Comparison of spectral methods for fatigue analysis in broad-band Gaussian random processes

The fatigue analysis of broad-band Gaussian random processes is discussed, with attention focused on the distribution of rainflow cycles and the fatigue damage under the linear rule. Several spectral methods are reviewed: the narrow-band approximation, the Wirsching–Light formula, Dirlik’s amplitude density, the Zhao–Baker technique, together with an approach recently developed by the authors, as well as a new (completely empirical) method. Analogies and differences amongst all cited methods are emphasised and commented on, such as the dependence existing on particular spectral parameters; general relations amongst bandwidth parameters are given in the Appendix. Numerical simulations are used to judge the accuracy of each method in estimating results from time-domain calculations and an error index is defined to quantify all deviations: the Zhao–Baker, Dirlik’s and the new method are seen to be the most precise approaches, as well as the new empirical method.