Enhanced anisotropic radius basis function metamodel based on recursive evolution Latin hypercube design and fast K -fold cross-validation

Metamodels are popular approaches to improve design efficiency in practical-engineering problems through replacing the time-consuming simulation models with easy-to-evaluate numerical models. To improve the generalization performance of the radial basis function (RBF) metamodel, this work sets up an anisotropic radial basis function metamodeling algorithm enhanced by recursive evolution Latin hypercube design and fast K -fold cross-validation method. First, the recursive evolution Latin hypercube design method splits the large-sample design into several small-sample designs to reduce computation cost and naturally splits the training samples into several folds for K -fold cross-validation. Then, the training samples are utilized to build the anisotropic RBF model, where the sensibility of model to each dimension is considered. In anisotropic RBF method, the optimization of hyperparameters in RBF model is transformed to anisotropic-scaling factors to improve the performance and computational efficiency. Afterwards, the evolutionary algorithm and fast K -fold cross-validation method are employed to optimize the anisotropic-scaling factors, and thus, the final metamodel is constructed. Finally, several numerical functions and an engineering case of cylindrical stiffened shell performance prediction are conducted to test the proposed enhanced anisotropic RBF metamodel. Results indicate that the proposed method is competitive compared with other popular metamodel methods and state-of-the-art multi-width RBF modeling methods, and can effectively deal with practical-engineering problems.