Update stiffness matrix using the displacement output feedback technique

The analytical matrices of a finite element model are generally symmetric and positive definite (semidefinite). How to ensure that the coefficient matrices of the adjusted model have such properties is an important yet challenging task in the process of model updating. In this paper, we put forward a direct method to update the stiffness matrix of the undamped structural systems by means of the displacement output feedback technique. Utilizing the QR-decomposition and the singular value decomposition, the required displacement output feedback gain matrix is found, and the explicit representation of the optimal adjusted stiffness matrix is achieved. The introduced method can ensure that the updated stiffness matrix is symmetric and positive semidefinite. Finally, two numerical examples verify the accuracy of the results obtained.