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.

中文翻译：

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根据估算的功率谱密度计算出的“单矩”疲劳损伤的置信区间

本文开发了一种理论方法来解决疲劳损伤的不确定性，疲劳损伤是由有限长度固定记录估计的功率谱密度的采样变异性引起的。获得估计频谱矩的矩生成函数，并将其用于与具有新选择的自由度数的卡方随机变量的概率分布近似。这种近似分布可以导出“真实”谱矩和“单矩”损伤的置信区间。最后给出一个数值例子，以证明所提出解决方案的正确性。