Direct approach in inverse problems for dynamic systems

A direct and effective approach is presented for the inverse problem of dynamic structural systems, which is related to structural optimization, system identification, and damage detection. The structural modifications are sought for the characteristic changes assigned from the design goals or modal measurements. A finite element method is used for the system analysis and inverse problem. Mathematical programming techniques are applied for the minimization of the deviation of the finite element model from the desired inverse system, along with an objective function of least structural change. The modal method is based on the perturbation equations of a set of selected degrees of freedom and the energy equation associated with the frequency change. The mode shape change is expressed as the sum of the baseline mode shape and complementary vector, which plays a very important role in the search for the inverse solution. The linear perturbation equation is employed to get an initial approximation, which can be improved through iterations with the nonlinear perturbation equation. The proposed method does not involve the system reduction. Therefore, it is believed to be superior to conventional methods, which suffer from the residual error due to transformation of the eigenproblem.