Development of an optimized trend kriging model using regression analysis and selection process for optimal subset of basis functions

Lee, Hakjin; Lee, Duck-Joo; Kwon, Hyung-Il

doi:10.1016/j.ast.2018.01.042

Cited by 17 publications

(2 citation statements)

References 25 publications

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“…The number of active basis functions in the final model is N active and has to meet the constraint N active ≤ min 1≤k≤K (n k ) −1 (Lee et al [28]).…”

Section: Traditional Prs Modeling Methods Based On Cross Validationmentioning

confidence: 99%

Polynomial Response Surface based on basis function selection by multitask optimization and ensemble modeling

Zhao

Chen

et al. 2021

Complex Intell. Syst.

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Polynomial Regression Surface (PRS) is a commonly used surrogate model for its simplicity, good interpretability, and computational efficiency. The performance of PRS is largely dependent on its basis functions. With limited samples, how to correctly select basis functions remains a challenging problem. To improve prediction accuracy, a PRS modeling approach based on multitask optimization and ensemble modeling (PRS-MOEM) is proposed for rational basis function selection with robustness. First, the training set is partitioned into multiple subsets by the cross validation method, and for each subset a sub-model is independently constructed by optimization. To effectively solve these multiple optimization tasks, an improved evolutionary algorithm with transfer migration is developed, which can enhance the optimization efficiency and robustness by useful information exchange between these similar optimization tasks. Second, a novel ensemble method is proposed to integrate the multiple sub-models into the final model. The significance of each basis function is scored according to the error estimation of the sub-models and the occurrence frequency of the basis functions in all the sub-models. Then the basis functions are ranked and selected based on the bias-corrected Akaike’s information criterion. PRS-MOEM can effectively mitigate the negative influence from the sub-models with large prediction error, and alleviate the uncertain impact resulting from the randomness of training subsets. Thus the basis function selection accuracy and robustness can be enhanced. Seven numerical examples and an engineering problem are utilized to test and verify the effectiveness of PRS-MOEM.

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“…The number of active basis functions in the final model is N active and has to meet the constraint N active ≤ min 1≤k≤K (n k ) −1 (Lee et al [28]).…”

Section: Traditional Prs Modeling Methods Based On Cross Validationmentioning

confidence: 99%

Polynomial Response Surface based on basis function selection by multitask optimization and ensemble modeling

Zhao

Chen

et al. 2021

Complex Intell. Syst.

View full text Add to dashboard Cite

show abstract

“…Kriging surrogate model 36–41 was initially developed in the field of geostatistics, and it could be regarded as an interpolation model since it interpolates responses at all sample data points. By using this model, the estimation of the unknown response function of interest y(x) can be expressed as where x is a vector of design variable.…”

Section: Optimization Strategymentioning

confidence: 99%

Rotor blade aerodynamic shape optimization based on high-efficient optimization method

Qing

Zhao

2019

Proceedings of the Institution of Mechanical Engineers, Part G:

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In order to design a high-performance rotor, a high-efficient optimization method is established by coupling Kriging model and sequential quadratic programming with high-accuracy computational fluid dynamics method. In order to obtain the global optimal design point, the initial blade shape is optimized by using the Kriging model coupled with genetic algorithm based on the baseline rotor blade (Helishape 7A rotor). After that, the modified sequential quadratic programming method is employed to search the final blade shape based on the initial blade shape deeply. In the optimal process, the regions of design variables are restricted considering rotor dynamic characteristics. As a result, a new shape of rotor blade with characters of nonlinear twist, variational chord length, complex swept, and anhedral distributions is obtained. Compared with the baseline rotor, blade-tip vortex of the final optimized rotor is significantly weakened, the figure of merit of the final optimized rotor increases about 3.42%, and the peak of sound pressure decreases about 16.9%. At the same time, it is demonstrated that the final optimized rotor has better forward flight characteristics.

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A regularization method for constructing trend function in Kriging model

Zhang

Yao²,

et al. 2018

Struct Multidisc Optim

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Development of an optimized trend kriging model using regression analysis and selection process for optimal subset of basis functions

Cited by 17 publications

References 25 publications

Polynomial Response Surface based on basis function selection by multitask optimization and ensemble modeling

Polynomial Response Surface based on basis function selection by multitask optimization and ensemble modeling

Rotor blade aerodynamic shape optimization based on high-efficient optimization method

A regularization method for constructing trend function in Kriging model

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