Tensor Decomposition Theory And Its Application In Mechanical Fault Diagnosis

The mechanical equipment fault signals collected in engineering practice are usually the result of coupled vibration of different excitation sources and multiple components,which present the typical characteristics of multi-interference,nonlinear and non-stationary.In addition,the early weak faults are easy to be submerged by strong background noise.Moreover,the fault information obtained by a single sensor is insufficient.Therefore,weak fault feature extraction under the strong background noise and multi-component interference as well as the multi-sensor joint diagnosis are the hot issues in fault diagnosis research.The complex dynamic characteristics of signal can be effectively demonstrated in the reconstructed high-dimensional phase space.As the high-dimensional extension of matrix representation,tensor is the most natural representation of high-dimensional data.The signal processing method based on tensor decomposition model can mine the potential feature information in the tensor data,which has been widely used in various types of signal processing in recent years.Aiming at the several typical problems mentioned above,this thesis takes the mechanical equipment as the research object,deeply studies and improves the tensor decomposition theory,so as to provide a new theoretical system for mechanical fault diagnosis.The main work of this thesis includes the following aspects:(1)A signal denoising method based on Tensor Nuclear Norm Canonical Polyadic Decomposition is proposed against the problem of strong noise interference.The signal denoising problem can be transformed into the low-rank approximation solution of signal feature subspace,and the low-rank representation of one-dimensional signals in the high-order tensor space was realized via tensor nuclear norm minimization.Moreover,the global optimal convergence solution was obtained by using convex optimization algorithm,so as to achieve robust elimination of strong noise.On this basis,the proposed method is combined with the Multi-Scale Permutation Entropy for the fault diagnosis of gear signal,and the Back Propagate neural network is selected as the classifier to realize intelligent identification of different gear fault types.(2)A signal subspace separation method based on Local Tensor Robust Principal Component Analysis is proposed against the problem of fault feature extraction under multi-component interference.For the second-order trajectory tensor reconstructed via one-dimensional signals,on the basis of providing good noise reduction performance,the local low-rank model of signals is established by smoothing kernel function and distance function.This model supports that the signal attractor phase space is a linear mixture of multiple subspaces representing different feature components,and their corresponding locally trajectory matrices have typical low-rank characteristics.These low-rank matrices can be effectively separated by solving a convex optimization framework about the joint minimization of the matrix nuclear norm and the penalty function regularization.Then,the Teager energy operator is employed to calculate the time-frequency distribution of signal and the fault-related subspace components can be identified via time-frequency characteristics of the fault feature,so as to effectively separate the fault characteristic components from the multi-component signals.(3)A weak fault feature signal energy maintained method based on Generalized Non-Convex Tensor Robust Principal Component Analysis is proposed against the problem of multi-sensor joint analysis and early weak fault feature extraction.Firstly,the signal is reconstructed to the three-order trajectory tensor via phase space reconstruction to obtain the high-order tensor representation of multi-channel signals.Then,the nonlinear filtering is performed to the obtained tensor via the classical Tensor Singular Value Decomposition model to mine the joint fault features of multi-channel signals.And a generalized non-convex relaxation is applied to the strong convex constraint of the tensor nuclear norm in the convex optimized denoising framework adopted by the filtering,so as to effective avoid the amplitude reduction of useful Singular Value Tubes.Moreover,based on the sensitivity of kurtosis to the impact signal,a Tensor Singular Value Kurtosis index is defined to determine adaptively the optimal reconstruction order of Singular Value Tubes,so as to achieve effective reconstruction and energy maintained of weak fault feature.(4)Aiming at the problem of weak fault diagnosis under multi-component interference and strong noise,the local low-rank model is extended to the three-order tensor space to further improve the Generalized Non-Convex Tensor Robust Principal Component Analysis,and a weak fault diagnosis method based on Local Generalized Non-Convex Tensor Robust Principal Component Analysis is proposed.The three-order trajectory tensor reconstructed from real multi-channel signal in phase space is modeled as linear combination of several local low-Tubal-rank subspaces contaminated by noise,and these feature subspaces can be effectively separated by solving a generalized non-convex optimization framework.Meanwhile,a Multivariate Kurtosis is introduced to identify the fault-related subspace components,so as to effectively remove the interference components and maintain the energy of the extracted fault feature,so as to realize the feature extraction and accurate diagnosis of early weak fault of real multi-channel signal.