Enhanced RBF neural network metamodelling approach assisted by sliced splitting-based K-fold cross-validation and its application for the stiffened cylindrical shells

Abstract

To build an enhanced radial basis function neural network (RBFNN) metamodel with improved generalization capabilities, this paper presents a novel sliced splitting-based K-fold cross-validation (SSKCV) method. Cross-validation is a promising method to construct the RBFNN metamodel but suffers the high variance and loss of information of observed sample points. To overcome the intrinsic deficiency, a sliced splitting strategy is proposed to allocate the observed sample points into K mutually exclusive and collectively exhaustive folds as evenly as possible. Further, the novel average expected prediction error (AEPE), analogous to a bias-variance tradeoff, is introduced as the loss function in SSKCV, which is more capable to evaluate the generalization error of the RBFNN metamodel. Finally, the optimal parameters in the RBFNN metamodels are determined by the SSKCV method, which enhances the metamodelling efficiency and precision. Compared with other variants of SSKCV and the state-of-art blind Kriging, the benefits of the SSKCV method in achieving excellent generalization performance are both validated in the high dimensional numerical benchmarks and the stiffened cylindrical shells.