The role of uncertainty of power spectral density data in estimating the fatigue damage of random uniaxial loadings through frequency-domain methods

This work treats of the statistical uncertainty of fatigue damage evaluated in frequencydomain, coming from the sampling variability of power spectral density data estimated from finite length records. The article derives the expression for the moment generating function (mgf) of the sample spectral moment of order q. The mgf permits the probability distribution of the sample spectral moment to be approximated by the distribution of a scaled chi-square random variable. This introduces the concept of “equivalent degrees of freedom” for a power spectrum. The confidence interval for both the q-th order spectral moment and the fatigue damage estimated by the “single-moment spectral method” are then obtained in closed form. A Monte Carlo study is finally used to verify the correctness of the proposed expressions