Frequency-domain characterization of varying random vibration loading by a non-stationarity matrix

Abstract

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.