Multiway Kernel Research Articles

Fault diagnosis of microbial pharmaceutical fermentation process with non-Gaussian and nonlinear coexistence

A large Proportion of batch processes commonly have traits of non-Gaussian and nonlinear. In this work, Multiway Kernel Entropy Independent Component Analysis (MKEICA) algorithm was developed to formulate more accurate model for process monitoring so as to enhance the monitoring performance. The original process data with three-dimension were first expanded into two-dimensional data matrix by using AT variable expansion method. The Kernel Entropy Component Analysis (KECA) was then employed to preprocess the data in order to reduce data redundancy. Such approach can also retain the information of cluster structure and maximize the essential characteristics of data. After that, a monitoring model of MKEICA was established for production process monitoring. Once a fault is detected, a nonlinear contribution plots method would be utilized to diagnose the fault variables. Consequently, to illustrate the superiority and feasibility, the proposed method was conducted on the penicillin simulation platform and the actual pharmaceutical production process.

Rolling bearing diagnosis method based on WMKPCA-LSTM network

The monitoring data from large machinery have characteristics of high dimensions, non-linearity and correlation. In the traditional fault diagnosis, it is hard to extract features and complex to build the model. In order to solve these problems, the rolling bearing diagnosis method based on a weighted mixed kernel principal component analysis (WMKPCA) and long-short-term memory (LSTM) network is proposed. The method uses WMKPCA algorithm to reduce the dimensionality of the vibration signal. The method not only effectively reduces the correlation of the original data, but also improve the diagnostic accuracy; The LSTM neural network has a memory function that can be used to extract temporal features. Experimental results show that the proposed algorithm has higher diagnostic accuracy and higher efficiency than traditional methods of principal component analysis (PCA), kernel principal component analysis (KPCA) and multiway kernel principal component analysis (MKPCA).

A novel MDFA-MKECA method with application to industrial batch process monitoring

For the complex batch process with characteristics of unequal batch data length, a novel data-driven batch process monitoring method is proposed based on mixed data features analysis and multi-way kernel entropy component analysis &#x0028 MDFA-MKECA &#x0029 in this paper. Combining the mechanistic knowledge, different mixed data features of each batch including statistical and thermodynamics entropy features, are extracted to finish data pre-processing. After that, MKECA is applied to reduce data dimensionality and finally establish a monitoring model. The proposed method is applied to a reheating furnace industry process, and the experimental results demonstrate that the MDFA-MKECA method can reduce the calculated amount and effectively provide on-line monitoring of the batch process.

Online monitoring method for multiple operating batch processes based on local collection standardization and multi‐model dynamic PCA

AbstractTo handle multiple operations and non‐Gaussian problems which widely exist in complex industry processes, a new online monitoring method for multi‐operation batch processes is proposed by combing local collection standardization and multi‐model dynamic principal component analysis (LCS‐MMDPCA). Since a series of operations are often manually manipulated by operators, in general, the statistics of each batch data do not follow Gaussian distribution, which results in a failure for the construction of a multivariate statistical model. To target multiple operations and non‐Gaussian problems, we first split the complex batch processes into a sequence of stages. Subsequently, the data in each stage are clustered according to the operations. Then, we exploit the Local Collection Standardization (LCS) method to make the data belonging to the same cluster obey Gaussian distribution. At last, we adopt MMDPCA to model the complex industry processes with multiple operations and non‐Gaussian features. Experimental results on fault detection in ladle furnace steelmaking process showed the advantages of the proposed method in comparison to multiway kernel principal component analysis (MKPCA) and multiway dynamic principal component analysis (MDPCA).

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.

On - line Fault Detection and Diagnosis of Sequencing Batch Reactor Using MKICA

Considering the data of Sequencing Batch Reactor (SBR) having the characteristics of non-Gaussian distribution and highly nonlinearity, this research applies Multi-way Kernel Independent Component Analysis (MKICA) to the on-line process monitoring of SBR. Meanwhile, a novel contribution analysis scheme named bar plot is developed for MKICA to diagnose faults. Above all, the three-dimensional data of SBR is expanded into two-dimensional by a new data expanding method; then, Kernel Principal Component Analysis (KPCA) is utilized to map the two-dimensional data into a high dimensional feature space, and make use of Independent Component Analysis (ICA) to extract Independent Components (ICs) in feature space; finally, if MKICA detects a fault occurs during on-line monitoring stage, the bar plot is used to identify the variables causing the fault. The method is successfully applied to an 80L lab-scale SBR. The experimental results demonstrate that, compared with traditional MICA, the proposed method exhibit better performance in fault detection and diagnose.

Fault Diagnosis Model of Beer Fermentation Process Based on Multiway Kernel Principal Component Analysis

Aiming at the limitation of the application of principal component analysis model for fault diagnosis in nonlinear time-varying process, kernel transformation theory is introduced into the data feature extraction of nonlinear space, on the basis of the periodic characteristics of the batch process, putting forward a kind of improved multi-way kernel principal component analysis fault diagnosis model, which effectively solves the nonlinear problem of process data and ensures integrity of data and information extraction. By comparing with other methods in experiment, the results show that the proposed method has good real-timing and accuracy to slow time-varying of batch process.

Quality relevant nonlinear batch process performance monitoring using a kernel based multiway non-Gaussian latent subspace projection approach

Multiway kernel partial least squares method (MKPLS) has recently been developed for monitoring the operational performance of nonlinear batch or semi-batch processes. It has strong capability to handle batch trajectories and nonlinear process dynamics, which cannot be effectively dealt with by traditional multiway partial least squares (MPLS) technique. However, MKPLS method may not be effective in capturing significant non-Gaussian features of batch processes because only the second-order statistics instead of higher-order statistics are taken into account in the underlying model. On the other hand, multiway kernel independent component analysis (MKICA) has been proposed for nonlinear batch process monitoring and fault detection. Different from MKPLS, MKICA can extract not only nonlinear but also non-Gaussian features through maximizing the higher-order statistic of negentropy instead of second-order statistic of covariance within the high-dimensional kernel space. Nevertheless, MKICA based process monitoring approaches may not be well suited in many batch processes because only process measurement variables are utilized while quality variables are not considered in the multivariate models. In this paper, a novel multiway kernel based quality relevant non-Gaussian latent subspace projection (MKQNGLSP) approach is proposed in order to monitor the operational performance of batch processes with nonlinear and non-Gaussian dynamics by combining measurement and quality variables. First, both process measurement and quality variables are projected onto high-dimensional nonlinear kernel feature spaces, respectively. Then, the multidimensional latent directions within kernel feature subspaces corresponding to measurement and quality variables are concurrently searched for so that the maximized mutual information between the measurement and quality spaces is obtained. The I2 and SPE monitoring indices within the extracted latent subspaces are further defined to capture batch process faults resulting in abnormal product quality. The proposed MKQNGLSP method is applied to a fed-batch penicillin fermentation process and the operational performance monitoring results demonstrate the superiority of the developed method as apposed to the MKPLS based process monitoring approach.

Nonlinear and Non-Gaussian Dynamic Batch Process Monitoring Using a New Multiway Kernel Independent Component Analysis and Multidimensional Mutual Information Based Dissimilarity Approach

Batch or semibatch process monitoring is a challenging task because of various factors such as strong nonlinearity, inherent time-varying dynamics, batch-to-batch variations, and multiple operating phases. In this article, a novel nonlinear and non-Gaussian dissimilarity method based on multiway kernel independent component analysis (MKICA) and multidimensional mutual information (MMI) is developed and applied to batch process monitoring and abnormal event detection. MKICA models are first built on the normal benchmark and monitored batches to characterize the nonlinear and non-Gaussian variable relationship of batch processes. Then, the kernel independent component (IC) subspaces are extracted from the benchmark and monitored batches. Further, a multidimensional mutual information based dissimilarity index is defined to quantitatively evaluate the statistical dependence between the benchmark and monitored subspaces through the moving-window strategy. With the corresponding control limit estimated from th...

A Multiway Gaussian Mixture Model based Adaptive Kernel Partial Least Squares Regression Approach for Inferential Quality Predictions of Batch Processes

Soft sensor technique has become increasingly important to provide reliable on-line measurements, facilitate advanced process control and improve product quality in process industries. The conventional soft sensors are normally single-model based and thus may not be appropriate for processes with shifting operating conditions or phases. In this study, a multiway Gaussian mixture model (MGMM) based kernel partial least squares (PLS) method is proposed to handle multiple operating phases in batch or semibatch processes. The measurement data are first projected onto high-dimensional kernel feature space to account for the process nonlinearity. Then the multiway Gaussian mixture model is estimated with multiple Gaussian clusters in the kernel space. Thus various localized PLS models can be built within each Gaussian cluster to characterize the dynamics in the particular operating phase. Using Bayesian inference strategy, the soft sensor models for all the test samples are adaptively selected from the multiple localized kernel PLS models representing different phases and further used for online quality predictions. The presented soft sensor method is applied to the multiphase penicillin fermentation process and the computational results demonstrate that its performance is superior to the conventional multiway kernel PLS model.

Nonlinear Bioprocess Monitoring Using Multiway Kernel Localized Fisher Discriminant Analysis

A novel batch bioprocess monitoring approach based on multiway kernel localized Fisher discriminant analysis (MKLFDA) is proposed in this article. For the routine bioprocess operation with some abnormal events, a supervised monitoring method is needed to handle the training data set that includes various types of faulty samples. Because of the inherent process nonlinearity and multimodality among normal and faulty clusters, the traditional multiway Fisher discriminant analysis (MFDA) method becomes inappropriate and unable to effectively detect or classify faulty samples. The newly developed MKLFDA approach, however, combines kernel function with the localized Fisher discriminant analysis so that the “kernel” feature can retain the process nonlinearity while the “localized” characteristic is able to extract the multi-Gaussianity within data clusters. Furthermore, the integrated multiway analysis uses batch-wise unfolding to convert the three-dimensional data set into a two-dimensional matrix that can be f...

Nonlinear Batch Process Monitoring Using Phase-Based Kernel-Independent Component Analysis−Principal Component Analysis (KICA−PCA)

In this article, the statistical modeling and online monitoring of nonlinear batch processes are addressed on the basis of the kernel technique. First, the article analyzes the conventional multiway kernel algorithms, which were just simple and conservative kernel extensions of the original multiway linear methods and thus inherited their drawbacks. Then, an improved nonlinear batch monitoring method is developed. This method captures the changes of the underlying nonlinear characteristics and accordingly divides the whole batch duration into different phases. Then, focusing on each subphase, both nonlinear Gaussian and non-Gaussian features are explored by a two-step modeling strategy usingkernel-independent component analysis−principal component analysis (KICA−PCA). Process monitoring and fault detection can be readily carried out online without requiring the estimation of future process data. Meanwhile, the dynamics of the data are preserved by exploring time-varying covariance structures. The idea and performance of the proposed method are illustrated using a real three-tank process and a benchmark simulation of fed-batch penicillin fermentation production.

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.

Fault Detection of Nonlinear Processes Using Multiway Kernel Independent Component Analysis

In this paper, a new nonlinear process monitoring method that is based on multiway kernel independent component analysis (MKICA) is developed. Its basic idea is to use MKICA to extract some dominant independent components that capture nonlinearity from normal operating process data and to combine them with statistical process monitoring techniques. The proposed method is applied to the fault detection in a fermentation process and is compared with modified independent component analysis (MICA). Applications of the proposed approach indicate that MKICA effectively captures the nonlinear relationship in the process variables and show superior fault detectability, compared to MICA.

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.