Quantification of a concentrated point mass by Haar wavelets and machine learning

Abstract

The inverse problem of determining location and mass ratio of a concentrated point mass attached to the homogeneous Euler – Bernoulli beam was considered in this article. Under the assumption that the size of the point mass was small compared to the total mass of the beam, it was shown that the problem could be solved in terms of point-mass-induced changes in the natural frequencies or mode shapes. Predictions of the point mass location and its mass ratio were made by the artificial neural networks or the random forests. The dimensionless natural frequency parameters or the first mode shape transformed into the Haar wavelet coefficients were used at the inputs of the machine learning methods. The simulation studies indicated that the combined approach of the natural frequencies, Haar wavelets and neural networks produced accurate predictions. The results presented in this article could help in understanding the behaviour of more complex structures under similar conditions and provide apparent influence on design of beams.