Fatigue damage assessment for Sine-on-Random: a comparative analysis of the predictive capability and application limits of spectral methods

Abstract

Mechanical and electronic components, mainly in aerospace and rotating machinery environments, are generally subjected to Sine-on-Random (SoR) excitations, where deterministic sinusoidal tones are superimposed on a broadband random vibration. While international testing standards require the validation of components under these complex profiles, the numerical evaluation of fatigue damage poses a major analytical challenge. The time-domain rainflow counting method is computationally prohibitive. Conversely, frequency-domain spectral methods rely on Gaussian assumptions that are explicitly violated by SoR loads, leading to inaccurate damage estimates. To bridge this gap, researchers have developed two main strategies: practical approaches that synthesize an equivalent random Power Spectral Density (PSD) based on damage or energy equivalence, and rigorous theoretical methods deriving analytical cycle distributions. This paper evaluates and compares the available methodologies, aiming to highlight the benefits and limitations of each. Ultimately, this comparative study serves as a practical guide for engineers to select the most appropriate tool for fatigue damage assessment under SoR vibrations