Methods for estimating the statistical variability of the fatigue damage computed in one single stationary or non-stationary random time-history record

The fatigue damage D(T) of a random time-history x(t) of finite length T is a random variable that follows a certain probability distribution with expected value E[D(T)], which represents an average over an infinite population of damage values computed from infinite time-histories ‒ clearly not obtainable in practice. Most often, in engineering applications only one single time-history record of finite length is available e.g. from measurements or simulations, and its fatigue damage D(T) is the only quantity that can be used to infer about the expected damage E[D(T)]. This paper shows how to address this issue by means of confidence intervals for E[D(T)]. Solutions are developed for two families of time-history: stationary and non-stationary ‒ the latter focused in particular to the subclass of switching loadings, formed by a sequence of stationary states. The proposed confidence intervals are verified first by numerical simulations and then by experiments in which a time-history record is measured on a bicycle travelling at a prescribed speed on a track with specific succession of road surfaces. A small subset of time-histories (called “calibrator set”) is also generated or collected with the aim order to compute a sample mean damage, used to approximate the expected damage in the verification of confidence intervals. In all considered examples, the confidence intervals enclose the expected damage, which demonstrates the correctness of the proposed approach.