Spectral analysis of randomly distributed scatterers for ultrasonic grain size estimation

Abstract

Since the average grain size is an important parameter in material characterization, the non-destructive evaluation of the microstructure in polycrystalline materials using ultrasonic backscattered echoes has significant practical implications. However, the complexity of the ultrasonic backscattered signal, which consists of interrering multiple echoes with random positions and amplitudes, makes accurate grain size evaluation difficult with conventional signal processing techniques. This Paper introduces an alternative approach which examines the spectrum of an ensemble of randomly distributed scatterers with known distribution to establish a relationship between the spectral and temporal statistical properties of the scatterers. Theoretical derivations based on a one-dimensional point scattered model show that the average grain size can be extracted from the power spectrum of the backscattered echoes. Using a non-linear least-squares technique, the theoretical grain power spectrum is curve-fitted to the sample grain power spectrum to estimate the mean and standard deviation of the grain size. Computer simulations based on this technique show that the average grain size can be extracted from the power spectrum of the backscattered echoes, indicating the potential feasibility of this technique for material characterization.