Modeling Multiresponse Surfaces for Airfoil Design with Multiple-Output-Gaussian-Process Regression

Liu, X.; Zhu, Qi‐Zhi; Lu, Hao

doi:10.2514/1.c032465

Cited by 42 publications

(19 citation statements)

References 18 publications

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“…Before model training, the data pre-processing is performed by normalizing y and each column of X to N (0, 1). In modeling, we employ the SE kernel in (2), and initialize the length-scales l 1 , · · · , l d as 0.5, the signal variance σ 2 f as 1.0, and the noise variance σ 2 ǫ as 0.1. All the scalable GPs except SVGP employ the CGD for inference with the maximum number of iterations as 100.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Surrogate-assisted modeling and optimization have been extensively deployed to facilitate modern aeroengine design [1,2,3,4] due to the representational capability of complex features. Among current surrogates (also known as machine learning models), as a non-parametric Bayesian model, Gaussian process (GP) [5] (also known as Kriging or emulator), has gained popularity.…”

Section: Introductionmentioning

confidence: 99%

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Understanding and comparing scalable Gaussian process regression for big data

Liu

Cai

Ong

et al. 2019

Knowledge-Based Systems

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As a non-parametric Bayesian model which produces informative predictive distribution, Gaussian process (GP) has been widely used in various fields, like regression, classification and optimization. The cubic complexity of standard GP however leads to poor scalability, which poses challenges in the era of big data. Hence, various scalable GPs have been developed in the literature in order to improve the scalability while retaining desirable prediction accuracy. This paper devotes to investigating the methodological characteristics and performance of representative global and local scalable GPs including sparse approximations and local aggregations from four main perspectives: scalability, capability, controllability and robustness. The numerical experiments on two toy examples and five real-world datasets with up to 250K points offer the following findings. In terms of scalability, most of the scalable GPs own a time complexity that is linear to the training size. In terms of capability, the sparse approximations capture the long-term spatial correlations, the local aggregations capture the local patterns but suffer from over-fitting in some scenarios. In terms of controllability, we could improve the performance of sparse approximations by simply increasing the inducing size. But this is not the case for local aggregations. In terms of robustness, local aggregations are robust to various initializations of hyperparameters due to the local attention mechanism. Finally, we highlight that the proper hybrid of global and local scalable GPs may be a promising way to improve both the model capability and scalability for big data.

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Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Understanding and comparing scalable Gaussian process regression for big data

Liu

Cai

Ong

et al. 2019

Knowledge-Based Systems

View full text Add to dashboard Cite

show abstract

“…1) As in SOCPL1, the bias term b is solved by another optimization problem (12). 2) Both the primal and dual problems belong to the SOCP problem and this formulation is named as SOCPL2.…”

Section: B Second-order Cone Program With the Second-order Loss (Socmentioning

confidence: 99%

“…Despite the success in various fields, however, the use of the SVR is limited because the standard SVR has a single output and does not fit well with multiple output regression problems such as time series prediction [8], localization in wireless sensor networks [3], [9], pose estimation in computer vision [10], robot control and identification [11], airfoil design [12], and biological data prediction [13].…”

Section: Introductionmentioning

confidence: 99%

General Dimensional Multiple-Output Support Vector Regressions and Their Multiple Kernel Learning

Chung

Kim

Lee

et al. 2015

IEEE Trans. Cybern.

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Support vector regression has been considered as one of the most important regression or function approximation methodologies in a variety of fields. In this paper, two new general dimensional multiple output support vector regressions (MSVRs) named SOCPL1 and SOCPL2 are proposed. The proposed methods are formulated in the dual space and their relationship with the previous works is clearly investigated. Further, the proposed MSVRs are extended into the multiple kernel learning and their training is implemented by the off-the-shelf convex optimization tools. The proposed MSVRs are applied to benchmark problems and their performances are compared with those of the previous methods in the experimental section.

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“…In recent years, finding a surrogate model with high accuracy and which needs only a small number of samples has been of great concern, and many new models have appeared including the kriging model (Namura et al, 2015), the radial basis function model (Wu Z.Y. et al, 2015), the artificial neural network model, the multiple output Gaussian process (MOGP) (Liu et al, 2014), and so on. Among all of the surrogate models, the polynomial-based response surface model (P-RSM) is the most mature one, which has been employed successfully in aerodynamic design and reverse design (Wu X.J.…”

Section: Sampling and Modeling Approachmentioning

confidence: 99%

A study of airfoil parameterization, modeling, and optimization based on the computational fluid dynamics method

Zhang

Huang

Wang

et al. 2016

J. Zhejiang Univ. Sci. A

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An excellent airfoil with a high lift-to-drag ratio may decrease oil consumption and enhance the voyage. Based on NACA 0012, an improved airfoil is explored in this paper. The class/shape function transformation has been proved to be a good method for airfoil parameterization, and in this paper it is modified to improve imitation accuracy. The computational fluid dynamics method is applied to obtain numerically the aerodynamic parameters of the parameterized airfoil, and the result is proved credible by comparison with available experimental data in the open literature. A polynomial-based response surface model and the uniform Latin hypercube sampling method are employed to decrease computational cost. Finally, the nonlinear programming by quadratic Lagrangian method is utilized to modify the multi-island genetic algorithm, which has an improved optimization effect than the method used on its own. The obtained result shows that the modified class/shape function transformation method produces a better imitation of an airfoil in the nose and tail regions than the original method, and that it will satisfy the tolerance zone of the model in a wind tunnel. The response surface model based on the uniform Latin hypercube sampling method gives an accurate prediction of the lift-to-drag ratio with changes in the design variables. The numerical result of the flow around the airfoil shows reasonable agreement with the experimental data graphically and quantitatively. Ultimately, an airfoil with better capacity than the original one is acquired using the multi-island genetic algorithm based nonlinear programming by quadratic Lagrangian optimization method. The pressure contours and lift-to-drag ratio along with the attack angle have been compared with those of the original airfoil, and the results demonstrate the strength of the optimized airfoil. The process for exploring an improved airfoil through parameterization to optimization is worth referencing in future work.

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Modeling Multiresponse Surfaces for Airfoil Design with Multiple-Output-Gaussian-Process Regression

Cited by 42 publications

References 18 publications

Understanding and comparing scalable Gaussian process regression for big data

Understanding and comparing scalable Gaussian process regression for big data

General Dimensional Multiple-Output Support Vector Regressions and Their Multiple Kernel Learning

A study of airfoil parameterization, modeling, and optimization based on the computational fluid dynamics method

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