Objective Due to the limited number of measurement points in the machinery space, the longitudinal vibration of the propulsion shaft system can only be measured at a few locations, which makes it difficult to comprehensively assess the longitudinal vibration status of the entire shaft system. This study aims to propose a novel method for accurately predicting the longitudinal vibration displacement of the entire propulsion shaft system based on a limited number of measurement points.

Method This study innovatively integrates Kalman filtering technology with the longitudinal vibration model of the propulsion shafting to develop a new prediction method for the longitudinal vibration displacement. This method is a time-domain prediction approach that combines deterministic analysis with stochastic factors, fully accounting for the effects of dynamic model errors and measurement data errors. Using a minimum variance unbiased estimation strategy, it effectively enhances the accuracy of displacement prediction. Especially in complex scenarios where the propeller excitation force is unknown and the measurement signals are heavily contaminated by noise, this method can accurately predict the longitudinal vibration displacement at any position of the propulsion shafting using data from just two measurement points.

Results The results show that the method maintains high accuracy even in challenging environments with a signal-to-noise ratio as low as 0 dB. The root mean square error (RMSE) between the predicted and theoretical displacements at the propeller is only 8.85 μm, and the RMSE at the thrust bearing is only 5.49 μm. These results fully illustrate the high-precision prediction ability of this method in low signal-to-noise ratio environments.

Conclusion The method proposed in this paper provides a new solution for real-time, online assessment of the longitudinal vibration state of ship propulsion shafting, with significant practical value. It has the potential for widespread application in ship propulsion system monitoring and fault diagnosis, contributing to improved safety and reliability of ship operations.