基于核Fisher判别分析方法的非线性统计过程监控与故障诊断

化工过程中大量的生产数据反应了生产过程的内在变化和系统的运行状况,基于数据驱动的统计方法可以有效地对生产过程进行监控。对于复杂的化工和生化过程,其过程变量之间的相关关系往往具有很强的非线性特性,传统的线性统计过程监控方法显得无能为力。本文提出了基于核Fisher判别分析的非线性统计过程监控方法,首先利用非线性核函数将数据从原始空间映射到高维空间,在高维空间中利用线性的Fisher判别分析方法提取数据最优的Fisher特征矢量和判别矢量来实现过程监控与故障诊断,能有效地捕获过程变量之间的非线性关系,通过对流化催化裂化（FCCU）过程的仿真表明该方法的有效性。     

A novel multimode process monitoring method integrating LCGMM with modified LFDA

Complex processes often work with multiple operation regions, it is critical to develop effective monitoring approaches to ensure the safety of chemical processes. In this work, a discriminant local consistency Gaussianmixture model (DLCGMM) for multimode process monitoring is proposed for multimode process monitoring by integrating LCGMMwith modified local Fisher discriminant analysis (MLFDA).Different fromFisher discriminant analysis (FDA) that aims to discover the global optimal discriminant directions, MLFDA is capable of uncovering multimodality and local structure of the data by exploiting the posterior probabilities of observations within clusters calculated fromthe results of LCGMM. This may enableMLFDA to capturemoremeaningful discriminant information hidden in the high-dimensional multimode observations comparing to FDA. Contrary to most existing multimode process monitoring approaches, DLCGMMperforms LCGMMandMFLDA iteratively, and the optimal subspaces with multi-Gaussianity and the optimal discriminant projection vectors are simultaneously achieved in the framework of supervised and unsupervised learning. Furthermore, monitoring statistics are established on each cluster that represents a specific operation condition and two global Bayesian inference-based faultmonitoring indexes are established by combining with all themonitoring results of all clusters. The efficiency and effectiveness of the proposed method are evaluated through UCI datasets, a simulated multimode model and the Tennessee Eastman benchmark process.     

Local component based principal component analysis model for multimode process monitoring

For plant-wide processes with multiple operating conditions,the multimode feature imposes some chal-lenges to conventional monitoring techniques.Hence,to solve this problem,this paper provides a novel local component based principal component analysis(LCPCA)approach for monitoring the status of a multimode process.In LCPCA,the process prior knowledge of mode division is not required and it purely based on the process data.Firstly,LCPCA divides the processes data into multiple local components using finite Gaussian mixture model mixture(FGMM).Then,calculating the posterior probability is applied to determine each sample belonging to which local component.After that,the local component information(such as mean and standard deviation)is used to standardize each sample of local component.Finally,the standardized samples of each local component are combined to train PCA monitoring model.Based on the PCA monitoring model,two monitoring statistics T2 and SPE are used for monitoring multimode pro-cesses.Through a numerical example and the Tennessee Eastman(TE)process,the monitoring result demonstrates that LCPCA outperformed conventional PCA and LNS-PCA in the fault detection rate.     

Fault Diagnosis in Chemical Process Based on Self-organizing Map Integrated with Fisher Discriminant Analysis

Fault diagnosis and monitoring are very important for complex chemical process. There are numerous methods that have been studied in this field, in which the effective visualization method is still challenging. In order to get a better visualization effect, a novel fault diagnosis method which combines self-organizing map （SOM） with Fisher discriminant analysis （FDA） is proposed. FDA can reduce the dimension of the data in terms of maximizing the separability of the classes. After feature extraction by FDA, SOM can distinguish the different states on the output map clearly and it can also be employed to monitor abnormal states. Tennessee Eastman （TE） process is em- ployed to illustrate the fault diagnosis and monitoring performance of the proposed method. The result shows that the SOM integrated with FDA method is efficient and capable for real-time monitoring and fault diagnosis in complex chemical process.     

ISOMAP-LDA方法用于化工过程故障诊断

针对化工连续生产过程的时序性及非线性等特征,提出一种新的基于数据驱动的化工过程故障诊断方法：ISOMAP-LDA。首先实行流形学习算法ISOMAP,在保持量测数据几何结构特性下完成非线性降维,然后基于提取的嵌入变量张成的低维空间,选用线性判别分析（LDA）构造故障模式类的判别函数,负责各采样个体故障类型的判定。将该方法用于仿真化工Tennessee Eastman 过程的故障诊断,结果表明,ISOMAP-LDA方法不仅拥有较高的故障诊断能力,而且取得采样在低维空间的可视化表示。     

A support vector clustering‐based probabilistic method for unsupervised fault detection and classification of complex chemical processes using unlabeled data

A new support vector clustering (SVC)‐based probabilistic approach is developed for unsupervised chemical process monitoring and fault classification in this article. The spherical centers and radii of different clusters corresponding to normal and various kinds of faulty operations are estimated in the kernel feature space. Then the geometric distance of the monitored samples to different cluster centers and boundary support vectors are computed so that the distance–ratio–based probabilistic‐like index can be further defined. Thus, the most probable clusters can be assigned to the monitored samples for fault detection and classification. The proposed SVC monitoring approach is applied to two test scenarios in the Tennessee Eastman Chemical process and its results are compared to those of the conventional K‐nearest neighbor Fisher discriminant analysis (KNN‐FDA) and K‐nearest neighbor support vector machine (KNN‐SVM) methods. The result comparison demonstrates the superiority of the SVC‐based probabilistic approach over the traditional KNN‐FDA and KNN‐SVM methods in terms of fault detection and classification accuracies. © 2012 American Institute of Chemical Engineers AIChE J, 59: 407–419, 2013     

Fault diagnosis based on imbalance modified kernel Fisher discriminant analysis

Process data with imbalance class distribution has brought a significant drawback to most existing pattern recognition based fault diagnosis algorithms, which have assumed that the process data have an equal misclassification cost and relatively balanced class distribution. The frequent occurrence of the imbalance problem in real industrial process indicates the need for extra research efforts. In this paper, three novel imbalance modified kernel Fisher discriminant analysis (IM-KFDA) approaches are proposed to handle this problem. Two sample-level approaches, over-sampling KFDA and under-sampling KFDA, are presented along with proper stochastic sampling strategies. One algorithm-level approach, inductive bias KFDA, is also proposed with incorporating a novel regular weighted matrix (RWM) into the minimum Euclid distance based pattern classification rule. To improve the fault diagnosis performance, model updating modes for the sample-level and algorithm-level approaches are described, respectively. A simulation case study of Tennessee Eastman (TE) process is conducted to evaluate the proposed fault diagnosis approaches.     

A combined canonical variate analysis and Fisher discriminant analysis (CVA–FDA) approach for fault diagnosis

This paper proposes a combined canonical variate analysis (CVA) and Fisher discriminant analysis (FDA) scheme (denoted as CVA–FDA) for fault diagnosis, which employs CVA for pretreating the data and subsequently utilizes FDA for fault classification. In addition to the improved handling of serial correlations in the data, the utilization of CVA in the first step provides similar or reduced dimensionality of the pretreated datasets compared with the original datasets, as well as decreased degree of overlap. The effectiveness of the proposed approach is demonstrated on the Tennessee Eastman process. The simulation results demonstrate that (i) CVA–FDA provides better and more consistent fault diagnosis than FDA, especially for data rich in dynamic behavior; and (ii) CVA–FDA outperforms dynamic FDA in both discriminatory power and computational time.     

复杂故障判定的基于结构化残差的多层次分析法

In industrial processes,there exist faults that have complex effect on process variables.Complex and simple faults are defined according to their effect dimensions.The conventional approaches based on structured residuals cannot isolate complex faults.This paper presents a multi-level strategy for complex fault isolation.An extraction procedure is employed to reduce the complex faults to simple ones and assign them to several levels.On each level,faults are isolated by their different responses in the structured residuals.Each residual is obtained insensitive to one fault but more sensitive to others.The faults on different levels are verified to have different residual responses and will not be confused.An entire incidence matrix containing residual response characteristics of all faults is obtained,based on which faults can be isolated.The proposed method is applied in the Tennessee Eastman process example,and the effectiveness and advantage are demonstrated.     

Balanced multiple weighted linear discriminant analysis and its application to visual process monitoring

Visual process monitoring is important in complex chemical processes. To address the high state separation of industrial data, we propose a new criterion for feature extraction called balanced multiple weighted linear discriminant analysis(BMWLDA). Then, we combine BMWLDA with self-organizing map(SOM) for visual monitoring of industrial operation processes. BMWLDA can extract the discriminative feature vectors from the original industrial data and maximally separate industrial operation states in the space spanned by these discriminative feature vectors. When the discriminative feature vectors are used as the input to SOM, the training result of SOM can differentiate industrial operation states clearly.This function improves the performance of visual monitoring. Continuous stirred tank reactor is used to verify that the class separation performance of BMWLDA is more effective than that of traditional linear discriminant analysis, approximate pairwise accuracy criterion, max–min distance analysis, maximum margin criterion, and local Fisher discriminant analysis. In addition, the method that combines BMWLDA with SOM can effectively perform visual process monitoring in real time.     

基于Fisher子空间特征提取的间歇过程监控和故障诊断

1 INTRODUCTION Process monitoring and fault diagnosis are the most important tasks that determine the successful operation and the final product quality. In batch proc- ess, small changes in the operating conditions may impact the final product quality, which is often exam- ined off-line in a laboratory. If the quality variable does not satisfy a specified criterion, then it is not possible to examine the causes of fault and the time of its occurrence[1]. Therefore, early fault detection …     

基于KECA的化工过程故障监测新方法

针对化工过程数据复杂、非线性的特点,提出一种基于核熵成分分析(KECA)的化工过程故障监测算法。首先,KECA算法按照Renyi熵值的大小选取特征值及特征向量,相比传统的KPCA监测算法,其保留主元个数更少,可以有效减少运算量。同时,仿真研究表明KECA算法选取的主元具有角度结构特性,据此,提出一种新的统计量--CS(Cauchy-Schwarz)统计量,其对应到核特征空间中即为向量间的角度余弦值,可以较好表述不同概率密度分布之间的相似度。最后,将KECA和KPCA算法分别应用于TE(Tennessee Eastman)过程,结果表明KECA在故障检测延迟与检出率相比KPCA都有很大的优势。     

Topological preservation techniques for nonlinear process monitoring

This work proposes a novel approach for the offline development and online implementation of data-driven process monitoring (PM) using topological preservation techniques, specifically self-organizing maps (SOM). Previous topological preservation PM applications have been restricted due to the lack of monitoring and diagnosis tools. In the proposed approach, the capabilities of SOM are further extended so that all aspects of PM can be performed in a single environment. First for fault detection, using SOM's vector quantization abilities, an SOM-based Gaussian mixture model (GMM) is proposed to define the normal region. For identification, an SOM-based contribution plot is proposed to identify the variables most responsible for the fault. This is done by analyzing the residual of the faulty point and an SOM model of the normal region used in fault detection. The data points are projected on the model by locating the best matching unit (BMU) of the point. Finally, for fault diagnosis a procedure is formulated involving the concept of multiple self-organizing maps (MSOM), creating a map for each fault. This allows the ability to include new faults without directly affecting previously characterized faults. A Tennessee Eastman Process (TEP) application is performed on dynamic faults such as random variations, sticky valves and a slow drift in kinetics. Previous studies of the TEP have considered particular feed-step-change faults. Results indicate an excellent performance when compared to linear and nonlinear distance preservation techniques and standard nonlinear SOM approaches in fault diagnosis and identification.     

一种基于改进MPCA的间歇过程监控与故障诊断方法

针对基于不同展开方式的多向主元分析(MPCA)方法在线应用时各自存在的缺陷,提出一种改进的基于变量展开的MPCA方法,实现间歇过程的在线监控与故障诊断。该方法采用随时间更新的主元协方差代替固定的主元协方差进行T²统计量的计算,充分考虑了主元得分向量的动态特性;同时引入主元显著相关变量残差统计量,避免SPE统计量的保守性,且该统计量能提供更详细的过程变化信息,对正常工况改变或过程故障引起的T²监控图变化有一定的识别能力;最后提出一种随时间变化的贡献图计算方法用于在线故障诊断。该方法和MPCA方法的监控性能在一个青霉素发酵仿真系统上进行了比较。仿真结果表明：该方法具有较好的监控性能,能及时检测出过程存在的故障,且具有一定的故障识别和诊断能力。     

基于互信息的PCA方法及其在过程监测中的应用

主元分析(PCA)是一种经典的特征提取方法,已被广泛用于多变量统计过程监测,其算法的本质在于提取过程数据各变量之间的相关性。然而,传统PCA算法中定义的相关性矩阵局限于计算变量间的线性关系,无法衡量两个变量间相互依赖的强弱程度。为此,提出一种新的基于互信息的PCA方法(MIPCA)并将之应用于过程监测。与传统PCA所不同的是,MIPCA通过计算两两变量间的互信息来定义相关性,将原始相关性矩阵取而代之为互信息矩阵,并利用该互信息矩阵的特征向量实现对过程数据的特征提取。在此基础上,可以建立相应的统计监测模型。最后,通过实例验证MIPCA用于过程监测的可行性和有效性。     

Multiway discrete hidden Markov model‐based approach for dynamic batch process monitoring and fault classification

A new multiway discrete hidden Markov model (MDHMM)‐based approach is proposed in this article for fault detection and classification in complex batch or semibatch process with inherent dynamics and system uncertainty. The probabilistic inference along the state transitions in MDHMM can effectively extract the dynamic and stochastic patterns in the process operation. Furthermore, the used multiway analysis is able to transform the three‐dimensional (3‐D) data matrices into 2‐D measurement‐state data sets for hidden Markov model estimation and state path optimization. The proposed MDHMM approach is applied to fed‐batch penicillin fermentation process and compared to the conventional multiway principal component analysis (MPCA) and multiway dynamic principal component analysis (MDPCA) methods in three faulty scenarios. The monitoring results demonstrate that the MDHMM approach is superior to both the MPCA and MDPCA methods in terms of fault detection and false alarm rates. In addition, the supervised MDHMM approach is able to classify different types of process faults with high fidelity. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

A quality relevant non‐Gaussian latent subspace projection method for chemical process monitoring and fault detection

Partial least‐squares (PLS) method has been widely used in multivariate statistical process monitoring field. The goal of traditional PLS is to find the multidimensional directions in the measurement‐variable and quality‐variable spaces that have the maximum covariances. Therefore, PLS method relies on the second‐order statistics of covariance only but does not takes into account the higher‐order statistics that may involve certain key features of non‐Gaussian processes. Moreover, the derivations of control limits for T² and squared prediction error (SPE) indices in PLS‐based monitoring method are based on the assumption that the process data follow a multivariate Gaussian distribution approximately. Meanwhile, independent component analysis (ICA) approach has recently been developed for process monitoring, where the goal is to find the independent components (ICs) that are assumed to be non‐Gaussian and mutually independent by means of maximizing the high‐order statistics such as negentropy instead of the second‐order statistics including variance and covariance. Nevertheless, the IC directions do not take into account the contributions from quality variables and, thus, ICA may not work well for process monitoring in the situations when the quality variables have strong influence on process operations. To capture the non‐Gaussian relationships between process measurement and quality variables, a novel projection‐based monitoring method termed as quality relevant non‐Gaussian latent subspace projection (QNGLSP) approach is proposed in this article. This new technique searches for the feature directions within the measurement‐variable and quality‐variable spaces concurrently so that the two sets of feature directions or subspaces have the maximized multidimensional mutual information. Further, the new monitoring indices including I² and SPE statistics are developed for quality relevant fault detection of non‐Gaussian processes. The proposed QNGLSP approach is applied to the Tennessee Eastman Chemical process and the process monitoring results of the present method are demonstrated to be superior to those of the PLS‐based monitoring method. © 2013 American Institute of Chemical Engineers AIChE J 60: 485–499, 2014     

Robust fault detection and monitoring of hybrid process systems with uncertain mode transitions

A methodology for fault detection and monitoring of a class of hybrid process systems modeled by switched nonlinear systems with control actuator faults, uncertain continuous dynamics, and uncertain mode transitions is presented. A robust hybrid monitoring scheme that distinguishes reliably between faults, mode transitions, and uncertainty is developed using tools from unknown input observer theory and results from Lyapunov stability theory. The monitoring scheme consists of (1) a family of dedicated mode observers that locate the active operating mode at any given time and detect mode switches, (2) a family of robust Lyapunov‐based fault detection schemes that detect the faults within the continuous modes, and (3) a supervisor that synchronizes the switching between different controllers and different fault detectors as the process transitions from one mode to another. A key idea of the developed framework is to design the mode observers in a way that facilitates the identification of the active mode without information from the controllers and renders the residuals insensitive to the faults and uncertainties in the constituent subsystems. The implementation of the developed monitoring scheme is demonstrated using a simulated model of a chemical reactor that switches between multiple operating modes. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Data‐based linear Gaussian state‐space model for dynamic process monitoring

This article develops a data‐based linear Gaussian state‐space model for monitoring of dynamic processes under noisy environment. The Kalman filter is introduced for construction of the linear Gaussian state‐space model, and an iterative expectation‐maximization algorithm is used for model parameters learning. With the incorporation of the dynamic data information, a new fault detection and identification approach is proposed. The feasibility and effectiveness of the two monitoring statistics in the new method are theoretically evaluated and further confirmed through two case studies. Furthermore, detailed fault smearing effect analysis of the proposed method is provided and compared with other identification methods. Based on the simulation results of two case studies, the superiority of the proposed method is explored. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Multiway independent component analysis mixture model and mutual information based fault detection and diagnosis approach of multiphase batch processes

Batch process monitoring is a challenging task, because conventional methods are not well suited to handle the inherent multiphase operation. In this study, a novel multiway independent component analysis (MICA) mixture model and mutual information based fault detection and diagnosis approach is proposed. The multiple operating phases in batch processes are characterized by non‐Gaussian independent component mixture models. Then, the posterior probability of the monitored sample is maximized to identify the operating phase that the sample belongs to, and, thus, the localized MICA model is developed for process fault detection. Moreover, the detected faulty samples are projected onto the residual subspace, and the mutual information based non‐Gaussian contribution index is established to evaluate the statistical dependency between the projection and the measurement along each process variable. Such contribution index is used to diagnose the major faulty variables responsible for process abnormalities. The effectiveness of the proposed approach is demonstrated using the fed‐batch penicillin fermentation process, and the results are compared to those of the multiway principal component analysis mixture model and regular MICA method. The case study demonstrates that the proposed approach is able to detect the abnormal events over different phases as well as diagnose the faulty variables with high accuracy. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2761–2779, 2013