Confidence interval of the ‘single-moment’ fatigue damage calculated from an estimated power spectral density

This article develops a theoretical approach to account for the uncertainty of the fatigue damage caused by the sampling variability of a power spectral density estimated from a finite length stationary record. The moment generating function of the estimated spectral moments is obtained and used to approximate their probability distribution with that of a chi-square random variable with a newly chosen number of degrees of freedom. This approximate distribution allows the confidence interval of both the ‘true’ spectral moments and ‘single-moment’ damage to be derived. A numerical example is finally presented to demonstrate the correctness of the proposed solutions