基于多阶段多向核熵成分分析的间歇过程故障检测方法

针对间歇过程的非线性、多阶段特性,提出一种基于多阶段多向核熵成分分析（multistage-MKECA,MsMKECA）的故障检测方法。针对间歇过程的多阶段特性,建立一种时序核熵主元关联度的矩阵相似性阶段划分方法,实现对间歇生产过程的多阶段划分;针对传统批次展开方式在线监控需要预估批次未来值的缺陷,进一步引入一种批次-变量三维数据展开方式建立每个阶段的MKECA非线性统计模型,实现对间歇过程的分阶段监控。最后对盘尼西林发酵过程开展仿真研究,结果表明所提方法能够比传统MKECA方法更为快速地进行故障检测。     

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。     

Batch process monitoring using multiway Laplacian autoencoders

In this paper, a novel nonlinear method named multiway Laplacian autoencoder (MLAE) is proposed for batch process monitoring. Autoencoder (AE) is an effective unsupervised learning neural network for nonlinear feature extraction. Compared with traditional AEs, the proposed method has two main advantages. Firstly, traditional AEs usually ignore the local structure of the original dataset. The proposed MLAE method integrates graph Laplacian regularization to the loss function, and, thus, the local structure of the normal process data is fully considered. Secondly, the Laplacian matrix of the regularization term is constructed by an average local affinity matrix of all batch runs, which contains the information of the stochastic deviations among batches. Furthermore, two statistics, ie, H² and SPE statistics, are developed based on the extracted hidden representation and the retained reconstruction error. The effectiveness and advantages of the MLAE-based monitoring strategy are illustrated by a benchmark penicillin fermentation process and a real E. coli fermentation process.     

Fault detection in nonlinear chemical processes based on kernel entropy component analysis and angular structure

Considering that kernel entropy component analysis (KECA) is a promising new method of nonlinear data transformation and dimensionality reduction, a KECA based method is proposed for nonlinear chemical process monitoring. In this method, an angle-based statistic is designed because KECA reveals structure related to the Renyi entropy of input space data set, and the transformed data sets are produced with a distinct angle-based structure. Based on the angle difference between normal status and current sample data, the current status can be monitored effectively. And, the confidence limit of the angle-based statistics is determined by kernel density estimation based on sample data of the normal status. The effectiveness of the proposed method is demonstrated by case studies on both a numerical process and a simulated continuous stirred tank reactor (CSTR) process. The KECA based method can be an effective method for nonlinear chemical process monitoring.     

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     

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。     

基于KECA的非线性工业过程故障检测与诊断新方法

提出了一种基于核熵成分分析（kernel entropy component analysis，KECA）的非线性过程故障检测与诊断新方法。该方法首先利用KECA获取过程数据的得分向量及非线性特征子空间；然后鉴于KECA可以以角结构的方式揭示数据中潜在的集群结构，设计了基于角度的监测指标VoA。该指标通过各得分向量之间的角度方差来描述变换后数据间的结构差异,并根据角度方差的变化情况实现故障检测；接着，为了在检测到故障后有效地进行故障识别，构建了KECA相似度因子来度量特征子空间的相似程度以识别故障模式；最后，以非线性数值案例及Tennessee Eastman过程进行仿真测试研究，结果验证了所提方法的可行性及有效性。     

Statistics pattern analysis: A new process monitoring framework and its application to semiconductor batch processes

In the semiconductor industry, process monitoring has been recognized as a critical component of the manufacturing system. Multivariate statistical process monitoring (SPM) techniques, such as multiway principal component analysis and multiway partial least squares, have been extend to monitor semiconductor processes. These SPM methods require extensive, often off‐line data preprocessing such as data unfolding, trajectory mean shift, and trajectory alignment. This requirement is probably not an issue for the traditional chemical batch processes but it poses a significant challenge for semiconductor batch processes. This is because data preprocessing makes model building and maintenance extremely labor intensive due to the large number of models in a typical semiconductor fab. In addition, semiconductor process data often show more severe nonnormality compared to those of the traditional chemical process under closed‐loop control, which results in suboptimal performance in many applications. To address these challenges, several pattern classification based monitoring (PCM) methods have been developed recently, but some limitations remain and trajectory alignment is still required. In this article, we analyze the fundamental reasons for the limitations of the SPM and PCM methods when applied to monitor semiconductor processes. In addition, we propose a new statistics pattern analysis (SPA) framework to address the challenges associated with semiconductor processes. By monitoring batch statistics, the proposed SPA framework not only eliminates all data preprocessing steps but also provides superior fault detection performance. Finally, we use an industrial example to demonstrate the advantages of the proposed SPA framework, and examine the fundamental reasons for the improved performance from SPA. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

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     

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。     

基于特征样本核主元分析的TE过程快速故障辨识方法

核主元分析（KPCA）在非线性系统的故障检测方面明显优于普通的PCA方法,但存在无法进行故障辨识以及在故障诊断过程常常出现核矩阵K计算困难等难题。针对上述问题,提出了一种基于特征样本核主元分析方法（FS-KPCA）非线性故障辨识方法。首先采用特征样本（FS）提取方法有效解决核矩阵K的计算量问题。然后利用计算核函数的偏导方法求取KPCA监控中每个原始变量对统计量T²和SPE的贡献率,利用每个变量对监控统计量贡献程度的不同,可以辨识出故障源。将上述方法应用到TE过程,仿真结果表明该方法不仅能够有效辨识故障,而且提高了故障检测和辨识速度。     

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。     

基于核Fisher包络分析的间歇过程故障诊断

随着间歇过程越来越受重视,其过程监控和故障诊断技术也成为研究热点。以核Fisher判别分析为基础,提出了基于核Fisher的正常工况与故障包络面模型,给出了基于该模型的在线故障诊断流程。此方法利用了Fisher判别分析对类别的划分特点,分别针对正常工况数据和各故障类型数据建立包络曲面模型。与多向Fisher判别分析相比,该方法按批次方向将数据展开,能够解决生产周期不一致问题,在线故障诊断时也不需要预报完整的生产轨迹,并且加入核函数来处理复杂的非线性。最后在青霉素发酵过程的仿真平台上对该方法进行测试,与改进多向Fisher判别分析方法进行对比,该方法获得了满意的诊断效果：能够及早诊断出故障的发生,并在有效识别已有故障的同时还具有对新故障的自学习能力。     

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 contribution (RBC) model that paves the way for determining the cause of the fault are proposed. The proposed fault diagnosis model was applied to Tennessee Eastman (TE) process and penicillin fermentation process for fault diagnosis. And compare with other fault diagnosis methods. The results show that the proposed method has better detection effects than other methods. Finally, the reconstruction-based contribution (RBC) model method is used to accurately locate the root cause of the fault and determine the fault path.     

非高斯建模方法的间歇过程的在线预测监控和预测模型

A new on-line predictive monitoring and prediction model for periodic biological processes is proposed using the multiway non-Gaussian modeling. The basic idea of this approach is to use multiway non-Gaussian modeling to extract some dominant key components from daily normal operation data in a periodic process, and subsequently combining these components with predictive statistical process monitoring techniques. The proposed predictive monitoring method has been applied to fault detection and diagnosis in the biological wastewater-treatment process, which is based on strong diurnal characteristics. The results show the power and advantages of the proposed predictive monitoring of a continuous process using the multiway predictive monitoring concept, which is thus able to give very useful conceptual results for a daily monitoring process and also enables a more rapid detection of the process fault than other traditional monitoring methods.     

基于MKECA的非高斯性和非线性共存的间歇过程监测

多向核独立成分分析（multiway kernel independent component analysis,MKICA）在监测间歇过程非高斯性和非线性方面取得了广泛应用,其仅仅是将线性独立成分分析（independent component analysis,ICA）方法利用核主成分分析（kernel principal component analysis,KPCA）白化扩展到非线性领域,但数据经KPCA白化后只考虑数据信息最大化未考虑数据簇结构信息的不足,为解决此问题,采用核熵成分分析（kernel entropy component analysis,KECA）代替KPCA白化的过程监测方法。该方法首先利用AT展开方法将过程三维数据变为二维数据;其次用KECA进行白化处理的同时解决数据的非线性;然后建立ICA监测模型用于非高斯生产过程监测;最后将该方法应用到青霉素发酵仿真和实际的工业过程并与MKICA方法进行对比,验证该方法的有效性。     

基于核独立元分析的间歇过程在线监控

针对间歇过程独特的数据特点,提出了一种基于核独立元分析(kernelICA)的局部在线建模监控方法。核独立元分析通过规范相关性将比较函数扩展到一个再生的核希尔伯特空间,并用核的方法在此空间对比较函数进行计算和寻优。对含有多种分布的过程源数据,核独立元分析是一种比独立元分析(ICA)更有效的特征提取方法。对于按批次方向展开的间歇过程历史建模数据,在每一个时间间隔点应用核独立元分析算法提取独立元用于建模,并计算I2和SPE统计量及相应的控制限。此方法不需要对未来测量值进行估计,更重要的是解决了核独立元分析不能直接处理间歇过程高维历史建模数据的难题。仿真结果验证了所提出方法的可行性和有效性,并显示出比传统MICA更好的监控效果。     

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。