An Adaptive Meta-Modelling Approach for Multi-Dimensional Correlated Flow Field Responses

It has become common practice to build inexpensive surrogate models to supplant time-consuming numerical simulations. By gradually increasing the number of training samples, the efficiency of model construction can be significantly improved. This study proposes an adaptive meta-modelling approach for multi-dimensional correlated responses within the framework of proper orthogonal decomposition (POD) and the Kriging model. The algorithm begins with the adaptive sampling algorithm for each reduced-dimension response, which integrates the prediction variance, distances between samples, and sensitivity indicator of each parameter. The adaptive sampling criterion for each reduced-dimension response is weighted by the energy of the modal, forming the adaptive sampling algorithm for multi-dimensional correlated responses. Tests on an analytical function and M6 wing simulation show that, under the same number of training samples, the proposed adaptive algorithm results in a model with lower prediction error than the random sampling algorithm, offering a more efficient model for flow field prediction.