Aiming at the vibration safety of hydropower stations, a prediction method based on AVMD(adapative variational mode decomposition) and BSA-KELM(bird swarm algorithm-kernel extreme learning machine) was proposed to study the vibration response of the plant structure combined with the intelligent learning algorithm, which shed some light on the intelligent monitoring of structural vibration. Firstly, the vibration signals were decomposed into multi-order IMF(intrinsic mode function) components using AVMD. Then the KELM prediction model was established for each IMF component, and the model parameters were optimized by BSA optimization algorithm. Finally, the structural vibration time-history curves were obtained through the reconstruction of the vibration signals. Based on the prototype observation data, the prediction model of a hydropower station was established using this method, with the signals of the generator and water pressure pulsation as the input and the signals of hydropower plant structure vibration as the output. Compared with the test signals, the determination coefficients of the prediction results were all greater than 0.8, the root mean square errors of the vibration amplitude were all less than 0.3 μm, and the average absolute errors were all less than 0.2 μm, indicating that the prediction method has high accuracy and excellent performance.