Toward the robust establishment of variable-fidelity surrogate models for hierarchical stiffened shells by two-step adaptive updating approach

Since the high-fidelity model (HFM) of hierarchical stiffened shells is time-consuming, the sampling points based on HFM are generally few, which would result in a certain randomness of the sampling process. In some cases, the prediction accuracy of the variable-fidelity surrogate model (VFSM) is prone to be not robust and reliable. In order to improve the robustness of the prediction accuracy of VFSM, a two-step adaptive updating approach is proposed for the robust establishment of VFSM. In the first step, the leave-one-out (LOO) cross validation is carried out for sampling points of the low-fidelity model (LFM), aiming at finding out those with large prediction error. Then, these points are evaluated by HFM and then added into the original HFM set. In the second step, another LOO cross validation is performed on sampling points of the hybrid bridge function linking HFM and LFM. Based on the Voronoi diagram method, new updating points are chosen from where the largest prediction error of the bridge function lies, and then the VFSM is updated. After above two-step updating process, the VFSM is established. Three simple examples of test functions are firstly presented to verify the effectiveness and efficiency of the proposed method. Further, the proposed method is applied to an engineering example of hierarchical stiffened shells. In order to provide evaluation indexes for prediction accuracy and robustness of VFSM, the VFSM is established by multiple times, and the mean value and the standard deviation of the relative root mean square error (RRMSE) values of the multiple sets of VFSM are calculated. Results indicate that, under the similar computational cost, the mean value and the standard deviation of the RRMSE values of the proposed method decrease by 24.1% and 82.0% than those of the traditional VFSM based on the direct sampling method, respectively. Therefore, the high prediction accuracy and robustness of the proposed method is verified. Additionally, the total computational time of the proposed VFSM decreases by 70% than that of the surrogate model based on HFM when achieving the similar prediction accuracy, indicating the high prediction efficiency of the proposed VFSM.