Quantification of cracks in beams on the Pasternak foundation using Haar wavelets and machine learning

Abstract

The inverse problem of crack identification, localisation and severity quantification is addressed in this article. The open cracks are simulated numerically in a homogeneous Euler–Bernoulli beam. The beam rests on the Pasternak foundation. Under the assumption that the size of the crack is small compared to the height of the beam, it is shown that the problem can be solved in terms of crack-induced changes in the natural frequencies or mode shapes. Predictions of the crack characteristics (location and severity) are made by artificial neural networks or random forests. The dimensionless natural frequency parameters or the first mode shape transformed into the Haar wavelet coefficients are used at the inputs of the machine learning methods. The numerical examples indicate that the combined approach of the natural frequencies, Haar wavelets, and machine learning produces accurate predictions. The results presented in the article can help in understanding the behaviour of more complex structures under similar conditions and provide apparent influence on the design of beams.

Keywords

• open cracks
• euler–bernoulli beam
• pasternak foundation
• haar wavelets
• neural network
• random forest.