Research On Locally-Linear-Embedding-Based Fault Feature Extraction Technology For Rolling Bearing

Mechanical machine is a combination of multiple components and it can complete certain tasks through coordinating with each component under driven by power source.Rolling bearing is the most commonly used mechanical part in mechanical machine,which breaks down more frequently in the real-world operation process.Whether the rolling bearing can work steadily not only determines the working efficiency and product quality of mechanical machine,but also influences the smooth and safe operation of industrial production processes.Therefore,in-depth analysis of common failures of rolling bearing during equipment operation,timely warning in the early stages of failure,and repair and maintenance are the keys to ensuring the normal operation of the equipment and extending the service life of the equipment.Rolling bearing will inevitably generate some vibration signals during operation,and the vibration signals contain abundant useful information reflecting the working stage of mechanical machine.It is difficult to recognize the faults directly from the collected vibration signals due to the complex working conditions and the influence of various noises in the field.How to extract the significant features of various faults by analyzing vibration signals to improve the recognition accuracy and reduce the computational complexity of the recognition algorithms is an important research direction of fault diagnosis methods.In this paper,the classical non-linear dimensionality reduction method,Locally Linear Embedding(LLE)algorithm,is researched in depth.Based on the characteristics of rolling bearing fault signals,a series of rolling bearing fault feature extraction methods based on LLE algorithm are proposed.The main work is as follows:Considering the existence of a large amount of redundant information in the collected rolling bearing data,which increases the complexity of the data and affects the recognition accuracy and recognition efficiency.Thus we utilize LLE algorithm to eliminate the redundant dimensions of data.On the other hand,combining regularization theory to address the problems simultaneously that local structure calculation and neighbors selection are sensitive to noise in LLE algorithm.More specifically,constructing a more practical local reconstruction model in the original high-dimensional devotes to proposing an adaptive non-linear dimensionality reduction method,which is named as ALLE algorithm.In the local reconstruction model,ALLE algorithm flexibly adjusts the roles of regularmethod of 7)1and 7)2in the optimization process according to the relationship between the embedding dimensionality of samples (9 and the number of neighbor points 6)to limit the optimal solution to a desired region;In order to solve the reconstructed model more effectively and avoid losing important information of original data simultaneously,we integrate the least-angel regression technique into ALLE algorithm to find the optimal solution with a more conservative search strategy.Moreover,the experimental results show that the ALLE algorithm can reduce the dimensionality of data effectively when applying it to the standard rolling bearing data set of Case Western Reserve University(CWRU).Generally,it is difficult to extract meaningful features for rolling bearing data sets in traditional time and frequency space.To overcome this problem,we propose a method called single tensor high order singular value decomposition-ALLE(STHALL).It firstly uses a single tensor high order singular value decomposition(STH)algorithm incorporated high order singular value decomposition(HOSVD)algorithm to extract the original features of rolling bearing data set,which comprehensively analyses the properties of rolling bearing signals in different subspaces.In this paper,the rolling bearing signals are projected into three subspaces by phase space reconstruction,empirical mode decomposition and wavelet transform,and then are united into a tensor model for described.Moreover,we employ ALLE algorithm to reduce the dimensionality of the decomposed features and obtain meaningful features that can truly reflect the original data.It can be noted that STHALLE algorithm not only realizes the multi-information integration of data set,but also solves the problems of loss structural information and small samples cased by traditional vector patterns.The single-sample tensor high-order singular value decomposition ALLE algorithm is applied to the numerical experiments of rolling bearings and Case Western Reserve bearing data set.Experimental results demonstrate that the proposed algorithm can extract intrinsic characteristics of rolling bearing signal.Aiming at the high speed of diagnosis in the real rolling bearing fault diagnosis,the ALLE algorithm belongs to a batch processing method and cannot meet the problem of real-time monitoring of the running status of the rolling bearing.From the two aspects of the ALLE algorithm’s own characteristics and the nonlinear approximation of the function,the linear projection ALLE algorithm and the ALLE algorithm based on BP neural network are proposed,respectively.In the linear projection ALLE algorithm,learning from the idea of linear discriminant analysis algorithm,that is,combining ALLE with linear discriminant analysis algorithm,while mining the structural information and cate-gory information of the data.This method can not only improve the recognition of the embedded results,but also learn an explicit mapping matrix between high dimensional space and low dimensional space.Based on the explict projection,the new caming samples can be projected into the low dimensional feature space.In this method,we can not only improve the recognition of embedded results,but also learn an explicit mapping matrix from high-dimensional space to low ones,and new sample points can be easily projected into low-dimensional feature space.The superiority of the two algorithms in processing new coming samples was verified using the Case Western Reserve rolling bearing data set.Combining the above research fruits with support vector machine,we propose a complete rolling bearing fault diagnosis method.Firstly,the tensor model of each rolling bearing sample is constructed by multi-sensor or space transformation method;Secondly,HOSVD algorithm is used to extract the initial features of the tensor model;Then LPALLE algorithm is employed to reduce the dimensionality of the initial features to get the final embedding results,and then obtained a mapping function between high dimensional space and low dimensional space;Furthermore,the training of support vector machine model is gained by employing the existing samples and the corresponding embedded results;Finally,an on-line real-time monitoring of rolling bearing operations is constructed by using a mapping function and support vector machine.