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.     

基于深度残差网络的化工过程故障诊断

本工作提出了一种基于深度残差网络(DRN)的化工过程故障诊断方法,可从大量化工过程运行数据中自动提取故障特征。模型采用快捷连接缓解传统深度神经网络训练困难的问题,且使用批归一化(BN)方法,可有效缓解梯度消失/爆炸的问题。以田纳西?伊斯曼(TE)过程为实验对象对所提方法进行诊断性能评价实验,并与以往的基于传统深度学习模型的TE过程故障诊断方法进行对比,进一步探究了模型层数、BN技术和残差结构对故障诊断率的影响,最后,通过t分布随机邻域嵌入(t-SNE)方法对网络部分层的输出进行可视化。结果表明,模型对21种工况取得了94%的平均故障诊断率和0.30%的平均假阳率,表现出更加卓越的诊断性能。输出层的二维散点图显示了清晰的聚类,表明所提出的DRN模型能够对故障进行准确诊断。     

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.     

A fault detection method based on sparse dynamic canonical correlation analysis

Fault detection based on canonical correlation analysis (CCA) has received increased attention due to its efficiency in exploring the relationship between input and output. However, traditional CCA may generate redundant features in both the input and output projections while maximizing the correlations. In this paper, sparse dynamic canonical correlation analysis (SDCCA) is developed for dealing with the fault detection of dynamic processes. Through posing sparsity in the extraction of features, the interpretability of canonical variates is enhanced attributed to the sparsity of canonical weights. Based on the SDCCA model, the $$ monitoring metric is established for fault detection. Moreover, the upper control limit (UCL) based on $$ monitoring metrics is determined by the kernel density estimation (KDE) method to avoid the violation of the Gaussian assumption. The superiority of the proposed SDCCA-based fault detection method is illustrated through a comparative study of the Tennessee Eastman process benchmark.     

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.     

基于GLSAFIS的氟化工过程操作单元可靠性监测

氟化工产物的剧毒特性,使得对于氟化工过程设备的运行可靠性监控异常重要。为此,提出了基于全局-局部结构分析的模糊推理系统（GLSAFIS）在线评估氟化工过程操作单元运行可靠性。依据氟化工工艺流程选取操作单元过程变量后,通过全局-局部结构分析算法（GLSA）对操作单元过程变量进行全局-局部特征提取。这些低维的全局-局部特征代替原始变量作为模糊推理系统（FIS）的输入,不仅可以克服噪声的影响,降低对专家知识的依赖,同时可以通过特征空间的降维压缩,大大加速后续模糊推理系统的逻辑设计。最后模糊推理系统的实施,使得本方法可以对化工过程操作单元可靠性进行在线评估。国内某氟化工厂二氟一氯甲烷（R-22）生产过程的实际应用以及田纳西伊斯曼模拟过程的仿真结果均证实了所提方法可以准确地反映实际化工过程操作单元的运行状况,大大提高了对实际化工过程的安全监控力度。     

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.     

Dynamic stationary subspace analysis based on Gaussian mixture models for ironmaking process monitoring

Blast furnace ironmaking process monitoring is an important and challenging task. Due to the influence of hot blast stove switching and large fluctuations in the quality of raw materials, the measurements of ironmaking processes show obvious non-stationary characteristics, and in addition, the observed data are also characterized by time-series dynamic and non-Gaussian characteristics. In this paper, a dynamic stationary subspace analysis method based on the Gaussian mixture model (DSSA–GMM) is proposed to address the difficulties in blast furnace ironmaking process monitoring. The time-series dynamic relationship of the data is conducted by introducing a sliding time window. The Gaussian mixture model (GMM) is used to deal with the non-Gaussian characteristics of the data, and the parameters of the GMMs are estimated using the expectation–maximization algorithm. The stationary projection matrix is obtained by optimizing the Kullback–Leibler (K–L) divergence between GMMs of different periods to realize the stationary subspace separation. Finally, the convex hull of the stationary subspace is established for fault detection, thus realizing the monitoring for non-stationary and non-Gaussian dynamic processes. The effectiveness of the DSSA–GMM method is verified by a numerical simulation and a dataset collected from an actual blast furnace ironmaking process.     

Multimodal process monitoring based on transition-constrained Gaussian mixture model

Reliable process monitoring is important for ensuring process safety and product quality. A production process is generally characterized by multiple operation modes, and monitoring these multimodal processes is challenging. Most multimodal monitoring methods rely on the assumption that the modes are independent of each other, which may not be appropriate for practical application. This study proposes a transition-constrained Gaussian mixture model method for efficient multimodal process monitoring. This technique can reduce falsely and frequently occurring mode transitions by considering the time series information in the mode identification of historical and online data. This process enables the identified modes to reflect the stability of actual working conditions, improve mode identification accuracy, and enhance monitoring reliability in cases of mode overlap. Case studies on a numerical simulation example and simulation of the penicillin fermentation process are provided to verify the effectiveness of the proposed approach in multimodal process monitoring with mode overlap.     

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。