Improved Multivariate Empirical Mode Decomposition And Its Application To Mechanical Fault Diagnosis

With the improvement of comprehensive strength and the progress of science and technology in China,the demand for safe production in modern industry is increasing.It is of great significance to develop and study mechanical fault diagnosis technology to ensure the safe and efficient operation of mechanical equipment.With the development of multi-sensor acquisition system,the synchronous processing of multivariate signals becomes particularly important.In the research of mechanical fault diagnosis,the multivariate signal processing method can describe the dynamic information of the fault components more comprehensively,which is beneficial to the realization of mechanical fault diagnosis.Therefore,on the basis of in-depth study of multiple empirical mode decomposition(MEMD),aiming at the problems of mode aliasing,power imbalance between multiple channels and high-dimensional extraction of hidden features of onedimensional signals in MEMD,this paper proposes improved MEMD theories.The main purpose of this paper is to optimize the decomposition performance of MEMD in processing multivariate signals,so that the decomposed multivariate IMF can accurately depict the dynamic information of the system,and make use of its decomposition characteristics and dynamic characterization attributes to carry out mechanical fault diagnosis.The effectiveness and superiority of the improved MEMD theory are illustrated by theoretical derivation,simulation analysis and practical experiments.In this dissertation,the rolling bearing is taken as the research object,and the improved MEMD theory is successfully applied to mechanical fault feature extraction and fault classification.The main contents of this paper include the following five aspects:1.Conduct the indepth study of MEMD theory,the effectiveness and superiority of MEMD are illustrated by simulation analysis and practical experiments.It shows that MEMD as a multi-signal synchronization processing method can be well applied to the study of mechanical fault diagnosis,laying a solid foundation for the improved MEMD theory and its application in mechanical fault diagnosis.2.Aiming at the problem of mode aliasing in MEMD,noise-assisted multivariate empirical mode decomposition(NAMEMD)is proposed based on the in-depth study of the filter bank property of MEMD.By adding the Gaussian white noise channels as auxiliary channels,the Gaussian white noise with uniform spectrum distribution can be used as a reference for MEMD in the frequency adaptive decomposition process.Two methods of adding noise are proposed.One is to add Gaussian white noise channel as auxiliary channel until the iteration is completed.The other is to add the Gauss white noise channel step by step to generate IMF of each order,to guarantee the same number of modes.3.Aiming at the power imbalance between multiple channels in MEMD,an adaptive projection multivariate empirical mode decomposition(APITMEMD)is proposed by using the adaptive nonuniform projection strategy.The principal component direction is used to represent the maximum direction of power imbalance between multi-channels adaptively,and the correlation between different channels is taken into account.The adaptive projection direction vector is used to iteratively decompose the power imbalance between different channels of multi-channel signals,thus reducing the sub-optimal local estimation caused by power imbalance between different channels of multi-channel signals.At the same time,we study the filter bank characteristics of APITMEMD under the aid of white noise,and further propose a noise aided adaptive projection multivariate empirical mode decomposition(NAAPITMEMD).4.To solve the problem of high-dimensional extraction of one-dimensional signal hiding features in MEMD,phase space reconstruction is proposed to optimize NAAPITMEMD.The reconstructed high-dimensional phase space is differentially homeomorphic to the original dynamical system,and the hidden evolution rules in the original dynamical system can be displayed in the high-dimensional phase space.The multivariate IMF decomposed by NAAPITMEMD is reconstructed in phase space,and the high-dimensional IMF can represent the inherent and hidden dynamic information of onedimensional signals.Through the study of high-dimensional phase points in highdimensional IMF,the dynamic information and evolution law of one-dimensional signal hiding are extracted,and the intrinsic dynamic feature extraction of one-dimensional signal in high-dimensional phase space is realized.5.The improved MEMD theories are successfully applied to mechanical fault feature extraction and fault classification.The method of composite fault feature extraction of rolling bearing based on NAAPITMEMD and an intelligent fault diagnosis method for rolling bearings under different working conditions are proposed.NAAPITMEMD is used to reduce the adverse effects caused by modal aliasing and power imbalance between multi-channels in extracting composite fault features of rolling bearings,and the composite fault features of rolling bearings are extracted from the decomposed multivariate IMF.In the classification of rolling bearing faults,the intelligent fault diagnosis of rolling bearings under different working conditions is carried out by using neural network.On the one hand,the dynamic information of the faulty rolling bearings is represented by partial multivariate IMF,and the entropy value of multivariate IMF is used as the input of the neural network.Because of the complexity of the time series measured by the entropy value,the intelligent fault diagnosis of rolling bearings under different working conditions can be realized.On the other hand,the high-dimensional IMF is obtained by phase space reconstruction.The feature of the high-dimensional IMF is used as the input of the neural network.By selecting the high-dimensional feature which is insensitive to the abnormal value,the intelligent fault diagnosis of rolling bearings under different working conditions is realized.