Stochastic single crack identification of a continuous beam like structure

This paper considers identification of a crack in continuous beam like structures. The crack location and its depth are identified by employing experimental modal test results performed on the structure. The crack is modeled using generic elements to include the coupling effects between shear forces and bending moments at the crack section. In the identification procedure eigen- sensitivity analysis of continuous structure is performed by implicit differentiation of structure characteristic equation. The experimentally obtained modal results contain several sources of errors including measurement errors, uncertainties in model order determination and curve fitting errors. A stochastic model updating is preformed on the structure using multiple sets of modal data. The crack location and the depth are set to be unknown parameters of the model to be identified using model updating. The updating of the continuous model parameters is performed from the stochastic point of view. Stochastic distributions of multiple measurements are determined and via the desired uncertainty propagation method the distribution of model modal predictions is also formed. The model random parameters are determined by matching the distributions of these two sets modal data. The identification process is mainly divided into two adjustment steps of matching the parameters mean value and their related covariance matrix adjustments. Here, the uncertainty propagation is performed by the so-called Monte-Carlo simulation for simulating the random processes.

Keywords:

Crack identification , Stochastic model updating , Uncertainty , Eigen-value sensitivity