Batch process monitoring with tensor factorization

A batch process monitoring method using tensor factorization, tensor locality preserving projections (TLPP), is proposed. In many existing vector-based methods on batch process monitoring such as MPCA and MLPP, a batch data is represented as a vector in high-dimensional space. But vectorizing batch data will lead to information loss. Essentially, a batch data is presented as a second order tensor, or a matrix. In this case, tensor factorization may be used to deal with the two-way batch data matrix directly instead of performing vectorizing procedure. Furthermore, tensor representation has some advantages such as low memory and storage requirements and less estimated parameters for normal operating condition (NOC) model. On the other hand, different from principal component analysis (PCA) which aims at preserving the global Euclidean structure of the data, the TLPP aims to preserve the local neighborhood information and to detect the intrinsic manifold structure of the data. Consequently, TLPP may be used to find more meaningful intrinsic information hidden in the observations. The effectiveness and advantages of the TLPP monitoring approach are tested with the data from a benchmark fed-batch penicillin fermentation and two industrial fermentation processes, penicillin and cephalosporin, respectively.     

A novel process monitoring and fault detection approach based on statistics locality preserving projections

Data-driven fault detection technique has exhibited its wide applications in industrial process monitoring. However, how to extract the local and non-Gaussian features effectively is still an open problem. In this paper, statistics locality preserving projections (SLPP) is proposed to extract the local and non-Gaussian features. Firstly, statistics pattern analysis (SPA) is applied to construct process statistics and grasp the non-Gaussian statistical property using high order statistics. Then, locality preserving projections (LPP) method is used to discover local manifold structure of the statistics. In essence, LPP tries to map the close points in the original space to close in the low-dimensional space. Lastly, T² and squared prediction error (SPE) charts of SLPP model are used to detect process faults. One simple simulated system and the Tennessee Eastman process show that the proposed SLPP method is more effective than principal component analysis, LPP and statistics principal component analysis in fault detection performance.     

基于改进的局部保持投影高光谱图像分类研究*

针对高光谱图像分类中基于流形的降维方法进行了研究。提出一种改进的局部保持投影（LPP）方法即MLPP方法。该方法利用标签信息避免了传统LPP在邻接图构建中很难确定的邻域大小的选择问题,同时采用更能反映高维数据间相关性的统计特征量相关系数来衡量数据之间的相似程度。设计的权重矩阵既保持类内数据的几何结构,又最大化类间距离。而且MLPP不依赖任何参数和先验知识。在两个高光谱图像上的实验结果表明MLPP增加了不同光谱特征地物之间的可分性,在提高分类性能上明显优于其他传统的降维方法。     

基于变量展开和时变协方差的连续更新的MPCA及其在批过程故障监测中的应用

针对传统的多向主元分析（MPCA）模型批过程监测的缺陷,提出了一种基于变量展开和协方差随时间变化的连续更新的MPCA批过程故障监测方法。该方法将基于批次展开能够去除采样数据的主要非线性动态性的优点与基于变量展开不需要对被监测的新批次的未反应完的数据进行预估的优点结合起来,用于批过程的故障监测,一旦因此判断出某一新批次过程正常,则模型参考数据库就随之更新。在实时监测新的批过程时,只需利用已收集到的数据信息,并且在线连续地更新模型参考数据库,提高了批过程性能监测的准确性,克服了MPCA不能处理非线性过程和实时性问题。通过采用该方法与传统的MPCA方法对青霉素补料分批发酵过程的实时监测,结果表明该方法比传统的MPCA更适合于对缓慢变化的批过程进行监测,具有更可靠的监测性能。     

Predictive on-line monitoring of continuous processes

For safety and product quality, it is important to monitor process performance in real time. Since traditional analytical instruments are usually expensive to install, a process model can be used instead to monitor process behavior. In this paper, a monitoring approach using a multivariate statistical modeling technique, namely multi-way principal component analysis (MPCA), is studied. The method overcomes the assumption that the system is at steady state and it provides a real time monitoring approach for continuous processes. The monitoring approach using MPCA models can detect faults in advance of other monitoring approaches. Several issues which are important for the proposed approach, such as the model input structure, data pretreatment, and the length of the predictive horizon are discussed. A multi-block extension of the basic methodology is also treated and this extension is shown to facilitate fault isolation. The Tennessee Eastman process is used for demonstrating the power of the new monitoring approach.     

基于判别正则化的局部保留投影

局部保留投影（Locality preserving projections,LPP）是一种常用的线性化流形学习方法,其通过线性嵌入来保留基于图所描述的流形数据本质结构特征,因此LPP对图的依赖性强,且在嵌入过程中缺少对图描述的进一步分析和挖掘。当图对数据本质结构特征描述不恰当时,LPP在嵌入过程中不易实现流形数据本质结构的有效提取。为了解决这个问题,本文在给定流形数据图描述的条件下,通过引入局部相似度阈值进行局部判别分析,并据此建立判别正则化局部保留投影（简称DRLPP）。该方法能够在现有图描述的条件下,有效突出不同流形结构在线性嵌入空间中的可分性。在人造合成数据集和实际标准数据集上对DRLPP以及相关算法进行对比实验,实验结果证明了DRLPP的有效性。     

Statistical process monitoring with independent component analysis

In this paper we propose a new statistical method for process monitoring that uses independent component analysis (ICA). ICA is a recently developed method in which the goal is to decompose observed data into linear combinations of statistically independent components [1 and 2]. Such a representation has been shown to capture the essential structure of the data in many applications, including signal separation and feature extraction. The basic idea of our approach is to use ICA to extract the essential independent components that drive a process and to combine them with process monitoring techniques. I², I_e² and SPE charts are proposed as on-line monitoring charts and contribution plots of these statistical quantities are also considered for fault identification. The proposed monitoring method was applied to fault detection and identification in both a simple multivariate process and the simulation benchmark of the biological wastewater treatment process, which is characterized by a variety of fault sources with non-Gaussian characteristics. The simulation results clearly show the power and advantages of ICA monitoring in comparison to PCA monitoring.     

A Minimal Line Property Preserving Representation of Line Images

In line image understanding a minimal line property preserving (MLPP) graph of the image compliments the structural information in geometric graph representations like the run graph. With such a graph and its dual it is possible to efficiently detect topological features like loops and holes and to make use of relations like containment. We present a new rule based method on dual graph contraction for transforming the run graph and its dual into MLPP graphs. A parallel O(log(longest curve)) algorithm is presented and results given. Received: May 28, 1998; revised November 17, 1998     

Nonlinear process monitoring based on kernel global–local preserving projections

A new nonlinear dimensionality reduction method called kernel global–local preserving projections (KGLPP) is developed and applied for fault detection. KGLPP has the advantage of preserving global and local data structures simultaneously. The kernel principal component analysis (KPCA), which only preserves the global Euclidean structure of data, and the kernel locality preserving projections (KLPP), which only preserves the local neighborhood structure of data, are unified in the KGLPP framework. KPCA and KLPP can be easily derived from KGLPP by choosing some particular values of parameters. As a result, KGLPP is more powerful than KPCA and KLPP in capturing useful data characteristics. A KGLPP-based monitoring method is proposed for nonlinear processes. T² and SPE statistics are constructed in the feature space for fault detection. Case studies in a nonlinear system and in the Tennessee Eastman process demonstrate that the KGLPP-based method significantly outperforms KPCA, KLPP and GLPP-based methods, in terms of higher fault detection rates and better fault sensitivity.     

改进的MPCA及其在批过程实时故障监测中的应用

针对多向主元分析（MPCA）模型批过程在线监测的缺陷,提出了一种基于变量展开和主元协方差随时间变化的MPCA方法,该方法按变量展开,不需要对新批次未反应完的数据进行预估,而数据之间的动态联系通过时变主元协方差得以保存,并且不需要建模批次的长度相等;将该力法应用于青霉素补料分批发酵过程的实时监测中．结果表明该方法比传统的MPCA方法具有更可靠的监测性能。     

Local and global principal component analysis for process monitoring

In this paper, a novel data projection method, local and global principal component analysis (LGPCA) is proposed for process monitoring. LGPCA is a linear dimensionality reduction technique through preserving both of local and global information in the observation data. Beside preservation of the global variance information of Euclidean space that principal component analysis (PCA) does, LGPCA is characterized by capturing a good linear embedding that preserves local structure to find meaningful low-dimensional information hidden in the high-dimensional process data. LGPCA-based T² (D) and squared prediction error (Q) statistic control charts are developed for on-line process monitoring. The validity and effectiveness of LGPCA-based monitoring method are illustrated through simulation processes and Tennessee Eastman process (TEP). The experimental results demonstrate that the proposed method effectively captures meaningful information hidden in the observations and shows superior process monitoring performance compared to those regular monitoring methods.     

基于分层分块DLPPCA-SVM的复杂工业过程监测与故障诊断方法

针对工业过程动态性及非线性强等特点,提出一种基于动态局部保持主成分分析法的过程监测方法.该方法通过构造扩展矩阵来解决动态过程中各采样点间相关性强的问题,并将局部保持投影(LPP)与主成分分析法(PCA)相结合从而实现提取流形结构的最大方差信息.在此基础上,针对复杂工业过程变量复杂多变、呈不同特性的特点,提出基于分层分块DLPPCA-SVM(dynamic locality preserving principal component analysis-support vector machine, DLPPCA-SVM)的过程监测及故障诊断方法,该方法针对不同特性的子块分别采用DLPPCA和PCA进行建模,并利用支持向量机进行故障诊断.将该方法用于田纳西-伊斯曼(TE)化工过程和发电机组的在线监测和故障诊断,仿真结果验证了所提出方法的有效性.     

Intelligent process monitoring by interfacing knowledge-based systems and multivariate statistical monitoring

An intelligent process monitoring and fault diagnosis environment has been developed by interfacing multivariate statistical process monitoring (MSPM) techniques and knowledge-based systems (KBS) for monitoring multivariable process operation. The real-time KBS developed in G2 is used with multivariate SPM methods based on canonical variate state space (CVSS) process models. Fault detection is based on T ² charts of state variables. Contribution plots in G2 are used for determining the process variables that have contributed to the out-of-control signal indicated by large T ² values, and G2 Diagnostic Assistant (GDA) is used to diagnose the source causes of abnormal process behavior. The MSPM modules developed in Matlab are linked with G2. This intelligent monitoring and diagnosis system can be used to monitor multivariable processes with autocorrelated, crosscorrelated, and collinear data. The structure of the integrated system is described and its performance is illustrated by simulation studies.     

Exponential locality preserving projections for small sample size problem

Locality preserving projections (LPP) is a widely used manifold reduced dimensionality technique. However, it suffers from two problems: (1) small sample size problem and (2) the performance is sensitive to the neighborhood size k. In order to address these problems, we propose an exponential locality preserving projections (ELPP) by introducing the matrix exponential in this paper. ELPP avoids the singular of the matrices and obtains more valuable information for LPP. The experiments are conducted on three public face databases, ORL, Yale and Georgia Tech. The results show that the performances of ELPP is better than those of LPP and the state-of-the-art LPP Improved1.     

Local structure based supervised feature extraction

In the past few years, the computer vision and pattern recognition community has witnessed the rapid growth of a new kind of feature extraction method, the manifold learning methods, which attempt to project the original data into a lower dimensional feature space by preserving the local neighborhood structure. Among them, locality preserving projection (LPP) is one of the most promising feature extraction techniques. However, when LPP is applied to the classification tasks, it shows some limitations, such as the ignorance of the label information. In this paper, we propose a novel feature extraction method, called locally discriminating projection (LDP). LDP utilizes class information to guide the procedure of feature extraction. In LDP, the local structure of the original data is constructed according to a certain kind of similarity between data points, which takes special consideration of both the local information and the class information. The similarity has several good properties which help to discover the true intrinsic structure of the data, and make LDP a robust technique for the classification tasks. We compare the proposed LDP approach with LPP, as well as other feature extraction methods, such as PCA and LDA, on the public available data sets, FERET and AR. Experimental results suggest that LDP provides a better representation of the class information and achieves much higher recognition accuracies.     

CUIMWMPCA方法及其在批过程故障监测中的应用*

针对传统的多向主元分析(multiway principal component analysis,MPCA)批过程监测的缺陷,提出了一种连续更新的改进移动窗多向主元分析(consecutively updated improved moving window MPCA,CUIMWMPCA)方法。该方法采用连续更新的多模型非线性结构代替传统的MPCA固定的单模型线性化结构,一旦通过改进的移动窗多向主元分析(improved moving window MPCA,IMWMPCA)判断出某一新批次过程正常,则     

基于多时段MPCA的半导体蚀刻过程监测方法

针对MPCA方法在具有多时段的间歇过程中的故障监测效果不佳的问题,提出一种新的多时段建模方法,首先根据各时间片上的主元个数不同,对过程进行模糊划分,然后利用K均值算法对样本数据聚类得到精确划分,最后按照划分结果在各阶段建立代表性统计分析模型对整个过程进行监控。将该方法用于半导体蚀刻过程的故障监测,并与MPCA方法进行了比较证明该方法具有良好的监控性能,能够及时准确及时的监测出引起产品质量发生变化的故障。     

基于改进的MPCA与DTW方法及其在批过程故障诊断中的应用

针对传统的多向主元分析(Multiway Principal Component Analysis,MPCA)常会导致误诊断,且对批生产过程难以保证在线状态监测和故障诊断的实时性,提出了一种改进的MPCA与动态时间错位(Dynamitc Time Warping,DTW)方法,该方法采用多模型非线性结构代替传统的MPCA单模型线性化结构,并利用对称式DTW算法解决了多元轨迹同步化的问题。将该方法应用到青霉素发酵批过程的在线故障监测中,结果表明它克服了MPCA不能处理非线性过程和实时性问题,并避免了MPCA在线应用时预报未来测量值带来的误差,提高了批过程性能监测和故障诊断的准确性。     

Supervised optimal locality preserving projection

In the past few years, the computer vision and pattern recognition community has witnessed a rapid growth of a new kind of feature extraction method, the manifold learning methods, which attempt to project the original data into a lower dimensional feature space by preserving the local neighborhood structure. Among these methods, locality preserving projection (LPP) is one of the most promising feature extraction techniques. Unlike the unsupervised learning scheme of LPP, this paper follows the supervised learning scheme, i.e. it uses both local information and class information to model the similarity of the data. Based on novel similarity, we propose two feature extraction algorithms, supervised optimal locality preserving projection (SOLPP) and normalized Laplacian-based supervised optimal locality preserving projection (NL-SOLPP). Optimal here means that the extracted features via SOLPP (or NL-SOLPP) are statistically uncorrelated and orthogonal. We compare the proposed SOLPP and NL-SOLPP with LPP, orthogonal locality preserving projection (OLPP) and uncorrelated locality preserving projection (ULPP) on publicly available data sets. Experimental results show that the proposed SOLPP and NL-SOLPP achieve much higher recognition accuracy.     

BDPCA在线过程监测方法

针对基于多向主元分析(Muhiway Principal Component Analysis,MPCA)的方法在批过程故障监测中以样本观测相互独立作为假设前提条件,没有考虑到时间序列相关性的影响及需要对新批次未反应完的数据进行预估的缺陷,提出一种枇过程动态主元分析(Batch Dy-namic PCA,BDPCA)在线监测方法.该方法采用时滞变量将过程的静态和动态特征相结合,有效地去除了测量变量时间序列的自相关关系,并通过时滞窗口提供了在线监测方案,避免了对新批次未反应完的数据进行预估的需要,提出确定时滞变量的算法.将BDPCA应用于β-甘露聚糖酶发酵批过程的仿真监测,与移动窗多向主元分析(Moving Window MPCA.MWMPCA)法相比,仿真结果表明该方法能够更精确地对过程故障行为进行描述,具有良好的准确性和实时性.