On-line Monitoring Of Batch Processes Research Articles

Online monitoring of batch processes combining subspace design of latent variables with support vector data description

Online monitoring of batch processes combining subspace design of latent variables with support vector data description

Data-driven soft-sensors for online monitoring of batch processes with different initial conditions

A soft-sensing methodology applicable to batch processes operated under changeable initial conditions is presented. These cases appear when the raw materials specifications differ from batch to batch, different production scenarios should be managed, etc. The proposal exploits the capabilities of the machine learning techniques to provide practical soft-sensing approach with minimum tuning effort in spite of the fact that the inherent dynamic behavior of batch systems are tracked through other online indirect measurements. Current data modeling techniques have been also tested within the proposed methodology to demonstrate its advantages. Two simulation case-studies and a pilot-plant case-study involving a complex batch process for wastewater treatment are used to illustrate the problem, to assess the modeling approach and to compare the modeling techniques. The results reflect a promising accuracy even when the training information is scarce, allowing significant reductions in the cost associated to batch processes monitoring and control.

On-line monitoring of batch processes using generalized additive kernel principal component analysis

Based on analyzing the special structure of three-way array and generalizing the concept of additive kernels, this paper proposes the generalized additive kernel principal component analysis (GAKPCA) method for on-line monitoring of batch processes. The proposed method is a special nonlinear principal component analysis (PCA) method which can handle the nonlinear relationships between different monitoring variables and/or time intervals. It inherits the good properties of traditional multiway PCA (MPCA) method for on-line monitoring, and solves some problems that exist in traditional multiway kernel PCA (MKPCA) method. For example, based on the decomposition of batch samples in the feature space, the total squared prediction error (SPE) statistic of an entire batch can be divided into K components corresponding to K time intervals respectively, and its score vectors can be directly estimated on-line by the least squares approach without filling the unknown observations. As a special case, when the Gaussian kernel is used as the kernel function at each time interval, the proposed method is connected with the concept of correntropy which can bring robustness to our method. The experimental results on a fed-batch penicillin fermentation process demonstrate the validity of the proposed GAKPCA-based on-line monitoring method.

Phase analysis and statistical modeling with limited batches for multimode and multiphase process monitoring

For multimode batch processes, the conventional modeling methods in general require that sufficient batches should be available for every mode, which, however, cannot be guaranteed in practice. It may be impractical to conduct enough trial runs and wait until sufficient batches are available before development of monitoring models for each mode. Starting from limited batches, how to derive reliable process information and develop monitoring models has been an important question for successful online multimode batch process monitoring. To address this problem, this article proposes a phase analysis and statistical modeling strategy with limited batches. One mode which has obtained sufficient batches is chosen as the reference mode while the other modes which can only get limited batches work as alternative modes. Starting from limited batches, the proposed algorithm addresses two issues, concurrent phase partition and analysis of between-mode relative changes. First, for each alternative mode, generalized time-slices are constructed by combining several consecutive time-slices within a short time region to explore local process correlations. The time-varying characteristics are then concurrently analyzed across modes so that multiple sequential phases are identified simultaneously for all modes. Then phase-representative data units are arranged by variable-unfolding the conventional time-slices for the reference mode and the generalized time-slices for each alternative mode respectively. Between-mode statistical analysis is performed within each phase where the relative changes from the reference mode to each alternative mode are analyzed. From the between-mode perspective, different types of relative variations in each alternative mode are separated and modeled for online monitoring. Starting from limited batches, online batch process monitoring can be conducted, providing reliable fault detection performance. The proposed algorithm is illustrated with a typical multiphase batch process with multiple modes.

On-line Batch Process Monitoring with Improved Multi-way Independent Component Analysis

In the past decades, on-line monitoring of batch processes using multi-way independent component analysis (MICA) has received considerable attention in both academia and industry. This paper focuses on two troublesome issues concerning selecting dominant independent components without a standard criterion and determining the control limits of monitoring statistics in the presence of non-Gaussian distribution. To optimize the number of key independent components, we introduce a novel concept of system deviation, which is able to evaluate the reconstructed observations with different independent components. The monitored statistics are transformed to Gaussian distribution data by means of Box-Cox transformation, which helps readily determine the control limits. The proposed method is applied to on-line monitoring of a fed-batch penicillin fermentation simulator, and the experimental results indicate the advantages of the improved MICA monitoring compared to the conventional methods.

Online Monitoring for Uneven Length Batch Processes using Function Space Principal Component Analysis

Online batch process monitoring has been a challenging task, as batch processes do not operate around a nominal steady state operating point. Various monitoring approaches where future batch trajectory is filled with average (nominal) batch trajectory have been proposed. Predicting future trajectory for a batch process is a difficult task. Recently a multiway principal component analysis (MPCA) based approach that does not involve future trajectory prediction was proposed. In this paper a new technique based on function space principal component analysis (FSPCA) is proposed for online batch process monitoring. The main advantage of the proposed FSPCA based methodology is its ability to detect incipient and small to medium magnitude faults and its relevance for uneven length batch processes. Efficiency and effectiveness of the proposed algorithm is demonstrated via a fed-batch penicillin cultivation process simulation. The diagnostic performance of the proposed approach is significantly better compared to MPCA based approaches.

Real-time synchronization of batch trajectories for on-line multivariate statistical process control using Dynamic Time Warping

This paper addresses the real-time monitoring of batch processes with multiple different local time trajectories of variables measured during the process run. For Unfold Principal Component Analysis (U-PCA)—or Unfold Partial Least Squares (U-PLS)-based on-line monitoring of batch processes, batch runs need to be synchronized, not only to have the same time length, but also such that key events happen at the same time. An adaptation from Kassidas et al .'s approach [1] will be introduced to achieve the on-line synchronization of batch trajectories using the Dynamic Time Warping (DTW) algorithm. In the proposed adaptation, a new boundaries definition is presented for accurate on-line synchronization of an ongoing batch, together with a way to adapt mapping boundaries to batch length. A relaxed greedy strategy is introduced to avoid assessing the optimal path each time a new sample is available. The key advantages of the proposed strategy are its computational speed and accuracy for the batch process context. Data from realistic simulations of a fermentation process of the Saccharomyces cerevisae cultivation are used to illustrate the performance of the proposed strategy.

On-line batch process monitoring using batch dynamic kernel principal component analysis

In this paper, a new dynamic and nonlinear batch process monitoring method, referred to as BDKPCA, is developed for on-line batch process monitoring, tactfully integrating kernel PCA and ARMAX time series model through estimating the Average Kernel Matrix (AKM) of all batch runs. AKM is an average of I, the batch number, Single-Batch Kernel Matrixes (SBKM). Each of the I SBKM is also an average of I kernel matrixes for each batch. The AKM contains the information of the stochastic variations and deviations among batches. This information will be very useful for the BDKPCA model to characterize the batch process in detail. The structure of BDKPCA model is very simple, and BDKPCA calculates the Hotelling's T 2 statistic and the Q-statistic for every time point, enhancing the method's sensitivity to the faults. Two cases are used to investigate the potential application of the proposed method, and its application to on-line batch process monitoring shows better performance than MKPCA.

On-line multivariate statistical monitoring of batch processes using Gaussian mixture model

This paper considers multivariate statistical monitoring of batch manufacturing processes. It is known that conventional monitoring approaches, e.g. principal component analysis (PCA), are not applicable when the normal operating conditions of the process cannot be sufficiently represented by a multivariate Gaussian distribution. To address this issue, Gaussian mixture model (GMM) has been proposed to estimate the probability density function ( pdf) of the process nominal data, with improved monitoring results having been reported for continuous processes. This paper extends the application of GMM to on-line monitoring of batch processes. Furthermore, a method of contribution analysis is presented to identify the variables that are responsible for the onset of process fault. The proposed method is demonstrated through its application to a batch semiconductor etch process.

The best approaches in the on-line monitoring of batch processes based on PCA: Does the modelling structure matter?

Much work has been devoted to the on-line multivariate statistical process control (MSPC) of batch processes based on bilinear models such as principal component analysis (PCA). The data collected from a batch process have 3-way structure and they have to be arranged in 2-way matrices prior to PCA. Several transformation methods have been proposed reporting contradictory conclusions regarding monitoring performance. The aim of this paper is to run an objective research to assess the influence of 3-way to 2-way transformations on the monitoring performance. Batch-wise, variable-wise, batch-dynamic, local and multi-phase approaches are compared using simulated data from a pair of ‘toy’ processes with quite different and perfectly known dynamics. Several realistic types of faults are simulated. The main conclusions regarding fault detection performance are: (i) the best monitoring approach depends more on the type of fault than on the process dynamics; (ii) the information considered in the model structure will determine which faults are detectable; (iii) in general, a good monitoring performance is achieved with a parsimonious model; (iv) proper identification of the changes in the correlation structure -the phases of the process- is crucial for parsimonious models; (v) it can be advisable to combine several unfolding methods to improve the detection ability of predefined types of faults. These results were coherently explained from the theoretically known features of the models and validate the conclusions in previous investigations with real batch processes and realistic simulations.

On-line statistical monitoring of batch processes using Gaussian mixture model

The statistical monitoring of batch manufacturing processes is considered. It is known that conventional monitoring approaches, e.g. principal component analysis (PCA), are not applicable when the normal operating conditions of the process cannot be sufficiently represented by a Gaussian distribution. To address this issue, Gaussian mixture model (GMM) has been proposed to estimate the probability density function of the process nominal data, with improved monitoring results having been reported for continuous processes. This paper extends the application of GMM to on-line monitoring of batch processes, and the proposed method is demonstrated through its application to a batch semiconductor etch process.

Multiway kernel independent component analysis based on feature samples for batch process monitoring

Most batch processes generally exhibit the characteristics of nonlinear variation. In this paper, a nonlinear monitoring technique is proposed using a multiway kernel independent component analysis based on feature samples (FS-MKICA). This approach first unfolds the three-way dataset of a batch process into the two-way one and then chooses representative feature samples from the large two-way input training dataset. The nonlinear feature space abstracted from the unfolded two-way data space is then transformed into a high-dimensional linear space via kernel function and an independent component analysis (ICA) model is established in the mapped linear space. The proposed FS-MKICA method can significantly reduce the computational cost in extracting the kernel ICA model since it is based on the small subset of feature samples rather than on the entire input sample set. We supply two statistics, the I 2 statistic of process variation and the squared prediction error statistic of residual, for on-line monitoring of batch processes. The proposed method is applied to detecting faults in the fed-batch penicillin fermentation process. The standard linear ICA method for batch process monitoring, known as the multiway independent component analysis (MICA), is also applied to the same benchmark batch process. The simulation results obtained in this nonlinear batch process application clearly demonstrate the power and superiority of the new nonlinear monitoring method over the linear one. The FS-MKICA approach can extract the nonlinear features of the batch process while the MICA method cannot.

Online monitoring of multi-phase batch processes using phase-based multivariate statistical process control

Online monitoring of batch processes using multivariate statistical methods has attracted enormous research interests due to its practical importance. In this paper, we focus on an important issue that continues to confound online batch process monitoring—run-to-run variations that do not confirm to a normal distribution around a reference trajectory. Here, we show that a phase-based decomposition of the trajectory offers a systematic way to overcome this challenge. In our approach, phase changes are detected online using Singular points in key variables. Run-to-run variations among different instances of a phase are synchronized by using time warping. Finally, phased-based multivariate statistical process control models are used to monitor the execution of the batch and detect abnormalities. This phase-based monitoring approach is robust to run-to-run variations arising from changes in initial conditions and event timings as is illustrated using a well-known fermentation process simulation.

Online monitoring of batch processes using multi-phase principal component analysis

Unfold Principal Component Analysis (u-PCA) has been successfully applied in the monitoring of batch processes. The traditional online monitoring strategy is based on the same unfolding procedure used for end-of-batch monitoring. This procedure may distort the interval where the process is out of normal operation, with delays in the detection of a fault or in the return to normal operation of a faulty batch. In this paper, a new strategy for the generation of a model specially suited for on-line monitoring is presented. This method is based on the combination of four ideas: mean trajectory subtraction and auto-scaling as preprocessing, variable-wise unfolding, addition of lagged variables to fit the dynamics and multi-phase modelling with multi-phase PCA. Evolving and local models have been included in the comparative analysis of the different approaches.

MONITORING OF BATCH PROCESSES WITH VARYING DURATIONS BASED ON THE HAUSDORFF DISTANCE

In some industrial situations, the classical assumption used in the batch process monitoring that all batches have equal durations and are synchronized does not hold. A batch process is carried out in sequential phases and a significant variability generally occurs in the duration of the phases such that events signifying the beginning or the end of a phase are generally misaligned in time within the various batches. The consequence is that the variable trajectories, in the different runs of the same batch process, are unsynchronized. In this case, data analysis from process for performing the multivariate statistical process control can be difficult. In this paper, we propose several innovative methods for the off-line and on-line monitoring of batch processes with varying durations, all based on the Hausdorff distance. These methods have been successfully tested on a simulated example and on an industrial case example. The conclusion is that these methods are able to efficiently discriminate between nominal and non-nominal batches.

AN ADJOINED MULTI-DPCA APPROACH FOR ONLINE MONITORING OF FED-BATCH PROCESSES

Batch processes are common in the manufacturing of high value-added products. Monitoring with the highly popular principal components analysis (PCA) approaches do not function adequately in the face of the sequential nature of batch processes, as the basic assumptions that its monitoring statistics (SPE and Hotelling's T2) are developed upon – stationary, normal distribution of source data - are violated. Consequently, these monitoring techniques become prone to Type-I (false positives) and Type-II Errors (false negatives). In this article, an extension of PCA, called adjoined dynamic principal component analysis (ADPCA), is proposed for online monitoring of batch processes by using multiple dynamic-PCA (DPCA) models. The ADPCA models are developed by first clustering process data using fuzzy c-means algorithm and developing a DPCA model for each cluster. Each cluster is selected so that it satisfies the PCA's assumption. The problem of switching between the models which normally confounds multiple model-based approaches is overcome by allowing adjoining models to overlap and thus enabling smooth switching from one model to another during the course of batch operations. As shown in this paper, the proposed methodology reduces both Type-I and Type-II errors compared to single block methods.

Two‐dimensional dynamic PCA for batch process monitoring

Batch processes play an important role in many industriesfor flexible manufacturing of high value-added products. On-line monitoring of batch processes is of critical importance inensuring operation safety and quality consistency. Multivariatestatistical methods for continuous processes, such as principalcomponent analysis (PCA) and partial least square (PLS), havebeen extended to batch process monitoring with some suc-cesses, for example, multiway PCA/PLS,

Framework for regression‐based missing data imputation methods in on‐line MSPC

AbstractMissing data are a critical issue in on‐line multivariate statistical process control (MSPC). Among the different scores estimation methods for future multivariate incomplete observations from an existing principal component analysis (PCA) model, the most statistical efficient ones are those that estimate the scores for the new incomplete observation as the prediction from a regression model. We have called them regression‐based methods. Several approximations have been proposed in the literature to overcome the singularity or ill‐conditioning problems that some of the mentioned methods can suffer due to missing data. This is particularly acute in on‐line batch process monitoring. In order to ease the comparison of the statistical performance of these methods and to improve the understanding of their relationships, in this paper we propose a framework that allows to write these regression‐based methods by an unique expression, function of a key matrix. From this framework a statistical performance index (PRESV) is introduced as a way to compare the statistical efficiency of the different framework members and to predict the impact of specific missing data combinations on scores estimation without requiring real data. The results are illustrated by application to several continuous and batch industrial data sets. Copyright © 2005 John Wiley & Sons, Ltd.

Genetic algorithms (GA) applied to the orthogonal projection approach (OPA) for variable selection

Multivariate curve resolution (MCR) and especially the orthogonal projection approach (OPA) can be applied to spectroscopic data and were proved to be suitable for process monitoring. To improve the quality of the on-line monitoring of batch processes, it is interesting to get as many as possible spectra in a given period of time. Nevertheless, hardware limitations could lead to the fact that it is not possible to acquire more than a certain number of spectra in this given period of time. Wavelength selection could be a good way to limit this problem since it decreases size, and consequently the acquisition time, of each recorded spectrum. This paper details an industrial application of genetic algorithms (GA) coupled with a curve resolution method (OPA) for such purpose.

On-line monitoring of batch processes using multiway independent component analysis

Batch processes play an important role in the production of low-volume, high-value products such as polymers, pharmaceuticals, and biochemical products. Multiway principal component analysis (MPCA), a multivariate projection method, has been widely used to monitor batch processes. But in-control data of non-stationary processes in fact contain inherent non-Gaussian distributed data due to ramp changes, step changes, and even weak levels of autocorrelation. Monitoring charts obtained by applying MPCA to such non-Gaussian data may contain nonrandom patterns corresponding to the data characteristics. To obtain better monitoring performance in a batch process with non-Gaussian data, on-line batch monitoring method with multiway independent component analysis (MICA) is developed in this paper. MICA is based on a recently developed feature extraction method, called independent component analysis (ICA), whereas PCA looks for Gaussian components, whereas ICA searches for non-Gaussian components. MICA projects the multivariate data into a low-dimensional space defined by independent components (ICs). When the measured variables have non-Guassian distributions, MICA provides more meaningful statistical analysis and on-line monitoring compared to MPCA because MICA assumes that the latent variables are not Gaussian distributed. The proposed method was applied to the on-line monitoring of a fed-batch penicillin production. The simulation results demonstrate the power and advantages of MICA.