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Mao, J., Xian, Z., Wang, X., Hu, D., Pan, J., Wang, R., et al. (2025) Fatigue Life Prediction of Cold Expansion Hole Using Physics-Enhanced Data-Driven Method. International Journal of Fatigue, 190, Article 108634.
https://doi.org/10.1016/j.ijfatigue.2024.108634

has been cited by the following article:

• TITLE: Non-Stationary Load Extrapolation over Long Horizons Based on a Frequency-Consistent Diffusion Model

  AUTHORS: Yu Bai, Fei Meng

  KEYWORDS: Diffusion Model, Load Extrapolation, Frequency-Consistency

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.16 No.4, April 7, 2026

  ABSTRACT: This study proposes a frequency-consistent diffusion model (FCDM) for long-horizon extrapolation of non-stationary bearing load signals. Condition tokens and spectral-consistency constraints are introduced to preserve spectral and fatigue-related characteristics during tenfold extrapolation. The generated signals are evaluated using PSD, band-energy proportion, Range-Mean distribution, and unit pseudo-damage. Compared with DDPM, FCDM better preserves dominant frequencies, harmonic structure, and band-energy allocation. The dominant frequency error is 1.02%, and the mean harmonic error is 0.52%. FCDM also shows smaller band-energy allocation errors across all frequency bands. In addition, it reproduces the bimodal clustering pattern in the Range-Mean distribution more accurately. The unit pseudo-damage is 1.0978 for FCDM and 1.1280 for DDPM. These results indicate that FCDM improves spectral fidelity and fatigue-related consistency in long-sequence load extrapolation.