The hydropower generator unit (HGU) is a vital piece of equipment for frequency and peaking modulation in the power grid. Its vibration signal contains a wealth of information and status characteristics. Therefore, it is important to predict the vibration tendency of HGUs using collected real-time data, and achieve predictive maintenance as well. In previous studies, most prediction methods have only focused on enhancing the stability or accuracy. However, it is insufficient to consider only one criterion (stability or accuracy) in vibration tendency prediction. In this paper, an intelligence vibration tendency prediction method is proposed to simultaneously achieve strong stability and high accuracy, where vibration signal preprocessing, feature selection and prediction methods are integrated in a multi-objective optimization framework. Firstly, raw sensor signals are decomposed into several modes by empirical wavelet transform (EWT). Subsequently, the refactored modes can be obtained by the sample entropy-based reconstruction strategy. Then, important input features are selected using the Gram-Schmidt orthogonal (GSO) process. Later, the refactored modes are predicted through kernel extreme learning machine (KELM). Finally, the parameters of GSO and KELM are synchronously optimized by the multi-objective salp swarm algorithm. A case study and analysis of the mixed-flow HGU data in China was conducted, and the results show that the proposed model performs better in terms of predicting stability and accuracy.