Crack fault diagnosis based on wavelet finite elements

The additional flexibility near the crack vicinity is evaluated according to linear and elastic fracture mechanics theory. The wavelet finite element stiffness matrix of crack is constructed and the algorithm for crack fault diagnosis based on wavelet finite elements is proposed, which overcomes the deterioration in the performance of classical finite element method caused by the crack top singularity. Graphs of crack equivalent stiffness versus crack location are plotted by providing the first three natural frequencies as an input. The intersection of the three curves predicts the crack location and size. The numerical examples of cracked shafts are presented to verify the accuracy of the method. It is observed that the identification error of crack location and size are both less than 2%. The new method for prognosis and diagnosis of incipient small crack can be applied to engineering practice effectively.