Characterization and prediction of the backscattered form function of an immersed cylindrical shell using hybrid fuzzy clustering and bio-inspired algorithms

The acoustic scattering of a plane wave by an elastic cylindrical shell is studied. A new approach is developed to predict the form function of an immersed cylindrical shell of the radius ratio b/a (‘b’ is the inner radius and ‘a’ is the outer radius). The prediction of the backscattered form function is investigated by a combined approach between fuzzy clustering algorithms and bio-inspired algorithms. Four famous fuzzy clustering algorithms: the fuzzy c-means (FCM), the Gustafson-Kessel algorithm (GK), the fuzzy c-regression model (FCRM) and the Gath-Geva algorithm (GG) are combined with particle swarm optimization and genetic algorithm. The symmetric and antisymmetric circumferential waves A, S 0 , A 1 , S 1 and S 2 are investigated in a reduced frequency ( k 1 a ) range extends over 0.1 k 1 a 225 ( k 1 is the wave number). The time-frequency representation of Smoothed Pseudo Wigner-Ville (SPWV) is applied on the predicted and calculated acoustic backscattered form functions. This representation is used as a comparison criterion between the calculated form function by the analytical method and that predicted by the proposed approach on the one hand and is used to extract the predicted cut-off frequencies on the other hand. Moreover, the transverse velocity of the material constituting the cylindrical shell is extracted. The computational results show that the proposed approach is very efficient to predict the form function and consequently, for acoustic characterization purposes.