A regularization method for constructing trend function in Kriging model

Zhang, Yi; Yao, Wen; Ye, Siyu; Chen, Xiaoqian

doi:10.1007/s00158-018-2127-8

Cited by 24 publications

(7 citation statements)

References 49 publications

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“…This work uses the global gaussian interpolation (Gong et al (2021b)), kriging (Zhang et al (2018)), support vector regression (SVR) (Schulz et al (2018)) and neural network(NN) (Erichson et al ( 2020)) as baselines. The number of test samples is set to 4000 for all methods and the number of training samples is set to 16000 for the supervised learning methods including the SVR, NN and the porposed method.…”

Section: Comparisons With Other Methodsmentioning

confidence: 99%

“…The other one takes advantage of the surrogate model-based methods to cope with those problems. The methods concerned about TFR is teeming with polynomial regression (Leon et al (2018)), kriging (Zhang et al (2018)), radial basis function(RBF) (Yao et al (2012)), support vector regression(SVR) (Yan et al (2018)), gappy proper orthogonal decomposition (GPOD) (Lei and Liu (2013)), Kalman filtering (Tian et al (2019)), Extreme Learning Machine(ELM) (Lei and Liu (2017)), neural network(NN) (Yan et al (2011);Erichson et al (2020)). However, these traditional surrogate model-based methods can hardly solve the high dimensional nonlinear problems well subject to a limited number of parameters, which means limited representation ability.…”

Section: Introductionmentioning

confidence: 99%

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A deep learning method based on patchwise training for reconstructing temperature field

Peng¹,

Li²,

Gong³

et al. 2022

Preprint

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Physical field reconstruction is highly desirable for the measurement and control of engineering systems. The reconstruction of the temperature field from limited observation plays a crucial role in thermal management for electronic equipment. Deep learning has been employed in physical field reconstruction, whereas the accurate estimation for the regions with large gradients is still diffcult. To solve the problem, this work proposes a novel deep learning method based on patchwise training to reconstruct the temperature field of electronic equipment accurately from limited observation. Firstly, the temperature field reconstruction (TFR) problem of the electronic equipment is modeled mathematically and transformed as an image-to-image regression task. Then a patchwise training and inference framework consisting of an adaptive UNet and a shallow multilayer perceptron (MLP) is developed to establish the mapping from the observation to the temperature field. The adaptive UNet is utilized to reconstruct the whole temperature field while the MLP is designed to predict the patches with large temperature gradients. Experiments employing finite element simulation data are conducted to demonstrate the accuracy of the proposed method. Furthermore, the generalization is evaluated by investigating cases under different heat source layouts, different power intensities, and different observation point locations. The maximum absolute errors of the reconstructed temperature field are less than 1K under the patchwise training approach.

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Section: Comparisons With Other Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A deep learning method based on patchwise training for reconstructing temperature field

Peng¹,

Li²,

Gong³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Step-by-Step Variable Selection Methods. Although the kriging model has a character of interpolator due to its stochastic process, penalty methods still could be used to select the important variables from the candidates to improve prediction accuracy [13].…”

Section: 2mentioning

confidence: 99%

Step-by-Step Penalized Blind Kriging Methods for Surrogate Modeling

Feng

Wang

et al. 2022

Mathematical Problems in Engineering

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When building a surrogate model, it is important to identify a proper mean function for the kriging model. The commonly used variable selection method is the penalized blind kriging (PBK) method. But this method could lead to a low time efficiency, which is not suitable for experiments with time-sensitive data. In this paper, we propose three step-by-step approaches for constructing an appropriate mean function to improve the prediction accuracy and time efficiency of the PBK method. Several functions and two engineering examples are used to prove the effectiveness of the proposed methods. From simulation results, we can see that Method 1 (M1) and Method 2 (M2) have been significantly improved in both the prediction accuracy and the time efficiency compared with PBK. Especially, in the Test function, compared with the traditional PBK method, the prediction accuracy of M2 is improved by 69.08 % and 26.13 % , respectively, under the penalty of Lasso and Elastic Net, and the time efficiency of M1 is improved by 85.15 % and 90.33 % , respectively, under the penalty of Lasso and Elastic Net. In addition, Method 3 (M3) has been significantly improved in prediction accuracy compared with PBK.

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“…The Kriging model assumes that the true deterministic response y(x) is realized with a trend function and a stochastic process z(x). The formulation can be written as [24]…”

Section: Krigingmentioning

confidence: 99%

An Effective Surrogate Ensemble Modeling Method for Satellite Coverage Traffic Volume Prediction

Zhang

Yao³

et al. 2019

Applied Sciences

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The satellite constellation network is a powerful tool to provide ground traffic business services for continuous global coverage. For the resource-limited satellite network, it is necessary to predict satellite coverage traffic volume (SCTV) in advance to properly allocate onboard resources for better task fulfillment. Traditionally, a global SCTV distribution data table is first statistically constructed on the ground according to historical data and uploaded to the satellite. Then SCTV is predicted onboard by a data table lookup. However, the cost of the large data transmission and storage is expensive and prohibitive for satellites. To solve these problems, this paper proposes to distill the data into a surrogate model to be uploaded to the satellite, which can both save the valuable communication link resource and improve the SCTV prediction accuracy compared to the table lookup. An effective surrogate ensemble modeling method is proposed in this paper for better prediction. First, according to prior geographical knowledge of the SCTV distribution, the global earth surface domain is split into multiple sub-domains. Second, on each sub-domain, multiple candidate surrogates are built. To fully exploit these surrogates and combine them into a more accurate ensemble, a partial weighted aggregation method (PWTA) is developed. For each sub-domain, PWTA adaptively selects the candidate surrogates with higher accuracy as the contributing models, based on which the ultimate ensemble is constructed for each sub-domain SCTV prediction. The proposed method is demonstrated and testified with an air traffic SCTV engineering problem. The results demonstrate the effectiveness of PWTA regarding good local and global prediction accuracy and modeling robustness.

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A regularization method for constructing trend function in Kriging model

Cited by 24 publications

References 49 publications

A deep learning method based on patchwise training for reconstructing temperature field

A deep learning method based on patchwise training for reconstructing temperature field

Step-by-Step Penalized Blind Kriging Methods for Surrogate Modeling

An Effective Surrogate Ensemble Modeling Method for Satellite Coverage Traffic Volume Prediction

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