An improved sufficient dimension reduction-based Kriging modeling method for high-dimensional evaluation-expensive problems

Song, Zhouzhou; Liu, Zhao; Zhang, Hanyu; Zhu, Ping

doi:10.1016/j.cma.2023.116544

Cited by 17 publications

(2 citation statements)

References 51 publications

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“…Surrogate models are commonly utilized to enhance the computational efficiency of the reliability analysis by approximating the relationship between inputs and outputs [23,24]. Popular surrogate models include the Kriging model [25][26][27], neural network (NN) [28,29], polynomial chaos expansion (PCE) [30,31], support vector machine (SVM) [32,33], etc. Among them, the Kriging model is widely used as an exact interpolation model with the convenience of obtaining the predicted value and prediction deviation simultaneously.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Kriging-Based Fourth-Moment Reliability Analysis Method for Engineering Structures

Wang,

Xie

et al. 2024

Applied Sciences

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The fourth-moment method can accurately perform a reliability analysis when it is challenging to determine the distribution of the random variable due to limited available samples. This method only utilizes the first four moments of the random variable and constructs the fourth-moment reliability index. However, it cannot be applied in engineering cases where the state function cannot be expressed explicitly, as it becomes difficult to establish a correlation between the first four moments of the random variable and the state function. Simplifying the state function forcefully may result in significant reliability prediction errors. To address this limitation, this study proposes an adaptive Kriging-based fourth-moment method for reliability analysis under complex state equations. The proposed method demonstrates better applicability and efficiency compared to existing methods. Several numerical examples are provided to validate the effectiveness and accuracy of the proposed method.

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Section: Introductionmentioning

confidence: 99%

An Adaptive Kriging-Based Fourth-Moment Reliability Analysis Method for Engineering Structures

Wang,

Xie

et al. 2024

Applied Sciences

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“…The computational burden can be reduced by using metamodels, also known as surrogate models, which approximate the behavior of complex models with simpler ones [28,29]. Methods such as polynomial response surface [30,31], response surface based multi-fidelity model [32], polynomial chaos expansion (PCE) [33,34], Gaussian process [35,36], Kriging [37,38], and neural network [39,40,41] are used to the creation of such metamodels. While the use of metamodels significantly reduces computational burden by approximating complex models with simpler ones, there are some critical drawbacks to this approach [42,43,44].…”

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confidence: 99%

Global Sensitivity Analysis of Structural Reliability Using Cliff Delta

Kala

2024

Preprint

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This paper introduces innovative sensitivity indices based on Cliff's Delta for global sensitivity analysis of structural reliability. These indices build on Sobol's method, using binary outcomes (success or failure), but avoid the need to calculate failure probability Pf and the associated distributional assumptions of resistance R and load F. Cliff's Delta, originally for ordinal data, evaluates the dominance of resistance over load without specific assumptions. The mathematical formulations for computing Cliff's Delta between R and F quantify structural reliability by assessing the random realizations of R > F using a double-nested-loop approach. The derived sensitivity indices, based on the squared value of Cliff's Delta, exhibit properties analogous to those in Sobol's sensitivity analysis, including first-order, second-order, and higher-order indices. This provides a comprehensive framework for evaluating the contributions of input variables and their interactions on structural reliability. This method is particularly significant for FEM applications, where repeated simulations of R or F are computationally intensive. The double-nested-loop algorithm of Cliff's Delta maximizes the extraction of information about structural reliability from these simulations. However, the high computational demand of Cliff's Delta is a disadvantage. Future research should optimize computational demands, especially for small Pf, where the inner loop may often be unnecessary.

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Data reduction in big data: a survey of methods, challenges and future directions

Khoei,

Singh

2024

Int J Data Sci Anal

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An improved sufficient dimension reduction-based Kriging modeling method for high-dimensional evaluation-expensive problems

Cited by 17 publications

References 51 publications

An Adaptive Kriging-Based Fourth-Moment Reliability Analysis Method for Engineering Structures

An Adaptive Kriging-Based Fourth-Moment Reliability Analysis Method for Engineering Structures

Global Sensitivity Analysis of Structural Reliability Using Cliff Delta

Data reduction in big data: a survey of methods, challenges and future directions

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