Fault Detection Of Batch Processes Research Articles

Efficient batch process monitoring based on random nonlinear feature analysis

AbstractEfficient batch process monitoring is a challenging task because of the large data scale, the strong process nonlinearity, and the complicated local behaviours. To handle this issue, this paper presents a random nonlinear feature analysis method, called two‐level localized ensemble random Fourier feature analysis (TLERFFA), for effective batch process fault detection. Considering the large data scale of the nonlinear batch process, the random Fourier feature analysis (RFFA) is introduced to develop the statistical model, which is more efficient than the traditional kernel modelling method in terms of computation loads. Furthermore, for overcoming the model uncertainty resulting from the random mapping weights, the ensemble learning based on Bayesian inference is used to integrate multiply RFFA models with different weight settings. To further mine the rich local information of batch process data, a two‐level localization strategy is designed from the perspectives of the variables and the statistics. At the first level, the monitored variables are divided into several sub‐groups according to their maximal information coefficients, while at the second level, the local monitoring statistics are constructed based on the temporal–spatial neighbour analysis. Lastly, one case study on the benchmark process is given to demonstrate the effectiveness of the proposed methods.

Deep Convolutional Feature-Based Probabilistic SVDD Method for Monitoring Incipient Faults of Batch Process

Support vector data description (SVDD) has been widely applied to batch process fault detection. However, it often performs poorly, especially when incipient faults occur, because it only considers the shallow data feature and omits the probabilistic information of features. In order to provide better monitoring performance on incipient faults in batch processes, an improved SVDD method, called deep probabilistic SVDD (DPSVDD), is proposed in this work by integrating the convolutional autoencoder and the probability-related monitoring indices. For mining the hidden data features effectively, a deep convolutional features extraction network is designed by a convolutional autoencoder, where the encoder outputs and the reconstruction errors are used as the monitor features. Furthermore, the probability distribution changes of these features are evaluated by the Kullback-Leibler (KL) divergence so that the probability-related monitoring indices are developed for indicating the process status. The applications to the benchmark penicillin fermentation process demonstrate that the proposed method has a better monitoring performance on the incipient faults in comparison to the traditional SVDD methods.

A sequential resampling approach for imbalanced batch process fault detection in semiconductor manufacturing

Fault detection is one of the most important research topics to guarantee safe operation and product quality consistency especially in the batch process of semiconductor manufacturing. However, the imbalanced fault data bring great challenges to extract the high nonlinearity and inherently time-varying dynamics of the batch process. Motivated by these, we propose a sequential oversampling discrimination approach for imbalanced batch process fault detection. Especially, different from the traditional oversampling methods, which extract temporal features from the whole process, we transform a whole batch sequence into multiple fixed-length sequences each batch by a sliding window, to extract the robust time-varying dynamics features. Then, an oversampling neural network is performed to balance both sequences of minority and majority classes. The needed sequences of the minority class are generated by an improved combination model of variational auto-encoder and generative adversarial network. Finally, a simplified sequential neural network is learned by the balanced-class sequences to perform the discrimination. We conduct extensive experiments based on two datasets of semiconductor manufacturing. One is a benchmark dataset and the other is a dataset from a real production line. The results achieved significant improvement, compared with other state-of-art fault detection methods and oversampling techniques.

Dynamic nonlinear batch process fault detection and identification based on two‐directional dynamic kernel slow feature analysis

AbstractThe batch process generally covers high nonlinearity and two‐directional dynamics: time‐wise dynamics, which correspond to inherently time‐varying dynamics resulting from the slowly varying underlying driving forces within each batch duration; and batch‐wise dynamics, which are associated with different operating modes among different batches. However, most existing dynamic nonlinear monitoring methods cannot extract the slowly varying underlying driving forces of the nonlinear batch process and rarely tackle the batch‐wise dynamic characteristics among batch runs. In order to address these issues, a new monitoring scheme based on two‐directional dynamic kernel slow feature analysis (TDKSFA) is developed by combining kernel SFA with a global modelling strategy. In the TDKSFA method, kernel SFA is integrated with the ARMAX time series model to mine the nonlinear and time‐wise dynamic properties within a batch run due to its capability of extracting the slowly varying underlying driving forces. Furthermore, the global modelling strategy is presented to handle the batch‐wise dynamics among batches by calculating the total average kernel matrix of all training batches. After the slow features are extracted, Hotelling's T2 and SPE statistics are built to detect faults. To solve the issue of fault variable nonlinear identification, a novel nonlinear contribution plot inspired by the pseudo‐sample variable projection trajectories in the TDKSFA model is further proposed to identify fault variables. Finally, the feasibility and effectiveness of the TDKSFA‐based fault diagnosis strategy is demonstrated through a numerical system and the penicillin fermentation process.

Nonlinear fault detection for batch processes via improved chordal kernel tensor locality preserving projections

The quality and stability of products are seriously influenced by the process conditions. A large number of modern production processes can be considered as batch processes, with nonlinear relationships between the process variables. How to troubleshoot batch processes has attracted considerable attention in the literature. The research object of batch processes is expressed as the third-order tensor data of batch × variable × time. The traditional methods convert the tensors into second-order forms through matrix expansion. A novel method named improved chordal kernel tensor locality preserving projections (ICK-TLPP) is proposed for fault detection of batch processes. First, the chordal distance is introduced as a measurement of the similarity of matrix, and an improved method is proposed for describing the variation of time series data. Then, the chordal kernel function is introduced to preserve the spatial structure of the tensor data without the information loss caused by vectorization, and describe the nonlinear correlation during the multivariate control system. Next, the locality preserving projections algorithm is applied to detect the intrinsic manifold structure. Parallel analysis is applied to optimize the hyper-parameters in the model. Finally, Granger causality analysis is performed to locate the root cause of the process fault. The proposed method is validated on two datasets, penicillin fermentation process and the hot strip rolling process. The best results of false alarm rate and fault detection rate are 16% and 94% respectively. The proposed method performs better compared with the traditional algorithms.

Batch process fault detection for multi-stage broad learning system

In the real industrial production process, some minor faults are difficult to be detected by multivariate statistical analysis methods with mean and variance as detection indicators due to the aging equipment and catalyst deactivation. With structural characteristics, deep neural networks can better extract data features to detect such faults. However, most deep learning models contain a large number of connection parameters between layers, which causes the training time-consuming and thus makes it difficult to achieve a fast-online response. The Broad Learning System (BLS) network structure is expanded without a retraining process and thus saves a lot of training time. Considering that different stages of the batch production process have different production characteristics, we use the Affinity Propagation (AP) algorithm to separate the different stages of the production process. This paper conducts research on a multi-stage process monitoring framework that integrates AP and the BLS. Compared with other monitoring models, the monitoring results in the penicillin fermentation process have verified the superiority of the AP-BLS model.

Nonlinear Fault Detection of Batch Processes Using Functional Local Kernel Principal Component Analysis

In order to guarantee and improve the product quality, the data-driven fault detection technique has been widely used in industry. For three-way datasets of batch process in industry process (i.e., batch × variable × time), a novel method named functional local kernel principal component analysis (FLKPCA) is proposed. Since the variables' trajectories often show functional nature and can be considered as smooth functions rather than just vectors. Firstly, the variables' trajectory is expressed as the combination of smooth basis functions using functional data analysis (FDA), which means that the datasets of batches process would be transformed from the three-ways array into two-ways function matrix. Then, kernel locality preserving projections (LKPCA) is used to perform dimensionality reduction on two-way function matrix directly. Different from kernel principal component analysis (KPCA). LKPCA aims at preserving the both local and global structure of the data in a new optimization objective. Consequently, FLKPCA could more effectively seek the potential information that hidden in the three-ways datasets. Lastly, the effectiveness of the proposed approach is illustrated by the benchmark of fed-batch penicillin fermentation process and the hot strip rolling process.

Incipient Fault Detection for Multiphase Batch Processes With Limited Batches

Sufficient batches are in general, required for fault detection of batch processes. However, sometimes, it is difficult and may be impractical to conduct multiple cycles and wait until enough batches are available. Without batch-wise normalization step, the nonstationary cannot be efficiently removed by time-wise normalization. The mean values of the nonstationary variables are still time varying and the interval of fault-free data is very wide in each phase. Therefore, the incipient fault, which has a small magnitude including early changing and the slow developing, may be buried by nonstationary trends resulting in low fault detection rate. To address the above issue, a two-layer fault detection method is proposed to detect the incipient fault for multiphase batch processes with limited batches. First, a concurrent variable separation strategy is proposed to distinguish nonstationary variables from stationary variables for multiple batches in each phase. Second, a two-layer fault detection model is constructed to detect the incipient fault. Cointegration analysis-based fault detection model is built to investigate the relationship between nonstationary variables, which can effectively distinguish the incipient fault from the normal trend of the nonstationary variables. Principal component analysis is adopted to describe the correlation of stationary variables. Afterward, a total fault detection model is constructed to monitor the relation between nonstationary variables and stationary variables. To illustrate the feasibility and effectiveness, the proposed algorithm is applied to two multiphase batch processes including fed-batch penicillin fermentation process and semiconductor etch process.

Nonlinear fault detection of batch processes based on functional kernel locality preserving projections

Data-driven fault detection technique has exhibited its wide applications in industrial process monitoring. The batch dataset is often organized as a special three-way array (i.e., batch × variable × time), and the research of data-based batch process monitoring has attracted considerable attention in the literature. A novel method named functional kernel locality preserving projections (FKLPP) is proposed for batch process monitoring. Since the variables' trajectories often show functional nature and can be considered as smooth functions rather than just vectors, then the three-way data can be transformed into a two-way function matrix. Firstly, the variables’ trajectories are expressed by using the functional data analysis (FDA). By doing so, the original batch process data can be transformed into a two-way manner (batches × functions of the variable trajectories) by describing each variable trajectory as a function of time. Then, kernel locality preserving projections is used to perform dimensionality reduction on two-way function matrix directly. Different from principal component analysis (PCA) which aims at preserving the global Euclidean structure of the data, the FKLPP aims to preserve the local neighborhood information and to detect the intrinsic manifold structure of the data. The kernel trick is applied to the construction of nonlinear kernel model. Consequently, FKLPP may be useful to seek more meaningful intrinsic information hidden in the observations. Lastly, the effectiveness and potentials of the FKLPP-based monitoring approach are illustrated by a benchmark fed-batch penicillin fermentation process and the hot strip rolling process.

Batch process fault detection and identification based on discriminant global preserving kernel slow feature analysis

As an attractive nonlinear dynamic data analysis tool, global preserving kernel slow feature analysis (GKSFA) has achieved great success in extracting the high nonlinearity and inherently time-varying dynamics of batch process. However, GKSFA is an unsupervised feature extraction method and lacks the ability to utilize batch process class label information, which may not offer the most effective means for dealing with batch process monitoring. To overcome this problem, we propose a novel batch process monitoring method based on the modified GKSFA, referred to as discriminant global preserving kernel slow feature analysis (DGKSFA), by closely integrating discriminant analysis and GKSFA. The proposed DGKSFA method can extract discriminant feature of batch process as well as preserve global and local geometrical structure information of observed data. For the purpose of fault detection, a monitoring statistic is constructed based on the distance between the optimal kernel feature vectors of test data and normal data. To tackle the challenging issue of nonlinear fault variable identification, a new nonlinear contribution plot method is also developed to help identifying the fault variable after a fault is detected, which is derived from the idea of variable pseudo-sample trajectory projection in DGKSFA nonlinear biplot. Simulation results conducted on a numerical nonlinear dynamic system and the benchmark fed-batch penicillin fermentation process demonstrate that the proposed process monitoring and fault diagnosis approach can effectively detect fault and distinguish fault variables from normal variables.

Order-Information-Based Phase Partition and Fault Detection for Batch Processes

Batch processes have significantly different properties across different phases. It is essential to divide batch processes reasonably and model corresponding phases correctly for fault detection. Order information is critical for phase partition. Different from traditional phase partition methods, which customarily adopt the results of PCA for advanced research, a novel method called Markov-chain-based spectral partition (MCSP) is proposed in this paper, which takes the sequence (order) information into consideration for phase partition. Due to the combination of neighborhood information and order information, MCSP can separate each batch into major phases automatically. The time-varying characteristics remain relatively stable in each phase, which is suitable for following a Gaussian-mixture-model-based fault detection model to reflect the phase properties. Due to its simple and intuitive format, our proposed method has superior performance in fault detection. The effectiveness of MCSP is illustrated in ...

Time Sequential Phase Partition and Modeling Method for Fault Detection of Batch Processes

Different operation phases in batch processes cover distinguishing behaviors, so establishing statistical models for each identical phase become an effective way for batch monitoring. In this paper, a new adaptive phase partition and online fault detection method is proposed, which can track the phase’s transition by time sequence and has less reliance on parameters’ selection. The discussion and analysis of this proposed method follows. In this proposed method, the information contained in every sample time will be evaluated, and the change tendency of feature is demonstrated on a batch prospect. Then, two control bounds are designed for the feature tendency, the stable, and the transitional phases that have a different feature level and play certainly roles in process operation, will be identified automatically. For online monitoring, the new fault detection strategy is composed of modeling the PCA and PLS statistical methods for each identified phase, three statistics are established to ensure the data-decomposing reliable. The proposed method is applied to the industrial penicillin fermentation process, and the experimental result shows better performance in phase partition and fault detection.

Feature extraction for batch process monitoring and fault detection via simultaneous data scaling and training of tensor based models

This contribution presents a novel framework for process monitoring and fault detection of batch processes. The batch platform is key for the full scale production of specialty chemicals, active pharmaceutical ingredients, biochemical products and other high added value products, where flexibility is required due to the relatively limited life span of the products and/or the diversity on big product portfolios of relatively small scale. Traditional approaches for fault identification in batch processes require unfolding the third order structure of the data (variables × time × batches). In this contribution a tensor based approach is considered because it applies a more comprehensive multilinear analysis of the data. The novel approach allows to impose independence relations through knowledge based structural sparsity constraints on the tensor decomposition. Additionally, a novel methodology is presented for simultaneous data scaling and model training. This allows finding the optimal data scale to exploit the variability present in all directions (i.e., from every variable). The combination of the two proposed methods results in an improved framework to extract interpretable features from the data. The application of the proposed novel framework to the dynamic simulation of the fed-batch penicillin production (Pensim) allows to evaluate its advantages over traditional methods for multivariate statistical process monitoring (MSPM). Some identified advantages of the novel framework are a better distribution on the approximation of the data with lower noise propagation and bias, as well as a higher interpretability of the extracted features and the fault detection. This results in an enhanced capability for monitoring batch processes and fault detection.

Discriminant diffusion maps based k‐nearest‐neighbour for batch process fault detection

In this paper, a novel discriminant diffusion maps based k‐nearest‐neighbour rule (DDM‐kNN) is developed for the high‐dimensional data of batch process and nonlinear characteristics of the data, and the traditional multivariate statistical process control and monitoring methods is less effective. Firstly, a discriminant kernel parameter is applied to the framework of the diffusion maps, and the Gaussian kernel width is selected from the within‐class width and the between‐class width according to discriminating sample class labels, which can make kernel function effectively extract data correlation features and exactly describe the structure characteristics of data original space in the low‐dimensional feature. Subsequently, the adapted kNN rule is applied to the low‐dimensional manifold feature space for fault detection. The effectiveness of DDM for the performance of data dimension reduction and feature extraction is verified in 3 arm spiral test data experiments compared with other dimensionality reduction methods, and successfully shows the high‐dimensional data in the low‐dimensional space and optimally preserves the original intrinsic nonlinear structure of the dataset. In addition, DDM‐kNN is applied to penicillin fermentation process monitoring and fault detection, and results also verify the effectiveness of the proposed method by integrating discriminant diffusion maps with k‐nearest‐neighbour rule.

Quality-Relevant Batch Process Fault Detection Using a Multiway Multi-Subspace CVA Method

For batch process fault detection, regular data-driven methods cannot distinguish quality-irrelevant faults from quality-relevant faults. To solve such problem, we propose a multiway multi-subspace canonical variate analysis (MMCVA) method for the batch processes. First, the combination of batch-wise unfolding and variable-wise unfolding is adopted to unfold the three-way process and quality data in to two-way data. Then, we use CVA to project the process and quality data spaces to three subspaces, a process-quality correlated subspace, a quality-uncorrelated process subspace, and a process-uncorrelated quality subspace. Fault detection statistics are developed based on the three subspaces. The proposed MMCVA method is capable of indicating the normality or abnormality of the quality variables, while detecting a process fault. The simulation results of a fed-batch penicillin fermentation process illustrate the effectiveness of the proposed method.

Fault detection of batch processes based on multivariate functional kernel principal component analysis

In some batch processes, the variables' trajectories often show obviously functional nature and can be considered as smooth functions rather than just vectors, then the collected three-way data array essentially can be transformed into a two-way function matrix. For this purpose, the approach of functional data analysis (FDA) is introduced to express the variables' functions in this article, which can highlight the subtle differences in the shape of variables' trajectories between normal batches and faulty ones, and can also easily handle the problems of irregular three-way data array, such as unequal batch length, different sampling rates, missing data, etc. Based on the function matrix, a novel monitoring method called multivariate functional kernel principal component analysis (MFKPCA) is proposed for fault detection of batch processes, which directly eigen-decomposes the two-way function matrix in the function space and uses the kernel trick to handle the nonlinear correlations. Different from the traditional PCA method, MFKPCA designs three complementary control charts for batch process monitoring based on three statistics including Hotelling's T2, squared prediction error (SPE) and mean squared error (MSE). Finally, some simulations and an industrial semiconductor etch process are used to illustrate the validity of the proposed monitoring method.

Fault Detection for Batch Processes Based on Segmentation MPCA

Aiming at the dynamic characteristic of batch production process changes fast and the accurate modeling of it is difficult, so this paper proposes an intermittent fault detection method of the principal component analysis based on process segment. According to the different dynamic characteristics of process data, the process is divided into multiple stages, with the method of piecewise linear approximation of nonlinear modeling to model different stages of the process, in order to make up the deficiency of traditional MPCA fault diagnosis methods. Through the fault detection of the beer fermentation process experiments to verify that the method can detect process faults promptly and improve the speed and accuracy of process monitoring.

Fault detection of batch processes using multiway kernel principal component analysis

Batch processes are very important in most industries and are used to produce high-quality materials, which causes their monitoring and control to emerge as essential techniques. Several multivariate statistical analyses, including multiway principal component analysis (MPCA), have been developed for the monitoring and fault detection of batch process. In this paper, a new batch monitoring method using multiway kernel principal component analysis (MKPCA) is proposed. Three-way batch data of normal batch process are unfolded batch-wise, and then KPCA is used to capture the nonlinear characteristics within normal batch processes. The proposed monitoring method was applied to fault detection in the simulation benchmark of fed-batch penicillin production. In both off-line analysis and on-line batch monitoring, the proposed approach can effectively capture the nonlinear relationships among process variables. In on-line monitoring, MKPCA can detect significant deviation which may cause a lower quality of final products. MPCA, however, has a limit to detect faults.

Fault detection of batch processes using multiway kernel principal component analysis

Batch processes are very important in most industries and are used to produce high-quality materials, which causes their monitoring and control to emerge as essential techniques. Several multivariate statistical analyses, including multiway principal component analysis (MPCA), have been developed for the monitoring and fault detection of batch process. In this paper, a new batch monitoring method using multiway kernel principal component analysis (MKPCA) is proposed. Three-way batch data of normal batch process are unfolded batch-wise, and then KPCA is used to capture the nonlinear characteristics within normal batch processes. The proposed monitoring method was applied to fault detection in the simulation benchmark of fed-batch penicillin production. In both off-line analysis and on-line batch monitoring, the proposed approach can effectively capture the nonlinear relationships among process variables. In on-line monitoring, MKPCA can detect significant deviation which may cause a lower quality of final products. MPCA, however, has a limit to detect faults.

On-line Batch Process Monitoring Using Different Unfolding Method and Independent Component Analysis.

In many industries, the effective monitoring and control of batch processes is crucial to the production of high-quality materials. Several techniques using multivariate statistical analysis have been developed for monitoring and fault detection of batch processes. Multiway principal component analysis (MPCA) has shown a powerful monitoring performance in many industrial batch processes. However, it has shortcomings that all batch lengths should be equalized and future values of batches should be estimated for on-line monitoring. In order to overcome these drawbacks and obtain better monitoring performance, we propose a new statistical method for on-line batch process monitoring that uses different unfolding method and independent component analysis (ICA). If the measured data set contains non-Gaussian latent variables, the ICA solution can extract the original source signal to a much greater extent than the PCA solution since ICA involves higher-order statistics and is not based on the assumption that the latent variables follow a multivariate Gaussian distribution. The proposed monitoring method was applied to fault detection and identification in the simulation benchmark of the fed-batch penicillin production, which is characterized by some fault sources with non-Gaussian characteristics. The simulation results clearly show the power and advantages of the proposed method in comparison to MPCA.