Bearings are the core components of ship propulsion shafting, and effective prediction of their working condition is crucial for reliable operation of the shaft system. Shafting vibration signals can accurately represent the running condition of bearings. Therefore, in this article, we propose a new model that can reliably predict the vibration signal of bearings. The proposed method is a combination of a fuzzy-modified Markov model with gray error based on particle swarm optimization (PGFM (1,1)). First, particle swarm optimization was used to optimize and analyze the three related parameters in the gray model (GM (1,1)) that affect the data fitting accuracy, to improve the data fitting ability of GM (1,1) and form a GM (1,1) based on particle swarm optimization, which is called PGM (1,1). Second, considering that the influence of historical relative errors generated by data fitting on subsequent data prediction cannot be expressed quantitatively, the fuzzy mathematical theory was introduced to make fuzzy corrections to the historical errors. Finally, a Markov model is combined to predict the next development state of bearing vibration signals and form the PGFM (1,1). In this study, the traditional predictions of GM (1,1), PGM (1,1), and newly proposed PGFM (1,1) are carried out on the same set of bearing vibration data, to make up for the defects of the original model layer by layer and form a set of perfect forecast system models. The results show that the predictions of PGM (1,1) and PGFM (1,1) are more accurate and reliable than the original GM (1,1). Hence, they can be helpful in the design of practical engineering equipment.

轴承是船舶推进轴系的核心组件，有效预测其工作状况对于轴系的可靠运行至关重要。轴振动信号可以准确表示轴承的运行状况。因此，在本文中，我们提出了一种可以可靠地预测轴承振动信号的新模型。所提出的方法是基于粒子群优化（PGFM（1,1））的具有灰色误差的模糊修正马尔可夫模型的组合。首先，使用粒子群优化算法对灰色模型（GM（1,1））中影响数据拟合精度的三个相关参数进行优化和分析，以提高GM（1,1）的数据拟合能力并形成一个基于粒子群优化的GM（1,1），称为PGM（1,1）。第二，考虑到数据拟合产生的历史相对误差对后续数据预测的影响无法定量表达，引入模糊数学理论对历史误差进行模糊校正。最后，结合马尔可夫模型来预测轴承振动信号的下一个发展状态，并形成PGFM（1,1）。在这项研究中，对同一组轴承振动数据进行了GM（1,1），PGM（1,1）和新提出的PGFM（1,1）的传统预测，以弥补将原始模型逐层构建并形成一组完善的预测系统模型。结果表明，PGM（1,1）和PGFM（1,1）的预测比原始GM（1,1）更准确和可靠。因此，它们可以对实际工程设备的设计有所帮助。