Estimation of low failure probability based on active learning Kriging model with a concentric ring approaching strategy

Yuan, Xufeng; Liu, Yongshou; Fang, Xiuyang; Cai-ying, MI

doi:10.1007/s00158-018-1960-0

Cited by 27 publications

(10 citation statements)

References 38 publications

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“…To search for the important failure regions, a concentric ring approaching (CRA) method was proposed by the authors based on the ALK model 39 . This method was called ALK‐CRA in 39 . The fusion of ALK model with the kernel‐density‐estimation‐based IS method (KDE‐IS) was researched and the method named ALK‐KDE‐IS was proposed in Reference 40.…”

Section: Introductionmentioning

confidence: 99%

“…39 This method was called ALK-CRA in. 39 The fusion of ALK model with the kernel-density-estimation-based IS method (KDE-IS) was researched and the method named ALK-KDE-IS was proposed in Reference 40. The fusion of ALK model and KDE-IS for hybrid reliability analysis was researched in Reference 41.…”

Section: Introductionmentioning

confidence: 99%

“…Firstly, Markov Chain Monte Carlo (MCMC) sampling is widely utilized to obtain important samples. [37][38][39][40] Because the acceptance ratio of new candidates shrinks along with the increase of dimension, the computational time of the learning process is remarkably increased during dealing with problems with a little more random variables. 38 Moreover, the samples generated by MCMC are frequently trapped in one failure region, 43 and the accuracy of the existing methods cannot be guaranteed.…”

Section: Introductionmentioning

confidence: 99%

“…. To search for the important failure regions, a concentric ring approaching (CRA) method was proposed by the authors based on the ALK model 39 . This method was called ALK‐CRA in 39 .…”

Section: Introductionmentioning

confidence: 99%

“…Although a great deal of work has been done, some fatal issues remain unsolved during fusing the ALK model and IS methods. Firstly, Markov Chain Monte Carlo (MCMC) sampling is widely utilized to obtain important samples 37‐40 . Because the acceptance ratio of new candidates shrinks along with the increase of dimension, the computational time of the learning process is remarkably increased during dealing with problems with a little more random variables 38 .…”

Section: Introductionmentioning

confidence: 99%

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Active learning method combining Kriging model and multimodal‐optimization‐based importance sampling for the estimation of small failure probability

Yuan

Cheng

2020

Numerical Meth Engineering

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A novel method which combines the active learning Kriging (ALK) model with important sampling is proposed in this paper. The main aim of the proposed method is to solve problems with very small failure probability and multiple failure regions. A surrogate limit state surface (LSS) which strikes a balance between the Kriging mean and variance is proposed. In each iteration, important samples of the surrogate LSS are generated, optimal training points are chosen, the Kriging model is updated and the surrogate LSS is refined. After several iterations, the surrogate LSS will converge to the true LSS. To obtain all the local and global most probable points (MPPs) on the surrogate LSS in each iteration, a recently proposed evolutionary algorithm from the field of multimodal optimization is introduced. In this way, none of the potential failure regions is missed and the unbiasedness of the proposed method is guaranteed. The contribution factor of each MPP is defined and a weighted multimodal instrumental sampling density is formulated. In this way, more attention is paid to the more important failure regions and training points are further saved. The performance of the proposed method is verified by six case studies.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…. To search for the important failure regions, a concentric ring approaching (CRA) method was proposed by the authors based on the ALK model 39 . This method was called ALK‐CRA in 39 .…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Active learning method combining Kriging model and multimodal‐optimization‐based importance sampling for the estimation of small failure probability

Yuan

Cheng

2020

Numerical Meth Engineering

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An efficient hybrid reliability analysis method based on active learning Kriging model and multimodal‐optimization‐based importance sampling

Wang

Yuan

Cai-ying

2021

Numerical Meth Engineering

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A novel method is proposed, which aims to solve rare‐event hybrid reliability problems with random and interval variables, where the performance function has various failure zones. It combines the active learning Kriging (ALK) model with importance sampling (IS) and evolutionary multimodal‐based multiobjective optimization (EMO‐MMO). The surrogate limit state surfaces (LSS) for the upper and lower failure probability bounds are respectively defined considering the Kriging variance. Failure candidate solutions located in different failure regions are generated by the EMO‐MMO method. Subsequently, all the most probable failure points (MPPs) are identified from those candidate solutions. The IS samples are simulated around the MPPs using the MPP‐based IS method. The IS samples located in unimportant regions are removed in order to improve the efficiency of approximating the surrogate LSSs. The optimal training points are selected from the truncated IS samples to update the Kriging model. After several training iterations, the surrogate LSSs are convergent. Ultimately, a reliable and unbiased estimation of the upper and lower failure probability bounds is provided. The performance of the ALK‐EMO‐IS‐HRA approach is verified through five application examples.

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Multi-fidelity Surrogate Assisted Reliability Design Optimization

Zhou¹,

Zhao²,

Hu³

et al. 2022

Multi-Fidelity Surrogates

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Estimation of low failure probability based on active learning Kriging model with a concentric ring approaching strategy

Cited by 27 publications

References 38 publications

Active learning method combining Kriging model and multimodal‐optimization‐based importance sampling for the estimation of small failure probability

Active learning method combining Kriging model and multimodal‐optimization‐based importance sampling for the estimation of small failure probability

An efficient hybrid reliability analysis method based on active learning Kriging model and multimodal‐optimization‐based importance sampling

Multi-fidelity Surrogate Assisted Reliability Design Optimization

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