An improved spectral discretization method for fatigue damage assessment of bimodal Gaussian processes

Abstract Fatigue damage assessment of narrow-banded (NB) Gaussian processes in frequency domain has been a classical problem since the 1960s, in that the frequency-domain approach is more efficient than the time-domain approach such as the Monte-Carlo simulation based rainflow counting. However, when the random process of stress is wide-banded (WB) and particularly contains two or more peaks well apart in the spectrum, it is still difficult to accurately assess the fatigue damage by spectral methods, even if the process is Gaussian. On the basis of the single-moment method and the spectral discretization idea, this paper presents an efficient and accurate method for the bimodal Gaussian fatigue assessment. In this method, the mutual influence between the narrow-banded low-frequency (LF) stress and the high-frequency (HF) stress is reflected by a coefficient ξ dependent on the high-low frequency ratio γ, the energy ratio β and the slope parameter k of material’s S-N curve. Time-domain rainflow counting is used as the reference to judge the accuracy of this new method against several popular spectral methods, i.e., Jiao-Moan (JM) method, single moment (SM) method, Low’s bimodal method (LOW) and Tovo-Benasciutti (TB) method. For wide ranges of γ, β, k and all bimodal patterns (NB-LF with NB-HF, WB-LF with NB-HF, NB-LF with WB-HF and WB-LF with WB-HF), the proposed method is most accurate among all methods, demonstrating its great potential in engineering practice.