A fast approximate modeling method and application for sample cluster enhancement

To improve the analysis and optimization efficiency of stiffened composite cylindrical shells, a novel fast modeling method for the Augmented Radial Basis Function (ARBF) approximate model is proposed by fusing sample clustering and improved K-fold cross-validation. The K-means clustering algorithm is used to determine the optimal sample clustering, and the reference shape parameters of the samples are determined based on the local density of the samples. The scaling coefficient is introduced into each cluster to adjust the shape parameters adaptively, which effectively balance the optimization efficiency and accuracy of the shape parameters. The ARBF auxiliary approximation model is established by sample subset, and then the evaluation criteria of ARBF auxiliary approximation model generalization performance is established based on bias-variance decomposition, addressing the problem of insufficient utilization of traditional K-fold cross-validation sample information. Based on the block matrix inversion technique, a fast inversion method of the high-order coefficient matrix of the ARBF auxiliary approximation model is derived, and the scaling coefficient optimization method based on the improved K-fold cross-validation is proposed, which greatly reduces the computational complexity of determining the optimal shape parameters and improves the efficiency and accuracy of ARBF approximation modeling. Numerical and engineering examples validate that the optimal sample clustering and fast cross-validation have significant contributions to the approximate modeling efficiency and accuracy, and reduce the sensitivity of modeling efficiency to sample size and problem dimension. Moreover, using the same number of training samples, the modeling accuracy of the proposed method is significantly superior to that of other typical methods. The results verifies the effectiveness, advancemen and practical engineering value of the proposed method.