Multi-stage batch process monitoring

On-line batch process monitoring using a consecutively updated multiway principal component analysis model

Process Monitoring Using Principal Component Analysis in Different Operating Time Processes

Dynamic model-based fault diagnosis for (bio)chemical batch processes

Complex-valued neural networks for nonlinear complex principal component analysis

Photoluminescence spectroscopic probes offer the potential for differentiation among plant species in real-time. Spectral emission signatures (excitation at 365 nm) from three different pH (2.2, 7.5 and 12.5) phosphate buffered saline (PBS) extracts from two grasses, Sporobolus flexuosus (Thurb. ex Vasey) Rydb., [mesa dropseed], and Pleuraphis mutica Buckley [tobosa], two forbs, Dimorphocarpa wislizenii (Engelm.) Rollins [spectacle pod], and Sphaeralcea incana Torrey [pale globemallow], and leaves and twigs from two shrubs Flourensia cernua DC. [tarbush], and Atriplex canescens (Pursh) Nutt., [fourwing saltbush] were examined. Since pH has been shown to be pivotal in affecting extraction efficiency of other plant compounds pH seemed appropriate as an additional dimension within our multi-way principal component analysis (MPCA) to differentiate among six different plant species. In particular, MPCA allowed differentiation between Sporobolus and Pleuraphis that was not possible using only principal component analysis (PCA). This research suggests MPCA may be a more appropriate tool than PCA when attempting to discriminate among plant species.

The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal variables and that it can handle and discover nonlinear relationships between variables. Also, nonlinear PCA can deal with variables at their appropriate measurement level; for example, it can treat Likert-type scales ordinally instead of numerically. Every observed value of a variable can be referred to as a category. While performing PCA, nonlinear PCA converts every category to a numeric value, in accordance with the variable's analysis level, using optimal quantification. The authors discuss how optimal quantification is carried out, what analysis levels are, which decisions have to be made when applying nonlinear PCA, and how the results can be interpreted. The strengths and limitations of the method are discussed. An example applying nonlinear PCA to empirical data using the program CATPCA (J. J. Meulman, W. J. Heiser, & SPSS, 2004) is provided.

Two improvements to the Non‐linear Principal Component Analysis (NLPCA) method are presented. In the normal application of this method, a non‐linear curve C is found that best fits the data. The method provides a projection function mapping from the data space to the curve C. However, this projection function is faulty in that points in the data space are generally not projected onto their closest neighbours on C. Here, a new projection function is introduced which ensures that the data points are projected onto their closest neighbours on C, resulting in an increase in the amount of variance explained by the NLPCA mode. This is illustrated by an analysis of the sea surface temperature anomaly data from the tropical Pacific, where the El Niño‐Southern Oscillation (ENSO) phenomenon is manifested. A second shortcoming of the NLPCA method is that the curve C comes with a parametrization which is arbitrary and has no physical interpretation. Here, the curve is re‐parametrized by arc length. This allows the computation of more meaningful time series, which we illustrate through an analysis of the Quasi‐Biennial Oscillation (QBO) in the equatorial stratospheric zonal wind data.

There has been a lot of research activity in the area of batch process analysis and monitoring for abnormal situation detection since the pioneer work of Nomikos and MacGregor []. However, some of the key ideas and the thought process that led to those first papers have been forgotten. Batch process data are dynamic data. The whole philosophy of looking at batch process data with latent variables was developed because batch process variables are both autocorrelated and cross‐correlated. Statistical process control by definition checks deviations from a nominal behavior (a target). Therefore for statistical process control of batch processes we should look at deviations of process variable trajectories from their nominal trajectories and from their nominal auto/cross‐correlations. An added advantage to modeling the deviations from the target trajectory is that a non‐linear problem is converted to a linear one that it is easy to tackle with linear latent variable methods such as principal component analysis (PCA) and partial least squares (PLS). This paper first takes a critical look at the true nature of batch process data. The general case where variables are not present during the entire duration of the batch is addressed. It is then illustrated how proper centering (by taking the deviations from the target trajectory) can retain valuable information on auto‐ and cross‐correlation of the process variables. This auto‐ and cross‐correlation is only modeled with a certain types of models. Topics such as scaling and trajectory alignment are revisited and issues arising when using the indicator variable approach are addressed. The development of control charts for multiblock, multiway PCA/PLS is discussed. Practical issues related to applications in industry are addressed. Then some of the methods that have appeared in the literature are examined as to their assumptions, their advantages and disadvantages and their range of applicability. Finally the nature of transition data (start‐ups, grade transitions) is discussed and issues related to aligning, centering and scaling such types of data are presented. Copyright © 2003 John Wiley & Sons, Ltd.

Biological processes exhibit different behavior depending on the influent loads, temperature, microorganism activity, and so on. It has been shown that a combination of several models can provide a suitable approach to model such processes. In the present study, we developed a multiple statistical model approach for the monitoring of biological batch processes. The proposed method consists of four main components: (1) multiway principal component analysis (MPCA) to reduce the dimensionality of data and to remove collinearity; (2) multiple models with a posterior probability for modeling different operating regions; (3) local batch monitoring by the T(2)- and Q-statistics of the specific local model; and (4) a new discrimination measure (DM) to identify when the system has shifted to a new operating condition. Under this approach, local monitoring by multiple models divides the entire historical data set into separate regions, which are then modeled separately. Then, these local regions can be supervised separately, leading to more effective batch monitoring. The proposed method is applied to a pilot-scale 80-L sequencing batch reactor (SBR) for biological wastewater treatment. This SBR is characterized by nonstationary, batchwise, and multiple operation modes. The results obtained for the pilot-scale SBR indicate that the proposed method has the ability to model multiple operating conditions, to identify various operating regions, and also to determine whether the biosystem has shifted to a new operating condition. Our findings show that the local monitoring approach can give more reliable and higher resolution monitoring results than the global model.

The problem of using time-varying trajectory data measured on many process variables over the finite duration of a batch process is considered. Multiway principal-component analysis is used to compress the information contained in the data trajectories into low-dimensional spaces that describe the operation of past batches. This approach facilitates the analysis of operational and quality-control problems in past batches and allows for the development of multivariate statistical process control charts for on-line monitoring of the progress of new batches. Control limits for the proposed charts are developed using information from the historical reference distribution of past successful batches. The method is applied to data collected from an industrial batch polymerization reactor.

Batch process data can be arranged in a three-way matrix (batch × variable × time). This paper provides a critical discussion of various aspects of the treatment of these multiway data. First, several methods that have been proposed for decomposing three-way data matrices are discussed in the context of batch process data analysis and monitoring. These methods are multiway principal component analysis (MPCA)—also called Tucker1—parallel factor analysis (PARAFAC) and Tucker3. Secondly, different ways of unfolding, mean centering and scaling the three-way matrix are compared and discussed with respect to their effects on the analysis of batch data. Finally, the role of the time variable in batch process data is considered and methods suggested to predict the per cent completion of batch runs with unequal duration are discussed. Copyright © 1999 John Wiley & Sons, Ltd.

Batch process data contain between‐run and within‐run sources of variation, which complicates data analysis and process monitoring. Multilevel methods, such as multilevel simultaneous component analysis, greatly enhance the interpretation of large sets of batch process data by separating the between‐run and within‐run variation. Using a multilevel approach in batch process monitoring greatly reduces the occurrence of false alarms that are caused by trivial variations and process changes that were made on purpose. This also reduces the need for model updating, which often is a large effort and causes downtime of the monitoring system. Furthermore, relevant phenomena that are masked by larger but uninteresting sources of variation when standard batch process monitoring methods are applied can often be detected if the multilevel approach is used. Chemical batch process data are used to illustrate the methods. Copyright © 2012 John Wiley & Sons, Ltd.

Nonlinear principal component analysis (NLPCA) is known as a nonlinear generalization of the standard principal component analysis (PCA). Since nonlinear PCA is a non-unique concept, it is discussed, how nonlinear PCA can be defined as a nonlinear feature extraction technique most similar to linear PCA. The nonlinear reduction of a data set from its original dimension to the intrinsic dimension of the data is one aspect, but we also request that the nonlinear features spanning this intrinsic data space are hierarchically arranged similar to the linear features of PCA. Thus, such nonlinear PCA is a powerful pre-processing step. It can be used as nonlinear sphering (whitening) or it can be considered as a smoothing method which removes nonlinear correlations between variables. Nonlinear PCA can be performed by minimizing a hierarchical error function. This error function is applied to the autoencoder which is a multi-layer perceptron used in auto-associative mode to perform the identity mapping.

Traditional single model based soft sensors may have poor performance on quality prediction for batch processes because of the strong nonlinearity, multiple-phase, and time-varying characteristics. Therefore, a phase partition based ensemble learning framework upon least squares support vector regression (LSSVR) is proposed for soft sensor modeling. Firstly, multiway principal component analysis (MPCA) is employed to handle high-dimensional datasets and extract essential correlation information. Then, different operation phases of the process can be identified by the phase partition strategy based on Gaussian mixture model (GMM) method. Meanwhile, the optimal Gaussian component number is determined by Bayesian information criterion (BIC) technique. Further, multiple localized LSSVR models are constructed to characterize the various dynamic relationships between quality and process variables for local regions, while the grid search (GS) and ten-fold cross-validation methods are introduced to parameter optimization for each local model. Finally, the posterior probability for each test sample with respect to different phases can be estimated by Bayesian inference strategy, and local outputs are integrated to produce the final quality prediction results. Feasibility and superiority of the proposed soft sensor are validated through a case study for penicillin fermentation process. It can achieve satisfactory prediction accuracy and effectively tackle nonlinear and multi-phase modeling problems in chemical and biological processes.

This paper investigates fault diagnosis in batch processes and presents a comparative study of feature extraction and classification techniques applied to a specific biotechnological case study: the fermentation process model by Birol et al. (Comput Chem Eng 26:1553-1565, 2002), which is a benchmark for advanced batch processes monitoring, diagnosis and control. Fault diagnosis is achieved using four approaches on four different process scenarios based on the different levels of noise so as to evaluate their effects on the performance. Each approach combines a feature extraction method, either multi-way principal component analysis (MPCA) or multi-way independent component analysis (MICA), with a classification method, either artificial neural network (ANN) or support vector machines (SVM). The performance obtained by the different approaches is assessed and discussed for a set of simulated faults under different scenarios. One of the faults (a loss in mixing power) could not be detected due to the minimal effect of mixing on the simulated data. The remaining faults could be easily diagnosed and the subsequent discussion provides practical insight into the selection and use of the available techniques to specific applications. Irrespective of the classification algorithm, MPCA renders better results than MICA, hence the diagnosis performance proves to be more sensitive to the selection of the feature extraction technique.