Modeling the Cut-off Frequency of Acoustic Signal with an Adaptative Neuro-Fuzzy Inference System (ANFIS)

An Adaptative Neuro-Fuzzy Inference System (ANFIS), new flexible tool, is applied to predict the cut-off frequencies of the symmetric and the anti-symmetric circumferential waves (Si and Ai, i=1,2) propagating around an elastic aluminum cylindrical shell of various radius ratio b/a (a: outer radius and b: inner radius). The time-frequency of Wigner-Ville and the proper modes theory are used in this study to compare and valid the frequencies values predicted by the ANFIS model. The useful data, of the cut-off frequencies (ka)c, are used to train and to test the performances of the model. These data are determined from the values calculated using the proper modes theory of resonances and also from those determined using the time-frequency images of Wigner-Ville. The material density, the radius ratio b/a, the index i of the symmetric and the anti-symmetric circumferential waves, and the longitudinal and transverse velocities of the material constituting the tube, are selected as the input parameters of the ANFIS model. This technique is able to model and to predict the cut-off frequencies, of the symmetric and the anti-symmetric circumferential waves, with a high precision, based on different estimation errors such as mean relative error (MRE), mean absolute error (MAE) and standard error (SE). A good agreement is obtained between the output values predicted using the propose model and those computed by the proper modes theory.