PSI - Issue 54

Arvid Trapp et al. / Procedia Structural Integrity 54 (2024) 521–535 Arvid Trapp / Structural Integrity Procedia 00 (2023) 000–000

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element models. However, these come with a central limitation that is connected to the PSD-based description, as it provides a full statistical characterization exclusively for stationary Gaussian loading. Deviations from these condi tions commonly lead to non-conservative discrepancies in the predicted structural lifetimes (Palmieri et al. (2017)).

Fig. 1. Schematic comparison of sampling-based and statistical approach to a fatigue assessment; in red proposal of this paper

Given this restriction, it is popular to utilize the kurtosis as a concise indicator of non-Gaussianity and several re searchers have proposed correction approaches based on the kurtosis. These either aim to correct the damage value in reference to a process of same PSD (Braccesi et al. (2009); Cianetti et al. (2018); Bo¨hm and Kowalski (2018)) or they transform non-Gaussian into Gaussian stress series using distinct transformation models (Winterstein (1985, 1988); Sarkani et al. (1994); Benasciutti and Tovo (2006)). Common to all these approaches is their reliance on the response kurtosis, which is only accessible by obtaining the response stress series, involving the corresponding computational e ff ort of a sampling-based assessment. As this contradicts the principles of a statistical approach, some researchers propose to use the input kurtosis, which introduces the strong assumption that the dynamic structural behavior will have no e ff ect on the non-Gaussianity. Another of their common features is the assumption that the scalar-valued kur tosis — sometimes accompanied with the skewness — are su ffi cient for characterizing non-Gaussianity and relating it to fatigue damage. Because of this limited characterization, the methods converting non-Gaussian into ’equivalent’ Gaussian series (’inversion formulas’) don’t always ensure actual significance and come with inherent limitations and constraints, such as frequency distortions. On the other hand, (Braccesi et al. (2009); Cianetti et al. (2018)) presented damage correction factors based on least squares fitting of reference data. Both further float the idea of relating input kurtosis to modal analysis in order to base the correction on better estimates of stress kurtosis. From variance to kurtosis: Independent of the quality of correction, the central issue is that the standard method of calculating kurtosis is based on time-domain realizations, which is not available in a statistical approach. Crucial is the dynamic behavior of structures — just as it defines how the loads’ PSD, the spectral decomposition of variance, transfers into structural stress / strain responses. So for obtaining response kurtosis statistically it requires a spectral rep resentation of the kurtosis, indicating non-Gaussianity, to estimate how this characteristic a ff ects structural responses