Research On Gear Fault Detection Based On Compressive Sensing

Compressed sensing theory breaks through the deficiency of Nyquist sampling theorem that the signal sampling frequency must be more than twice the highest cut-off frequency,then directly samples signal randomly and compresses,so it has been applied in many fields.In this paper,aiming at the problems that the Toplitz measurement matrix is easy to be implemented by hardware,but the signal compression sampling is insufficient and the reconstruction is poor,the corresponding improvements were carried out to meet the use requirements.Secondly,in view of the complexity of timefrequency analysis and difficulty in finding fault points after the restoration and reconstruction of compressed signals,it was proposed to directly extract the features of the compressed signals on the sparse matrix,instead of completely restoring and reconstruction of signals,so as to realize the classification and discrimination of fault signals.Therefore,it was proposed to extract the features of the vibration signal directly on the discrete cosine domain for state discrimination and fault location based on the constructed block redundancy matrix.The research contents of this paper are as follows:(1)In this paper,Toplitz matrix was optimized by Schmidt orthogonalization in view of the poor performance of real signals,then it was applied to signal compression measurement restoration.In view of the complexity of the measured signals and the difficulty of fault differentiation by time-frequency analysis after restoration,a variational modal decomposition(VMD)was proposed for the restored signals,and then feature extraction was carried out for the information of each layer component.Finally,the fault categories of the signals were determined by comparing the eigenvalues.(2)The common discrete cosine matrix is not ideal for sparse expression of measured vibration signals.Therefore,it was proposed to filter the measured vibration signals first to obtain the information near the actual operating frequency of the equipment,then sparse expression was carried out based on the discrete cosine matrix,and fault mechanism was identified according to the change of sparse cardinal value.Feature extraction of discrete cosine basis for 5 kinds of vibration signals of gear box was proposed,then the gearbox state was identified according to the characteristic value.(3)The dictionary learning method was used to construct a block redundancy matrix,which solveed the problem that the vibration signals of gearbox cannot be sparsely decomposed based on the conventional redundancy matrix.According to the comparison of the redundancy error value of each vibration signal in the block redundancy matrix,the fault classification and discrimination of the gearbox were carried out.To sum up,this paper proposed to improve the Schmidt orthogonalization of the current structural measurement matrix,and applied it to the observation of planetary gearbox signals.At the same time,a new idea of gear fault prediction based on kurtosis feature extraction was proposed for the sparse variation of signals in discrete cosine domain.The dictionary learning method was used to construct a block redundancy matrix for sparse decomposition of gearbox signals,and the classification and discrimination of gearbox vibration signals based on this matrix was proposed.