Joint Measurement And Reconstruction Of Vibration Signals At Multiple Monitoring Points Based On Compressed Sensing Theory

The vibration signals generated during the operation of mechanical equipment can provide important information support for fault diagnosis,full life cycle prediction and reliability analysis of mechanical equipment.With the rapid development of modern mechanical equipment,the frequency contained in its vibration signal is also increasing.The traditional signal acquisition method based on the Nyquist sampling theorem has fallen into the dilemma caused by the collection of large amounts of data.Applying compression sensing theory to the vibration signal collection of mechanical equipment can help solve many problems caused by the traditional signal collection method of collecting large amounts of data.In actual production,multiple sensors have been commonly used to collect signals at different monitoring points of mechanical equipment.Therefore,in this paper,through sparse representation,joint sparse representation,and joint compression measurement reconstruction,we focus on the research of multi-point vibration signal joint compression measurement reconstruction method,and carry out the following related work.(1)Firstly,the basic knowledge of compressed sensing theory,distributed compressed sensing theory and commonly used sparse representation orthogonal basis and learning dictionary algorithm are introduced respectively.Through simulation experiments,the reconstruction performance of the compressed and reconstructed signals of the vibration signals at different monitoring points under the orthogonal basis and the sparse representation of the learning dictionary is analyzed.Simulation experiment results show that K-SVD learning dictionary is more suitable for compression and reconstruction of vibration signals at different monitoring points than discrete cosine orthogonal basis and MOD learning dictionary.(2)Secondly,analyze the joint sparsity of the vibration signals of multiple monitoring points under the discrete cosine orthogonal basis in the same period,and use the MMV model to perform joint compression and reconstruction.Through simulation experiments,the effectiveness of the joint compression and reconstruction method for the vibration signals of multiple monitoring points in the same time period and the reconstruction performance of the reconstructed signals under different measurement matrices and joint reconstruction algorithms are analyzed.Simulation experiment results show that,compared with the traditional compression and reconstruction scheme,joint compression and reconstruction of the vibration signals of multiple monitoring points in the same period can improve the reconstruction performance of the reconstructed signal.Gaussian random measurement matrix,random Bernoulli measurement matrix,random sparse measurement matrix,and focal underdetermined system solver are more suitable for joint compression measurement reconstruction of vibration signals at multiple monitoring points in the same time period.The Gaussian random measurement matrix,random Bernoulli measurement matrix,random sparse measurement matrix and the underdetermined system localized solution method of the MMV model are more suitable for combined compression measurement reconstruction of vibration signals at multiple monitoring points in the same time period.(3)Finally,the K-SVD learning dictionary is applied to the joint compression measurement reconstruction of vibration signals at multiple monitoring points.Simulation experiment results show that the K-SVD learning dictionary is used to jointly compress and reconstruct the vibration signals of multiple monitoring points in the same period to effectively improve the reconstruction performance of the reconstructed signal.Aiming at the problem that the K-SVD algorithm takes too long to train and learn the dictionary,through the study of the SGK algorithm and the joint sparse representation characteristics of the vibration signals of multiple monitoring points in the same period,a fast dictionary learning algorithm is proposed to train and learn the dictionary.The simulation experiment results show that the reconstruction performance of the combined compression and reconstruction signal of the learning dictionary trained by K-SVD,SGK and the fast dictionary learning algorithm is almost the same,but the time for the fast dictionary learning algorithm to train the learning dictionary is significantly reduced.