Modeling of statistical and spectral properties of non-Gaussian random vibration fatigue loads using Higher Order Spectra

Abstract

A theoretical analysis of random vibration fatigue is possible in time- or frequency-domain. In time-domain, sampled signal realizations are used, whereas the power spectral density (PSD) method is based on second-order statistics in frequency-domain. PSDs have important advantages over the sampled time-domain signals: (i) PSDs use a statistical model, enabling sound modeling of extreme value statistics, (ii) PSDs come along with a beneficial data reduction in computational analysis. However, PSD models rely on the hypothesis of Gaussianity. Practical applications often deviate from this assumption causing significantly false fatigue load estimations. Various improvements were proposed in the past, based on simplifying assumptions or with limited validity, not yet providing a theoretically sound solution for general non-Gaussian random fatigue loads. This paper follows the hypothesis that higher-order spectra (HOS) can model general non-Gaussian random fatigue loads. HOS extend the second-order PSD model in spectral domain. Using typical, different non-Gaussian signal types, the paper demonstrates significant improvements based on the trispectrum (4th-order HOS). To achieve this goal, a novel method for the synthetic generation of non-Gaussian time realizations from a HOS description is presented. The results lay the foundation for further work, such as the development of estimation methods for load-spectra from HOS.