Crack fault quantitative diagnosis based on finite element of B-spline wavelet on the interval

The model-based forward and inverse problems in the diagnosis of structural crack fault were studied. The forward problem is to solve the natural frequencies through cracked structural model and the inverse problem is to quantitatively determine the crack parameters using the experimentally metrical frequencies. Then, The one- dimension crack element of B-spline wavelet on the interval was built to solve the forward problem. Graphs of crack equivalent stiffness versus crack location were plotted by providing the first three natural frequencies as an input. The intersection of the three curves predicted the crack location and size. The experimental study verified the validity of the crack element in solving crack singular problems to overcome the disadvantages of traditional FEM (finite element method), such as low efficiency, insufficient accuracy, slow convergence to correct solutions etc. At the same time, it had adequate identification precision. The new method can be applied to prognosis and quantitative diagnosis of incipient cracks.