A novel underdetermined source number estimation for coupled vibration sources of mechanical fault based on variational mode decomposition

The number of fault sources is helpful for accurately extracting fault features. The existing source number estimation methods have certain difficulties when realizing the source estimation of mechanical vibration signals and acoustic signals in a strong background noise environment. A variety of the fault source signals are coupled with each other, resulting in that the number of fault sources in the actual working conditions is unknown, and sometimes the number of observation signals is less than the number of fault source signals due to the limitation of sensor installation condition. A novel method for underdetermined source number estimation based on the combination of morphological filtering (MF), adaptive variational modal decomposition (AVMD) and singular value decomposition (SVD), named MF-AVMD-SVD, is proposed. First, MF is used to filter out background noise signals and enhance the impact characteristics of fault signals. Second, AVMD is used to resolve the filtered observation signals to obtain intrinsic mode function (IMF); these IMFs are recombined to obtain the covariance matrix of multidimensional observation signals. Finally, new non-zero eigenvectors are obtained by SVD, and the accurate number of rolling bearing fault source signals is determined according to the maximum value of the adjacent eigenvalue ratio. This method is applied to the simulation signal; the number of four sources can be accurately estimated by the two-channel simulation mixed signal under the condition that the signal to noise ratio (SNR) is −15 dB or even −21 dB. It can also be effectively estimated that the number of vibration sources is three from the vibration signals and acoustic signals of the double-channel rolling bearing composite fault.