An active learning kriging model for hybrid reliability analysis with both random and interval variables

Yuan, Xufeng; Liu, Yongshou; Gao, Yi; Zhang, Yishang; Gao, Zongzhan

doi:10.1007/s00158-014-1189-5

Cited by 174 publications

(78 citation statements)

References 31 publications

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“…In Equations (30) and (31), I is an m-dimensional unit vector, r(θ, x) and R(θ) are the correlation vector and correlation matrix, respectively, g denotes the response vector of x, i.e., [30].…”

Section: Erf Based-active Learning Kriging Surrogate Modelmentioning

confidence: 99%

“…Yang et al [28] proved that only a surrogate model that correctly predicts the sign of limit state function can meet the requirements of random-evidence hybrid reliability analysis. Based on this viewpoint, an extreme value symbol theorem and an expected risk function (ERF) [29,30] are introduced to construct an efficient active learning kriging (ALK) model under the framework of random-evidence hybrid reliability analysis. In order to screen out those JFEs on which the limit state function is monotone, a Karush-Kuhn-Tucker-based optimization (KKTO) method [28] is used in the proposed method to decrease the optimization burden.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Regional Sensitivity Analysis Method Based on Failure Probability with Hybrid Uncertainty

Zhang

et al. 2018

Energies

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Abstract:The application of reliability sensitivity analysis (RSA) to the high voltage direct current (HVDC) transmission systems is one of the hot topics in the future. A regional RSA method, the contribution to failure probability (CFP) plot, is investigated in this paper. This CFP plot contains both aleatory and epistemic uncertain variables modeled as random variables by probability theory and interval variables by evidence theory, respectively. A surrogate model of second-level limit state function needs to be established for each joint focal element (JFE), which is a time-consuming process. Additionally, an excessive number of Monte Carlo simulations (MCS) and optimizations may exceed the computing power of modern computers. In order to deal with the above problems and further decrease the computational cost, a more effective CFP calculation method under the framework of random-evidence hybrid reliability analysis is proposed. Three important improvements in the proposed method make the calculation of CFP more efficient and easy to implement. Firstly, an active learning kriging (ALK) based on the symbol prediction idea is employed to directly establish a surrogate model rather than a second-level limit state function with fewer function calls, which greatly simplifies construction of the model. Secondly, a random set-based Monte Carlo simulation (RS-MCS) is used to handle the issue of oversized optimization caused by too many JFEs. Thirdly, for further reducing the size of optimizations and improving the efficiency of the CFP calculation, a Karush-Kuhn-Tucker-based optimization (KKTO) method is recommended in the proposed method to solve the extreme value of performance function. A numerical example and an engineering example were studied to verify the accuracy, effectiveness and practicality of the proposed method. It can be seen from the results that regardless of whether it is modeling or computational efficiency, the proposed method is better than the original method.

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Section: Erf Based-active Learning Kriging Surrogate Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Efficient Regional Sensitivity Analysis Method Based on Failure Probability with Hybrid Uncertainty

Zhang

et al. 2018

Energies

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“…This paper aims to develop an effective method to calculate the bounds of failure probability in the framework of UUA. In our recent work , we have proved that, in terms of interval variables, the signs of maximum (minimum) of a Kriging model and that of the true performance function are the same if the Kriging model can rightly predict the sign of performance function. This indicates that constructing a Kriging model with right sign prediction will help to obtain sufficiently accurate results in UUA.…”

Section: Introductionmentioning

confidence: 98%

Unified reliability analysis by active learning Kriging model combining with random‐set based Monte Carlo simulation method

Yuan

Liu

Gao

2016

Numerical Meth Engineering

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Summary Reliability analysis with both aleatory and epistemic uncertainties is investigated in this paper. The aleatory uncertainties are described with random variables, and epistemic uncertainties are tackled with evidence theory. To estimate the bounds of failure probability, several methods have been proposed. However, the existing methods suffer the dimensionality challenge of epistemic variables. To get rid of this challenge, a so‐called random‐set based Monte Carlo simulation (RS‐MCS) method derived from the theory of random sets is offered. Nevertheless, RS‐MCS is also computational expensive. So an active learning Kriging (ALK) model that only rightly predicts the sign of performance function is introduced and closely integrated with RS‐MCS. The proposed method is termed as ALK‐RS‐MCS. ALK‐RS‐MCS accurately predicts the bounds of failure probability using as few function calls as possible. Moreover, in ALK‐RS‐MCS, an optimization method based on Karush–Kuhn–Tucker conditions is proposed to make the estimation of failure probability interval more efficient based on the Kriging model. The efficiency and accuracy of the proposed approach are demonstrated with four examples. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Because it requires large data samples and many repeated function evaluations to guarantee the convergence of the simulation results, the MCS is difficult to be applied in engineering applications. However, the MCS is often used as a standard solution to test the accuracy for other new methods [26].…”

Section: Fundamentals Of Evidence Theorymentioning

confidence: 99%

“…In addition, Luo et al [25] presented a combined probabilistic and set-valued description based on the multiellipsoid convex model description for grouped uncertain-but-bounded variables. Yang et al [26] developed an efficient and accurate method for hybrid reliability analysis with both random and interval variables based on active learning Kriging model. Xie et al [27] proposed an efficient hybrid reliability analysis method with random and interval variables, by decomposing the nested probability analysis loop and interval analysis loop into two separate loops.…”

Section: Introductionmentioning

confidence: 99%

Discretization Analysis Method of Hybrid Reliability Based on Evidence Theory

Tang

2018

Mathematical Problems in Engineering

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Aiming at the problem that various types of uncertainties, such as randomness, fuzziness, and interval, coexist in structure reliability analysis, a discretization analysis method of hybrid reliability for uncertain structures is proposed based on evidence theory (ET) in this article. Firstly, in order to establish a hybrid reliability model based on ET, a generalized density method (GDM) is developed to transform the fuzzy variables into equivalent random variables on the basis of the entropy equivalent method (EEM). Based on the discrete property of the basic probability assignment (BPA) in evidence theory, the random variables and fuzzy variables (equivalent random variables) are both discretized into subintervals according to six-sigma rule. Then, the BPA of each subinterval is solved and all focal elements are assigned BPA, so the evidence structure characterization of random and fuzzy variables is realized. Secondly, using Fmincon function based on the sequential quadratic programming (SQP) algorithm in MATLAB, the minimum and maximum values of performance function over each focal element can be acquired directly. Meanwhile, the production rules are used to judge the belonging of focal elements and classify them, so the numerical calculation of belief measure and plausibility measure is also realized. Finally, combined with the Monte Carlo Simulation (MCS) method, an engineering example is provided to demonstrate the feasibility and accuracy of the proposed method.

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An active learning kriging model for hybrid reliability analysis with both random and interval variables

Cited by 174 publications

References 31 publications

An Efficient Regional Sensitivity Analysis Method Based on Failure Probability with Hybrid Uncertainty

An Efficient Regional Sensitivity Analysis Method Based on Failure Probability with Hybrid Uncertainty

Unified reliability analysis by active learning Kriging model combining with random‐set based Monte Carlo simulation method

Discretization Analysis Method of Hybrid Reliability Based on Evidence Theory

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