Testing for Nongaussian Fluctuations in Grain Noise
In ultrasonic nondestructive evaluation (NDE), grain noise corrupts the scattered wave field from a flaw in a polycrystalline material. Many probabilistic approaches associated with flaw detection and characterization utilize stochastic models in which grain noise is assumed uncorrected and zero-mean Gaussian distributed. Typically, the Gaussian assumptions is justified via heuristic arguments based on the central limit theorem. This paper presents the kurtosis test and the Shapiro-Wilk W test as methods to quantitatively test time domain noise ensembles for deviations from Gaussian statistics. We will establish, through the application of these hypothesis tests to grain noise, a quantitative tool which can be used to consider “how Gaussian” grain noise signals must be for Gaussian noise based signal processing procedures to out perform alternative approaches.