A novel support vector regression algorithm incorporated with prior knowledge and error compensation for small datasets

Liu, Zhenyu; Xu, Yunkun; Qiu, Chao; Tan, Jianrong

doi:10.1007/s00521-018-03981-1

Cited by 14 publications

(3 citation statements)

References 25 publications

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“…where the coefficients w and b are the weight vector and bias term, respectively. This linear function can be constrained to the following optimization problem [10,11,52]. Using ε as the insensitive loss function, the corresponding SVR, which is called ε-SVR, can be represented as follows:…”

Section: Conflicts Of Interestmentioning

confidence: 99%

“…Therefore, a surrogate modeling method has been developed rapidly over the last three decades as an alternative for computationally expensive simulations that consumes less time [1]. A wide variety of surrogate models have been used in engineering design, such as polynomial response surface (PRS) [2,3], Kriging (KRG) [3][4][5][6], radial basis function (RBF) [7,8], and support vector regression (SVR) [8][9][10][11][12][13]. The PRS and SVR models can identify global trends for a given input data set; whereas, owing to the interpolation characteristics, KRG and RBF have higher local accuracy around the training points.…”

Section: Introductionmentioning

confidence: 99%

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A Least Squares Ensemble Model Based on Regularization and Augmentation Strategy

Zhang¹,

Zhang²,

Liu³

et al. 2019

Applied Sciences

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Surrogate models are often used as alternatives to considerably reduce the computational burden of the expensive computer simulations that are required for engineering designs. The development of surrogate models for complex relationships between the parameters often requires the modeling of high-dimensional functions with limited information, and it is challenging to choose an effective surrogate model over the unknown design space. To this end, the ensemble models—combined with different surrogate models—offer effective solutions. This paper presents a new ensemble model based on the least squares method, which is a regularization strategy and an augmentation strategy; we call the model the regularized least squares ensemble model (RLS-EM). Three individual surrogate models—Kriging, radial basis function, and support vector regression—are used to compose the RLS-EM. Further, the weight factors are estimated by the least squares method without using the global or local error metrics, which are used in most existing methods. To solve the collinearity in the least squares calculation process, a regularization strategy and an augmentation strategy are developed. The two strategies help explore the unknown regions and improve the accuracy on one hand; on the other hand, the collinearity can be reduced, and the overfitting phenomenon that may occur can be avoided. Six numerical functions, from two-dimensional to 12-dimensional, and a computer numerical control (CNC) milling machine bed design problem are used to verify the proposed method. The results of the numerical examples show that RLS-EM saves a considerable amount of computation time while ensuring the same level of robustness and accuracy compared with other ensemble models. The RLS-EM used for the CNC milling machine bed design problem also shows good accuracy characteristics compared with other ensemble methods.

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Section: Conflicts Of Interestmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Least Squares Ensemble Model Based on Regularization and Augmentation Strategy

Zhang¹,

Zhang²,

Liu³

et al. 2019

Applied Sciences

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show abstract

“…The antenna theories and Feko are used for the calculation of power pattern with position errors. 12 Prediction models are built based on a linear programming support vector regression (LPSVR) [13][14][15] algorithm. Section 4 presents the evaluation results on measured data and Section 5 reports our conclusions.…”

Section: Introductionmentioning

confidence: 99%

A γ‐conical position error representation method considering high‐order position relevance of array elements

Guo

Liu

et al. 2021

Micro & Optical Tech Letters

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The position errors of array elements, which include systematic and random errors, are inevitable and could lead to the degradation of the radiation performance. For an array antenna, the systematic errors come from the continuous deformation of the reflector while the random errors come from the manufacturing and assembly of array elements. The accurate representation of position errors is important to evaluate the effects of position errors on performance in the design of an array antenna. In previous studies, many methods have been proposed to represent the systematic and random errors. However, few studies have considered the high-order position relevance of array elements resulting from the systematic errors, which could lead to the inaccurate representation of position errors. Here, a γ-conical representation method is proposed to consider the γ-order position relevance of successive array elements. The existing conical representation method and the proposed γ-conical representation method are used as comparisons to generate simulation data of position errors. The corresponding electrical performance of position errors is calculated with antenna theories and Feko. Prediction models are built based on a linear programming support vector regression algorithm to evaluate the ability of different representation methods. Finally, experiments are conducted on a platform with 8 Â 8 array elements to demonstrate the superiority of the γ-conical representation method.

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Synergy evaluation model of container multimodal transport based on BP neural network

Zhu

Wang

Zhang

2021

Neural Comput & Applic

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A novel support vector regression algorithm incorporated with prior knowledge and error compensation for small datasets

Cited by 14 publications

References 25 publications

A Least Squares Ensemble Model Based on Regularization and Augmentation Strategy

A Least Squares Ensemble Model Based on Regularization and Augmentation Strategy

A γ‐conical position error representation method considering high‐order position relevance of array elements

Synergy evaluation model of container multimodal transport based on BP neural network

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