04.2 - Aerostructures Design, Structural Dynamics, Aeroelasticity
IMPROVED STOCHASTIC PERTURBATION ALGORITHM FOR GENERALIZED REPEATED EIGENVALUES PROBLEM BASED ON SURROGATE MODEL
H.-C. Qiu¹, W.-C. Fan¹, Y.-N. Fang¹; ¹COMAC Shanghai Aircraft Manufacturing Co., Ltd., China
In order to investigate the uncertainty and its propagation in the problems of generalized repeated eigenvalues, within the uncertainties of design variables taking into account, an improved method based on stochastic perturbation method and surrogate model approach is presented in this work. Initially repeated eigenvalue undergoing changes of design variables is expressed by the perturbation expansions, in which the first-order perturbation term of repeated eigenvalue could be calculated by solving a standard eigenvalue equation; then, to avoid solving the eigenvalue equation repeatedly in structural uncertainty analysis, a surrogate model which consists of polynomial chaos expansions (PCE) is established to approximate the first-order perturbation term of repeated eigenvalue; omitting the second and higher-order perturbation terms, perturbed repeated eigenvalue is expressed as the combination of original repeated eigenvalue and the surrogate model; lastly, the statistical quantities of perturbed repeated eigenvalue are calculated directly on the basis of the surrogate model. Via this proposed method, not only the uncertainty propagation analysis, but also the dynamic reanalysis, structural design optimization and importance measure for structures associated with repeated eigenvalues can be performed and accomplished expediently. The accuracy and efficiency of the proposed method have been validated thoroughly by three numerical examples.