Multi-source Signal Adaptive Sparse Representation Separation Method And Its Application

Mechanical equipment often operates under more complicated working conditions such as high temperatures and heavy loads,and its core components will inevitably fail.In actual situations,the source of failure is often not a single fault,but a composite fault caused by different damage in different parts.It will greatly increase the difficulty of fault diagnosis,seriously affect the normal operation of the enterprise,and may even bring catastrophic consequences.Therefore,the complex fault diagnosis of rotating machinery is one of the important links of enterprise equipment condition monitoring and fault diagnosis,and it is the top priority to ensure the safe,reliable and stable operation of machinery and equipment.In order to solve the problem that mechanical multi-source fault signals are difficult to extract,an adaptive sparse representation separation algorithm based on multi-source signals and its application research were carried out in this paper.The main research contents are presented as follows:Aiming at the problems of complicated working conditions such as limited number of sensors in the actual operation of mechanical equipment,a blind source separation method based on intrinsic mode decomposition was developed.First,adaptive intrinsic mode decomposition is performed on the collected fault vibration signals.In the traditional decomposition process,the target decomposition signal is a stationary signal,and the discrimination conditions are strict.However,in actual cases,most of the collected signals are carried noise.Noisy vibration signals and rigid discrimination conditions will cause the algorithm to fail to converge.Aiming at this situation,the judgment conditions suitable for the vibration signal are reset.During the iteration process,an energy factor index is constructed as the termination condition of the algorithm.An improved intrinsic mode decomposition method is proposed,which improves the signal decomposition efficiency.At the same time,it also provides help for compound fault diagnosis.Aiming at the difficulty of the traditional blind source separation algorithm to perform in the underdetermined occasion,a new underdetermined blind source separation framework was proposed.Based on the above-mentioned intrinsic mode decomposition method,the observation signal is adaptively decomposed,and the under-determined problem that is difficult to solve is converted into a positive-determined or over-determined problem.Because non-negative matrix factorization can better solve practical problems,an underdetermined blind separation method based on improved intrinsic mode decomposition method and non-negative matrix factorization is proposed for bearing composite fault diagnosis.Firstly,the fault signal is processed through adaptive intrinsic mode decomposition to obtain a certain number of components.Then the number of source signals is estimated by the potential function method to determine the matrix dimensions in the non-negative matrix factorization process.In addition,by combining the improved intrinsic mode decomposition method with the independent component analysis method and the sparse component analysis method,the blind source separation of signals is realized.Aiming at the problem of insufficient vibration signal sparseness,a signal separation method based on sparse blind source separation was developed.In view of the prerequisites of the independent component analysis algorithm,it is more demanding in actual situations and has many calculation links.The non-negative matrix factorization method is a time-consuming problem.Considering the advantages of the sparse representation algorithm in processing big data problems,the research focuses blind separation algorithm for sparse component analysis.Aiming at the problems that the vibration signals are not sparse enough and it is difficult to deal with them with traditional sparse representations,the sparse component analysis algorithm of sparse components is first studied.The sparsity promotion methods of wavelet modulus maxima is used to obtain sparse observation signals.The potential function is then used to estimate the number of source signals and mixed matrix based on the sparse signal.Finally,the source signal can be separated according to the shortest path method.In addition,the traditional potential function is convenient to calculate but can only deal with the two-dimensional plane in the mixed matrix estimation method.Fuzzy cluster estimation and other methods are not limited by the dimensions but the results have some randomness.Therefore,A new mixed matrix estimation is proposed.By mapping a two-dimensional plane into a three-dimensional space,a new set of spatial potential functions are constructed based on the spherical coordinate system,and the matrix estimation problem is converted into a function extreme value solving problem.The mixed model of convolution coupling in the actual process is further studied.Compound fault diagnosis is carried out based on the mapping relationship between the three-dimensional potential function and the convolution model.Aiming at the problem of the results will be inaccurate based on insufficient signal sparsity or deviation of estimation matrix.A method based on optimized sparse component analysis is carried out,and a step-by-step optimization sparse component analysis strategy is proposed.First,the majorization-minimization method is used to represent the vibration signal in sparse way,then the three-dimensional potential function is used to estimate the mixed matrix,and finally the reference signal is constructed to achieve separation.In the sparse representation process,a convex regular term is usually used to ensure that the problem has a global optimal solution during the optimization process.However,in many practical applications,non-convex regularization can often achieve better sparsity,that is,further enhance sparsity.Therefore,the non-convex regular term is constructed,and the structure of the non-convex regular term is adjusted by introducing parameterized coefficients,so as to determine its expression under the premise of satisfying the global optimality.On the basis of obtaining a good sparse representation effect,by improving the three-dimensional potential function method,it can be used to estimate the mixture matrix without low dimensional restrictions,and in the process of recovering the signal,the algorithm efficiency is improved by selecting the basis vector.In this paper,the blind separation of mechanical faults is used as a starting point.The adaptive decomposition method,intrinsic mode decomposition method,independent component analysis,non-negative matrix factorization,and blind separation algorithm for sparse component analysis in mechanical fault diagnosis are thoroughly and systematically studied.The research,especially from the perspective of sparsity,deeply studies the sparse components analysis based on three-dimensional potential function and non-convex regularization.The research results are of great engineering significance and practical value for the health monitoring and fault diagnosis of mechanical equipment.