Assessment of fatigue damage induced by Non-Gaussian bimodal processes with emphasis on spectral methods

Abstract

The stress on an engineering structure tends to be random and is usually assumed to be Gaussian or weakly non-Gaussian. In some situations, the power spectrum of stress also exhibits two distinct peaks in a bimodal profile. This study focuses on the fatigue damage estimation of softening non-Gaussian bimodal processes (kurtosis >3) with emphasis on spectral methods. Several classical spectral methods for Gaussian problems and a newly developed method by authors are examined. Correction factors derived from the Hermite transformation are used to handle the non-Gaussianity. Through comprehensive case studies, including ideal bimodal spectra and practical bimodal spectra in ocean engineering, the accuracy of the underlying Gaussian fatigue damage and the corresponding correction factor for each spectral method is investigated separately. The results demonstrate that when the non-Gaussianity is weak (kurtosis between 3 and 6), the correction factor is dominated by the nonlinear mapping between the non-Gaussian stress and the underlying Gaussian stress while the bandwidth effect is relatively limited. Under this situation, the narrow-banded correction factor proposed by Winterstein is conservatively accurate in most cases. Among all spectral methods, the newly developed method coupled with the Winterstein's correction factor renders the best accuracy of non-Gaussian fatigue damage estimation.