Acoustic characterization and prediction of the cut-off dimensionless frequency of an elastic tube by neural networks

A neural network is developed to predict cut-off dimensionless frequencies of the antisymmetric circumferential waves (A
_i
) propagating around an elastic circular cylindrical shell of different radius ratio b/a (a, outer radius; b, inner radius). The useful data to train and test the performances of the model are determinated from calculated trajectories of natural modes of resonances or extracted from time-frequency representations of Wigner-Ville of the acoustic backscattered time signal obtained from a computation. In this work, the studied tubes are made of aluminum or stainless steel. The material density, the radius ratio b/a, the index i of the antisymmetric waves, and the propagation velocities in the tube, are selected like relevant entries of the model of neural network. During the development of the network, several configurations are evaluated. The optimal model selected is a network with two hidden layers. This model is able to predict the cut-off dimensionless frequencies with a mean relative error (MRE) of about 1%, a mean absolute error (MAE) of 3.10
^-3
k
₁
a, and a standard error (SE) of 10
^-3
k
₁
a(k
₁
a is the dimensionless frequency, k
₁
is the wave number in water)