Variability of the fatigue damage due to the randomness of a stationary vibration load

Variance of fatigue damage in narrowband Gaussian random loadings: Exact solution and approximations

“…Nevertheless, in [1] the range of validity of this expression was incorrectly extended to values of 𝑚 other than two [4]. Although theoretically not correct, this use of 𝜌 𝑑 0 𝑑 𝑙 (𝑙) yielded estimations that deviated not very much from the simulation results of [1].…”

“…Recently, it has nevertheless been discovered that the formula used in [1] for the method of Madsen et al's, though being in theory only valid for 𝑚=2, was incorrectly applied also to values greater than two [4]. Despite this unfortunate circumstance, the simulations did not highlight exaggerated errors.…”

“…where 𝑁 is the number of cycles counted in 𝑥(𝑡), 𝑑 i = Following [1,3,6], the expected value and variance of fatigue damage in a narrowband process are:…”

“…In a recent article in this journal [1], the authors surveyed four methods used for estimating the variance and coefficient of variation of damage 𝐷(𝑇) in a narrowband Gaussian random time-history 𝑥(𝑡) with duration 𝑇. The methods rely on the concept of random process 𝑋(𝑡), formed by an infinite ensemble of time-histories with infinite length.…”

“…Among the methods considered in [1], the two with fewer assumptions in the estimation of 𝑉𝑎𝑟[𝐷(𝑇)] were those of Madsen et al [2] and of Low [3]. Both methods showed a comparable good accuracy when benchmarked against Monte Carlo simulations with various types of narrowband random loadings.…”