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A new response surface method based on the adaptive bivariate cut-HDMR

Wenliang Fan (School of Civil Engineering, Chongqing University, Chongqing, China and Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Ministry of Education, Chongqing, China)
Wei Shen (Department of Architecture and Architectural Engineering, Kyoto Daigaku, Kyoto, Japan)
Qingbin Zhang (School of Civil Engineering, Chongqing University, Chongqing, China)
Alfredo H.-S. Ang (Department of Civil and Environmental Engineering, University of California Irvine, Irvine, California, USA)

Engineering Computations

ISSN: 0264-4401

Article publication date: 17 May 2021

Issue publication date: 15 June 2021




The purpose of this study is to improve the efficiency and accuracy of response surface method (RSM), as well as its robustness.


By introducing cut-high-dimensional representation model (HDMR), the delineation of cross terms and the constitution analysis of component function, a new adaptive RSM is presented for reliability calculation, where a sampling scheme is also proposed to help constructing response surface close to limit-state.


The proposed method has a more feasible process of evaluating undetermined coefficients of each component function than traditional RSM, and performs well in terms of balancing the efficiency and accuracy when compared to the traditional second-order polynomial RSM. Moreover, the proposed method is robust on the parameter in a wide range, indicating that it is able to obtain convergent result in a wide feasible domain of sample points.


This study constructed an adaptive bivariate cut-HDMR by introducing delineation of cross-terms and constitution of univariate component function; and a new sampling technique is proposed.



The research presented in this paper was conducted with the support of the National Key R&D Program of China (Project 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.

Data availability statement: Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.


Fan, W., Shen, W., Zhang, Q. and Ang, A.H.-.-S. (2021), "A new response surface method based on the adaptive bivariate cut-HDMR", Engineering Computations, Vol. 38 No. 3, pp. 1402-1431.



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