Online process monitoring for complex systems with dynamic weighted principal component analysis☆

Conventional multivariate statistical methods for process monitoring may not be suitable for dynamic processes since they usually rely on assumptions such as time invariance or uncorrelation. We are therefore motivated to propose a new monitoring method by compensating the principal component analysis with a weight approach. The proposed monitor consists of two tiers. The first tier uses the principal component analysis method to extract cross-correlation structure among process data, expressed by independent components. The second tier estimates auto-correlation structure among the extracted components as auto-regressive models. It is therefore named a dynamic weighted principal component analysis with hybrid correlation structure. The essential of the proposed method is to incorporate a weight approach into principal component analysis to construct two new subspaces, namely the important component subspace and the residual subspace, and two new statistics are de-fined to monitor them respectively. Through computing the weight values upon a new observation, the proposed method increases the weights along directions of components that have large estimation errors while reduces the influences of other directions. The rationale behind comes from the observations that the fault information is associated with online estimation errors of auto-regressive models. The proposed monitoring method is exem-plified by the Tennessee Eastman process. The monitoring results show that the proposed method outperforms conventional principal component analysis, dynamic principal component analysis and dynamic latent variable. ? 2016 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. Al rights reserved.     

在线自适应批次过程监视的双滑动窗口MPCA方法

Online monitoring of chemical process performance is extremely important to ensure the safety of a chemical plant and consistently high quality of products. Multivariate statistical process control has found wide applications in process performance analysis, monitoring and fault diagnosis using existing rich historical database. In this paper, we propose a simple and straight forward multivariate statistical modeling based on a moving window MPCA （multiway principal component analysis） model along the time and batch axis for adaptive monitoring the progress of batch processes in real-time. It is an extension to minimum window MPCA and traditional MPCA. The moving window MPCA along the batch axis can copy seamlessly with variable run length and does not need to estimate any deviations of the ongoing batch from the average trajectories. It replaces an invariant fixed-model monitoring approach with adaptive updating model data structure within batch-to-batch, which overcomes the changing operation condition and slows time-varying behaviors of industrial processes. The software based on moving window MPCA has been successfully applied to the industrial polymerization reactor of polyvinyl chloride （PVC） process in the Jinxi Chemical Company of China since 1999.     

PVC生产过程故障传感器的检测与重构

Based on principal component analysis, this paper presents an application of faulty sensor detection and reconstruction in a batch process, polyvinylchloride (PVC) making process. To deal with inconsistency in process data, it is proposed to use the dynamic time warping technique to make the historical data synchronized first,then build a consistent multi-way principal component analysis model. Fault detection is carried out based on squared prediction error statistical control plot. By defining principal component subspace, residual subspace and sensor validity index, faulty sensor can be reconstructed and identified along the fault direction. Finally, application results are illustrated in detail by use of the real data of an industrial PVC making process.     

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.     

A Robust Statistical Batch Process Monitoring Framework and Its Application

In order to reduce the variations of the product quality in batch processes, multivariate statistical process control methods according to multi-way principal component analysis (MPCA) or multi-way projection to latent structure (MPLS) were proposed for on-line batch process monitoring. However, they are based on the decomposition of relative covariance matrix and strongly affected by outlying observations. In this paper, in view of an efficient projection pursuit algorithm, a robust statistical batch process monitoring (RSBPM) framework, which is resistant to outliers, is proposed to reduce the high demand for modeling data. The construction of robust normal operating condition model and robust control limits are discussed in detail. It is evaluated on monitoring an industrial streptomycin fermentation process and compared with the conventional MPCA. The results show that the RSBPM framework is resistant to possible outliers and the robustness is confirmed.     

间歇生产过程鲁棒统计监控及其应用

In order to reduce the variations of the product quality in batch processes, multivariate statistical process control methods according to multi-way principal component analysis (MPCA) or multi-way projection to latent structure (MPLS) were proposed for on-line batch process monitoring. However, they are based on the decomposition of relative covariance matrix and strongly affected by outlying observations. In this paper, in view of an efficient projection pursuit algorithm, a robust statistical batch process monitoring (RSBPM) framework, which is resistant to outliers, is proposed to reduce the high demand for modeling data. The construction of robust normal operating condition model and robust control limits are discussed in detail. It is evaluated on monitoring an industrial streptomycin fermentation process and compared with the conventional MPCA. The results show that the RSBPM framework is resistant to possible outliers and the robustness is confirmed.     

Balanced multiple weighted linear discriminant analysis and its application to visual process monitoring

Visual process monitoring is important in complex chemical processes. To address the high state separation of industrial data, we propose a new criterion for feature extraction called balanced multiple weighted linear discriminant analysis(BMWLDA). Then, we combine BMWLDA with self-organizing map(SOM) for visual monitoring of industrial operation processes. BMWLDA can extract the discriminative feature vectors from the original industrial data and maximally separate industrial operation states in the space spanned by these discriminative feature vectors. When the discriminative feature vectors are used as the input to SOM, the training result of SOM can differentiate industrial operation states clearly.This function improves the performance of visual monitoring. Continuous stirred tank reactor is used to verify that the class separation performance of BMWLDA is more effective than that of traditional linear discriminant analysis, approximate pairwise accuracy criterion, max–min distance analysis, maximum margin criterion, and local Fisher discriminant analysis. In addition, the method that combines BMWLDA with SOM can effectively perform visual process monitoring in real time.     

自适应MPCA方法在链霉素过程监控中的应用

Multi-way principal component analysis (MPCA) had been successfully applied to monitoring the batch and semi-batch process in most chemical industry. An improved MPCA approach, step-by-step adaptive MPCA (SAMPCA), using the process variable trajectories to monitoring the batch process is presented in this paper. It does not need to estimate or fill in the unknown part of the process variable trajectory deviation from the current time until the end. The approach is based on a MPCA method that processes the data in a sequential and adaptive manner. The adaptive rate is easily controlled through a forgetting factor that controls the weight of past data in a summation. This algorithm is used to evaluate the industrial streptomycin fermentation process data and is compared with the traditional MPCA. The results show that the method is more advantageous than MPCA, especially when monitoring multi-stage batch process where the latent vector structure can change at several points during the batch.     

基于变长度移动窗口和HMM的工业过程故障在线诊断

An integrated framework is presented to represent and classify process data for on-line identifying abnormal operating conditions. It is based on pattern recognition principles and consists of a feature extraction step, by which wavelet transform and principal component analysis are used to capture the inherent characteristics from process measurements, followed by a similarity assessment step using hidden Markov model (HMM) for pattern comparison. In most previous cases, a fixed-length moving window was employed to track dynamic data, and often failed to capture enough information for each fault and sometimes even deteriorated the diagnostic performance. A variable moving window, the length of which is modified with time, is introduced in this paper and case studies on the Tennessee Eastman process illustrate the potential of the proposed method.     

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     

Online Flooding Supervision in Packed Towers: An Integrated Data‐Driven Statistical Monitoring Method

The development of simple and efficient monitoring methods for flooding supervision is an important but difficult task for the safe operation of packed towers. A data‐driven online flooding monitoring method named Bayesian integrated dynamic principal component analysis (IDPCA) is assessed. In the first step of IDPCA, using the fuzzy c‐means clustering method, the multivariate samples collected during plant operation are first classified into several groups. Then, in each subset a dynamic principal component analysis (DPCA) model is constructed to extract the process characteristics. To improve the monitoring performance, Bayesian inference is utilized to combine these DPCA models in a suitable manner. Consequently, the control limits are formulated using the probabilistic analysis. The superiority of IDPCA is illustrated using a lab‐scale packed tower by comparison with the conventional principal component analysis (PCA) and DPCA methods.     

Fault detection and diagnosis for chemical processes using dynamic global–local preserving projections

Most traditional multivariate statistical monitoring methods require an assumption that the observation values at a certain moment and a past moment are statistically independent. However, in actual chemical and biological processes, the sample at a certain moment is often affected by the previous moment. Therefore, given the problem of more false alarms and poor detection ability based on the traditional principal component analysis, this article proposes a dynamic global–local preserving projections (DGLPP) algorithm. Unlike dynamic local preserving projections (DLPP) and dynamic principal component analysis (DPCA), DGLPP controls the global and local information retained in the dimensionality reduction data by introducing weight coefficients, which makes the algorithm applicable to more types of industrial processes. Moreover, new parameter determination methods are also proposed for improved detection and diagnosis. Through the improved contribution graph method, we can see the influence degree of each variable on the fault, to monitor and isolate the fault. Finally, by verifying the operation of the multivariable process and two practical cases, the results show that compared with DPCA, DLPP, and global local retained projection (GLPP) methods, the performance under this method has been significantly improved.     

A novel fault detection scheme for a nonlinear dynamic process based on generalized non-negative matrix projection-maximum mean discrepancy: Application on the DAMADICS benchmark process

In order to address the issue of minor fault detection in nonlinear dynamic processes, this paper proposes a fault detection method based on generalized non-negative matrix projection-maximum mean discrepancy (GNMP-MMD). Firstly, the GNMP is employed to acquire the residual scores of the samples. Subsequently, a sliding window approach is integrated with MMD for real-time monitoring of sample status within the residual subspace. In this study, GNMP is utilized to mitigate the impact of non-Gaussianity in data distribution, while MMD serves to alleviate autocorrelation among samples. A numerical case and experimental data collected from the DAMADICS process are utilized to simulate and validate the proposed method. Compared to traditional principal component analysis (PCA), dynamic principal component analysis (DPCA), dynamic kernel principal component analysis (DKPCA), non-negative matrix factorization (NMF), GNMP, and MMD, the experiment results clearly illustrate the feasibility of the proposed method.     

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.     

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.     

Layered monitoring of xylenol tail gas treatment process based on stationary subspace analysis

To deal with the inaccurate monitoring caused by the non-stationary characteristics of the xylenol tail gas treatment process, a layered monitoring scenario utilizing stationary subspace analysis has been presented in the present study. First, principal component analysis (PCA) is applied to establish the upper-level stationary monitoring model. Then the sliding time window is used to capture the dynamic information of the remaining non-stationary features, update the model, and establish the lower non-stationary monitoring model. Next, the Bayesian information criterion is employed to build the global monitoring model according to the detection results of the upper and lower layers. Finally, the industrial data collected from the industrial boiler is used to evaluate the effectiveness and applicability of the proposed method. It is demonstrated that layered monitoring has higher accuracy than conventional non-stationary process monitoring techniques. Moreover, it can capture the faults in the stationary features masked by the non-stationary features.     

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.     

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.     

Dynamic simulation of a cascade fluidized-bed membrane reactor in the presence of long-term catalyst deactivation for methanol synthesis

In this work, a dynamic model for a cascade fluidized-bed hydrogen permselective membrane methanol reactor (CFBMMR) has been developed in the presence of long-term catalyst deactivation. In the first catalyst bed, the synthesis gas is partly converted to methanol in a water-cooled reactor, which is a fluidized-bed. In the second bed, which is a membrane assisted fluidized-bed reactor, the reaction heat is used to preheat the feed gas to the first bed. This reactor configuration solves some observed drawbacks of new conventional dual type methanol reactor (CDMR) and even fluidized-bed membrane dual type methanol reactor (FBMDMR) such as pressure drop, internal mass transfer limitations, radial gradient of concentration and temperature in both reactors. A dynamic two-phase theory in bubbling regime of fluidization is used to model and simulate the proposed reactor. The proposed model has been used to compare the performance of a cascade fluidized-bed membrane methanol reactor with fluidized-bed membrane dual-type methanol reactor and conventional dual-type methanol reactor. The simulation results show a considerable enhancement in the methanol production due to the favorable profile of temperature and activity along the CFBMMR relative to FBMDMR and CDMR systems.