Multiple Failure Modes Reliability Modeling and Analysis in Crack Growth Life Based on JC Method

Sun, Yuan; Liu, Chao; Zhang, Qing; Qin, Xianrong

doi:10.1155/2017/2068620

Cited by 9 publications

(3 citation statements)

References 5 publications

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“…This theory deals with the problem of choosing the best time to take a specific action. It covers a broad group of problems investigated in various branches of engineering [ 20 , 21 , 22 , 23 , 24 ]. Here, we focus on the so-called blackjack-type stopping problems, which were studied in [ 25 , 26 ].…”

Section: Blackjack-type Optimal Stopping Problemsmentioning

confidence: 99%

Optimal Stopping Rules for Preventing Overloading of Multicomponent Systems

2023

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When random-strength components work as an interconnected parallel system, then its carrying capacity is random as well. In a case where such a multicomponent system is a subject of the stepwise-growing workload, some of its components fail and their loads are taken over by the ones that are intact. When the loading process is continued, the additional loads trigger consecutive failures that degrade the system, eventually leading to a complete failure. If the goal of the system is to carry as much load as possible, then the loading process should be continued, but no longer than until the loading capacity of the whole system is reached. On the other hand, with every additional load step, a failure of the system becomes more probable, as the carrying capacity is random and known solely through its probability distribution. In such cases, the decision on when to cease the loading process is not obvious. We introduce and analyse a minimal model of failure spreading in an array of progressively loaded pillars controlled by a decision-maker who stops the process when a required load is attained. We show how to construct an optimal stopping rule. Under some additional assumptions regarding the adopted loss function, it is argued that the optimal stopping rule is of the threshold type and it significantly depends on the shape of the load-step probability distribution.

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Section: Blackjack-type Optimal Stopping Problemsmentioning

confidence: 99%

Optimal Stopping Rules for Preventing Overloading of Multicomponent Systems

2023

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“…Kriging models can be built in MATLAB by means of the Dace toolbox proposed by Nielsen [12] . 2.2 Mean point method and Monte Carlo method BP neural network method [13] , JC interface method [14] , Monte-Carlo method, and first second order moment method are all probabilistic methods to solve the reliability index, and each probabilistic method has a different range of adaptation and the accuracy of the obtained reliability index is different. After the experimental verification of the selected probabilistic models, the mean point method (MEAN) and Monte-Carlo Simulation (MCS) are the most suitable for solving the reliability index of specimens with the required accuracy.…”

Section: 𝜃The Key Parameters Based On Gaussian Modelmentioning

confidence: 99%

Reliability analysis of structures containing cracks based on kriging model

Liao,

Zhang,

Zhang

2023

Preprint

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The fatigue reliability of structural elements with penetration cracks under stress loading is analysed using the Kriging model. The model is established using the “FEM + M integral” stress intensity factor modelling method, and the reliability of the numerical modelling is determined by comparing the theoretical and simulated values of the stress intensity factor. A kriging probability model is established, and the reliability of the cracked structure is obtained based on the mean point method and the Monte Carlo method. The influence law of the statistical characteristics of the random parameters on the reliability of crack containment specimens is investigated. It is concluded that the stress P is the most sensitive to the influence of the reliability of the cracked structure, followed by the crack length a, and the plate width W is the least sensitive to the influence of the reliability.

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“…Among these methods, RF method and NATAF are the most popular ones in the realistic engineering applications, as they only require partial probability information including the marginal distributions and correlation matrix. In the early days, compared with the nonlinear NATAF, the RF method, which is based on equivalent Normal conditions, is more popular and often recommended for uncorrelated non-Normal reliability problems because of its simplicity and easiness [Huang et al (2014); Sun et al (2017)]. In China, the design code "unified standard for reliability design of engineering structures (GB50153-2008)" [2008] also adopts RF method to deal with uncorrelated non-Normal variables.…”

Section: Introductionmentioning

confidence: 99%

Improvements of Rackwitz–Fiessler Method for Correlated Structural Reliability Analysis

Zhou

Xiao

Zhang

et al. 2019

Int. J. Comput. Methods

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Rackwitz–Fiessler (RF) method is well accepted as an efficient way to solve the uncorrelated non-Normal reliability problems by transforming original non-Normal variables into equivalent Normal variables based on the equivalent Normal conditions. However, this traditional RF method is often abandoned when correlated reliability problems are involved, because the point-by-point implementation property of equivalent Normal conditions makes the RF method hard to clearly describe the correlations of transformed variables. To this end, some improvements on the traditional RF method are presented from the isoprobabilistic transformation and copula theory viewpoints. First of all, the forward transformation process of RF method from the original space to the standard Normal space is interpreted as the isoprobabilistic transformation from the geometric point of view. This viewpoint makes us reasonably describe the stochastic dependence of transformed variables same as that in Nataf transformation (NATAF). Thus, a corresponding enhanced RF (EnRF) method is proposed to deal with the correlated reliability problems described by Pearson linear correlation. Further, we uncover the implicit Gaussian copula hypothesis of RF method according to the invariant theorem of copula and the strictly increasing isoprobabilistic transformation. Meanwhile, based on the copula-only rank correlations such as the Spearman and Kendall correlations, two improved RF (IRF) methods are introduced to overcome the potential pitfalls of Pearson correlation in EnRF. Later, taking NATAF as a reference, the computational cost and efficiency of above three proposed RF methods are also discussed in Hasofer–Lind reliability algorithm. Finally, four illustrative structure reliability examples are demonstrated to validate the availability and advantages of the new proposed RF methods.

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Multiple Failure Modes Reliability Modeling and Analysis in Crack Growth Life Based on JC Method

Cited by 9 publications

References 5 publications

Optimal Stopping Rules for Preventing Overloading of Multicomponent Systems

Optimal Stopping Rules for Preventing Overloading of Multicomponent Systems

Reliability analysis of structures containing cracks based on kriging model

Improvements of Rackwitz–Fiessler Method for Correlated Structural Reliability Analysis

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