit states of a given failure region. FSF better represents the limit state functions for reliability assessment than conventional linear or quadratic approximations on the most probable point (MPP). Assumptions, definitions, and benefits of FSF are discussed first in detail. Then, a discriminative sampling based algorithm was proposed to identify FSF, from which reliability is assessed. Test results on well known problems show that reliability can be accurately estimated with high efficiency. The algorithm is also effective for problems of multiple failure regions, multiple most probable points (MPP), or failure regions of extremely small probability.

Extreme Value Metamodeling for System Reliability With Time-Dependent Functions

2015 ◽  
Author(s):  
Zhifu Zhu ◽  
Xiaoping Du
Keyword(s):  
Computational Efficiency ◽  
System Reliability ◽  
Extreme Values ◽  
Random Variables ◽  
Probability Of Failure ◽  
High Accuracy ◽  
Extreme Value ◽  
Time Dependent ◽  
System Failure ◽  
Kriging Method

The reliability of a system is usually measured by the probability that the system performs its intended function in a given period of time. Estimating such reliability is a challenging task when the probability of failure is rare and the responses are nonlinear and time variant. The evaluation of the system reliability defined in a period of time requires the extreme values of the responses in the predefined period of time during which the system is supposed to function. This work builds surrogate models for the extreme values of responses with the Kriging method. For the sake of computational efficiency, the method creates Kriging models with high accuracy only in the region that has high contributions to the system failure; training points of random variables and time are sampled simultaneously so that their interactions could be considered automatically. The example of a mechanism system shows the effectiveness of the proposed method.

Failure Surface Frontier for Reliability Assessment on Expensive Performance Function

2006 ◽  
Vol 128 (6) ◽  
pp. 1227-1235 ◽  
Author(s):  
Songqing Shan ◽  
G. Gary Wang
Keyword(s):  
State Of The Art ◽  
Reliability Assessment ◽  
Failure Surface ◽  
Test Results ◽  
Approximation Model ◽  
Limit States ◽  
Performance Function ◽  
Failure Region ◽  
Novel Concept ◽  
Quadratic Approximations

This work proposes a novel concept of failure surface frontier (FSF), which is a hyper-surface consisting of the set of non-dominated failure points on the limit states of a failure region. Assumptions, definitions, and benefits of FSF are described first in detail. It is believed that FSF better represents the limit states for reliability assessment (RA) than conventional linear or quadratic approximations on the most probable point. Then, a discriminative sampling based algorithm is proposed to identify FSF, based on which the reliability can be directly assessed for expensive performance functions. Though an approximation model is employed to approximate the limit states, it is only used as a guide for sampling and a supplementary tool for RA. Test results on well-known problems show that FSF-based RA on expensive performance functions achieves high accuracy and efficiency, when compared with the state-of-the-art results archived in literature. Moreover, the concept of FSF and proposed RA algorithm are proved to be applicable to problems of multiple failure regions, multiple most probable points, or failure regions of extremely small probability.

A New Numerical Method for General Failure Probability with Fuzzy Failure Region

2007 ◽  
Vol 353-358 ◽  
pp. 997-1000 ◽  
Author(s):  
Lei Chen ◽  
Zhen Zhou Lu
Keyword(s):  
Numerical Method ◽  
Failure Probability ◽  
High Efficiency ◽  
Joint Probability ◽  
Line Sampling ◽  
Failure Region ◽  
Random Failure ◽  
Total Integral ◽  
Variable Space ◽  
General Reliability

For general reliability analysis with fuzzy failure region F % , the general failure probability F P% is defined as the integral of product of μF% [g( y)] , the membership of performance function ( ) g y to F % , and joint Probability Density Function (PDF) f ( y) over , the total variable space, i.e. [ ( )] ( ) F F P μ g f d % = ∫ ∫ % y y y L . On the basis of line sampling, an efficient method for random failure probability analysis with clear failure region, a new numerical method is presented to calculate F P% . In the presented method, the total integral region is split into m clear sub-regions i F in a way that the value of g( y) in i F can be approximately viewed as i g , a constant independent of y , and the value of [ ( )] F μ % g y in i F can be viewed as a constant ( ) F i μ g % subsequently. Due to the closely invariant property of [ ( )] F μ g % x in i F and 1 2 m = F I F ILI F , F P% is transformed into the sum of ( ) F i μ g % ( ) i F ∫L∫ f y dy , where ( ) i F ∫L∫ f y dy is the random failure probability with the clear failure region i F and can be obtained by line sampling. The high efficiency of the presented method resulted from that of the line sampling is demonstrated by the illustration.

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