A variational approach for solving an inverse vibration problem

The present investigation is focused on the solution of a dynamic inverse problem which is concerned with the assessment of damage in structures by means of measured vibration data. This inverse problem has been presented as an optimization problem and has been solved through the use of the Variational Approach, i.e. the conjugate gradient method (CGM) coupled with the adjoint equation. The results have been presented in a satisfactory form when a small structure with few degrees of freedom (DOF) is considered, however, when a higher DOF structure is studied, the simple application of the variational approach is not any more satisfactory, being necessary the application of an additional methodology. In order to solve this difficulty, a new approach based on the use of the genetic algorithm (GA) method has been proposed. The GA method is used to generate a primary solution which is employed as the initial guess for the CGM. The application of this new approach has shown that better results can be achieved, although the computational time for the application analyzed here could be increased. The damage estimation has been evaluated using noiseless and noisy synthetic experimental data, and the reported results are concerned with both truss and beam-like structures, which have been modeled through a finite element technique. Moreover, in order to take into account the reduced set of experimental data to be employed in the optimization algorithm, a Guyan reduction technique has been adopted on the finite element formulation.