Mechanical Fault Diagnosis Method Based On Symplectic Geometry Mode Decomposition And Support Matrix Machine

At present,China is in the transition stage of intelligent manufacturing,which requires the development of mechanical equipment towards intelligent,precision and complexity.The structure of mechanical equipment is becoming more and more complex and precise.In the service process of mechanical equipment,once a component fails,it will affect the operation of the entire mechanical equipment,and even cause safety accidents.Therefore,the research on fault diagnosis of mechanical equipment is of great practical significance for ensuring the safe operation of equipment.Roller bearings,gears,etc.,are key components in mechanical equipment systems,and their service status is directly related to the reliability of mechanical equipment.Therefore,in order to ensure the reliability of mechanical equipment,real-time service status monitoring and fault diagnosis must be performed on key components of mechanical equipment.Traditional fault diagnosis methods are mainly based on signal processing and pattern recognition technology.However,due to the complexity of the mechanical structure and the harsh working environment,the collected vibration signal is often coupled by the vibration mode and noise of many other components.At the same time,traditional signal processing methods and pattern recognition methods have disadvantages such as instability and lack of robustness,which makes it difficult to effectively decompose,de-noise and discriminate complex signals.Therefore,this paper proposes a fault diagnosis method based on symplectic geometry and support matrix machine for mechanical equipment fault diagnosis.Funded by the Natural Science Foundation of China?No.51575168 and No.51875183?,this paper has conducted in-depth research on the theory of symplectic geometry and support matrix machines.On this basis,this paper proposes several symplectic geometry decomposition methods,symplectic geometric noise reduction methods and improved support matrix machine methods,and apply them in the mechanical fault diagnosis.The main researche works and innovations of this paper are shown as follows:?1?In view of the shortcomings of traditional signal decomposition methods in dealing with non-linear signals,especially noisy complex signals.For example,Local characteristic scale decomposition?LCD?and singular spectrum analysis?SSA?force component signals to be decomposed into several incomplete components.Wavelet transform?WT?and ensemble empirical mode decomposition?EEMD?requires subjective parameters,whose decomposition effect is extremely sensitive to parameters.Therefore,based on the symplectic geometry,the paper proposes the symplectic geometry mode decomposition?SGMD?method,which can decompose the time series into several Symplectic geometry components?SGCs?with independent modes.SGMD uses the symplectic geometry similarity transform to solve the eigenvalues of the Hamiltonian matrix and reconstructs the single component signal with its corresponding eigenvector.At the same time,SGMD does not require subjective parameters and can effectively reconstruct existing modalities and eliminate noise.The analysis results of the simulated signal and the gear experimental signal show that the SGMD method can accurately and effectively decompose the analyzed signal.?2?For the selection of the similarity threshold in the SGMD method,the adaptive symplectic geometric mode decomposition?ASGMD?method is proposed.Firstly,symplectic geometric similarity transform is used to transform the analysis signal,and several initial single component signals are obtained.Then,the superiority of power spectral density?PSD?and iterative Gaussian function?IGF?in processing similar modal components is analyzed,and the adaptive reconstructed bandwidth range is set by PSD and IGF.Finally,the initial single component signal conforming to the bandwidth range is reconstructed to obtain a number of symplectic geometry components.Applying ASGMD to the simulation signal and composite fault signal,the application effect of the proposed ASGMD method in actual fault diagnosis is verified.?3?Aiming at the problem that noise affects the accuracy of fault diagnosis,two kinds of symplectic geometry de-noising methods are proposed,namely,symplectic singular mode decomposition based on Lagrange multiplier?v-SSMD?and symplectic transformation based variational Bayesian Learning?ST-VBL?denoising methods.?1?Aiming at the shortcomings of the previous signal de-noising method,a v-SSMD de-noising method is proposed.Firstly,the constructed trajectory matrix is transformed by the symplectic geometry similarity transformation to obtain the eigenvalues and eigenvectors of the useful component and the noise component respectively.Then,the pure signal is approximated by linear estimation method,and the Lagrange multiplier is used to enhance the useful component and suppress the residual signal represented by noise.Finally,the weighted matrix is applied to the reconstructed noise reduction function,and the influence of the noise component on the reconstructed noise reduction matrix is weakened.The v-SSMD is applied to the gear tooth crack simulation signal and the actual signal,and the superior performance of the v-SSMD method in signal de-noising is verified.?2?For the unknown and known noise?1/f noise,Gaussian white noise,etc.?in the signal to be analyzed,a ST-VBL de-noising method is proposed.First,the ST-VBL method uses the symplectic geometry similarity transformation and the two-order correction contribution rate?TCCR?method to construct the initial de-noising matrix,which removes most of the noise.Then,by constructing the variational Bayesian learning framework,the distribution of elements in the low-order matrix and the sparse matrix is obtained.The final approximate solution is calculated to weaken the rigid noise.Finally,the Gaussian of Mixture?MOG?model is added to the variational Bayesian process,so that the components other than noise obey the Gaussian distribution,and the de-noising effect is maximized.Applying ST-VBL to the gear tooth crack simulation signal and actual signal,the superior performance of the ST-VBL method in dealing with various unknown and known noises is verified.?4?In many classification problems,the input samples are often two-dimensional matrices composed of vibration signals,and there is a strong correlation between rows or columns in the input matrix.Support matrix machine?SMM?is a new type of classifier with matrix input.It makes full use of the structural information of matrix to construct prediction model and has good diagnostic effect.Unfortunately,the SMM method has some limitations in dealing with complex input matrices,such as noise robustness and convergence.Therefore,this paper proposes the symplectic geometry matrix machine?SGMM?.In SGMM,this method not only protects the original structure of the signal,but also automatically extracts the noise-free features through the symplectic geometry similarity transformation,and establishes a weight coefficient model,which can realize multi-classification tasks.At the same time,since the weight coefficient model is established,the convergence problem can be avoided.The effectiveness of the SGMM is verified by the roller bearing fault signal.The analysis results show that the SGMM method has a good effect on the fault diagnosis of roller bearings.?5?In view of the limitations of SMM in analyzing complex data,two improved support matrix machines are proposed,namely symplectic incremental matrix machine?SIMM?and symplectic interactive support matrix machine?SISMM?.?1?Aiming at the limitations of the SMM in dealing with noise components and redundant features,a SIMM method is proposed.Firstly,SIMM uses the symplectic geometry similarity transform to obtain the de-noising symplectic geometry coefficient matrix,which realizes the effective fusion of feature extraction and classification recognition.Then,the sparse attribute is added to the objective function,and the influence of redundant features is weakened by l₁-norm.Finally,the Incremental proximal descent?IPD?method is used to solve the objective function,which greatly improves the efficiency of the algorithm under the premise of ensuring the recognition rate.The test results of two sets of roller bearings show that the SIMM method has a good application effect on the fault diagnosis of roller bearings.?2?SMM is a technology similar to support vector machine?SVM?whose core principle is to divide different types of data by two parallel hyperplanes.Unfortunately,two parallel hyperplanes may not maximize the spacing.Therefore,a SISMM method is proposed,which can construct the interactive hyperplane to maximize the interval between two types of data.When the interactive hyperplane divides two types of data,each hyperplane is closer to one of the two types and as far as possible from the other.The analysis results of the roller bearing signal show that the SISMM method has a good recognition performance.