航空学报2025，Vol.46Issue(22)：61-77,17.DOI:10.7527/S1000-6893.2025.31755
样本分簇增强的快速近似建模方法及应用
A fast approximate modeling method and application for sample cluster enhancement
摘要
Abstract
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 approxima-tion 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 insuffi-cient 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 re-duces the computational complexity of determining the optimal shape parameters and improves the efficiency and ac-curacy of ARBF approximation modeling.Numerical and engineering examples validate that the optimal sample clus-tering 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 num-ber 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.关键词
复合材料加筋圆柱壳/增广径向基函数近似模型/样本分簇/K折交叉验证/分块矩阵求逆Key words
stiffened composite cylindrical shell/augmented radial basis function approximation model/sample clus-tering/K-fold cross-validation/block matrix inversion分类
航空航天引用本文复制引用
王悦,王志祥,李道奎,雷勇军..样本分簇增强的快速近似建模方法及应用[J].航空学报,2025,46(22):61-77,17.基金项目
国家自然科学基金(52405301) （52405301）
湖南省自然科学基金(2024JJ6453) National Natural Science Foundation of China(52405301) （2024JJ6453）
Natural Science Foundation of Hunan Province(2024JJ6453) （2024JJ6453）
