Crack Identification of a Continuous Beam Like Structure in the Presence of Uncertain Modal Data by Stochastic Model Updating

The problem of crack identification in continuous beam like structures is considered. The cracks’ locations and their depths are identified by employing experimental modal test results performed on the structure. The cracks are 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 are exposed to uncertainty including measurement errors, uncertainties in model order determination and etc. Uncertainty may also originate from manufacturing tolerances that are irreducible. To quantify uncertainties, a stochastic model updating is preformed on the structure using multiple sets of modal data. The crack locations and the depths are set to be unknown parameters of the model to be identified using model updating. 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. Here, the uncertainty propagation is performed by the so-called Monte-Carlo simulation for simulating the random processes.