The paper presents a model-based approach for the detection of structural damage with respect to location and extent from measured vibration test data. The method which is tolerant to small modeling errors is based upon an analytically redundant mathematical model approximately representing the undamaged structure.
The motivation was that in many practical cases it is not possible to obtain perfect correlation between the undamaged system and the original model due to modeling uncertainties or excessive modeling cost.
On the other hand, in the early phase of damage evolution the changes of the dynamical characteristics are very small. If the changes due to the damage are superimposed by the effects of mismodeling it is nearly impossible to get reliable diagnostic results. Therefore, an approach is presented here for the case that a perfect model cannot be obtained.
The resulting inverse problem usually is ill-posed, so that special attention must be paid to its accurate numerical solution. The application to damage detection problems requires the reduction of a large set of damage parameter candidates to a small subset of one or two parameters really describing the local change of the system. An orthogonalization strategy is given to reduce the parameter set and Akaike’s information criterion is used to confirm the correct size of the parametrization.
The method is applied to two laboratory structures: a multi-story frame and a damaged plate. The results show that the algorithm is able to localize and quantify the damage also in the presence of modeling errors.