Systemidentifikation zur Modellierung mechanischer Strukturen : Markovparameter zur experimentellen Schadenserfassung

The present work serves to describe a new methodology how structural changes can be located on the basis of vibration measurements. So far, vibration-based methods often use modal data. For the localisation and quantification of detected structural changes a comparison with a finite element model then is often necessary. The determination of a limited number of sensitive model parameters as necessary, which is necessary for this purpose, is challenging and influences the model quality significantly. In deviation thereto, parameters are generated in this work which are interpretable from the structure-mechanical aspect, but which are generated direct on the basis of experimentally acquired vibration signals, so that a finite element model is not required.
Using a model approach based on system theory the transfer behaviour of linear structures is modelled as black-box-model in state-space formulation. The system identification is effected using linear algebra methods. Initially the model parameters gained are interpretable from the purely mathematical aspect. In this work it is explained how these black-box state-space models can be transferred to physically interpretable white-box models. First, on the basis of theoretical considerations and using the mechanical equation of motion it is shown how Markov parameters and structure-mechanical parameters (mass, damping, stiffness) are associated with each other. Furthermore, it is described which theoretically necessary boundary conditions are to be guaranteed during the experimental application. This can hardly be achieved with real application. Therefore, corresponding structure-mechanical quantities based on Markov parameters are introduced on the basis of which a localisation of damage is still possible.
After the functionality of the presented methodology was proved by means of analytical and simulated vibration data it is applied using experimental data. On the basis of laboratory tests the behaviour of a beam structure is represented in detail. The structural change was applied using differently positioned weights and saw cuts for a modification of structural mass and stiffness. Finally, the results of an experimental large-scale test are presented using the example of an arch bridge made of prestressed concrete, where the failure of a prestressed concrete hanger could be localised.