KURTOSIS AND SKEWNESS BASED COMPARISON OF HERMITE POLYNOMIAL AND JOHNSON TRANSFORMATIONS

In fatigue analyses and structural health monitoring applications, frequency domain theoretical fatigue life estimation models work best on Gaussian data, while many natural occurrences that influence the stress history have non-Gaussian properties. In order to handle realistic stress data, various transformations from non-Gaussian to Gaussian distributions are used. In this study, two transformation methods namely moment based Hermite polynomial model and Johnson transformation model were examined that have both a non-Gaussian to Gaussian transformation and a Gaussian to non-Gaussian transformation. These established transformation methods were compared for their distortion with reference to increasingly leptokurtic behavior and skewness. Normally distributed Gaussian data were distorted to a non-Gaussian form and then re-stored back to Gaussian form using parameters estimated from the non-Gaussian data were compared according to their kurtosis and skewness values. It was found that the restored da-ta contains significant deviation from Gaussian form the deviation depending on the distortion in the initial transformation and the deviations are more prominent in the Hermite Polynomial Transformation. These deviations in turn affect fatigue life estimations.