The Research On Sparse Decomposition Theory For Mechanical Vibration Signal Based On Compressed Sensing

Mechanical vibration signal transmits and carries important information of mechanical equipment in its working process.The signals' on-line monitoring and collection are key technologies in mechanical engineering field,especially in fault diagnosis or remote fault diagnosis.Compressed sensing theory is used to signal monitoring,which contributes to solve problems and difficulty of storage,transmission and large amount of vibration signal by traditional sampling theorem.Signal sparsity is the premise and foundation of compressed sensing theory that is applied to vibration signal detection.Therefore,this study mainly focuses on the problem of mechanical vibration signal's sparse decomposition.The main research results are as follows:(1)At first,compressed sensing theory is introduced.Then the sparse representation theory is summarized in detail,while K-SVD dictionary-training algorithm and Double Sparse dictionary-training algorithm is analyzed.Finally,orthogonal matching pursuit algorithm is introduced.(2)For the commonly used orthogonal basis dictionary can not be flexible to express the complexity of the vibration signal,the vibration signal in the sparse mode can not be enough sparse,affecting the accuracy of the compressed sensing reconstruction of vibration signal.Hence,a method of reconstruction of compressed measuring for mechanical vibration signal based on K-SVD dictionary-training algorithm sparse representation is proposed in this research.Firstly,the sparsity(also called compressibility)of the vibration signal based on over-complete dictionary by the developed K-Singular Value Decomposition(K-SVD)dictionary-training algorithm is analyzed;Then,gaussian random matrix is used as the sensing matrix to measure the vibration signal;Finally,orthogonal matching pursuit algorithm is utilized to reconstruct the original vibration signal,which is based on the compression measurements.The test results of simulated data demonstrate that the relative error of the compressed sensing reconstruction of vibration signal based on over-complete dictionary by the developed K-SVD dictionary-training algorithm is smaller than that of the method using over-complete dictionary of discrete cosine when the vibration signal compression rate is at 60%~90%.In the case of without losing vibration information,the proposed method not only obtains high compression rate of vibration signal and accuracy of signal reconstruction,but also reduces the original amount ofvibration data.(3)Aiming at the mechanical equipment in the condition monitoring and fault diagnosis process,the sparse representation of the K-SVD dictionary learning algorithm shows that the training time is long and the computational complexity is large when the vibration signal is compressed and reconstructed.Hence,a method of compressed sensing for mechanical vibration signal based on double sparse dictionary model is proposed in this research.Firstly,the sparsity of the vibration signal based on over-complete dictionary by double sparse dictionary model is analyzed;Then,Gaussian random matrix is used as the sensing matrix to measure the vibration signal;Finally,over-complete dictionary by double sparse dictionary model and orthogonal matching pursuit algorithm are combined to reconstruct the original vibration signal.The test results of simulated data demonstrate that at the same compression rate,when compared to the method using classical K-SVD dictionary-training algorithm,the proposed method obtains high accuracy of signal reconstruction and reconstruction time decreases by 50%.