Adaptive anisotropic response surface method based on univariate dimension-reduction model and its high-order revision
ISSN: 0264-4401
Article publication date: 28 April 2020
Issue publication date: 28 October 2020
Abstract
Purpose
Based on univariate dimension-reduction model, this study aims to propose an adaptive anisotropic response surface method (ARSM) and its high-order revision (HARSM) to balance the accuracy and efficiency for response surface method (RSM).
Design/methodology/approach
First, judgment criteria for the constitution of a univariate function are derived mathematically, together with the practical implementation. Second, by combining separate polynomial approximation of each component function of univariate dimension-reduction model with its constitution analysis, the anisotropic ARSM is proposed. Third, the high-order revision for component functions is introduced to improve the accuracy of ARSM, namely, HARSM, in which the revision is also anisotropic. Finally, several examples are investigated to verify the accuracy, efficiency and convergence of the proposed methods, and the influence of parameters on the proposed methods is also performed.
Findings
The criteria for constitution analysis are appropriate and practical. Obtaining the undetermined coefficients for every component functions is easier than the existing RSMs. The existence of special component functions is useful to improve the efficiency of the ARSM. HARSM is helpful for improving accuracy significantly and it is more robust than ARSM and the existing quadratic polynomial RSMs and linear RSM. ARSM and HARSM can achieve appropriate balance between precision and efficiency.
Originality/value
The constitution of univariate function can be determined adaptively and the nonlinearity of different variables in the response surface can be treated in an anisotropic way.
Keywords
Acknowledgements
The research reported in this paper was conducted with the support of the National Key R&D Program of China (No. 2019YFD1101003), the National Natural Science Foundation of China (Grant No. 51678092) and the Fundamental Research Funds for the Central Universities (Project No. 2019CDXYTM0032). These supports are gratefully acknowledged.
Citation
Fan, W., Zhang, W., Li, M., Ang, A.H.-.-S. and Li, Z. (2020), "Adaptive anisotropic response surface method based on univariate dimension-reduction model and its high-order revision", Engineering Computations, Vol. 37 No. 9, pp. 3097-3125. https://doi.org/10.1108/EC-12-2019-0552
Publisher
:Emerald Publishing Limited
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