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。     

Fault detection and diagnosis in a non-Gaussian process with modified kernel independent component regression

Quality-related fault detection and diagnosis are crucial in the data-driven process monitoring field. Most existing methods are based on principal component analysis (PCA) or partial least squares (PLS), which will miss high-order statistical information when the industrial process does not satisfy a Gaussian distribution. Meanwhile, the traditional contribution plot is difficult to directly apply to nonlinear processes in some cases due to its limitation of convergence. As such, a modified kernel independent component regression (MKICR) model, which considers high-order statistical information, is proposed for quality-related fault detection and faulty variable identification. First, the relationship between the independent components and quality variables is established by kernel independent component regression, and the correlation matrix is obtained. Then, the kernel independent components can be suitably divided into quality-related and quality-unrelated parts. Finally, an analysis of the contribution of each variable to the statistics based on Lagrange's mean value theorem is presented. In addition, a numerical case and the Tennessee Eastman process (TEP) demonstrate the efficacy and superiority of the proposed method.     

A local and global statistics pattern analysis method and its application to process fault identification☆

Traditional principal component analysis (PCA) is a second-order method and lacks the ability to provide higher-order representations for data variables. Recently, a statistics pattern analysis (SPA) framework has been incor-porated into PCA model to make full use of various statistics of data variables effectively. However, these methods omit the local information, which is also important for process monitoring and fault diagnosis. In this paper, a local and global statistics pattern analysis (LGSPA) method, which integrates SPA framework and locality pre-serving projections within the PCA, is proposed to utilize various statistics and preserve both local and global in-formation in the observed data. For the purpose of fault detection, two monitoring indices are constructed based on the LGSPA model. In order to identify fault variables, an improved reconstruction based contribution (IRBC) plot based on LGSPA model is proposed to locate fault variables. The RBC of various statistics of original process variables to the monitoring indices is calculated with the proposed RBC method. Based on the calculated RBC of process variables' statistics, a new contribution of process variables is built to locate fault variables. The simula-tion results on a simple six-variable system and a continuous stirred tank reactor system demonstrate that the proposed fault diagnosis method can effectively detect fault and distinguish the fault variables from normal variables.     

Nonlinear process monitoring using kernel principal component analysis

In this paper, a new nonlinear process monitoring technique based on kernel principal component analysis (KPCA) is developed. KPCA has emerged in recent years as a promising method for tackling nonlinear systems. KPCA can efficiently compute principal components in high-dimensional feature spaces by means of integral operators and nonlinear kernel functions. The basic idea of KPCA is to first map the input space into a feature space via nonlinear mapping and then to compute the principal components in that feature space. In comparison to other nonlinear principal component analysis (PCA) techniques, KPCA requires only the solution of an eigenvalue problem and does not entail any nonlinear optimization. In addition, the number of principal components need not be specified prior to modeling. In this paper, a simple approach to calculating the squared prediction error (SPE) in the feature space is also suggested. Based on T² and SPE charts in the feature space, KPCA was applied to fault detection in two example systems: a simple multivariate process and the simulation benchmark of the biological wastewater treatment process. The proposed approach effectively captured the nonlinear relationship in the process variables and showed superior process monitoring performance compared to linear PCA.     

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.     

A sparse PCA for nonlinear fault diagnosis and robust feature discovery of industrial processes

Pearson's correlation measure is only able to model linear dependence between random variables. Hence, conventional principal component analysis (PCA) based on Pearson's correlation measure is not suitable for application to modern industrial processes where process variables are often nonlinearly related. To address this problem, a nonparametric PCA model is proposed based on nonlinear correlation measures, including Spearman's and Kendall tau's rank correlation. These two correlation measures are also less sensitive to outliers comparing to Pearson's correlation, making the proposed PCA a robust feature extraction technique. To reveal meaningful patterns from process data, a generalized iterative deflation method is applied to the robust correlation matrix of the process data to sequentially extract a set of leading sparse pseudoeigenvectors. For online fault diagnosis, the T² and SPE statistics are computed and analyzed with respect to the subspace spanned by the extracted pseudoeigenvectors. The proposed method is applied to two industrial case studies. Its process monitoring performance is demonstrated to be superior to that of the conventional PCA and is comparable to those of Kernel PCA and kernel independent component analysis at a lower computational cost. The proposed PCA is also more robust in sparse feature extraction from contaminated process data. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1494–1513, 2016     

Dynamic nonlinear batch process fault detection and identification based on two‐directional dynamic kernel slow feature analysis

The batch process generally covers high nonlinearity and two‐directional dynamics: time‐wise dynamics, which correspond to inherently time‐varying dynamics resulting from the slowly varying underlying driving forces within each batch duration; and batch‐wise dynamics, which are associated with different operating modes among different batches. However, most existing dynamic nonlinear monitoring methods cannot extract the slowly varying underlying driving forces of the nonlinear batch process and rarely tackle the batch‐wise dynamic characteristics among batch runs. In order to address these issues, a new monitoring scheme based on two‐directional dynamic kernel slow feature analysis (TDKSFA) is developed by combining kernel SFA with a global modelling strategy. In the TDKSFA method, kernel SFA is integrated with the ARMAX time series model to mine the nonlinear and time‐wise dynamic properties within a batch run due to its capability of extracting the slowly varying underlying driving forces. Furthermore, the global modelling strategy is presented to handle the batch‐wise dynamics among batches by calculating the total average kernel matrix of all training batches. After the slow features are extracted, Hotelling's T² and SPE statistics are built to detect faults. To solve the issue of fault variable nonlinear identification, a novel nonlinear contribution plot inspired by the pseudo‐sample variable projection trajectories in the TDKSFA model is further proposed to identify fault variables. Finally, the feasibility and effectiveness of the TDKSFA‐based fault diagnosis strategy is demonstrated through a numerical system and the penicillin fermentation process.     

Improved dynamic kernel PCA based on local preserving projections and its application for electric submersible pump fault diagnosis

Dynamic kernel principal component analysis (DKPCA) has been frequently implemented for nonlinear and dynamic process monitoring of complex industrial processes. However, traditional DKPCA focuses only on the global structural analysis of data sets and strongly neglects the local information, which is equally essential for process detection and identification. In this paper, an improved DKPCA, referred to as the local DKPCA (LDKPCA), is proposed based on local preserving projections (LPP) for nonlinear dynamic process fault diagnosis. The method combines the advantages of LPP and DKPCA by utilizing the local structure feature to maintain the geometric structure of the data in a unified framework. To achieve a highly comprehensive feature extraction, the local characteristics are fused in DKPCA to produce an optimization objective. The neighbouring points of the new objective function projection in the feature space are still maintained in proximity, and the variance information is retained simultaneously. For the purpose of fault detection, two statistics, known as the T² and squared prediction error (SPE) statistics, are constructed, based on the LDKPCA model, and used to monitor the latent variable space and the residual space, respectively. In addition, the sensitivity analysis is brought in for fault identification of the two statistics. Based on the experimental analysis using the shaft breakage data of an offshore oilfield electric submersible pump (ESP), the proposed method outperforms the conventional DKPCA in terms of fault monitoring performance. The experimental results demonstrate the potential of the method in nonlinear dynamic process fault diagnosis.     

Nonlinear dynamic process monitoring based on dynamic kernel PCA

Nonlinear dynamic process monitoring based on dynamic kernel principal component analysis (DKPCA) is proposed. The kernel functions used in kernel PCA (KPCA) are profitable for capturing nonlinear property of processes and the time-lagged data extension is suitable for describing dynamic characteristic of processes. DKPCA enables us to monitor an arbitrary process with severe nonlinearity and (or) dynamics. In this respect, it is a generalized concept of multivariate statistical monitoring approaches. A unified monitoring index combined T² with SPE is also suggested. The proposed monitoring method based on DKPCA is applied to a simulated nonlinear process and a wastewater treatment process. A comparison study of PCA, dynamic PCA, KPCA, and DKPCA is investigated in terms of type I error rate, type II error rate, and detection delay. The monitoring results confirm that the proposed methodology results in the best monitoring performance, i.e., low missing alarms and small detection delay, for all the faults.     

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.     

Fault detection and identification using a Kullback-Leibler divergence based multi-block principal component analysis and bayesian inference

Considering the huge number of variables in plant-wide process monitoring and complex relationships (linear, nonlinear, partial correlation, or independence) among these variables, multivariate statistical process monitoring (MSPM) performance may be deteriorated especially by the independent variables. Meanwhile, whether related variables keep high concordance during the variation process is still a question. Under this circumstance, a multi-block technology based on mathematical statistics method, Kullback-Leibler Divergence, is proposed to put the variables having similar statistical characteristics into the same block, and then build principal component analysis (PCA) models in each low-dimensional subspace. Bayesian inference is also employed to combine the monitoring results from each sub-block into the final monitoring statistics. Additionally, a novel fault diagnosis approach is developed for fault identification. The superiority of the proposed method is demonstrated by applications on a simple simulated multivariate process and the Tennessee Eastman benchmark process.     

Nonlinear multiscale modelling for fault detection and identification

In order to detect abnormal events at different scales, a number of multiscale multivariate statistical process control (MSPC) approaches which combine a multivariate linear projection model with multiresolution analysis have been suggested. In this paper, a new nonlinear multiscale-MSPC method is proposed to address multivariate process performance monitoring and in particular fault diagnostics in nonlinear processes. A kernel principal component analysis (KPCA) model, which not only captures nonlinear relationships between variables but also reduces the dimensionality of the data, is built with the reconstructed data obtained by performing wavelet transform and inverse wavelet transform sequentially on measured data. A guideline is given for both off-line and on-line implementations of the approach. Two monitoring statistics used in multiscale KPCA-based process monitoring are used for fault detection. Furthermore, variable contributions to monitoring statistics are also derived by calculating the derivative of the monitoring statistics with respect to the variables. An intensive simulation study on a continuous stirred tank reactor process and a comparison of the proposed approach with several existing methods in terms of false alarm rate, missed alarm rate and detection delay, demonstrate that the proposed method for detecting and identifying faults outperforms current approaches.     

基于映射向量和加权Q贡献图的故障识别研究

在基于主元分析(PCA)的统计过程监控实施中,贡献图是一个常用的故障识别工具,但难以实现故障精确定位的缺点限制了贡献图的进一步推广。通过引入基于真实值的故障模型,推导出故障映射向量幅值与故障贡献准确性的关系,指出了传统Q贡献图的理论缺陷,并提出了一种加权Q贡献图故障识别法。在CSTR上的仿真证明,相比传统Q贡献图,该法可以更准确地识别传感器,消除了对操作员的误导。     

基于距离空间统计量分析的多模态过程无监督故障检测

工业过程往往运行于多个生产模态,针对多模态过程数据的空间分布特点,提出了一种新的基于样本距离空间统计量分析的故障检测方法(DSSA)。首先用每一个样本与其训练集样本中的邻居之间的k个最近邻距离之差来表示该样本,将样本从原始变量空间映射到对应的距离空间中。然后在距离空间中通过移动窗口的方式计算各阶统计量,最后对由各阶统计量组成的统计量样本进行主元分析(PCA)。将DSSA方法、PCA方法以及另一种基于k近邻规则的多模态故障检测方法(FD-kNN)应用于TE过程中,仿真结果表明DSSA方法对多模态故障检测更为有效。     

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.     

Fault detection, identification and diagnosis using CUSUM based PCA

In this paper, a cumulative sum based statistical monitoring scheme is used to monitor a particular set of the Tennessee Eastman Process (TEP) faults that could not be properly detected or diagnosed with other fault detection and diagnosis methodologies previously reported.T² and Q statistics based on the cumulative sums of all available measurements were successful in observing these three faults. For the purpose of fault isolation, contribution plots were found to be inadequate when similar variable responses are associated with different faults. Fault historical data is then used in combination with the proposed CUSUM based PCA model to unambiguously characterize the different fault signatures. The proposed CUSUM based PCA was successful in detecting, identifying and diagnosing both individual as well as simultaneous occurrences of these faults.     

基于多块信息提取的PCA故障诊断方法

传统的监控方法往往只利用传感器观测值信息进行过程的故障监测，而忽略了原始数据中包含的其他有效信息。为此，提出一种基于多块信息提取的PCA故障监测算法。首先，对过程变量的累计误差和变化率信息进行定义，从而能够从数据中提取新的特征信息，并基于每种特征将过程划分为3个子块；然后，利用PCA方法对每个子块进行建模与监测，通过贝叶斯方法对监测结果进行融合；最后，提出一种基于加权贡献图的故障诊断方法，分离出引发故障的源变量。通过数值例子与田纳西-伊斯曼（TE）过程监控中的应用证明了所提方法的有效性与可行性。     

Reconstruction in integrating fault spaces for fault identification with kernel independent component analysis

In the original fault identification methods, contribution plots are popular. However, it is not accurate because of the smearing effect. In addition, traditional contribution plots cannot be applied to nonlinear process because there seems no way to accurately calculate variable contributions. As a comparison, the reconstruction method is widely used in fault identification for finding the root causes of the fault. For fault detection and identification of actual industrial process with nonlinear and non-Gaussian features, a new reconstruction-based fault identification method with kernel independent component analysis (KICA) is developed in this article. The proposed method, reconstruction in integrating fault spaces (RIFSs), extends the classic reconstruction-based fault identification approach to KICA for the first time, and develops the reconstruction method from unidimensional faults to multidimensional ones for nonlinear cases. Furthermore, the number of reconstruction is effectively reduced on the basis of the integrating fault spaces (IFSs) which are composed of fault subspaces satisfying orthogonal to each other from the known fault set. In addition, fault magnitude, indicating the adjustment magnitude of a fault sample back to normal range, is used as index to identify faults, and it makes the fault identification problem become more straightforward than with the existing fault identification index, such as ratio (index I) or the reconstructed statistics (index II). Finally, the proposed method is applied to the fault detection and identification on cyanide leaching of gold, which shows its feasibility and efficiency for both sensor faults and complex process faults.     

A Kernel Time Structure Independent Component Analysis Method for Nonlinear Process Monitoring

Kernel independent component analysis (KICA) is a newly emerging nonlinear process monitoring method, which can extract mutually independent latent variables called independent components (ICs) from process variables. However, when more than one IC have Gaussian distribution, it cannot extract the IC feature effectively and thus its monitoring performance will be degraded drastically. To solve such a problem, a kernel time structure independent component analysis (KTSICA) method is proposed for monitoring nonlinear process in this paper. The original process data are mapped into a feature space nonlinearly and then the whitened data are calculated in the feature space by the kernel trick. Subsequently, a time structure independent component analysis algorithm, which has no requirement for the distribution of ICs, is proposed to extract the IC feature. Finally, two monitoring statistics are built to detect process faults. When some fault is detected, a nonlinear fault identification method is developed to identify fault variables based on sensitivity analysis. The proposed monitoring method is applied in the Tennessee Eastman benchmark process. Applications demonstrate the superiority of KTSICA over KICA.