Stiffness and damage identification with model reduction technique

For structural health monitoring, it is impractical to use full measurement to identify the unknown parameters. When one attempts to retrieve second-order parameters from the identified state space model, various methodologies impose different restrictions on the number of sensors and actuators employed, assuming that all the modes of the structure can be successfully identified. This paper explores the possibility of performing this inverse vibration problem without minimal restriction on the number of the measurements. Based on the numerical analysis of measured response due to known excitation, structural parameters such as stiffness values are identified and compared with the intended design values for damage detection. The proposed methodology is based on the Eigensystem Realization Algorithm (ERA) and the Observer/Kalman Filter Identification (OKID) approach to identify a first-order state space model. The first-order model is then transformed into a second-order model in order to evaluate the system stiffness. The focus is on estimation of all stiffness values from the condensed stiffness matrices by model reduction making use of System Equivalent Reduction Expansion Process (SEREP). The required optimization is accomplished by the Genetic Algorithm (GA). The efficiency of the proposed technique is shown by numerical examples for multi-storey shear building subjected to random excitation, taking into consideration the effects of noisy data. The results indicate that the proposed methodology offers reasonably accurate identification in terms of locating and quantifying damage.