Dynamic force identification considering modeling errors using modal expansion method and relevant vector regression algorithm

Abstract

Accurate identification and estimation of external forces on launch vehicles, aircraft, and other in-service engineering structures plays a vital role in structural design and health monitoring. Considering structural modeling errors, this paper develops a novel force identification method based on modal expansion and relevant vector regression (RVR). Initially, the incomplete and noisy experimental modal data are used to modify the stiffness and mass matrices of the finite element (FE) model, reducing the impact of modeling errors on force identification accuracy. Subsequently, to account for noise disturbances and potential information about unknown initial conditions in the measured acceleration responses, the external forces and the unknown initial conditions are respectively expanded using trigonometric functions and the mode shapes based on the function fitting technique. On this basis, the force identification equation is established for the updated model. The RVR algorithm is integrated into modal expansion and force identification. Firstly, the mode shapes of the FE model are utilized to expand the incomplete and noisy experimental mode shapes to their full degree of freedom, significantly enhancing the accuracy of the model updating. Secondly, by combining the measured acceleration responses, the base coefficients can be solved sparsely, effectively identifying the dynamic forces even when unknown initial conditions are present.