Improved Atomic Sparse Decomposition Algorithm And Its Application On Mechanical Fault Diagnosis

Atomic sparse decomposition algorithm based on Orthogonal matching Pursuit(Orthogonal Match Pursuit,OMP)has been widely applied in the fields of data compression,image processing,feature extraction for signal,etc.However,it exists the problem of dictionary selection and high computational complexity.The performance of atomic sparse decomposition algorithm is closely related to dictionary selection.In addition to achieve the fast signal sparse decomposition,on the one hand the domestic and foreign researchers has proposed some fast algorithms such as genetic algorithm,fish algorithm and the like.However,these intelligent algorithms has a certain randomness in searching process,and can affect the effect of signal sparse decomposition in some cases;on the other hand the national and international researchers has combined signal sparse decomposition with compression perception theory.This method exists the problem of sparseness selection due to that the sparseness selection has a significant effect on the signal sparse decomposition.Aiming at the above mentioned problems,the paper concerned about more effective of the fast sparse decomposition based on OMP algorithm is proposed.The specific contents are listed as follows:(1)The theory of mechanical fault is introduced firstly.The characteristic of bearing and gear fault is analyzed.Then,the shortage of the time-frequency analysis methods is pointed out.The principle of atomic sparse decomposition algorithm is proposed,and the characteristic and problems of atomic sparse decomposition algorithm are pointed out.Atomic sparse decomposition has the problem of dictionary selection and huge calculation cost through the application of the MP algorithm.This section in the paper is studied to deal with the above-mentioned problems.(2)Aiming at the problem of dictionary selection in atomic sparse decomposition,a new OMP method based on improved linear frequency modulation basis function is proposed.In this method,an improved linear frequency modulation basis function is used as atom in OMP algorithm.The results of numerical simulation show that the accuracy and computational efficiency is better than the traditional atom dictionary in OMP.(3)Facing the problem of huge computation in atomic sparse decomposition,a new fast OMP algorithm based on improved genetic algorithm.This algorithm combines the QGA with the OMP algorithm for high-effective atom selection and reducing calculated complexity of sparse algorithm on the consideration that the QGA can quickly solve the problem of multiple parameters optimization.The results of numerical simulation and measured data demonstrated that this algorithm is more sparse and higher operation efficiency than the traditional OMP algorithm.(4)In order to more effectively improve the calculation speed of atomic sparse decomposition algorithm,a new CSOMP method based on total variation(TV)is proposed.This method firstly uses a DHT basis as atoms.Then it combines total variation algorithm with the CSOMP algorithm for adaptive sparseness selection and reducing computational complexity of CSOMP algorithm due to that the TV quickly solve the convex optimization problem.Finally,it selects suitable characteristic coefficient with the purpose of noise reduction.The results of numerical simulation and measured data show that CSOMP-TV algorithm is higher precision and faster calculation speed than the traditional CSOMP algorithm.Moreover,the CSOMP-TV algorithm based on parameter optimization has a good effect on the signal feature extraction and denoising.