REAK: Reliability analysis through Error rate-based Adaptive Kriging

Wang, Zeyu; Shafieezadeh, Abdollah

doi:10.1016/j.ress.2018.10.004

Cited by 133 publications

(46 citation statements)

References 32 publications

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“…All the neighbors of u are bounded by a niche. The radius of niche is estimated by the density of current candidate solutions and adaptively changed along with generation t, as shown in Equation (18).…”

Section: Exploration Of Multiple Mppsmentioning

confidence: 99%

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: Exploration Of Multiple Mppsmentioning

confidence: 99%

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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“…The maximum (or minimum) point, also called as the best next point, is expected to maximally enhance the Kriging. Several learning functions have been proposed from different perspectives, including U function [41], the expected feasibility function (EFF) [29], cumulative confidence level (CCL) [32], the expected risk function (ERF) [42], information entropy-based function H [43], least improvement function [44], the reliability-based expected improvement function [45], and error rate-based adaptive Kriging [46]. In spite of their differences, all learning function intends to enhance Kriging with points in the vicinity of limit state surface.…”

Section: G T T Xzmentioning

confidence: 99%

Kriging Model for Time-Dependent Reliability: Accuracy Measure and Efficient Time-Dependent Reliability Analysis Method

et al. 2020

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As the performance function of a mechanical structure is usually based on time-consuming computer codes, predicting time-dependent reliability analysis requires a large number of costly simulations in engineering. To reduce the number of evaluations of time-consuming models and enhance efficiency of time-dependent reliability analysis, Kriging is employed as a surrogate of original performance function. Firstly, a quantitative measure of the error of Kriging-based estimation of time-dependent failure probability is obtained by derivation. Dividing the quantitative measure by the Kriging-based estimation, the associated relative error is approximately estimated. Secondly, to construct an accurate Kriging model using fewer samples, a DoE (the design of experiments) strategy is developed. The idea is to adaptively refresh Kriging model with the best next sample that could enhance Kriging model the most with regard to expectation. Finally, a Kriging-based time-dependent reliability analysis method is constructed. In the method, Kriging model is adaptively refreshed according to the proposed DoE strategy, until the relative error of estimated probability of failure below a given threshold. The threshold could be quantitatively adjusted to accuracy requirement of reliability analysis. The proposed method can predict the evolution of failure probability over time. Its advantage is validated by three numerical examples. INDEX TERMS Time-dependent reliability analysis, Kriging, Monte Carlo simulation, the best next sample.

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“…al [21]. Other methods have also been presented to address specific problems such as small failure probabilities (rare events) estimations [3,22,23,24,25,7,26] , multiple failure regions problems [27,28,29,30] or systems failure probabilities assessment [6,31,5,2,9,32].…”

Section: Introductionmentioning

confidence: 99%

Adaptive coupling of reduced basis modeling and Kriging based active learning methods for reliability analyses

Menz

Gogu

Dubreuil

et al. 2020

Reliability Engineering & System Safety

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Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive. Hence, advanced methods are required to reduce the number of calls to the expensive computer codes. Adaptive sampling based reliability analysis methods are one promising way to reduce computational costs. Reduced order modelling is another one. In order to further reduce the numerical costs of Kriging based adaptive sampling approaches, the idea developed in this paper consists in coupling both approaches by adaptively deciding whether to use reduced-basis solutions in place of full numerical solutions whenever the performance function needs to be assessed. Thus, a method combining such adaptive sampling based reliability analyses and reduced basis modeling is proposed using on an efficient coupling criterion. The proposed method enabled significant computational cost reductions, while ensuring accurate estimations of failure probabilities.

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REAK: Reliability analysis through Error rate-based Adaptive Kriging

Cited by 133 publications

References 32 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

Kriging Model for Time-Dependent Reliability: Accuracy Measure and Efficient Time-Dependent Reliability Analysis Method

Adaptive coupling of reduced basis modeling and Kriging based active learning methods for reliability analyses

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