Improved Dynamic Mode Decomposition Theory And Its Application In Bearing Fault Diagnosis

Rolling bearings are key basic components in the equipment manufacturing industry,and their working conditions during service directly determine the performance,quality and reliability of mainframe products.In the actual operation of rolling bearings,the collected signals are non-linear,non-stationary,and dynamically coupled with the strong background and strong noise components of the external environment.These complex response signals containing the rich dynamic information of the original system and the characteristics of the health status of the machine make it difficult to judge health status and identify fault types of rolling beaings.In recent years,various mode decomposition methods have become a research hotspot in bearing fault diagnosis.The mode decomposition algorithm can adapt to various forms of complex signal systems and effectively separate various modes in the signals of rotating machinery.As a data-driven mode decomposition technology,the theory of dynamic mode decomposition can accurately extract the spatiotemporal characteristics of complex dynamic systems.In recent years,it has been widely used in the field of time series state assessment,feature extraction,trend prediction,and system control in the fluid field.This thesis studies how to use and improve the dynamic mode decomposition theory,effectively extract the fault characteristics of rolling bearing vibration signals,perform fault diagnosis and state recognition on equipment,introducing a new diagnostic theory system for the analysis of complex mechanical fault signals.The main work done by this degree thesis is as follows:(1)The theory of dynamic mode decomposition is studied,and a dynamic mode decomposition method for one-dimensional mechanical vibration signals is proposed.The ability of the dynamic mode decomposition theory to extract the dynamic characteristics of the system is verified by linear and nonlinear signals.In a comparative study with the existing mode decomposition methods and reduced order algorithms in mechanical fault diagnosis,we conclude that the dynamic mode decomposition theory has advantages in terms of the time-frequency retention of the original signal mode components and the coincidence degree of the reconstructed signal.Further research found that although the dynamic mode decomposition algorithm was suitable for the fault feature extraction of mechanical vibration signals,there are still have many key problems need to be solved in the implementation of the algorithm and the practical application,such as noise sensitivity,manual selection of the number of mode components,lacking of filtering criteria for useful mode components,lacking of synchronous coupling characterization of channel signals.(2)The research finds that the Koopman operator can not effectively suppress the noise component during the algorithm process,and it is the key reason for the sensitivity of the dynamic mode decomposition method to noise,and then global operator and reciprocal operator improvements are proposed.Experiments show that global operator improvement method is more effective.(3)Aiming at the problem of artificially setting the number of modes in the dynamic mode decomposition algorithm,an adaptive truncated rank dynamic mode decomposition method is proposed,which solves the problem of artificially setting parameters in the dynamic mode decomposition algorithm.Combining two successive improved algorithms in the dynamic mode decomposition process,an adaptive dynamic mode decomposition method combing with global operators is proposed.Through experimental research on the measured bearing fault signals,the fault feature information is effectively extracted,which shows that the improved algorithm is effective and the decomposition effect of the improved algorithm is better than the results of other mode decomposition and reduced order algorithms.(4)Aiming at the problem that the series of single-frequency modes still contain the sparse noise components of interference and the lack of principles for selecting useful mode components,a dynamic mode decomposition method of multi-scale permutation entropy threshold for noise reduction is proposed.Based on the multi-scale approximate entropy,the complexity of each mode component is detected,and the original signal is reconstructed by the threshold method.The key parameters of multi-scale approximate entropy decomposition for bearing signal components were determined through bearing dynamic signal simulation experiments.The method of multi-scale permutation entropy threshold with dynamic model decomposition is more effective for feature extraction of measured bearing signals.(5)Aiming at the problem that weak fault mode components in early noisy signals are difficult to extract,a multi-resolution dynamic mode decomposition method is proposed.Using the multi-resolution recursive layering theory,the original signal is decomposed in different layers with different resolutions(sampling frequencies)to obtain dynamic sets of low-rank modes and sparse modes that reflecting the dynamic characteristics of the original system.The mode of bearing failure characteristics was reconstructed.Experimental research based on early bearing fault signals shows that the multi-resolution dynamic mode decomposition method can strengthen the characterization of fault features in early fault signals.Combining the multi-scale permutation entropy mode selection method with the multi-resolution dynamic mode decomposition method,a multi-resolution and multi-scale dynamic mode decomposition method is proposed.Coarse-grained mean processing is used to replace sparse sampling of signal matrices at different levels,and multi-scale entropy thresholds are used to replace the dichotomy used for low-rank and sparse mode division.Experimental research shows that the multi-resolution and multi-scale dynamic mode decomposition method is better than the multi-resolution dynamic mode decomposition method in the early feature extraction of fault features.(6)Aiming at the problem of lacking of coupled decomposition method for multi-channel one-dimensional signals,a multivariate dynamic model decomposition method was proposed.The original multi-channel signal is formed into a third-order tensor by increasing the spatial dimension.After the high-order singular value decomposition,the adaptive dynamic mode decomposition with global operator is performed on basis matrix,and the kernel function is updated and reconstructed to restore the noise reduction tensor.The multivariate dynamic mode decomposition method solves the problem of artificial selection of truncated rank of the basis matrix in the process of high-order singular value decomposition.Experimental research shows that the method can synchronously and effectively extract the dynamic characteristics of each channel signal.(7)For signal processing,due to bearing size error,installation error,sensor acquisition error,noise pollution,etc.,there is a deviation between the faulty frequency value of the bearing signal obtained from the dynamic mode decomposition and the theoretical calculation value,which affects the diagnosis process of manual frequency finding of the fault characteristics,a method of bearing failure mode recognition based on improved dynamic mode decomposition theory is proposed.The sparse mode and multi-scale permutation entropy values of low-rank mode are used as feature parameters in multi-resolution and multi-scale modes,and BP neural network is selected as a classifier to realize the mode recognition of early bearing failures.Experiments based on two common bearing datasets show that the proposed method can accurately identify the failure mode of bearings.