Spectral methods for lifetime prediction under wide-band stationary random processes

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Fatigue predictions in entire body of metallic structures from a limited number of vibration sensors using Kalman filtering (2011, methodology): “For Gaussian stochastic stress processes, the probability distribution of the stress range Ds 1⁄4 2s, taken to be twice the random amplitude at stress level within [s,s1ds] in a stress process, is given by the Dirlik formula [8,27,28] as”
Vibration fatigue using modal decomposition (2018, methodology): “Models by Dirlik [22] or Tovo-Benasciutti [23] dTB were shown to give accurate results: dTB = [ b+ (1− b)αk−12 ] α2 dNB, (24) where b is a factor determined through a numerical simulation, k is the S-N slope coefficient, α2 is the spectral width parameter and dNB is the narrow-band spectral moment m”
Stochastic fatigue damage modeling under variable amplitude loading (2007, background): “Also, most of the frequency domain approaches assume the linear fatigue damage accumulation rule [6,1,2], due to the loss loading sequence information during the computation of the power spectral density function from the loading history.”