基于加权统计特征KICA的故障检测与诊断方法

针对核独立元分析（kernel independent component analysis, KICA）在非线性动态过程中对微小故障检测率低的问题,提出一种基于加权统计特征KICA（weighted statistical feature KICA, WSFKICA）的故障检测与诊断方法。首先,利用KICA从原始数据中捕获独立元数据和残差数据;然后,通过加权统计特征和滑动窗口获取改进统计特征数据集,并由此数据集构建统计量进行故障检测;最后,利用基于变量贡献图的方法进行过程故障诊断。与传统KICA统计量相比,所提方法的统计量对非线性动态过程中的微小故障具有更高的故障检测性能。应用该方法对一个数值例子和田纳西-伊斯曼（Tennessee-Eastman, TE）过程进行仿真测试,仿真结果显示出所提方法相对于独立元分析（ICA）、KICA、核主成分分析（kernel principal component analysis, KPCA）和统计局部核主成分分析（statistical local kernel principal component analysis, SLKPCA）检测的优势。     

基于贝叶斯推理的PKPCAM的非线性多模态过程故障检测与诊断方法

针对一类非线性多模态的化工过程,提出一种基于概率核主元的混合模型(PKPCAM),并利用贝叶斯推理策略进行过程监控与故障诊断.在提出的模型中, 每个操作模态由一个局部化的概率核主元分量描述,从而构建的一系列分量对应了不同的操作模态.首先,将过程数据从原始的度量空间投影到高维特征空间;其次,在该特征空间建立概率主元混合模型,从概率角度刻画数据集的多个局部分量特征;最后,在提取的核主元分量内获得测试样本的后验概率,结合模态内的马氏距离贡献度,提出基于贝叶斯推理的全局概率指标进行故障检测,同时利用模态内变量的相对贡献度,基于全局贡献度指标进行故障诊断.利用TEP仿真平台,与基于k均值聚类的次级主元分析和核主元分析的方法进行了对比分析,验证了提出的贝叶斯推理的PKPCAM方法对非线性多模态过程进行故障检测与诊断的可行性和有效性.     

基于WPRKPCA的非线性化工过程微小故障检测

传统核主元分析法（KPCA）是一种广泛应用的非线性化工过程故障检测方法,但是其未充分利用过程数据的概率分布信息,往往难以有效检测过程中的微小故障。针对传统KPCA方法的局限性,本文提出了一种基于加权概率相关核主元分析（WPRKPCA）的非线性化工过程微小故障检测方法。与传统KPCA方法监控核成分的变化不同,该方法利用Kullback Leibler散度（KLD）度量核成分的概率分布变化,进而建立基于KLD成分的统计监控模型,以充分挖掘过程数据所包含的概率信息。进一步考虑到不同KLD成分承载故障信息的差异性,该方法设计了一种基于核密度估计的指数加权策略,根据KLD成分描述故障信息程度的差异分配相应的权值,以加强监控模型对微小故障检测的灵敏性。在一个数值例子和连续搅拌反应器（CSTR）系统上的仿真结果表明,本文所提方法具有比传统KPCA方法更好的微小故障检测性能。     

基于核主角的故障检测方法

基于主元分析（PCA）的统计检测方法已经被广泛应用于各种化工过程的故障检测和识别.移动主元分析（moving principal component analysis,简称MPCA）算法基于PCA,根据主元子空间的变化来判断故障是否发生.然而,基于主元分析的统计检测方法是线性方法,无法有效应用于非线性系统.因此,提出一种适合于非线性系统的故障检测方法——基于核主角(kernel principal angle,简称KPA)的故障检测方法,其基本思想与MPCA相似,主要内容包括构建特征子空间和核主角测量两部分.TE过程故障检测仿真实验证明,基于核主角的故障检测方法优于传统的多元统计检测方法（cMSPC）和MPCA.     

基于加权互信息主元分析算法的质量相关故障检测

质量相关的故障检测已成为近几年研究热点,它的目标是在过程监测中,对质量相关的故障检测率更高,对质量无关的故障少报警或不报警。传统主元分析算法的故障检测会对所有故障均报警,不能达到上述要求。另外,在实际工业生产中,质量变量通常难以实时获得,需要后续分析或延时得到。为此,提出一种融合贝叶斯推断与互信息的加权互信息主元分析算法。首先利用贝叶斯推断的加权方法将度量过程变量和质量变量之间相关关系的互信息进行融合,选出包含质量变量信息量最大的一组过程变量。然后对过程变量利用主元分析（principal component analysis,PCA）进行统计建模,再次根据加权互信息选出包含质量变量信息量最大的主元,建立统计量进行故障检测。最后,通过实验验证该方法的可行性和有效性。     

Cycle temporal algorithm-based multivariate statistical methods for fault diagnosis in chemical processes

Multivariate statistical process monitoring methods are often used in chemical process fault diagnosis. In this article,(I) the cycle temporal algorithm(CTA) combined with the dynamic kernel principal component analysis(DKPCA) and the multiway dynamic kernel principal component analysis(MDKPCA) fault detection algorithms are proposed, which are used for continuous and batch process fault detections,respectively. In addition,(II) a fault variable identification model based on reconstructed-based ...     

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     

Fault Detection of Non‐Linear Processes Using Kernel Independent Component Analysis

In this paper, a new non‐linear process monitoring method based on kernel independent component analysis (KICA) is developed. Its basic idea is to use KICA to extract some dominant independent components capturing non‐linearity from normal operating process data and to combine them with statistical process monitoring techniques. The proposed method is applied to the fault detection in the Tennessee Eastman process and is compared with PCA, modified ICA, and KPCA. The proposed approach effectively captures the non‐linear relationship in the process variables and showed superior fault detectability compared to other methods while attaining comparable false alarm rates.     

基于加权统计局部核主元分析的非线性化工过程微小故障诊断方法

传统统计局部核主元分析（statistical local kernel principal component analysis, SLKPCA）在构造改进残差时未考虑样本的差异性,使得故障样本信息易于被其他样本所掩盖,针对该问题,提出一种基于加权统计局部核主元分析（weighted statistical local kernel principal component analysis, WSLKPCA）的非线性化工过程微小故障诊断方法。该方法首先利用KPCA获取过程的得分向量和特征值并构建初始残差。然后设计了一种基于测试样本与训练样本之间距离的加权策略构建加权改进残差,对含有较强微小故障信息的样本赋予较大权值,以增强故障样本的影响。最后,采用基于测量变量与监控统计量之间的加权互信息构建贡献图以识别故障源变量。在连续搅拌反应釜和田纳西伊斯曼（Tennessee Eastman, TE）化工过程上的仿真结果表明,所提方法具有良好的微小故障检测与识别性能。     

一种基于KICA-GMM的过程故障检测方法

核独立元分析(kernel independent component analysis,KICA)故障检测方法的故障检测时间易受独立元顺序和主导独立元数目经验选取的影响,针对这个问题,提出基于KICA和高斯混合模型(Gaussian mixture model,GMM)的故障检测方法。采用KICA从正常工况测量数据中提取独立元,用GMM拟合各独立元的概率密度函数,建立基于GMM的监控量及其控制限;计算各独立元的监控量均值,以此判断其非高斯性强弱,对每个强非高斯独立元进行单独监控,对弱非高斯部分采用主元分析法进行监控。在Tennessee Eastman过程上的仿真结果说明,相比于KICA故障检测方法,所提方法不需要排序独立元和选取主导独立元数目,避免了其对故障检测时间的影响,能够有效利用过程信息,缩短故障检测的延迟时间。     

基于ICA混合模型的多工况过程故障诊断方法

针对工业过程数据的多模态和非高斯特性,提出一种基于独立元混合模型（independent component analysis mixture model,ICAMM）的多工况过程故障诊断方法。该方法将独立元分析与贝叶斯估计结合,同时完成各个工况的数据聚类和模型参数求取,并建立基于贝叶斯框架下的集成监控统计量实时监控过程变化。在检测到故障后,针对传统的变量贡献图方法无法表征变量之间信息传递关系的缺点,提出基于信息传递贡献图的故障识别方法。该方法首先计算各变量对独立元混合模型统计量的贡献度,进一步通过最近邻传递熵描述故障变量之间的传递性,挖掘故障变量之间的因果关系,从而确定故障源变量和故障传播过程。最后对一个数值系统和连续搅拌反应釜（CSTR）过程进行仿真研究,结果验证了本文所提出方法的有效性。     

基于核熵独立成分分析的故障检测方法

传统核独立成分分析（KICA）依据特征值的大小进行降维,但是特征值大并不一定取得的信息熵贡献度也是最大的。针对这个问题,提出一种基于核熵独立成分分析（KEICA）的故障检测方法。将训练数据集投影在高维核空间,通过对数据信息熵的贡献大小选取核主成分,并建立独立成分分析（ICA）模型。对训练样本求{\mathit{I}}^{\mathrm{2}}和\mathrm{S}\mathrm{P}\mathrm{E}统计量,并利用核密度估计计算统计量的控制限。计算测试数据对训练数据的核矩阵,将其投影在ICA模型上并计算测试样本的统计量,统计量超出控制限的样本即可被识别为故障样本。将该方法用于非线性数值例子和Tennessee Eastman（TE）过程的故障检测,并与传统的核主成分分析（KPCA）、核熵成分分析（KECA）和KICA方法进行对比,表明KEICA的监测效果优于其他三种方法。     

Multivariate statistical process monitoring using an improved independent component analysis

An approach for multivariate statistical monitoring based on kernel independent component analysis (Kernel ICA) is presented. Different from the recently developed KICA which means kernel principal component analysis (KPCA) plus independent component analysis (ICA), Kernel ICA is an improvement of ICA and uses contrast functions based on canonical correlations in a reproducing kernel Hilbert space. The basic idea is to use Kernel ICA to extract independent components and later to provide enhanced monitoring of multivariate processes. I² (the sum of the squared independent scores) and squared prediction error (SPE) are adopted as statistical quantities. Besides, kernel density estimation (KDE) is described to calculate the confidence limits. The proposed monitoring method is applied to fault detection in the simulation benchmark of the wastewater treatment process and the Tennessee Eastman process, the simulation results clearly show the advantages of Kernel ICA monitoring in comparison to ICA and KICA monitoring.     

基于核熵独立成分分析的故障检测方法

传统核独立成分分析（KICA）依据特征值的大小进行降维,但是特征值大并不一定取得的信息熵贡献度也是最大的。针对这个问题,提出一种基于核熵独立成分分析（KEICA）的故障检测方法。将训练数据集投影在高维核空间,通过对数据信息熵的贡献大小选取核主成分,并建立独立成分分析（ICA）模型。对训练样本求{\mathit{I}}^{\mathrm{2}}和\mathrm{S}\mathrm{P}\mathrm{E}统计量,并利用核密度估计计算统计量的控制限。计算测试数据对训练数据的核矩阵,将其投影在ICA模型上并计算测试样本的统计量,统计量超出控制限的样本即可被识别为故障样本。将该方法用于非线性数值例子和Tennessee Eastman（TE）过程的故障检测,并与传统的核主成分分析（KPCA）、核熵成分分析（KECA）和KICA方法进行对比,表明KEICA的监测效果优于其他三种方法。     

基于故障判别增强KECA算法的故障检测

基于核熵主成分分析方法的统计模型仅利用正常工况下数据进行建模,而忽略了监控系统数据库中一些已知类别的先前故障数据。为了利用先前故障数据中包含的故障信息来增强故障检测性能,提出了一种故障判别增强KECA (fault discriminant enhanced kernel entropy component analysis, FDKECA)算法。该法通过采用无监督学习和监督学习方法建立模型,同时监测非线性核熵主成分(kernel entropy component, KEC)和故障判别成分(fault discriminant component, FDC)两类数据特征。此外,利用贝叶斯推理将相应的监视统计信息转换为故障概率,并通过加权两个子模型的结果来构建基于总体概率的监视统计量。通过数值仿真和田纳西伊斯曼(Tennessee Eastman, TE)过程仿真实验,证明和传统KECA相比,FDKECA算法能够有效利用故障数据提高故障检测率。     

基于双层局部KPCA的非线性过程微小故障检测方法

针对传统核主元分析（KPCA）方法难以有效检测微小故障的问题,提出一种基于双层局部核主元分析（double-level local kernel principal component analysis,DLKPCA）的非线性过程微小故障检测方法。该方法从变量和样本两个角度来挖掘数据内部的局部信息,以提高故障检测能力。首先,利用变量分块思想,基于不同变量与核主元之间互信息相关度的相似性,将所有过程变量划分多个局部变量块。然后,构建基于得分向量和特征值的残差函数以挖掘样本局部信息。最后利用贝叶斯融合策略对各块的结果进行融合。在田纳西-伊斯曼基准过程的仿真结果表明,在微小故障检测方面,本文所提方法具有比传统KPCA方法更好的故障检测性能。     

Reducing smearing effect in contribution plots and improving fault detection via polynomial approximated isomap embeddings

Dimension reduction is an essential method used in multivariate statistical process monitoring for fault detection and diagnosis. Principal component analysis (PCA) and independent component analysis (ICA) are the most frequently used linear dimensional reduction tools, and the contribution plot is the most popular fault isolation method in the absence of any prior information on the faults. These methods, however, come with their shortcomings. The fault detection capability of linear methods may not be sufficient for non-linear processes, and smearing effect is known to deteriorate the diagnostics obtained from contribution plots. While the fault detection rate may be increased by kernelized methods or deep artificial neural network models, tuning data-dependent hyperparameter(s) and network structure with limited historical data is not an easy task. Furthermore, the resulting non-linear models often do not directly possess fault isolation capability. In the current study, we aim to devise a novel method named ICA_pIso-PCA, which offers non-linear fault detection and isolation in a rather straightforward manner. The rationale of ICA_pIso-PCA mainly involves building a non-linear scores matrix, composed of principal component scores and high-order polynomial approximated isomap embeddings, followed by implementation of the ICA-PCA algorithm on this matrix. Applications on a toy dataset and the Tennessee Eastman plant show that the I² index from ICA_pIso-PCA yields a high fault detection rate and offers accurate contribution plots with diminished smearing effects compared to those from traditional monitoring methods. Easy implementation and the potential for future research are further advantages of the proposed method.     

基于统计量模式分析的T-KPLS间歇过程故障监控

核函数的全影结构投影(total kernel projection to latent structures,T-KPLS)最近在故障监控领域取得了广泛应用, 其实质是对数据矩阵的协方差矩阵进行分解, 没有利用数据的高阶统计量等有用信息, 在进行特征提取时会造成数据有用信息的丢失, 导致故障识别效果差。为了解决此问题, 提出了统计量模式分析(statistics pattern analysis, SPA)与核函数的全影结构投影法(total kernel projection to latent structures, T-KPLS)相结合的多向统计量模式分析的核函数的全影结构投影法(multi-way statistics pattern analysis total kernel projection to latent structures, MSPAT-KPLS)。该方法首先构造样本的不同阶次统计量, 将数据从原始的数据空间映射到统计量样本空间, 然后利用核函数将统计量样本空间映射到高维核空间并在质量变量的引导下将特征空间分为过程变量与质量变量相关、过程变量与质量变量无关、过程变量与质量变量正交和残差4个子空间;最后针对与质量变量相关和残差空间建立联合监控模型, 当监控到有故障发生时进行故障变量追溯。最后将该方法应用到微生物发酵过程中, 并与传统方法进行比较, 发现该方法具有更好的监控性能。     

Application of fault monitoring and diagnosis in process industry based on fourth order moment and singular value decomposition

Principal component analysis (PCA) and partial least squares (PLS) have been frequently used for process industry monitoring; however, their application on industrial sites is limited because they cannot be used to process data with non-Gaussian distribution. Independent component analysis (ICA) has become a powerful modelling method for non-Gaussian process monitoring. However, the ICA-based modelling method has been found to contribute to double the amount of data loss in feature extraction. There are two reasons for this. First, when the PCA algorithm is used to whiten the original data, the smaller principal component is discarded. Second, when selecting independent components, some smaller independent components will be discarded according to the evaluation index. The abovementioned two data feature extraction methods may discard useful information for fault monitoring, which will inevitably lead to inaccurate fault monitoring. To solve this problem, a fault monitoring and diagnosis method based on fourth order moment (FOM) analysis and singular value decomposition (SVD) is proposed. First, the fourth order moments of each process variable were constructed separately. Then, the data space of the fourth order moments was decomposed by singular value decomposition to establish the global monitoring statistics. Finally, the contribution diagram was drawn and the fault diagnosis was performed based on the global monitoring results. The proposed method was applied to the Tennessee Eastman (TE) simulation platform, and its effectiveness and feasibility were verified by a comparison with PCA and ICA.     

一种基于改进KICA的非高斯过程故障检测方法

针对基于核独立元分析(kernel independent component analysis,KICA)的故障检测方法只考虑非高斯信息提取而忽略局部近邻结构保持的问题,提出基于改进KICA的过程故障检测方法。将KICA法中只考虑非高斯信息提取的负熵最大化准则转换为熵最小化准则,结合局部保持投影的相似局部近邻结构准则,提出了同时考虑非高斯信息提取和局部近邻结构保持的目标函数,通过粒子群优化算法进行全局寻优,然后建立监控统计量对过程进行监控。在Tennessee Eastman过程上的仿真结果说明,与基于KICA的故障检测方法相比,所提方法能够在保持数据集局部近邻结构的同时,提取非高斯信息,能够有效缩短故障检测的延迟时间,提高故障检测率。