Total Variational Model of Structure Tensor Based on Partial Differential Equation and Its Application in Planet-Bearing Fault Diagnosis

When planet bearing operates under a complex and variable environment, the fault signal is often coupled with signals from other transmission components and is influenced by the transmission path with time-varying characteristics. The angle domain resampling method reduces the phenomenon of spectral line smear caused by speed variation. However, the order spectral line of the fault feature remains surrounded by many modulation sidebands and interference components. To address the above situation, for one thing, a novel blind convolution method [minimum noise amplitude deconvolution (MNAD)] is adopted to preprocess the angular domain signal of planet-bearing inner ring. This method does not directly enhance the fault features but suppresses the noise in the marked area. For another, this article achieves the goal of fault feature extraction for planet-bearing inner ring, a total variation model based on partial differential equations is constructed. The traditional total variation model takes advantage of the local structural regularity for the matrix and treats the computed gradient directly as the regularization penalty term. This method utilizes the structure tensor (ST) as the regularization term, which could sense neighborhood information. The overall structural features are described based on the local neighborhood information of matrix elements. This achieves a better effect of noise suppression. Finally, based on the above research methods, this article demonstrates that they are superior to other research methods in fault feature extraction through the fault test data of the planet-bearing inner ring.