The intelligent design of launch vehicles requires the high calculation efficiency and accuracy of the approximation model, hence a fast cross-validation improved RBF approximation modeling method is proposed. Radial Basis Function (RBF) is one of the most widely-used approximation metamodeling methods for nonlinear multi-peak time-consuming models. Reasonable determination of the shape parameters could greatly improve the prediction accuracy of the RBF approximation model. To solve the problems that many variables are to be determined for RBF with multiple shape parameters and the calculations are complex, a shape parameters characterization method based on the local density of sampling points is proposed. With the proposed method, the determination of multiple RBF shape parameters is transformed into the determination of a single scale factor based on the local density of sampling points. Therefore, the shape parameters optimization problem in RBF is decoupled from the number of training samples. Furthermore, a general fast K-fold cross-validation algorithm is proposed to determine the scale factor of RBF. The fast higher-order inverse matrices formula and fast solution of cross-validation errors formula are derived, which further reduces the computational complexity of shape parameters determination of RBF from n3 to (n/k)3, and improves the efficiency and accuracy of the RBF approximation model. Different numerical examples and engineering examples are used to verify that the proposed method not only has competitive prediction accuracy and versatility but also has application value in the field of flight vehicle design.
WEN Qian
,
YANG Jiawei
,
WU Zeping
,
YANG Xixiang
,
ZHAO Hailong
,
WANG Zhixiang
. An approximation modeling method of launch vehicles improved by fast cross-validation[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022
, 43(9)
: 225967
-225967
.
DOI: 10.7527/S1000-6893.2021.25967
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