Wang, H., Zhang, Z., Zhang, J., Shen, Y. and Wang, J. (2024) A Novel Load Extrapolation Method for Multiple Non-Stationary Loads on the Drill Pipe of a Rotary Rig. Machines, 12, Article 75.
https://doi.org/10.3390/machines12010075

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.