Fractal Characterization of Ultrasonic Signals from Polycrystalline Materials

The concept of fractal geometry has been introduced to characterize discrete time domain ultrasonic signals scattered from two different polycrystalline materials, aluminium and brass, using the pulse echo method. The fractal dimensions of these scattered signals were evaluated by box-counting method and Hursts rescaled range analysis. These signals were found to possess unique fractal dimensions, which remained invariant even with the change in the sampling rate of signal capture. Observed variations of the fractal dimensions and the Hurst spectra of these scattered ultrasonic signals are interpreted in the light of acoustic scattering. It is seen that scattered ultrasonic signals from aluminium are self-similar in character and anti-persistent in nature but, in the case of brass, they are self-affine and persistent in nature. Hursts spectra revealed that scattered ultrasonic signals from brass possess multifractality.