Research On Latant Variable Models In Statistics Process Control

Statistical process control is a significant way to guarantee product quality by monitoring and optimizing the production process.By employing probability theory and mathematical statistics techniques,multivariate statistical analysis based on process data can extract main factors that affect the quality of the product from the changes in the number of process variables,and can provide theoretical basis for further improving the product quality and process capability.Due to its simple concept and strong generalization,statistical process control based on data-driven technique,in recent years,has been vigorously developed for process modeling,data analysis,data mining,feature extraction and process monitoring,etc.The basic main approaches of multivariate statistical process control include principal component analysis(PCA),partial least squares regression(PLS)and principal component regression(PCR),etc.As for the practical production process,nonlinear relationship always exist among variables,the nonlinear multivariate statistical analysis has become a hot topic in many research fields.The widely used nonlinear multivariate statistical methods include kernel principal component analysis(KPCA),kernel least squares regression(KPLS)algorithm.The internal model parameters should be taken into account when establishing a process model based on KPCA and KPLS.To this end,this thesis has proposed several methods for determining model parameters based on the process statistical models in the nonlinear process.The specific research work in this thesis including:(1)In order to solve the problem of determining the correct number of principal components,we first analyzed advantages and disadvantages of the CPV,RE and KPA methods for estimating the number of principal components in KPCA in the literature.A two-dimensional cross-validatory technique was then proposed for optimally estimating the number of principal components.The proposed technique first removes one variable in the data set out,and uses the remaining ones to predict this variable.In the meantime,a corresponding kernel principal component regression model has been derived.The number of principal components can be obtained by minimizing the objective function which is the average variance for removing each variable in turn.Finally,the simulation results for a simulation example and three application studies,compared with existing methods,confirm that the proposed method can correctly estimate the number of principal components.(2)Extracting detailed information about the underlying data structure has received little attention.We firstly proposed a novel method which utilizes the nonlinear principal components in the KPCA to reveal the underlying nonlinear data structure.The proposed method assists in separating variable sets into distinct meaningful variable groups and examining their interdependencies by applying the estimated principal components of each variable subset.A simulation example(known variable classsification)and three industrial data sets(unknown variable classification)verified the effectiveness of the proposed method for data structure uncovering.(3)A detailed analysis shows that existing work for determining the kernel parameter and the number of latent variables for KPCA and KPLS is neither optimal nor efficient and may even lead to erroneous estimates.In addition to that,most methods are not designed to simultaneously estimate both parameters,i.e.they require one parameter to be predefined.To address these practically important issues,a cross-validatory framework was introduced to optimally determine both the parameters simultaneously,respectively.For a simulation example,the sensitivity of the number of samples and segments are analyzed,respectively;and some conclusions are drawn based on the effects on the optimal kernel parameter for different number of samples and segments.Three application studies confirm that the cross-validatory framework outperforms existing methods and yields optimal estimations for both parameters.