Firstly

the fatigue damages associated with the random loadings were always deemed as high-cycle or very-high-cycle fatigue problems

and based on Chebyshev theorem

the number of rainflow cycles in a given time interval could be recognized as a constant by neglecting its randomness. Secondly

the randomness of fatigue damage induced by the distribution of rainflow cycles was analyzed. According to central limit theorem

the fatigue damage could be assumed to follow Gaussian distribution

and the statistical parameters: mean and variance

were derived from Dirlik's solution. Finally

the proposed method was used to a simulate Gaussian random loading and the measured random loading from an aircraft. Comparisons with observed results were carried out extensively. In the first example

the relative errors of the proposed method are 2.29%

3.52% and 1.16% for the mean

standard deviation and variation coefficient of fatigue damage

respectively. In the second example

these relative errors are 11.70%

173.32% and 18.20%

and the larger errors are attributable to non-stationary state of the measured loading to some extent.