Sensitivity-based adaptive sequential sampling for metamodel uncertainty reduction in multilevel systems

Xu, Can; Liu, Zhao; Zhu, Ping; Li, Mushi

doi:10.1007/s00158-020-02673-6

Cited by 9 publications

(1 citation statement)

References 53 publications

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“…They are mathematical tools that approximate coded simulations of a few well-chosen experiments (Wu et al, 2018). A number of surrogate models can be found in the literature, such as the radial basis function model (Chau et al, 2014), support vector regression (Huang et al, 2015), Kriging (Sacks et al, 1989;Xu et al, 2020), neural networks (Haykin, 1998;Li et al, 2022) and so on. Among them, the Kriging model, also known as Gaussian Process Regression (GPR), is one of the most famous models because it not only has a powerful function representation ability but also can provide an estimation of the model uncertainty.…”

Section: Introductionmentioning

confidence: 99%

An improved high-dimensional Kriging modeling method utilizing maximal information coefficient

Zhai,

Liu,

Song

et al. 2023

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PurposeKriging surrogate model has demonstrated a powerful ability to be applied to a variety of engineering challenges by emulating time-consuming simulations. However, when it comes to problems with high-dimensional input variables, it may be difficult to obtain a model with high accuracy and efficiency due to the curse of dimensionality. To meet this challenge, an improved high-dimensional Kriging modeling method based on maximal information coefficient (MIC) is developed in this work.Design/methodology/approachThe hyperparameter domain is first derived and the dataset of hyperparameter and likelihood function is collected by Latin Hypercube Sampling. MIC values are innovatively calculated from the dataset and used as prior knowledge for optimizing hyperparameters. Then, an auxiliary parameter is introduced to establish the relationship between MIC values and hyperparameters. Next, the hyperparameters are obtained by transforming the optimized auxiliary parameter. Finally, to further improve the modeling accuracy, a novel local optimization step is performed to discover more suitable hyperparameters.FindingsThe proposed method is then applied to five representative mathematical functions with dimensions ranging from 20 to 100 and an engineering case with 30 design variables.Originality/valueThe results show that the proposed high-dimensional Kriging modeling method can obtain more accurate results than the other three methods, and it has an acceptable modeling efficiency. Moreover, the proposed method is also suitable for high-dimensional problems with limited sample points.

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