Fault Diagnosis Of Rolling Bearings Based On Locally Linear Embedding

Mechanical equipment usually requires multiple components to coordinate and cooperate under the power drive to complete related work tasks.As one of the most critical components in rotating machinery,bearings directly affect the operating state of the machinery.The normal operation of the bearing not only ensure the working efficiency of rotating machinery and equipment,but also maintain the stability and safety of industrial production.Therefore,it is very important to monitor the running status of the bearing.It can provide early warning in the early stage of failure,which is conducive to subsequent repairs and maintenance and extends the service life of the equipment.The vibration signal collected from mechanical equipment contains a large amount of important information,which is useful for fault identification.However,a large amount of data and features will lead to information redundancy,which increases the difficulty of fault identification.High-dimensional data not only increases the computational complexity of the algorithm,but also leads to the"curse of dimensionality",which in turn degrades the performance of the recognition algorithm.Therefore,it is unrealistic to directly perform fault detection in a high-dimensional space.How to analyze the collected high-dimensional vibration data and accurately extract the intrinsic features of various bearing faults to improve the recognition accuracy of the recognition algorithm and reduce the computational complexity are the important direction for the research of bearing fault diagnosis methods.This paper conducts in-depth analysis and research on the local linear embedding（LLE）algorithm in manifold learning algorithms,and combines it with the classic classification algorithm support vector machine（SVM）algorithm to extract a complete series of bearings based on the LLE algorithm.Main contents in this research are summarized as follows:The LLE algorithm only extracts features by mining a single local structure of the original high-dimensional data set,and other important information of the original data is lost,resulting in the inability to accurately characterize the essential features of rolling bearings,reducing the effect of feature extraction,and resulting in low fault diagnosis accuracy.Based on the theory of multi-structure fusion,this paper proposes two LLE-based multi-structure fusion methods,called multi-structure locally linear embedding coefficient fusion（MS-LLECF）algorithm and multi-structure local linear embedding function fusion multi-structure locally linear embedding function fusion（MS-LLEFF）algorithm.In the MS-LLECF algorithm,the least squares structure and sparse structure are first combined with adjustment parameters to estimate multiple structures in the high-dimensional space to fully mine and utilize the structural information of the original data,and then,the essential features of various types of faults are extracted through preserving the multi-structure unchanged in the low-dimensional space;In the MS-LLEFF algorithm,the multi-structure of the original data is constructed by fusing the least square structure and the sparse structure in the low-dimensional space,so that the obtained low-dimensional features can accurately represent various rolling bearing faults.In addition,the relationship between the two multi-structure fusion methods is analyzed,and it is proved that the solution of MS-LLECF is a subset of MS-LLEFF.Experimental results prove that the multi-structure fusion algorithm can effectively extract the fault information of rolling bearings.For feature selection based on LLE feature selection algorithm,it is not only sensitive to noise,but also unable to adaptively select K-nearest neighbors of sample data.This paper proposes a robust locally linear embedding based voting（RLLE vote）algorithm.The l₁ and l₂ regularization techniques are introduced into the high-dimensional reconstruction model of LLE,which enables it to adaptively select the K-nearest neighbors of the sample,thereby improving the robustness of the graph retention framework;A relatively conservative least angle regression-elastic net（LARS-EN）iterative algorithm is used to calculate a sparse reconstruction weight matrix to achieve noise suppression;The most representative feature in the original high-dimensional data is selected by measuring the difference between the reconstructed feature and the original feature.Experiments on the bearing data set of Case Western Reserve University proved that RLLE vote can select the optimal low-dimensional subspace from the original high-dimensional feature space,which can fully reveal all kinds of fault information under different K values;Meanwhile,the visualization results indicate that the model has good robustness and effectiveness.Combining the above research results with support vector machines（SVM）,a complete set of fault diagnosis methods for rolling bearings is proposed.The method was applied to the rolling bearing data set of Case Western Reserve University and Jiangsu Qianpeng QPZZ-Ⅱmechanical equipment simulation platform for verification.The experimental results show that the MS-LLECF algorithm and the MS-LLEFF algorithm consider the least square structure and sparse structure of the original high-dimensional data when extracting features,and can extract the essential low-dimensional fault features of rolling bearings;Then the low-dimensional fault data is input to the support vector machine model for training,and realize the fault diagnosis of the rolling bearing according to the output category information.