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.
