A Fuzzy Model for Predicting the Group and Phase Velocities of Circumferential Waves Based on Subtractive Clustering

Acoustic scattering is a highly effective tool for non-destructive control and structural analysis. In many real-world applications, understanding acoustic scattering is essential for accurately detecting and characterizing defects, assessing material properties, and evaluating structural integrity without causing damage. One of the most critical aspects of characterizing targets—such as plates, cylinders, and tubes immersed in water—is the analysis of the phase and group velocities of antisymmetric circumferential waves (A1). Phase velocity helps identify and characterize wave modes, while group velocity allows for tracking energy, detecting, and locating anomalies. Together, they are essential for monitoring and diagnosing cylindrical shells. This research employs a Sugeno fuzzy inference system (SFIS) combined with a Fuzzy Subtractive Clustering (FSC) identification technique to predict the velocities of antisymmetric (A1) circumferential signals propagating around an infinitely long cylindrical shell of different b/a radius ratios, where a is the outer radius, and b is the inner radius. These circumferential waves are generated when the shell is excited perpendicularly to its axis by a plane wave. Phase and group velocities are determined by using resonance eigenmode theory, and these results are used as training and testing data for the fuzzy model. The proposed approach demonstrates high accuracy in modeling and predicting the behavior of these circumferential waves. The fuzzy model’s predictions show excellent agreement with the theoretical results, as confirmed by multiple error metrics, including the Mean Absolute Error (MAE), Standard Error (SE), and Mean Relative Error (MRE).