Under “dual-carbon” goals and rapid renewable energy growth, increasing start-stop frequency poses new challenges to safe operations of pumped-storage power plant equipment. Ensuring equipment safety and predictive maintenance under complex conditions urgently requires vibration warnings and trend forecasting for pumped-storage units. In this study, the measured vibration-signal characteristics of pumped-storage units in a strong background-noise environment are obtained using a noise-reduction method that integrates BA-VMD and wavelet thresholding. We monitored the vibration-signal data of hydroelectric units over a long period of time, and the measured vibration-signal characteristics of pumped-storage units in a strong background-noise environment are accurately obtained using a noise-reduction method that integrates BA-VMD and wavelet thresholding. In this paper, a BP neural network prediction model, a support vector machine (SVM) prediction model, a convolutional neural network (CNN) prediction model, and a long short-term memory network (LSTM) prediction model are used to predict the trend of vibration signals of the pumped-storage unit under different operating conditions. The model prediction effect is analyzed by using the different error evaluation functions, and the prediction results are compared with the predicted results of the four different methods. By comparing the prediction effects of the four different methods, it is concluded that LSTM has higher prediction accuracy and can predict the vibration trends of hydropower units more accurately.