Multivariate Statistical Process Monitoring Based On Local Feature Enhancement

The research of the main text is established upon the careful and deep analysis of multivariate statistical process monitoring(MSPM)methods.Against the shortcomings of existing methods,our research on MSPM is based on local feature enhancement,and includes the following aspects:1.Local or part component feature enhancement and fault detection based on NMF.Nonnegative matrix factorization(NMF)can produce local-based or parts-based factorization.Compared with methods producing holistic factorization,NMF can find the latent component structure feature of data more effectively and avoid introducing too much useless information.In the study of NMF-based fault detection,NMF is first modified from two aspects to improve the defects of NMF having no good statistical properties:(1)The first improvement of NMF is to make NMF have a certain ability to preserve the data variance.For this purpose,a variance-preserved NMF model based on variance-preserved regularization item is proposed with a numerical iterative algorithm for solving this model,and the validity of this algorithm is proved as well.On the basis of this model,the corresponding fault detection strategy is designed,and its monitoring performance is demonstrated by the simulation experiment.(2)The second improvement of NMF is to make NMF have the ability to reduce the correlation between the latent variables to some extent.For this target,a low-correlated NMF(LNMF)model is proposed.This model solves the NMF problem with a designed low rank approximate factorization algorithm named nonnegative matrix underapproximation(NMU).The verification experiments show that LNMF not only can make the variables of low dimensional data be mutually low correlated,but also can get base matrices with higher orthgonality and sparsity.On the basis of this model,the corresponding fault detection strategy is also designed and applied to some simulated processes.The simulatation results demonstrate the the monitoring performance of LNMF.2.Local nonlinear feature enhancement and process monitoring based on ensemble kernel principal component analysisAgainst the adverse influence on the performance of nonlinear process monitoring caused by kernel function selection,KPCA is taken as a research example,and combined with ensemble learning and Bayesian inference.First,based on the idea of ensemble learning,a series of Gaussian kernel functions are selected to get several different KPCA models;Then the conventional monitoring statistics are transferred into the posterior probabilities of different faults;Finally,the monitoring results of different KPCA models are combined into a final decision output with a weighted strategy which highlights the results of the alerting models.By doing so,the monitoring performance is not only more robust on the selection of kernel functions but also possible to be dramatically improved,which is demonstrated by simulation experiment.3.Spatial local feature enhancement and process monitoring based on spatial-statistical local approachThe existing manifold learning-based process monitoring methods do not make full use of the local information of new data and cannot detect the changes of the local strucuture of data.To addresss these defects,neighborhood preserving embedding(NPE)is taken as a research example.In this research example,a novel manifold learning-based process monitoring scheme is proposed by introducing statistical local approach into NPE.This scheme not only inherits the capacity of NPE digging the local structure of data,but also can implement process monitoring by detecting the changes of local structure of new data.Besides,introducing statistical local approach into NPE can also elimate the influence of data distribution,as the monitored data in this new scheme always approximately follows a multivariate Gaussian distribution.Thus,the control limit of each statistic can be easiliy estimated withc~2 or F distribution.Moreover,this scheme can improve the fault detection sensity greatly,as it has some characteristics similar to cumulative sum(CUSUM).At last,this scheme is applied to a simulated process,and the experiment results demonstrate its performance.