Research Based On Improved Discriminant Locality Preserving Projection Method And It's Application In Industrial Fault Diagnosis

Today's chemical industry systems are characterized by integration,high complexity,multiple variables,and strong coupling.A large number of high-dimensional and nonlinear data are generated during the operation process.Therefore,the principle challenge for fault diagnosis is how to extract effective information from the massive high-dimensional,non-linear process data produced in the process industry.The data-driven fault diagnosis method based on feature extraction technology is main method to deal with this problem.Discriminant locality preserving projection(DLPP),belonging to the manifold learning,can not only mine the information located on the manifold structure,but also achieve better data visualization and classification by minimizing the within-class manifold dispersion and maximizing between-class manifold dispersion.It has important research significance and application value in fault diagnosis field.However,DLPP suffers from serious small sample size(SSS)problem in practical applications and cannot be directly applied.In order to make DLPP better applied in the fault diagnosis,we analyzed the causes of SSS problem,proposed two solutions,and modeled the chemical process.The specific contents are as follows:(1)A fault diagnosis method based on Schur decomposition-orthogonal exponential discriminant locality preserving projection(Schur-OEDLPP)is proposed.This method not only retains the identification and classification superiorities of DLPP,but also overcomes the small sample problem of DLPP by introducing matrix exponentials properties,thereby extracting important discriminant information in the null space of between-class manifold scatter matrix.However,computation of exponential of the matrix will make elements of matrix very large,so the Frobenius norm is used to normalize the matrix.In addition,we use Schur's theorem to decompose the corresponding matrix exponential,which can acquire a group of standard orthogonal basis vectors,thereby solving the redundancy problem of the eigenvectors and achieving better fault separation.(2)A fault diagnosis method based on the Bootstrap discriminant locality preserving projection(Bootstrap-DLPP)is proposed.This method uses Bootstrap's pair sampling method to resample multiple numbers within a class to generate multiple inter-class mean samples,which makes the number of samples between classes larger than the number of features to overcome the SSS problem of DLPP.Besides,a novel adjacency graph consisting of a k-nearest-neighbor graph and a k-furthest neighbor graph is developed to enhance the separation effect of the projection data,and improve the accuracy of fault diagnosis.(3)In this paper,the Akaike information criterion is used to select the optimal order of dimensionality reduction for Schur-OEDLPP and Bootstrap-DLPP models.Then,the fault classification is carried out through the Bayesian discriminant model on maximum posterior probability.(4)Finally,this paper takes the two-dimensional synthetic data set and the Tennessee-Eastman(TE)process as the research object,and uses multiple cases to evaluate the performance of the two methods proposed in various aspects.Experimental results prove the presented two algorithms outperform other state-of-the-art feature extraction technologies in terms of visualization intuition and classification accuracy,especially when the distances between classes are unevenly distributed.