An improved weighted recursive PCA algorithm for adaptive fault detection

A novel weighted adaptive recursive fault detection technique based on Principal Component Analysis (PCA) is proposed to address the issue of the increment in false alarm rate in process monitoring schemes due to the natural, slow and normal process changes (aging), which often occurs in real processes. It has been named as weighted adaptive recursive PCA (WARP).The aforementioned problem is addressed recursively by updating the eigenstructure (eigenvalues and eigenvectors) of the statistical detection model when the false alarm rate increases given the awareness of non-faulty condition. The update is carried out by incorporating the new available information within a specific online process dataset, instead of keeping a fixed statistical model such as conventional PCA does. To achieve this recursive updating, equations for means, standard deviations, covariance matrix, eigenvalues and eigenvectors are developed. The statistical thresholds and the number of principal components are updated as well.A comparison between the proposed algorithm and other recursive PCA-based algorithms is carried out in terms of false alarm rate, misdetection rate, detection delay and its computational complexity. WARP features a significant reduction of the computational complexity while maintaining a similar performance on false alarm rate, misdetection rate and detection delay compared to that of the other existing PCA-based recursive algorithms. The computational complexity is assessed in terms of the Floating Operation Points (FLOPs) needed to carry out the update.     

Linear Multilayer ICA Using Adaptive PCA

Linear multilayer independent component analysis (LMICA) is an approximate algorithm for ICA. In LMICA, approximate independent components are efficiently estimated by optimizing only highly dependent pairs of signals when all the sources are super-Gaussian. In this paper, the nonlinear functions in LMICA are generalized, and a new method using adaptive PCA is proposed for the selection of pairs of highly dependent signals. In this method, at first, all the signals are sorted along the first principal axis of their higher-order correlation matrix. Then, the sorted signals are divided into two groups so that relatively highly correlated signals are collected in each group. Lastly, each of them is sorted recursively. This process is repeated until each group consists of only one or two signals. Because a well-known adaptive PCA algorithm named PAST is utilized for calculating the first principal axis, this method is quite simple and efficient. Some numerical experiments verify the effectiveness of LMICA with this improvement.     

A new integrated on-line fuzzy clustering and segmentation methodology with adaptive PCA approach for process monitoring and fault detection and diagnosis

A new on-line fuzzy clustering-based algorithm is developed using integration of an adaptive principal component analysis approach with a weighted fuzzy C-means (WFCM) methodology for process fault detection and diagnosis (FDD) applications. The proposed algorithm is based on the segmentation of measured multivariate time series process data through a sliding window scheme being realized in a bottom-up cluster merging approach to enable detection of probable changes embedded in their hidden structure. The method recursively maintain updated PCA models and their corresponding fuzzy membership functions based on the most recent arrival of each independent chunk of process data. The extracted chunk features are then retained in the memory to be merged using a new on-line fuzzy C-means methodology before incoming of the following chunks of data. A new formula is then presented for cluster merging improvement by incorporating an on-line weight to address the issue of cluster’s weight updating in the on-line WFCM methodology. The cluster merging mechanism is coordinated by a compatibility criterion, utilizing both similarities of the adapted clusters-based PCA models and their center closeness. The proposed algorithm has been evaluated on an artificial case study and Tennessee Eastman benchmark process plant. The observed performances demonstrate promising capabilities of the proposed algorithm to successfully detect and diagnose the introduced fault scenarios.     

基于数据分析的化工过程监测

为了改善主元分析对带噪声过程的监测性能，本文结合小波包分析消噪性能与主元分析提取变量间相关性能的特点，提出了一种小波包主元分析方法。给出了基于小波包主元分析的过程监测的算法实现。并在此基础上，对TE过程进行了监测性能仿真。结果表明小波包主元分析方法有较好的监测性能。     

Fault detection and isolation in transient states using principal component analysis

This paper proposes the use of principal component analysis (PCA) for process monitoring and fault detection and isolation in processes with several operation modes and long transient states and start-ups. The principal aspects of the PCA approach and the necessary transformations for dealing with this type of processes are presented. In this paper a classical PCA model is used for each steady state of the process and a modification of a batch PCA approach is applied to the transient states of the continuous process. So, in this last case, the PCA model is performed over a three way matrix arranged with the values of the measured variables of several past transitions with a nominal behaviour. This approach presents some problems, such as the unfolding, alignment and imputation. The methods proposed to deal with these problems are explained in detail and compared in order to design a fault detection and isolation method. Two examples are considered to perform the tasks explained. In both cases good results are obtained.     

Low complexity adaptive algorithms for Principal and Minor Component Analysis

This article introduces new low cost algorithms for the adaptive estimation and tracking of principal and minor components. The proposed algorithms are based on the well-known OPAST method which is adapted and extended in order to achieve the desired MCA or PCA (Minor or Principal Component Analysis). For the PCA case, we propose efficient solutions using Givens rotations to estimate the principal components out of the weight matrix given by OPAST method. These solutions are then extended to the MCA case by using a transformed data covariance matrix in such a way the desired minor components are obtained from the PCA of the new (transformed) matrix. Finally, as a byproduct of our PCA algorithm, we propose a fast adaptive algorithm for data whitening that is shown to overcome the recently proposed RLS-based whitening method.     

基于小波变换核主元分析和多支持向量机的过程监控

针对过程工业数据中所含的噪声和干扰信号、过程工业的非线性及基于主元分析(Principal Component Analysis,PCA)的统计性能监控法由于不用过程机理模型的信息从而对故障诊断问题难以在理论上作系统分析的缺陷,提出基于小波变换核主元分析和多支持向量机的过程监控方法,该方法首先采用基于小波变换的收缩阈值去噪法对建模数据进行预处理,以有效抑制过程数据中所含的噪声和干扰信号,然后利用核主元分析来进行故障特征的提取,从而提高非线性统计过程监控的准确性;最后提出多支持向量机用来对故障的来源进行分类,以避免求解核主元空间到原始空间的逆映射.将该方法应用到对TE(Tennessee Eastman,TE)过程的监控,表明了所提出方法的有效性,为过程的监控和故障诊断提供了一个新的方法.     

Adaptive process monitoring using scale cusum for serially correlated processes

We present an adaptive monitoring approach for serially correlated data. This algorithm uses the adaptive linear prediction lattice filter (ALPLF) which makes it compute process parameters and prediction errors in real time and recursively update their estimates. We propose to apply a scale CUSUM control chart to prediction errors as an omnibus method for detecting changes in process parameters. Results of computer simulations demonstrate that the proposed adaptive monitoring approach has great potentials for real-time industrial applications which vary frequently in their control environment.     

Variable reconstruction and sensor fault identification using canonical variate analysis

The detection and identification of faults in dynamic continuous processes has received considerable recent attention from researchers in academia and industry. In this paper, a canonical variate analysis (CVA)-based sensor fault detection and identification method via variable reconstruction is described. Several previous studies have shown that CVA-based monitoring techniques can effectively detect faults in dynamic processes. Here we define two monitoring indices in the state and noise spaces for fault detection and, for sensor fault identification, we propose three variable reconstruction algorithms based on the proposed monitoring indices. The variable reconstruction algorithms are based on the concepts of conditional mean replacement and object function minimization. The proposed approach is applied to a simulated continuous stirred tank reactor and the results are compared to those obtained using the traditional dynamic monitoring technique, dynamic principal component analysis (PCA). The results indicate that the proposed methodology is quite effective for monitoring dynamic processes in terms of sensor fault detection and identification.     

基于递归稀疏主成分分析的工业过程在线故障监测和诊断

提出一种基于递归稀疏主成分分析(recursive sparse principal component analysis,RSPCA)的工业过程故障监测与诊断方法,可用于时变工业过程的自适应故障监测与诊断.通过引入弹性回归网,将主成分问题转化为Lasso与Ridge结合的凸优化问题,采用秩-1矩阵修正对协方差矩阵进行递归分解,递归更新稀疏载荷矩阵和监测统计量的过程控制限,以实现连续工业过程长时间自适应故障监测,对检测出来的故障通过贡献图法实现对故障的诊断.在田纳西-伊斯曼(TE)过程进行实验验证,结果表明,与传统的故障监测方法相比,所提出的方法有效降低了故障漏检率和误报率,且时间复杂度低,确保了故障监测的灵敏度和实时性.     

Online monitoring of nonlinear multivariate industrial processes using filtering KICA–PCA

In this paper, a novel approach for processes monitoring, termed as filtering kernel independent component analysis–principal component analysis (FKICA–PCA), is developed. In FKICA–PCA, first, a method to calculate the variance of independent component is proposed, which is significant to make Gaussian features and non-Gaussian features comparable and to select dominant components legitimately; second, Genetic Algorithm is used to determine the kernel parameter through minimizing false alarm rate and maximizing detection rate; furthermore, exponentially weighted moving average (EWMA) scheme is used to filter the monitoring indices of KICA–PCA to improve monitoring performance. In addition, a novel contribution analysis scheme is developed for FKICA–PCA to diagnosis faults. The feasibility and effectiveness of the proposed method are validated on the Tennessee Eastman (TE) process.     

A multi-scale orthogonal nonlinear strategy for multi-variate statistical process monitoring

In this paper a multi-scale nonlinear PCA strategy for process monitoring is proposed. The strategy utilizes the optimal wavelet decomposition in such a way that only the approximation and the highest detail functions are used, thus simplifying the overall structure and making the interpretation at each scale more meaningful. An orthogonal nonlinear PCA procedure is incorporated to capture the nonlinear characteristics with a minimum number of principal components. The proposed nonlinear strategy also eliminates the requirement of nonlinear functions relating the nonlinear principal scores to process measurements for Q-statistics as in other nonlinear PCA process monitoring approaches. In addition, the strategy is considerably robust to the presence of typical outliers.     

Dynamics of Generalized PCA and MCA Learning Algorithms

Principal component analysis (PCA) and minor component analysis (MCA) are two important statistical tools which have many applications in the fields of signal processing and data analysis. PCA and MCA neural networks (NNs) can be used to online extract principal component and minor component from input data. It is interesting to develop generalized learning algorithms of PCA and MCA NNs. Some novel generalized PCA and MCA learning algorithms are proposed in this paper. Convergence of PCA and MCA learning algorithms is an essential issue in practical applications. Traditionally, the convergence is studied via deterministic continuous-time (DCT) method. The DCT method requires the learning rate of the algorithms to approach to zero, which is not realistic in many practical applications. In this paper, deterministic discrete-time (DDT) method is used to study the dynamical behaviors of the proposed algorithms. The DDT method is more reasonable for the convergence analysis since it does not require constraints as that of the DCT method. It is proven that under some mild conditions, the weight vector in these proposed algorithms will converge exponentially to principal or minor component. Simulation results are further used to illustrate the theoretical results.     

基于PCA硬阈值收缩的平滑投影Landweber图像压缩感知重构

利用压缩感知理论对图像进行测量和重构时,基于分块思想可有效提高重构速度,但同时会带来较强的块效应.为了解决该问题,在编码端提出了一种基于边缘检测的自适应分块压缩感知测量方案;在解码端提出了一种基于主成分分析(PCA)的平滑投影Landweber(SPL)重构法,该算法运用PCA训练出适合于图像结构的稀疏字典,用于进行硬阈值收缩,从而有效消除了块效应,提升了重构图像的质量.为了提高硬阈值收缩效率和减少训练复杂度,采用了3种基于块的PCA硬阈值收缩方案:全局PCA、局部PCA和分层PCA.仿真实验结果表明:所提出的自适应压缩感知测量方案与SPL重构法相结合,和传统分块压缩感知方案相比,峰值信噪比(PSNR)值均提升了1～3 dB;本文算法,无论在传统分块压缩感知方案下还是在自适应分块压缩感知方案下,与基于方向小波阈值收缩的SPL重构算法相比,均获得了更高的PSNR值.     

基于主元子空间故障重构技术的故障诊断研究

针对基于主元分析(PCA)的统计性能监控法,由于不用过程机理模型的信息,因此,对故障诊断问题有难以在理论上作系统分析的缺陷,于是提出了一种基于主元子空间故障重构技术的故障诊断方法。利用故障子空间的概念,在故障重构技术的基础上,研究基于T~2统计量的故障诊断问题,提出故障识别指标和诊断算法。通过对双效蒸发过程的仿真监测,验证该诊断方法的有效性。     

The application of principal component analysis and kernel density estimation to enhance process monitoring

This paper discusses the application of kernel density estimation (KDE) and principal component analysis (PCA) to provide enhanced monitoring of multivariate processes. Different KDE algorithms are studied and assessed in depth in the context of practical applications so that one bandwidth selection algorithm is recommended for process monitoring. The results of the case studies clearly demonstrate the power and advantages of the KDE approach over parametric density estimation which is still widely used. Statistical summary charts are suggested to raise early warning of faults and locate the physical variables which are the prime indicators of the faults.     

基于分层分块DLPPCA-SVM的复杂工业过程监测与故障诊断方法

针对工业过程动态性及非线性强等特点,提出一种基于动态局部保持主成分分析法的过程监测方法.该方法通过构造扩展矩阵来解决动态过程中各采样点间相关性强的问题,并将局部保持投影(LPP)与主成分分析法(PCA)相结合从而实现提取流形结构的最大方差信息.在此基础上,针对复杂工业过程变量复杂多变、呈不同特性的特点,提出基于分层分块DLPPCA-SVM(dynamic locality preserving principal component analysis-support vector machine, DLPPCA-SVM)的过程监测及故障诊断方法,该方法针对不同特性的子块分别采用DLPPCA和PCA进行建模,并利用支持向量机进行故障诊断.将该方法用于田纳西-伊斯曼(TE)化工过程和发电机组的在线监测和故障诊断,仿真结果验证了所提出方法的有效性.     

An adaptive multimode process monitoring strategy based on mode clustering and mode unfolding

A comprehensive monitoring framework is proposed for multimode processes in which mode clustering and mode unfolding are integrated within an adaptive strategy. To start, an aggregated k-means algorithm produces an optimal ensemble clustering solution for a multimode process dataset. Next, a mode unfolding (MU) scheme enables the development of a single principal component analysis (PCA) model for processes operating under multiple desired steady-states (modes). Finally, adaptive strategies for online mode identification and model updating are presented to address the challenges in fault detection in the presence of multiple operating modes. The validity and usefulness of the adaptive MU-PCA based monitoring framework is demonstrated through a study of the Tennessee Eastman benchmark process.     

A new subspace identification approach based on principal component analysis

Principal component analysis (PCA) has been widely used for monitoring complex industrial processes with multiple variables and diagnosing process and sensor faults. The objective of this paper is to develop a new subspace identification algorithm that gives consistent model estimates under the errors-in-variables (EIV) situation. In this paper, we propose a new subspace identification approach using principal component analysis. PCA naturally falls into the category of EIV formulation, which resembles total least squares and allows for errors in both process input and output. We propose to use PCA to determine the system observability subspace, the A, B, C, and D matrices and the system order for an EIV formulation. Standard PCA is modified with instrumental variables in order to achieve consistent estimates of the system matrices. The proposed subspace identification method is demonstrated using a simulated process and a real industrial process for model identification and order determination. For comparison the MOESP algorithm and N4SID algorithm are used as benchmarks to demonstrate the advantages of the proposed PCA based subspace model identification (SMI) algorithm.