Optimization of the Vibration Response of a Longitudinal-Transverse Stiffened Conical Shell Based on an Ensemble of Surrogates

The acceleration responses at certain points of the longitudinal-transverse stiffened conical shells in special frequency region are major matters of concern. Because the finite element models of the longitudinal-transverse stiffened conical shells have to be employed to calculate the vibration response of the structure at all frequencies under consideration, it requires a large amount of computational cost when the optimization is conducted. In order to optimize the vibration response of the longitudinal-transverse stiffened conical shell, the surrogate modeling method is used in this study to approximate the frequency-acceleration response function which makes the vibration response optimization affordable. Since different surrogate models often perform differently in different regions of the design space, an ensemble of surrogate models is utilized to maximize the overall accuracy over the whole design space. The ensemble of surrogates is a weighted combination of Kriging model, radial basis function (RBF) and support vector regression (SVR). The weights of the ensemble of surrogates vary in different regions and are determined by the estimated errors of the surrogate models at the study point. The smaller the estimated error is, the higher the weight is. Then the prediction of ensemble of surrogates is compared to the individual surrogate’s, and the results show that the accuracies of the ensemble of surrogates in peak regions are significant higher than its components. Based on the ensemble of surrogates, a vibration optimization of a longitudinal-transverse stiffened conical shell is conducted using genetic algorithm (GA). The design variables of the optimization are the thickness of the longitudinal-transverse stiffened conical shell and the height of stiffened structure. The objective is to minimize the highest acceleration of the shell and the calculations of the peak accelerations are approximated by the built ensemble of the surrogates. The constraints include the weight of the stiffened conical shell and structure size combination. The optimization results show that the proposed approach is efficient in optimization of the vibration response of longitudinal-transverse stiffened conical shells.