Component Extraction Techniques For Statistical Process Control And Applications

With the applications of computer integrated manufacturing system (CIMS) and thedemands of rigorous product quality, statistical process control (SPC) is playing a significantrole in the industria processes. Component extraction (CX) as a key supporting technologyof SPC is a statistical computational technique for revealing the multivariable statisticalcharacteristics and extracting the hidden components that underlie the observation of a setof variables and signals. The main goal of this dissertation are aimed at extracting theprincipal components (PC) and independent components (IC) from the observed mixturedata with optimal cost performance based on second and higher statistics. In this thesisapplications of these component techniques of SPC, such as process monitoring and faultdiagnosis, signal processing and dimension reduction, are also illustrated.Firstly, the optimal performance of principal component analysis (PCA) is demonstratedaccording to principles of minimum error estimation and maximum entropy. While for theobservation of a non-Gaussian stochastic distribution process system the optimal PCA modelshould have minimum error entropy (MEE). It is evident that the conventional PCA approachneeds to be refined to a PCA model for non-Gaussian distribution system. In this study amodified PCA (MEE-PCA) with the optimization for MEE for the dimensionality reductionof non-Gaussian system is proposed, and the corresponding optimizing method via geneticalgorithm (GA) is derived. A four-tank multivariable system is included to demonstrate theadvantages of MEE-PCA in SPC, and the promising results have been obtained.Neural network (NN) provides a feasible way for parallel online PCA. In this thesis theprincipal component neural networks (PCNN) with minimum squared error criteria to extractlinear and nonlinear principal component are expounded. It has shown that linear PCNNmodel with MSE can extract the subspace spanned by principal eigenvectors or the theoret-ical principal eigenvectors. But for non-Gaussian distribution system the PCNN model withMSE does not contain maximum information about original system definitely. In this thesisa generalized autoassociative PCNN model with minimum error entropy (MEE) and its gra-dient descent learning algorithm are proposed. A nonparametric estimator based on Parzenwindowing with the Gaussian kernel to estimate entropy is also provided. According to theInfomax principle the equivalence of the PCNN with cost performance of MSE and MEEin Gaussian case is analyzed. The advantages of nonlinear PCNN in dimensionality reduc-tion and the e?ectiveness of the proposed MEE-PCNN in maximum information componentextraction from observation are simulated through some examples.Considering a situation where the observations are the mixtures of a number of indepen-dent non-Gaussian signals whose channels of mixing are unknown, and what we need to do isto find the original independent sources from the mixture. Linear PCNNs which ignore thehigher order structure will not be able to separate these independent source from the mix-tures. The aim of ICA is to design structure that can separate a mixture of signals in a blindmanner and identify the unknown mixing channels with only a observed mixed data. Nonlin-ear decorrelation and maximum non-Gaussianity are two basic principles for ICA. In contrastto PCA based on the covariance structure, ICA not only decorrelates the components butalso reduces higher order statistical dependencies, in order to make the extracted componentas independent as possible. The powerful strength of ICA is that only mutual statistical in-dependence between the non-Gaussian source signals is assumed in ICA model and no prioriinformation about the characteristics of the source signals and the mixing matrix are known.The classical application of ICA is blind source separation (BSS) which refers to the prob-lem of recovering signals from several observed mixtures. In this study the techniques andalgorithms for ICA are described from the perspective of information theory.Subsequently aprincipal independent component neural network (PICNN) based on maximization of secondorder Renyi's entropy is proposed. An approximation method for the computation of theRenyi entropy criterion and the corresponding gradient learning algorithm are provided. Themotivation for using Renyi's entropy was the existence of an computationally simple esti-mator for Renyi's quadratic entropy, as well as the fact that Shannon's entropy is a specialcase of Renyi's entropy. For normally distributed data the maximization of the transformeddata variance indicates that the entropy or average information content of data is maximized.Simulation examples are included to show the e?ectiveness of the proposed approach for thedimensionality reduction and the advantages of the blind source separation over the generalprinciple component analysis.Based on the ideas of dimensionality reduction and component extraction as mentionedabove, a nonlinear principal component neural network (PCNN) model with the instanta-neous stochastic gradient descent learning algorithm for dimensionality reduction of a highdimensional dynamic control system is derived. A fault diagnosis method via an adaptiveobserver for the dimensionality-reduced system is proposed by using the linear residual sig-nal, where an adaptive tuning rule is established to insure the monotonically decreasing of aselected Lyapunov function. The e?ciency of the proposed approaches is illustrated througha simulation example.Finally, the advantages of SPC based on the component extraction techniques are demon-strated through a case study on the dispensing process in integrated circuit encapsulation.Through a comparison study of the performance of di?erent methods it has shown that MEEbased component extraction technique is better than the MSE base component extractiontechnique in fault diagnosis.