An active weight learning method for efficient reliability assessment with small failure probability

Meng, Zeng; Zhang, Zhuohui; Li, Gang; Zhang, Dequan

doi:10.1007/s00158-019-02419-z

Cited by 72 publications

(25 citation statements)

References 54 publications

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“…Through giving small weight to the sample points of larger density and balancing the probability of selected sample space, the selected sample points can be distributed uniformly. 53…”

Section: An Active Learning Methods Combining Adaptive Kriging and Weighted Penalty Modelmentioning

confidence: 99%

An active learning method combining adaptive kriging and weighted penalty for structural reliability analysis

You

Zhang

Tang

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part O:

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Reducing the surrogate model-based method computation without loss of prediction accuracy remains a significant challenge in structural reliability analysis. The unbalanced probability density, important information in critical region and information redundancy of added sample points are ignored in most of traditional surrogate-based methods, resulting in heavy computational burden. In this work, an active learning combining adaptive Kriging method and weighted penalty (AK-WP) is proposed to analyze the reliability of engineering structures. Firstly, an active learning and weighted penalty function (WPLF) is the result of integrating active learning method, weighted function and penalty function, which is proposed to find the most probable point (MPP). Meanwhile, to avoid redundant information, the best suitable MPP is determined by a proposed distance law established between the found MPP and the existing design of experiment (DoE). Secondly, the Kriging model is refined according to best suitable MPP in each iteration. Thirdly, the failure probability is estimated by the Monte Carlo sample points from the n-ball domain until the convergence condition is satisfied. The accuracy and efficiency of the proposed method are demonstrated by some numerical examples including the highly nonlinear, the small probability problems and implicit function, as well as a real engineering application.

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“…Through giving small weight to the sample points of larger density and balancing the probability of selected sample space, the selected sample points can be distributed uniformly. 53…”

Section: An Active Learning Methods Combining Adaptive Kriging and Weighted Penalty Modelmentioning

confidence: 99%

An active learning method combining adaptive kriging and weighted penalty for structural reliability analysis

You

Zhang

Tang

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part O:

View full text Add to dashboard Cite

show abstract

“…The second analytical example is a four branches series system with two-dimension input variable, it has been studied in Refs. 26 , 28,36 The performance function of this example is defined asWhere the basic variables xinormal (normali=1,2) are both subject to standard normal distribution and mutually independent.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Furthermore, Meng et al. 35 proposed an active weight learning method based on Kriging variance and PDF. Zhang et al.…”

Section: Introductionmentioning

confidence: 99%

An improved active learning method combing with the weight information entropy and Monte Carlo simulation of efficient structural reliability analysis

Wang

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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A significant challenge of surrogate model-based structural reliability analysis (SRA) is to construct an accurate approximated model of the nonlinear limit state function (LSF) with high order and high dimension effectively. As one of the sequential update-strategies of design of experiment (DoE), the active learning method is more attractive in recent years due to greatly reduces the burden of reliability analysis. Although the active learning method based on information entropy learning function H and the line simulation (AK-LS) is a powerful tool of SRA, the computational burden from the iterative algorithm is still large during the learning process. In this research, an improved learning criterion, named the weight information entropy function (WH), is developed to update the DoE of Kriging-based reliability analysis. The WH learning function consists of the information entropy function and an adaptive weight function (W). Locations in the variable space and probability densities of the samples are taken accounted into the WH learning function, which is the most important difference from the H learning function. The samples that are closer to the LSF and has a greater probability density can be preferentially selected into the DoE comparing to others by changing the weight of information entropy during the learning process. The WH learning function can efficiently match the limit state function in an important domain rather than the entire variable space. Consequently, the approximated model of LSF via Kriging interpolation can be constructed more effectively. The new active learning method is developed based on Kriging model, in which WH learning function and Monte Carlo simulation (MCS) are employed. Finally, several engineering examples with high non-linearity are analyzed. Results shown that the new method are very efficient when dealing with intractable problems of SRA.

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“…In general, the safety factor method is usually used in engineering design where design variables are regarded as deterministic variables according to experience. However, because of the influence of machining errors, internal dispersion of materials, and accidental factors, the dimensional parameters, material characteristics, and external loads of the structure all have certain uncertainties [1][2][3][4][5]. erefore, when there are many uncertain factors in structure design, it is difficult to ensure the reliability of the structures when using the safety factor method without considering these uncertain factors.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive First-Order Reliability Analysis Method for Nonlinear Problems

Wang

Zhang

Song

2020

Mathematical Problems in Engineering

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The HL-RF algorithm of the first-order reliability method (FORM) is a widely useful tool in structural reliability analysis. However, the iteration results of HL-RF algorithm may not converge due to periodic cycles for some highly nonlinear reliability problems. In this paper, an adaptive first-order reliability method (AFORM) is proposed to improve solution efficiency for some highly nonlinear reliability problems by introducing an adaptive factor. In AFORM, based on the two-parameter approximate first-order reliability method, the new iteration point and the previous iteration point are used to obtain the corresponding angle, and the result of convergence is judged by angle condition. According to the convergence degree of the results, two iteration parameters of the approximate reliability method are adjusted continuously by adaptive factor. Moreover, iteration step size is adjusted by changing the parameters to improve the efficiency and robustness of FORM. Finally, four numerical examples and one mechanical reliability analysis example are used to verify the proposed method. Compared with the different algorithms, the results show that AFORM has better efficiency and robustness for some highly nonlinear reliability problems.

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An active weight learning method for efficient reliability assessment with small failure probability

Cited by 72 publications

References 54 publications

An active learning method combining adaptive kriging and weighted penalty for structural reliability analysis

An active learning method combining adaptive kriging and weighted penalty for structural reliability analysis

An improved active learning method combing with the weight information entropy and Monte Carlo simulation of efficient structural reliability analysis

An Adaptive First-Order Reliability Analysis Method for Nonlinear Problems

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