Advanced time-dependent reliability analysis based on adaptive sampling region with Kriging model

Yan, Shi; Lü, Zhenzhou; He, Ruyang

doi:10.1177/1748006x20901981

Cited by 5 publications

(4 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proposed method is directly compared with crude MCS. The example is widely used in the literature as a benchmark example [23,30,39,52]. As shown by Fig.3, it deals with a steel bending and corroded beam.…”

Section: Validation Of the Proposed Methodsmentioning

confidence: 99%

“…To handle problems involving time-consuming codes, the idea of surrogate model-based methods for time-independent reliability analysis is usually adopted. Kriging [29][30][31] and polynomial chaos expansion [32][33][34] are used to reduce the number of evaluations of timeconsuming models. Their basic idea is to construct surrogate models using a limit number of design points, and then replace the original time-consuming model in time-variant reliability procedures.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Importance Sampling for Time-Variant Reliability Analysis

2021

View full text Add to dashboard Cite

Importance sampling methods are extensively used in time-independent reliability analysis. However, the kind of methods is barely studied in the field of time-variant reliability analysis. This paper presents an importance sampling method for time-variant reliability analysis. It increases the probability of sampling failure trajectories of a time-variant performance function. To develop the method, the instantaneous performance function at a predefined time instant is regarded as a time-independent one. A time-independent importance sampling is first implemented on the instantaneous performance function in order to obtain instantaneous samples of stochastic processes and random variables. Then, conditional trajectories of stochastic processes are generated on the condition of instantaneous samples achieved above, which utilizes the correlationship among instantaneous uncertainties at different time instants associated with stochastic processes. Subsequently, trajectories of the time-variant performance function are obtained. Validation results show that comparing with crude Monte Carlo simulation, the proposed method remarkably increases the probability of sampling failure trajectories. The efficiency and accuracy of the proposed method are demonstrated.

show abstract

Section: Validation Of the Proposed Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Importance Sampling for Time-Variant Reliability Analysis

2021

View full text Add to dashboard Cite

show abstract

“…6,26,27 Specifically, Zhou et al 28 developed a Kriging-based method to reduce the computational cost of the uncertainty analysis of motion errors by defining two motion errors. Shi et al 29 developed a novel time-dependent reliability analysis method based on active Kriging to estimate the time-dependent failure probability accurately and efficiently. Yang et al 30,31 reported two novel methods combined the active kriging model with IS to solve problems with very small failure probability.…”

Section: Introductionmentioning

confidence: 99%

An adaptive Kriging-based structural reliability analysis method combing dichotomy and improved convergence criterion

Zhou

Caixue

Yang

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part O:

View full text Add to dashboard Cite

Traditionally, analysis requires very large number of calculations; some engineering applications in particular require time-consuming numerical efforts. Classical reliability analysis methods with combinations of surrogate models can relieve the computational burden. An active learning reliability method that combines kriging and Monte Carlo simulation has drawn a great deal of attention in recent years. However, it is often challenging to find the most suitable sample point and speed up the convergence. In this paper, a method is proposed to deal with this problem, in which two strategies are employed: an active learning method is proposed to search the most suitable sample point in a specific region using the dichotomy method; an improved convergence criterion is developed based on standard deviation to improve the convergence speed. In addition, taking advantage of the excellent characteristics of Subset Simulation, a method for dealing with small failure probability problems is proposed based on the above strategies. The efficiency and accuracy of the proposed approaches are tested using three numerical examples and one finite element example. Results demonstrate its accuracy.

show abstract

“…Therefore, it is often combined with other methods to evaluate time-variant probability of failure, such as surrogate-model-based methods and a part of first-crossing-based methods. A great amount of the literature in regards to crude MCS as the benchmark compares efficiency and accuracy of other methods [6,24,25,30]. Subset simulations (SS), such as Markov Chain Monte Carlo (MCMC), SS with splitting method [31,32] and SS with splitting and partitioning in time [33], are efficient methods for precisely evaluating time-variant probability of failure.…”

Section: Introductionmentioning

confidence: 99%

An Importance Sampling Framework for Time-Variant Reliability Analysis Involving Stochastic Processes

2021

View full text Add to dashboard Cite

In recent years, methods were proposed so as to efficiently perform time-variant reliability analysis. However, importance sampling (IS) for time-variant reliability analysis is barely studied in the literature. In this paper, an IS framework is proposed. A multi-dimensional integral is first derived to define the time-variant cumulative probability of failure, which has the similar expression to the classical definition of time-invariant failure probability. An IS framework is then developed according to the fact that time-invariant random variables are commonly involved in time-variant reliability analysis. The basic idea of the proposed framework is to simultaneously apply time-invariant IS and crude Monte Carlo simulation on time-invariant random variables and stochastic processes, respectively. Thus, the probability of acquiring failure trajectories of time-variant performance function is increased. Two auxiliary probability density functions are proposed to implement the IS framework. However, auxiliary PDFs available for the framework are not limited to the proposed two. Three examples are studied in order to validate the effectiveness of the proposed IS framework.

show abstract

Advanced time-dependent reliability analysis based on adaptive sampling region with Kriging model

Cited by 5 publications

References 41 publications

Importance Sampling for Time-Variant Reliability Analysis

Importance Sampling for Time-Variant Reliability Analysis

An adaptive Kriging-based structural reliability analysis method combing dichotomy and improved convergence criterion

An Importance Sampling Framework for Time-Variant Reliability Analysis Involving Stochastic Processes

Contact Info

Product

Resources

About