An analytical formulation for the fatigue damage skewness relating to a narrowband process

In spectral fatigue analysis, the expected fatigue damage is customarily used to ascertain the design fatigue life. The uncertainty of the damage induced by the underlying stochastic process is typically disregarded in both theory and practice. Yet, this uncertainty may be consequential in many circumstances. Recently, the author developed an accurate analytical approach for quantifying the damage variance for a narrowband Gaussian process. This paper extends the statistical analysis to the skewness, as the damage probability distribution can be distinctly asymmetric when the coefficient of variation is sizeable. For a linear oscillator system, the damage skewness has a closed form result, which is demonstrated to be highly accurate when benchmarked against Monte Carlo simulation and rainflow counting. For a more general narrowband process, two variants of the method are presented. The simpler version entails merely a single summation, whereas the more sophisticated approach involves a double summation that is still tractable. Further, it is shown that using the first three statistical moments, a good approximation to the distribution can be obtained.