In order to solve the problems of variational mode decomposition

including presetting parameter of mode number and failure liability in signal decomposition under the condition of strong noise

an improved method for determining the number of modal decomposition modes and the center of frequency band based on the extreme point of power spectral density was proposed. The effectiveness of the method was verified by signal simulation analysis. Based on the adaptive parameter variational mode decomposition

a fault diagnosis procedure was applied to diagnose the second level sun gear crack of planetary gearbox test platform. Test results proved that the method can accurately decompose the vibration signal

effectively extract and identify the fault characteristic frequency

and achieve accurate diagnosis of the second-stage sun gear crack fault under the condition of strong background noise and weak fault signal.