Two-stage difference mode decomposition for noise frequency band elimination.

• Use local PSD to weaken the influence of noise spectral lines. • A pre-whitening technology is proposed to deal with colored noise. • TDMD still shows good performance in signals with SNR = −24.9 dB. • Achieve out-of-band and in-band noise cancellation. Difference mode decomposition (DMD) is an ideal decomposition method that can accurately separate the signal into fault components, natural components, and noise. However, DMD is proposed based on the assumption that the amplitude of the noise spectral line is 0, and it cannot analyze the signal with a low signal-to-noise ratio (SNR). To expand the application scenarios of DMD, the two-stage difference mode decomposition method (TDMD) is proposed for diagnosing rolling bearing and gear faults. The sum of the amplitudes of the power spectral density in a certain frequency band is expressed as the spectral line of the local power spectral density (LPSD). Taking advantage of that LPSD can weaken the influence of noise spectral lines covering fault spectral lines, inputting LPSD into the convex optimization function can locate the noise frequency band. Set the spectrum lines in the noise frequency band to zero, and preliminarily eliminate noise interference. Inputting the noise-reduced normalized spectrum to the convex optimization function can accurately extract the fault components. The proposed method can effectively eliminate noise bands and highlight the main different spectral lines between healthy signals and fault signals. Simulation and experimental verification show that this method can effectively analyze signals with a low SNR. TDMD still shows good performance in signals with SNR = −24.9 dB. [ABSTRACT FROM AUTHOR]