Batch Process Monitoring Research Articles

Multivariate fault isolation of batch processes via variable selection in partial least squares discriminant analysis

In recent years, multivariate statistical monitoring of batch processes has become a popular research topic, wherein multivariate fault isolation is an important step aiming at the identification of the faulty variables contributing most to the detected process abnormality. Although contribution plots have been commonly used in statistical fault isolation, such methods suffer from the smearing effect between correlated variables. In particular, in batch process monitoring, the high autocorrelations and cross-correlations that exist in variable trajectories make the smearing effect unavoidable. To address such a problem, a variable selection-based fault isolation method is proposed in this research, which transforms the fault isolation problem into a variable selection problem in partial least squares discriminant analysis and solves it by calculating a sparse partial least squares model. As different from the traditional methods, the proposed method emphasizes the relative importance of each process variable. Such information may help process engineers in conducting root-cause diagnosis.

Latent variable based concurrent multi‐trends analysis method for monitoring batch processes with irregular and limited batches

AbstractIn practice, two problems, limited batches and irregular batch trajectories, may simultaneously exist in batch processes, making process modelling and monitoring a great challenge. However, previous work did not solve the two problems simultaneously. Motivated by such cognition, for those processes with limited modelling batches and irregular batch durations, this work proposes a LV (Latent Variable)‐based concurrent multi‐trends analysis method, which combines the advantages of multi‐set variable correlation analysis and trend analysis. First, cross set correlation analysis is implemented to reduce the variable dimensionality and extract the latent variables. Then, temporal evolution trends of latent variables are described by multiple polynomials, formulating multi‐trends models. For online monitoring, the sequential nature also provides an easy but effective way to check the operation status of a new sample. Additionally, a trends based updating strategy is proposed to accommodate normal batch‐wise variations to develop a more reliable monitoring system. The application to a typical batch process with uneven‐length and limited batches illustrates the online monitoring performance of the proposed method.

Pseudo Time-Slice Construction Using a Variable Moving Window k Nearest Neighbor Rule for Sequential Uneven Phase Division and Batch Process Monitoring

Multiphase characteristics and uneven-length batch duration have been two critical issues to be addressed for batch process monitoring. To handle these issues, a variable moving window-k nearest neighbor (VMW-kNN) based local modeling, irregular phase division, and monitoring strategy is proposed for uneven batch processes in the present paper. First, a pseudo time-slice is constructed for each sample by searching samples that are closely similar to the concerned sample in which the variable moving window (VMW) strategy is adopted to vary the searching range and the k nearest neighbor (kNN) rule is used to find the similar samples. Second, a novel automatic sequential phase division procedure is proposed by similarity evaluation for local models derived from pseudo time-slices to get different irregular phases and ensure their time sequence. Third, the affiliation of each new sample is real-time judged to determine the proper phase model and fault status can be distinguished from phase shift event. The pr...

Batch Process Monitoring Based on Multiway Global Preserving Kernel Slow Feature Analysis

As an effective nonlinear dynamic data analysis tool, kernel slow feature analysis (KSFA) has achieved great success in continuous process monitoring field during recent years. However, its application to batch process monitoring is unexploited, which is a more challenging task because of the complicated characteristics of batch process data. In this paper, we propose a novel batch process monitoring method based on the modified KSFA method, referred to as multiway global preserving kernel slow feature analysis (MGKSFA), to capture high nonlinearity and inherently time-varying dynamics of process data. In the proposed method, a two-step multiway data unfolding strategy is first utilized to convert the three-way batch process training data set into a two-way matrix. Then, the global structure preserving-based kernel slow feature analysis (GKSFA) is used to build the nonlinear statistical monitoring model, which not only explores the local dynamic data relationships but also considers the mining of global data structure information. Furthermore, a rule based on the cumulative slowness contribution is designed to determine the number of the retained slow features. Last, two monitoring statistics T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and SPE are built to detect the process faults. Two case studies, including one simple numerical nonlinear system and the benchmark fed-batch penicillin fermentation process, are used to demonstrate that the proposed MGKSFA method has the superior fault detection performance over the traditional batch process monitoring methods.

Enhanced monitoring of batch process using just-in-time learning-based kernel independent component analysis

A new method is developed for batch process monitoring in this paper. In the developed method, just-in-time learning (JITL) and kernel independent component analysis (KICA) are integrated to build JITL-KICA monitoring scheme. JITL is employed to tackle with the characteristics of batch process such as inherent time-varying dynamics, multiple operating phases, and especially the case of uneven length stage. According to new coming test data, the most correlated segmentation is obtained from batch-wise unfolded training data by JITL. Then, KICA serves as the principal components extraction approach. Therefore, the non-Gaussian distributed data can also be addressed under this modelling framework. The effectiveness and superiority of JITL-KICA-based monitoring method is demonstrated through benchmark data of DuPont industrial batch polymerisation reactor.

Stability Monitoring of Batch Processes with Iterative Learning Control

In recent years, the iterative learning control (ILC) is widely used in batch processes to improve the quality of the products. Stability is a preoccupation of batch processes when the ILC is applied. Focusing on the stability monitoring of batch processes with ILC, a method based on innerwise matrix with considering the uncertainty of the model and disturbance was proposed. First, the batch process with ILC was derived as a two-dimensional autoregressive and moving average (2D-ARMA) model. Then two kinds of stability indices are constructed based on the innerwise matrix through the identification of the 2D-ARMA. Finally, the statistical process control (SPC) chart was adopted to monitor those stability indices. Numerical results are presented to demonstrate the effectiveness of the proposed method.

Enhanced monitoring of batch process using just-in-time learning-based kernel independent component analysis

A new method is developed for batch process monitoring in this paper. In the developed method, just-in-time learning (JITL) and kernel independent component analysis (KICA) are integrated to build JITL-KICA monitoring scheme. JITL is employed to tackle with the characteristics of batch process such as inherent time-varying dynamics, multiple operating phases, and especially the case of uneven length stage. According to new coming test data, the most correlated segmentation is obtained from batch-wise unfolded training data by JITL. Then, KICA serves as the principal components extraction approach. Therefore, the non-Gaussian distributed data can also be addressed under this modelling framework. The effectiveness and superiority of JITL-KICA-based monitoring method is demonstrated through benchmark data of DuPont industrial batch polymerisation reactor.

Window-Based Stepwise Sequential Phase Partition for Nonlinear Batch Process Monitoring

In this paper, a window-based stepwise sequential phase partition method is proposed to improve monitoring performance for nonlinear batch processes with multiphase operations. The three-dimensional information matrix of batch operation is unfolded and normalized in the batch-wise direction to facilitate establishing the kernel principal component analysis (KPCA) models for phase partition. A moving window is introduced to improve the partition performance, with respect to the process dynamics and time sequence for operation. Consequently, phase partition algorithms are developed for even- and uneven-length batch processes, respectively. Moreover, a traversal algorithm is given to determine the optimal choice of the KPCA parameters and the window size for phase partition. A numerical case and two industrial multiphase processes of injection molding and penicillin fermentation are used to demonstrate the effectiveness and merit of the proposed phase partition method.

A feasibility research on the monitoring of traditional Chinese medicine production process using NIR-based multivariate process trajectories

Traditional Chinese medicine (TCM) products are usually manufactured through batch processes. To improve the batch-to-batch reproducibility, practical approaches for the real-time monitoring of batch evolution need to be developed. In-line near-infrared (NIR) spectroscopy combined with multivariate statistical process control (MSPC) method, as an efficient process analytical technology, is presented for the real-time batch process monitoring. Two representative TCM technical processes, the alkaline precipitation of the compound E-Jiao oral liquid and the liquid preparation process of Tanreqing injection, were taken as examples. The NIR spectra collected in-line was “variable-wise” unfolded into two-dimensional matrix, and multi-way principal component analysis (MPCA) model were developed based on the rearranged data of the normal operation condition (NOC) batches. Three kinds of multivariate control charts (PC scores, Hotelling T2 and DModX) were used to monitor the evolution of test batches with artificial batch variations, including the change of starting material quality attributes and abnormal operation conditions. As illustrated with test batches, the established model can identify NOC or AOC (abnormal operation condition) batches accurately, and detect different kinds of deviations from NOC batches using these control charts. The results indicated that the NIR-based multivariate process trajectories can reflect the batch-to-batch reproducibility effectively, and can also help for the diagnosis of the failure batches in the TCM production.

Phase partition for nonlinear batch process monitoring

A window-based step-wise sequential phase partition method is proposed for monitoring nonlinear batch processes with multiphase operations. The three-dimensional batch data are unfolded in the batch-wise direction to facilitate establishing the kernel principle component analysis (KPCA) models. A moving window is introduced to maintain the kernel parameters unchanged for computation while preserving the time sequence of different phases, thus capable of significantly reducing the storage space of kernel matrices and the computation complexity. A numerical case and a penicillin fermentation process are used to demonstrate the effectiveness and merit of the proposed method.

Sparse Representation Residual Space Analysis and Its Application to Multimode Batch Process Monitoring

In this paper, a novel multimode batch process monitoring scheme called sparse representation residual space analysis (SR-RA) is proposed. The proposed SR-RA method first unfolds the three way batch data into a two way matrix, where each batch is represented as a vector. By utilizing robust sparse representation (SR), the proposed method decomposes the original high dimensional multimode data into three subspaces: the SR primal subspace which preserves all the mode relevant information, the Gaussian residual subspace which is single modal Gaussian distributed, and the outlier residual subspace which is sparsely distributed with only a few nonzero entries. As the fault information is all effectively captured in the two residual subspaces which are mode-irrelevant, fault detection is performed in the two residual subspaces. The proposed method can effectively deal with the multimode problem and it inherits the robustness of SR to large magnitude outliers. The superiority of the proposed SR-RA method is veri...

Assumption free modeling and monitoring of batch processes

Modeling strategies currently in use for the monitoring of batch processes where multivariate data are available have some limitations, particularly for batches where the true starting or end point are not the same on an absolute time scale, or the batch progression varies among batches. In this paper, a method capturing these differences and allowing modeling and monitoring of batches in relative time is proposed. Using scores from principal component analysis (PCA) models as a feature space the new methodology is better able to handle the challenges usually experienced in batch analysis. The feasibility of the relative time approach is demonstrated using data from a chemical synthesis and a pharmaceutical drying process.

An extensive reference dataset for fault detection and identification in batch processes

Close process monitoring (i.e., detection and identification of disturbances) is important to achieve high process efficiency and safety. The Tennessee Eastman process is an extensive benchmark dataset for fault detection and identification, but it is only representative for continuous processes because it does not contain the inherent non-stationarity that complicates monitoring of batch processes. Nevertheless, batch processes also play an important role in many types of industry. This paper therefore presents an extensive reference dataset for benchmarking data-driven methodologies for fault detection and identification in batch processes.The original Pensim model [10] is expanded with sensor noise. By changing the properties of the initial conditions and/or model parameters, four subsets of different complexity are generated, each containing 400 batches with normal operation. To correctly assess the fault detection and identification in batch processes, 15 faults are simulated with various amplitudes and onset times for a total of 22,200 faulty batches for each subset, or 90,400 batches in total.Analysis of the data indicates that the presented types of process faults and their various amplitudes in each of the four subsets present a suitable benchmark for fault detection and identification in batch processes. The dataset is freely available at http://cit.kuleuven.be/biotec/batchbenchmark.

Multivariate quality control of batch processes using STATIS

Industrial batch processes are commonly used in the production of a variety of items. Data emerging from such processes present a peculiar structure, and a number of customized multivariate control charts (CCs) have been proposed for their monitoring. In this paper, we propose CCs based on STATIS method, an exploratory technique for measuring similarities between data matrices. Data are arranged in such a way that the monitoring along time is prioritized. The methodology easily allows a nonparametric online monitoring of complex batch processes in time, in situations where a large number of variables are present. Besides its presentation, the new approach is illustrated using simulated data.

Sequence/batch monitoring and root cause analysis

Batch processes are commonly used in industry to produce semiconductor devices, drugs, polymers, speciality chemicals, or other high quality products. Large amounts of process data are collected during batch operations and stored in process historians. Today, this valuable resource is not used systematically because of the lack of dedicated tools and methods to extract reliable information from it. Detecting unintended deviations from normal operation or identifying the root cause of abnormal behaviour becomes difficult with the ever increasing amount and complexity of stored data. To overcome this challenge, this paper proposes a multi-level workflow based on a combination of standard monitoring techniques that enables a hierarchical approach to batch process monitoring. The batch level analysis is able to automatically detect an abnormal batch within a collection of recorded batch datasets. The time level analysis makes it possible to detect the time of occurrence of the batch abnormality and isolate the process variables that significantly contribute to the detected process or operation abnormality. A case study for a fluidized-bed granulation process shows that the proposed methodology leads to robust results in challenging environments.

Phase division and process monitoring for multiphase batch processes with transitions

In this paper, a new repeatability factor is introduced to achieve phase division for multiphase batch processes. Then a two-step feature vector selection based kernel variable correlation analysis (TSFVS-KVCA) method is proposed for batch processes with transitions monitoring. The TSFVS-KVCA method not only considers the within-phase nonlinear variable correlation but also between-phase one by extracting the common bases and the specific bases between two neighboring phases. The TSFVS method first selects feature vectors from each steady phase as within-phase subsets. Then between-phase subsets are selected from the within-phase subsets of two neighboring phases. These selected feature vectors have well capacity of description on original data so that they can substitute for original data in a feature space F. Thus the TSFVS method reduces the computational complexity and the instability of high-dimensional kernel in subsequent KVCA method. Moreover, each within-phase subset can be used as sub-bases in a feature space F, which simplify the objective function of KVCA method. In this way, the common bases can be extracted in an easier way. Based on the common bases, two neighboring steady phases can be separated into the common subspace and the specific subspace, in which nonlinear process monitoring method is carried out. Furthermore, an online monitoring method for transitions is proposed based on a just-in-time model. The model can be described by the common bases of two neighboring phases and specific bases of the dominant phase at current time interval. The dominant phase can be dynamically determined according to the correlation between current transition sample and neighboring phases. The results of simulation demonstrate effectiveness and superiority of the proposed method.

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.

Multivariate Trajectory-Based Local Monitoring Method for Multiphase Batch Processes

This paper proposes a new method combining the multivariate trajectory analysis and the principal component analysis (PCA) for multiphase batch process monitoring. To handle the uneven length problem, the trajectories of process variables are calculated instead of the original samples. For online monitoring, similar trajectories are extracted by just-in-time learning (JITL) with historical trajectories and the PCA model is constructed, which can deal with the missing data problem as well. Furthermore, to acquire a more reliable monitoring performance, a new distance-based measurement is proposed to show the location of samples. For performance evaluation, case studies of a numerical example and a simulated penicillin fermentation process are provided, with detailed comparisons to traditional methods.

SPC based on growth models for monitoring the process of hydrogenation of edible oil

On-line monitoring of an industrial batch process of hydrogenation of edible oil involves repeated determination of the melting point of a batch at certain intervals. The objective of this study is to use these measurements to develop an SPC procedure for detecting process shifts like abnormal growth in melting point and occurrence of dead batches. Two model-free and a model based approach are proposed for this purpose. The growth data is of the form (MPij, tij), where MPij is the melting point at time ti for the jth batch. A linear approximation of the monomolecular growth model is used for developing the model based procedure. It is shown that the proposed model based charts can detect the out-of-control situations of active batches as well as the occurrence of dead batches efficiently. The effects of a few important process parameters on the parameters of the growth model are also discussed.

The RAYMOND simulation package — Generating RAYpresentative MONitoring Data to design advanced process monitoring and control algorithms

This work presents the RAYMOND simulation package for generating RAYpresentative MONitoring Data. RAYMOND is a free MATLAB package and can simulate a wide range of processes; a number of widely-used benchmark processes are available, but user-defined processes can easily be added. Its modular design results in large flexibility with respect to the simulated processes: input fluctuations resulting from upstream variability can be introduced, sensor properties (measurement noise, resolution, range, etc.) can be freely specified, and various (custom) control strategies can be implemented. Furthermore, process variability (biological variability or non-ideal behavior) can be included, as can process-specific disturbances.In two case studies, the importance of including non-ideal behavior for monitoring and control of batch processes is illustrated. Hence, it should be included in benchmarks to better assess the performance and robustness of advanced process monitoring and control algorithms.