INTRODUCTION OF DYNAMICS TO AN APPROACH FOR BATCH PROCESS MONITORING USING INDEPENDENT COMPONENT ANALYSIS

Use of independent component analysis (ICA) in developing statistical monitoring charts for batch processes has been reported previously. This article extends the previous work by introducing time lag shifts to include process dynamics in the ICA model. Comparison of the dynamic ICA-based method with other batch process monitoring approaches based on static ICA, static principal component analysis (PCA), and dynamic PCA is made for an industrial batch polymerization reactor and a simulated fed-batch penicillin fermentation process. For both case studies, it was found that the dynamic ICA approach detected faults earlier than other approaches, with less ambiguity, and was the only approach that detected all the faults.     

基于多动态核聚类的间歇过程在线监控

针对传统的多元统计监测方法不能有效检测工业过程中由于初始条件波动较大所引发的弱故障问题,提出一种基于多动态核聚类的核主元分析(DKCPCA)监控策略,实现多阶段间歇过程的弱故障在线监控.该方法首先针对过程中各阶段每一批次数据结合自回归移动平均时间序列模型(ARMAX)和核主成分分析(KPCA)方法分别建立动态核PCA模型,然后根据各批次模型间载荷的相似性采用分层次聚类方法进行聚类,最后将聚在一起的批次数据进行展开重新再建立动态核PCA模型,随着聚类数目的不同从而建立多个类模型.当在线应用时给出了多模型选择策略,以提高监测精度.将此方法应用于青霉素发酵过程的监控中,监测结果表明此方法取得了比DKPCA和MKPCA更好的监测性能.     

A non-Gaussian pattern matching based dynamic process monitoring approach and its application to cryogenic air separation process

Principal component analysis (PCA) based pattern matching methods have been applied to process monitoring and fault detection. However, the conventional pattern matching approaches do not specifically take into account the non-Gaussian dynamic features in chemical processes. Furthermore, those techniques are more focused on fault detection instead of fault diagnosis. In this study, a non-Gaussian pattern matching based fault detection and diagnosis method is developed and applied to monitor cryogenic air separation process. First, independent component analysis (ICA) models are built on the normal benchmark and monitored data sets along sliding windows. The IC subspaces from the benchmark and monitored data are then extracted to evaluate the non-Gaussian patterns and detect process faults through a mutual information based dissimilarity index. Further, a difference subspace between the two IC subspaces is computed to characterize the divergence of the dynamic and non-Gaussian patterns between the benchmark and monitored data. Subsequently, the mutual information between the IC difference subspace and each process variable direction is defined as a new non-Gaussian contribution index for fault identification and diagnosis. The presented approach is applied to a simulated cryogenic air separation plant and the monitoring results are compared against those of PCA based pattern matching techniques and ICA based monitoring method. The application study demonstrates that the developed non-Gaussian pattern matching approach can effectively monitor the complex air separation process with superior fault detection and diagnosis capability.     

Statistical monitoring of dynamic processes based on dynamic independent component analysis

Most multivariate statistical monitoring methods based on principal component analysis (PCA) assume implicitly that the observations at one time are statistically independent of observations at past time and the latent variables follow a Gaussian distribution. However, in real chemical and biological processes, these assumptions are invalid because of their dynamic and nonlinear characteristics. Therefore, monitoring charts based on conventional PCA tend to show many false alarms and bad detectability. In this paper, a new statistical process monitoring method using dynamic independent component analysis (DICA) is proposed to overcome these disadvantages. ICA is a recently developed technique for revealing hidden factors that underlies sets of measurements followed on a non-Gaussian distribution. Its goal is to decompose a set of multivariate data into a base of statistically independent components without a loss of information. The proposed DICA monitoring method is applying ICA to the augmenting matrix with time-lagged variables. DICA can show more powerful monitoring performance in the case of a dynamic process since it can extract source signals which are independent of the auto- and cross-correlation of variables. It is applied to fault detection in both a simple multivariate dynamic process and the Tennessee Eastman process. The simulation results clearly show that the method effectively detects faults in a multivariate dynamic process.     

Localized Fisher discriminant analysis based complex chemical process monitoring

Complex chemical process is often corrupted with various types of faults and the fault‐free training data may not be available to build the normal operation model. Therefore, the supervised monitoring methods such as principal component analysis (PCA), partial least squares (PLS), and independent component analysis (ICA) are not applicable in such situations. On the other hand, the traditional unsupervised algorithms like Fisher discriminant analysis (FDA) may not take into account the multimodality within the abnormal data and thus their capability of fault detection and classification can be significantly degraded. In this study, a novel localized Fisher discriminant analysis (LFDA) based process monitoring approach is proposed to monitor the processes containing multiple types of steady‐state or dynamic faults. The stationary testing and Gaussian mixture model are integrated with LFDA to remove any nonstationarity and isolate the normal and multiple faulty clusters during the preprocessing steps. Then the localized between‐class and within‐class scatter mattress are computed for the generalized eigenvalue decomposition to extract the localized Fisher discriminant directions that can not only separate the normal and faulty data with maximized margin but also preserve the multimodality within the multiple faulty clusters. In this way, different types of process faults can be well classified using the discriminant function index. The proposed LFDA monitoring approach is applied to the Tennessee Eastman process and compared with the traditional FDA method. The monitoring results in three different test scenarios demonstrate the superiority of the LFDA approach in detecting and classifying multiple types of faults with high accuracy and sensitivity. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

多变量统计过程监控:进展及其在化学工业的应用

Multivariate statistical process monitoring and control (MSPM&C) methods for chemical process monitoring with statistical projection techniques such as principal component analysis (PCA) and partial least squares (PLS) are surveyed in this paper. The four-step procedure of performing MSPM&C for chemical process, modeling of processes, detecting abnormal events or faults, identifying the variable(s) responsible for the faults and diagnosing the source cause for the abnormal behavior, is analyzed. Several main research directions of MSPM&C reported in the literature are discussed, such as multi-way principal component analysis (MPCA) for batch process, statistical monitoring and control for nonlinear process, dynamic PCA and dynamic PLS, and on-line quality control by inferential models. Industrial applications of MSPM&C to several typical chemical processes, such as chemical reactor, distillation column, polymerization process, petroleum refinery units, are summarized. Finally, some concluding remarks an     

A new multivariate statistical process monitoring method using principal component analysis

Principal component analysis (PCA) has been used successfully as a multivariate statistical process control (MSPC) tool for detecting faults in processes with highly correlated variables. In the present work, a novel statistical process monitoring method is proposed for further improvement of monitoring performance. It is termed ‘moving principal component analysis’ (MPCA) because PCA is applied on-line by moving the time-window. In MPCA, changes in the direction of each principal component or changes in the subspace spanned by several principal components are monitored. In other words, changes in the correlation structure of process variables, instead of changes in the scores of predefined principal components, are monitored by using MPCA. The monitoring performance of the proposed method and that of the conventional MSPC method are compared with application to simulated data obtained from a simple 2×2 process and the Tennessee Eastman process. The results clearly show that the monitoring performance of MPCA is considerably better than that of the conventional MSPC method and that dynamic monitoring is superior to static monitoring.     

基于滚动MPCA的青霉素发酵过程的在线监控

To reduce the variations of the production process in penicillin cultivations, a rolling multivariate statistical approach based on multiway principle component analysis （MPCA） is developed and used for fault diagnosis of penicillin cultivations. Using the moving data windows technique, the static MPCA is extended for use in dynamic process performance monitoring. The control chart is set up using the historical data collected from the past successful batches, thereby resulting in simplification of monitoring charts, easy tracking of the progress in each batch run, and monitoring the occurrence of the observable upsets. Data from the commercial-scale penicillin fermentation process are used to develop the rolling model. Using this method, faults are detected in real time and the corresponding measurements of these faults are directly made through inspection of a few simple plots （t-chart, SPE-chart, and T2-chart）. Thus, the present methodology allows the process operator to actively monitor the data from several cultivations simultaneously.     

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.     

基于主元分析和核密度估计的多变量统计过程监控及在工厂聚丙烯催化剂反应器的应用

Abstract Data-driven tools, such as principal component analysis （PCA） and independent component analysis （ICA） have been applied to different benchmarks as process monitoring methods. The difference between the two methods is that the components of PCA are still dependent while ICA has no orthogonality constraint and its latentvariables are independent. Process monitoring with PCA often supposes that process data or principal components is Gaussian distribution. However, this kind of constraint cannot be satisfied by several practical processes. To ex-tend the use of PCA, a nonparametric method is added to PCA to overcome the difficulty, and kernel density estimation （KDE） is rather a good choice. Though ICA is based on non-Gaussian distribution intormation, .KDE can help in the close monitoring of the data. Methods, such as PCA, ICA, PCA.with .KDE（KPCA）, and ICA with KDE,（KICA）, are demonstrated and. compared by applying them to a practical industnal Spheripol craft polypropylene catalyzer reactor instead of a laboratory emulator.     

Two‐step principal component analysis for dynamic processes monitoring

In this study, a two‐step principal component analysis (TS‐PCA) is proposed to handle the dynamic characteristics of chemical industrial processes in both steady state and unsteady state. Differently from the traditional dynamic PCA (DPCA) dealing with the static cross‐correlation structure and dynamic auto‐correlation structure in process data simultaneously, TS‐PCA handles them in two steps: it first identifies the dynamic structure by using the least squares algorithm, and then monitors the innovation component by using PCA. The innovation component is time uncorrelated and independent of the initial state of the process. As a result, TS‐PCA can monitor the process in both steady state and unsteady state, whereas all other reported dynamic approaches are limited to only processes in steady state. Even tested in steady state, TS‐PCA still can achieve better performance than the existing dynamic approaches.     

Local dynamic partial least squares approaches for the modelling of batch processes

The application of multivariate statistical projection based techniques has been recognized as one approach to contributing to an increased understanding of process behaviour. The key methodologies have included multi‐way principal component analysis (PCA), multi‐way partial least squares (PLS) and batch observation level analysis. Batch processes typically exhibit nonlinear, time variant behaviour and these characteristics challenge the aforementioned techniques. To address these challenges, dynamic PLS has been proposed to capture the process dynamics. Likewise approaches to removing the process nonlinearities have included the removal of the mean trajectory and the application of nonlinear PLS. An alternative approach is described whereby the batch trajectories are sub‐divided into operating regions with a linear/linear dynamic model being fitted to each region. These individual models are spliced together to provide an overall nonlinear global model. Such a structure provides the potential for an alternative approach to batch process performance monitoring. In the paper a number of techniques are considered for developing the local model, including multi‐way PLS and dynamic multi‐way PLS. Utilising the most promising set of results from a simulation study of a batch process, the local model comprising individual linear dynamic PLS models was benchmarked against global nonlinear dynamic PLS using data from an industrial batch fermentation process. In conclusion the results for the local operating region techniques were comparable to the global model in terms of the residual sum of squares but for the global model structure was evident in the residuals. Consequently, the local modelling approach is statistically more robust.     

基于统计信号重构的传感器故障诊断

主元分析、偏最小二层等数据驱动的多元统计监控方法由于不依赖于精确的数学模型,在化工过程监控与故障检测方面取得了广泛应用.通过研究基于统计信号重构的传感器故障诊断算法,给出了统计信号重构算法的一般形式,并推导了基于统计信号重构算法进行传感器故障诊断的可检测与可分离性条件,定义了模型空间和余差空间的故障识别指标.通过CSTR仿真对象的应用比较了不同统计信号重构算法间的差异,验证了故障诊断算法的有效性.     

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。     

主元空间中的故障重构方法研究

主元分析 (PCA)作为一种数据驱动的统计建模方法,在化工产品质量控制与故障诊断方面获得了广泛研究和应用.利用故障子空间的概念,研究了基于T²统计量的故障重构问题,获得了主元空间中的完全重构、部分重构,以及可重构性的条件.为进一步在主元空间中进行故障分离和识别提供了可能.通过对双效蒸发过程的仿真监测,对不同传感器的故障类型、幅值等重要信息进行重构和波形估计,证实了所获结果的有效性.     

Fault isolation in nonlinear systems with structured partial principal component analysis and clustering analysis

Partial principal component analysis (PCA) and parity relations are proven to be useful methods in fault isolation. To overcome the limitation of applying partial PCA to nonlinear problems, a new approach utilizing clustering analysis is proposed. By dividing a partial data set into smaller subsets, one can build more accurate PCA models with fewer principal components, and isolate faults with higher precision. Simulations on a 2 × 2 nonlinear system and the Tennessee Eastman (TE) process show the advantages of using the clustered partial PCA method over other nonlinear approaches.     

Enhanced statistical analysis of nonlinear processes using KPCA, KICA and SVM

In this paper, some drawbacks of original kernel independent component analysis (KICA) and support vector machine (SVM) algorithms are analyzed for the purpose of multivariate statistical process monitoring (MSPM). When the measured variables follow non-Gaussian distribution, KICA provides more meaningful knowledge by extracting higher-order statistics compared with PCA and kernel principal component analysis (KPCA). However, in real industrial processes, process variables are complex and are not absolutely Gaussian or non-Gaussian distributed. Any single technique is not sufficient to extract the hidden information. Hence, both KICA (non-Gaussion part) and KPCA (Gaussion part) are used for fault detection in this paper, which combine the advantages of KPCA and KICA to develop a nonlinear dynamic approach to detect fault online compared to other nonlinear approaches. Because SVM is available for classifying faults, it is used to diagnose fault in this paper.For above mentioned kernel methods, the calculation of eigenvectors and support vectors will be time consuming when the sample number becomes large. Hence, some dissimilar data are analyzed in the input and feature space.The proposed approach is applied to the fault detection and diagnosis in the Tennessee Eastman process. Application of the proposed approach indicates that proposed method effectively captures the nonlinear dynamics in the process variables.     

PCA过程监测方法的故障检测行为分析

通过分别导出T2 和SPE统计量均值与过程数据统计参数之间的关系 ,分析了影响主元分析 (PCA)检测行为的因素以及工况变化与故障在PCA下的不同被检测行为 ,利用双效蒸发过程的仿真监测验证了获得的结果 ,指出了通常关于PCA检测行为的一些不准确的结论     

步进MPCA及其在间歇过程监控中的应用

针对多向主元分析法(MPCA)在间歇过程监控过程中需要预测过程未来输出的困难,提出了一种新的步进多向主元分析方法。该方法通过建立一系列的PCA模型,避免了对预估过程变量未来输出的需要,通过引入遗忘因子能够自然地处理多阶段间歇过程的情况。对于多阶段链霉素发酵过程的监控表明,相对于普通MPCA,步进MPCA能够更精确地对过程故障行为进行描述。     

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