Spectral analysis constitutes an essential technique for random vibration fatigue. The power spectral density (PSD) provides an efficient, statistically unique characterization of stationary Gaussian loading which can be effectively processed via linear systems theory and load-spectrum estimators such as the Dirlik formulation. The PSD represents vibration loading by its averaged intensity for frequency. However, if the intensity varies throughout a dataset, i.e. the loading is non-stationary, the PSD has a fundamental flaw – it conceals any information about its evolution. Consequently, the PSD is not qualified to describe non-stationary loading and thus cannot represent instantaneous highly damaging events in a fatigue assessment. Therefore, this article proposes a statistical characterization particularly formulated for the specifications of non-stationary random vibration fatigue. We introduce a non-stationarity matrix defined as the auto-correlation matrix of short-time Fourier transforms, which describes the average variation and interaction of intensity by frequency. This characterization can directly be related to fourth-order statistics (kurtosis, trispectrum, etc.) and allows to be processed via linear systems theory. Thereby the influence of a loading’s non-stationarity structure on structural responses, and thus fatigue damage, can be assessed. Furthermore, this article provides the basis for an accompanying article in which the non-stationarity matrix finds application to efficiently perform fatigue analyses for non-stationary loading via a statistical approach using load-spectrum estimators.

频谱分析是随机振动疲劳的基本技术。功率谱密度（PSD）提供了稳定的高斯负载的有效，统计上唯一的表征，可以通过线性系统理论和诸如Dirlik公式的负载谱估计器对其进行有效处理。PSD通过其平均频率强度表示振动负载。但是，如果整个数据集中的强度变化，即加载是不稳定的，则PSD就有一个根本的缺陷–它隐藏了有关其演变的任何信息。因此，PSD没有资格描述非静态载荷，因此不能代表疲劳评估中的瞬时高破坏性事件。因此，本文提出了专门针对非平稳随机振动疲劳规范制定的统计特征。我们引入一个非平稳矩阵，定义为短时傅立叶变换的自相关矩阵，它描述强度的平均变化和强度随频率的相互作用。此特征可以直接与四阶统计量（峰度，三光谱等）相关，并可以通过线性系统理论进行处理。因此，可以评估载荷的非平稳性结构对结构响应的影响，从而可以评估疲劳损伤。此外，