面向统计过程控制的成分提取技术研究与应用
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摘要
统计过程控制(SPC)借助统计成分提取技术监测生产过程的稳定性,是先进制造系统的重要组成部分,也是先进质量控制的重要工具。成分提取技术是一类研究多变量数据内部统计规律,揭示数据内在低维本质信息的统计分析技术,更是统计过程控制的关键支撑技术。本文以统计过程控制为应用背景,深入研究了以二阶统计量方差和高阶统计量为算法性能指标的主成分和独立成分提取技术,并应用于化工过程和半导体封装过程的监控、故障诊断和系统降维等方面。
论文首先分析了在高斯分布下经典主成分分析(MSE-PCA)建立的主成分模型具有最小均方误差和最小残差熵性质。熵是比方差更通用的系统不确定性度量,最大熵原理要求系统主成分模型应该具有最小残差熵,但MSE-PCA对非高斯数据所建立的主成分模型不具有最小残差熵。依据最大熵原理,论文提出了一种主成分模型具有最小残差熵的改进型主成分提取方法(MEE-PCA)。MEE-PCA先以MSE-PCA确定基本主成分模型,再利用遗传算法优化所保留的主特征向量,使得主成分模型的残差熵最小。并以多变量四水箱过程为实例,描述了MEE-PCA在统计过程监控及故障诊断中的应用,验证了MEE-PCA方法比MSE-PCA的优越性。
依据随机逼近理论和Hebb学习规则,论文深入分析了以神经网络实现主成分提取的算法,论述了具有更强非线性数据降维能力的非线性主成神经网络算法。结合自关联线性主成分提取神经网络(MSE-PCNN)和非线性主成分提取思想,提出一种以最小残差熵为指标的自关联非线性主成分提取神经网络(MEE-PCNN),给出基于Parzen窗口密度函数估计的微分熵近似计算方法。基于信息最大化(Infomax)原理,论证了MSE-PCNN方法和MEE-PCNN方法在高斯分布情况下的等价性。以四水箱过程为实例,对比分析了经典PCA和非线性主成分神经网络的降维能力。用非高斯数据仿真验证了MEE-PCNN方法能有效地进行非高斯数据降维和信号盲源提取。
针对独立非高斯性信号混和数据的压缩降维与盲源提取问题,总结了几种基于最大非高斯性或信息熵度量指标的独立成分分析(ICA)算法,论证了最大似然估计ICA算法、最大负熵ICA算法和最小互信息ICA算法之间的等价性。结合非线性主成分提取网络的降维思想和信息最大化(Infomax)原则,论文提出一种以Renyi熵最大化作为指标的主独立成分提取网络(PICNN)算法,用于同时对非高斯混和数据降维压缩和独立成分提取。以田纳西-伊斯曼过程为应用实例,验证了ICA算法在过程故障检测和诊断中应用的优越性。用非高斯数据仿真分析了PICNN算法在信号降维和盲信号重构中应用的有效性。
统计成分提取技术常被用于基于知识或信号的数值分析类故障诊断方法中,却难以被用于基于模型的数学解析类故障诊断方法中。论文提出一种高维随机动态系统降维和基于观测器的故障诊断算法。该算法首先用成分提取技术对高维解析模型降维逼近,然后设计状态观察器,通过选择适当的自适应调节规律,保证所选择的李亚普诺夫函数能单调递
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.
论文首先分析了在高斯分布下经典主成分分析(MSE-PCA)建立的主成分模型具有最小均方误差和最小残差熵性质。熵是比方差更通用的系统不确定性度量,最大熵原理要求系统主成分模型应该具有最小残差熵,但MSE-PCA对非高斯数据所建立的主成分模型不具有最小残差熵。依据最大熵原理,论文提出了一种主成分模型具有最小残差熵的改进型主成分提取方法(MEE-PCA)。MEE-PCA先以MSE-PCA确定基本主成分模型,再利用遗传算法优化所保留的主特征向量,使得主成分模型的残差熵最小。并以多变量四水箱过程为实例,描述了MEE-PCA在统计过程监控及故障诊断中的应用,验证了MEE-PCA方法比MSE-PCA的优越性。
依据随机逼近理论和Hebb学习规则,论文深入分析了以神经网络实现主成分提取的算法,论述了具有更强非线性数据降维能力的非线性主成神经网络算法。结合自关联线性主成分提取神经网络(MSE-PCNN)和非线性主成分提取思想,提出一种以最小残差熵为指标的自关联非线性主成分提取神经网络(MEE-PCNN),给出基于Parzen窗口密度函数估计的微分熵近似计算方法。基于信息最大化(Infomax)原理,论证了MSE-PCNN方法和MEE-PCNN方法在高斯分布情况下的等价性。以四水箱过程为实例,对比分析了经典PCA和非线性主成分神经网络的降维能力。用非高斯数据仿真验证了MEE-PCNN方法能有效地进行非高斯数据降维和信号盲源提取。
针对独立非高斯性信号混和数据的压缩降维与盲源提取问题,总结了几种基于最大非高斯性或信息熵度量指标的独立成分分析(ICA)算法,论证了最大似然估计ICA算法、最大负熵ICA算法和最小互信息ICA算法之间的等价性。结合非线性主成分提取网络的降维思想和信息最大化(Infomax)原则,论文提出一种以Renyi熵最大化作为指标的主独立成分提取网络(PICNN)算法,用于同时对非高斯混和数据降维压缩和独立成分提取。以田纳西-伊斯曼过程为应用实例,验证了ICA算法在过程故障检测和诊断中应用的优越性。用非高斯数据仿真分析了PICNN算法在信号降维和盲信号重构中应用的有效性。
统计成分提取技术常被用于基于知识或信号的数值分析类故障诊断方法中,却难以被用于基于模型的数学解析类故障诊断方法中。论文提出一种高维随机动态系统降维和基于观测器的故障诊断算法。该算法首先用成分提取技术对高维解析模型降维逼近,然后设计状态观察器,通过选择适当的自适应调节规律,保证所选择的李亚普诺夫函数能单调递
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.
引文
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