Mixture semisupervised principal component regression model and soft sensor application

Traditionally, data‐based soft sensors are constructed upon the labeled historical dataset which contains equal numbers of input and output data samples. While it is easy to obtain input variables such as temperature, pressure, and flow rate in the chemical process, the output variables, which correspond to quality/key property variables, are much more difficult to obtain. Therefore, we may only have a small number of output data samples, and have much more input data samples. In this article, a mixture form of the semisupervised probabilistic principal component regression model is proposed for soft sensor application, which can efficiently incorporate the unlabeled data information from different operation modes. Compared to the total supervised method, both modeling efficiency and soft sensing performance are improved with the inclusion of additional unlabeled data samples. Two case studies are provided to evaluate the feasibility and efficiency of the new method. © 2013 American Institute of Chemical Engineers AIChE J 60: 533–545, 2014     

Nonlinear process monitoring using kernel principal component analysis

In this paper, a new nonlinear process monitoring technique based on kernel principal component analysis (KPCA) is developed. KPCA has emerged in recent years as a promising method for tackling nonlinear systems. KPCA can efficiently compute principal components in high-dimensional feature spaces by means of integral operators and nonlinear kernel functions. The basic idea of KPCA is to first map the input space into a feature space via nonlinear mapping and then to compute the principal components in that feature space. In comparison to other nonlinear principal component analysis (PCA) techniques, KPCA requires only the solution of an eigenvalue problem and does not entail any nonlinear optimization. In addition, the number of principal components need not be specified prior to modeling. In this paper, a simple approach to calculating the squared prediction error (SPE) in the feature space is also suggested. Based on T² and SPE charts in the feature space, KPCA was applied to fault detection in two example systems: a simple multivariate process and the simulation benchmark of the biological wastewater treatment process. The proposed approach effectively captured the nonlinear relationship in the process variables and showed superior process monitoring performance compared to linear PCA.     

Block adaptive kernel principal component analysis for nonlinear process monitoring

On‐line modeling of multivariate nonlinear system based on multivariate statistical methods has been studied extensively due to its industrial requirements. In order to further improve the modeling efficiency, a fast Block Adaptive Kernel Principal Component Analysis algorithm is proposed. Comparing with the existing work, the proposed algorithm (1) does not rely on iterative computation in the calculating process, (2) combines the up‐ and downdating operations to become a single one (3) and describes the adaptation of the Gram matrix as a series of rank‐1 modification. In addition, (4) the updation of the eigenvalues and eigenvectors is of and high‐precision. The computational complexity analysis and the numerical study show that the derived strategy possesses better ability to model the time‐varying nonlinear variable interrelationships in process monitoring. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4334–4345, 2016     

Fault identification for process monitoring using kernel principal component analysis

In this research, we develop a new fault identification method for kernel principal component analysis (kernel PCA). Although it has been proved that kernel PCA is superior to linear PCA for fault detection, the fault identification method theoretically derived from the kernel PCA has not been found anywhere. Using the gradient of kernel function, we define two new statistics which represent the contribution of each variable to the monitoring statistics, Hotelling's T²and squared prediction error (SPE) of kernel PCA, respectively. The proposed statistics which have similar concept to contributions in linear PCA are directly derived from the mathematical formulation of kernel PCA and thus they are straightforward to understand. The main contribution of this work is that we firstly suggest a fault identification method especially applicable to process monitoring using kernel PCA. To demonstrate the performance, the proposed method is applied to two simulated processes, one is a simple nonlinear process and the other is a non-isothermal CSTR process. The simulation results show that the proposed method effectively identifies the source of various types of faults.     

Molecular reconstruction of complex hydrocarbon mixtures: An application of principal component analysis

Three methods for reconstruction of the detailed molecular composition of complex hydrocarbon mixtures, based on their global properties, are compared: a method based on the Shannon entropy criterion, an artificial neural network and a multiple linear regression model. In spite of the broad range of naphthas included in the training set, the application range of the last two methods proved to be limited. Principal component analysis allowed to identify their three‐dimensional ellipsoidal application range. In this subspace, the artificial neural network is more accurate than the multiple linear regression model and the Shannon entropy method. However, outside its application range, the performance of the neural network, as well as the regression model, decreases drastically. In contrast, the performance of the Shannon entropy method is not influenced by the characteristics of the considered naphtha, but rather depends on the number of available commercial indices. The Shannon entropy method yields comparable results to the artificial neural network, provided that a sufficient amount of distillation data is available to supply information on the carbon number distribution. Combining the reconstruction methods with a fundamental simulation model illustrates the necessity of having accurate feedstock reconstruction methods since they allow to capture the full power of fundamental simulation models for the simulation of industrial processes. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

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

Batch processes lie at the heart of many industries; hence the effective monitoring and control of batch processes is crucial to the production of high-quality materials. Multiway principal component analysis (MPCA) has been widely used for batch monitoring and has proved to be an effective method for monitoring many industrial batch processes. However, because MPCA is a fixed-model monitoring technique, it gives false alarms when it is used to monitor real processes whose normal operation involves slow changes. In this paper, we propose a simple on-line batch monitoring method that uses a consecutively updated MPCA model. The key to the proposed approach is that whenever a batch successfully remains within the bounds of normal operation, its batch data are added to the historical database of normal data and a new MPCA model is developed based on the revised database. The proposed method was applied to monitoring fed-batch penicillin production, and the results were compared with those obtained using conventional MPCA. The simulation results clearly show that the ability of the proposed method to adapt to new normal operating conditions eliminates the many false alarms generated by the fixed model and provides a reliable monitoring chart.     

A Robust Statistical Batch Process Monitoring Framework and Its Application

In order to reduce the variations of the product quality in batch processes, multivariate statistical process control methods according to multi-way principal component analysis (MPCA) or multi-way projection to latent structure (MPLS) were proposed for on-line batch process monitoring. However, they are based on the decomposition of relative covariance matrix and strongly affected by outlying observations. In this paper, in view of an efficient projection pursuit algorithm, a robust statistical batch process monitoring (RSBPM) framework, which is resistant to outliers, is proposed to reduce the high demand for modeling data. The construction of robust normal operating condition model and robust control limits are discussed in detail. It is evaluated on monitoring an industrial streptomycin fermentation process and compared with the conventional MPCA. The results show that the RSBPM framework is resistant to possible outliers and the robustness is confirmed.     

Process monitoring using principal components in parallel coordinates

Parallel coordinates is a recognized visualization technique in which data points, each defined by multiple coordinates, are represented by an unlimited number of adjoining parallel axes. This type of visualization technique is suitable for process monitoring applications in industrial facilities where a significant number of sensors are used to detect and identify abnormal operating conditions. This work makes use of principal component monitoring methods implemented in parallel coordinates plots, named PC². The PC² capabilities to visualize confidence regions of operations, evaluate models with different number of principal components, compare faulty events and determine the frequency of false alarms are here demonstrated. The monitoring visualization technology presented by PC² was successfully used for early detection of compressor surge and column flooding using actual process data. © 2012 American Institute of Chemical Engineers AIChE J, 59: 445–456, 2013     

Improved multi-scale kernel principal component analysis and its application for fault detection

In this paper the multiscale kernel principal component analysis (MSKPCA) based on sliding median filter (SFM) is proposed for fault detection in nonlinear system with outliers. The MSKPCA based on SFM (SFM-MSKPCA) algorithm is first proposed and applied to process monitoring. The advantages of SFM-MSKPCA are: (1) the dynamical multiscale monitoring method is proposed which combining the Kronecker production, the wavelet decomposition technique, the sliding median filter technique and KPCA. The Kronecker production is first used to build the dynamical model; (2) there are more disturbances and noises in dynamical processes compared to static processes. The sliding median filter technique is used to remove the disturbances and noises; (3) SFM-MSKPCA gives nonlinear dynamic interpretation compared to MSPCA; (4) by decomposing the original data into multiple scales, SFM-MSKPCA analyze the dynamical data at different scales, reconstruct scales contained important information by IDWT, eliminate the effects of the noises in the original data compared to kernel principal component analysis (KPCA). To demonstrate the feasibility of the SFM-MSKPCA method, its process monitoring abilities are tested by simulation examples, and compared with the monitoring abilities of the KPCA and MSPCA method on the quantitative basis. The fault detection results and the comparison show the superiority of SFM-MSKPCA in fault detection.     

基于GC-MS和主成分分析的蜂蜡质量控制方法研究

目的:为确保蜂蜡质量稳定可控,建立建全蜂蜡的质量控制方法。方法:收集14个不同产地的蜂蜡,利用柱前衍生化气质联用技术对蜂蜡中成分进行分析,利用指纹图谱对14个不来源不同的蜂蜡样品进行鉴定分析,随后采用主成分分析进行结果验证,并找出引起质量差异的化合物,建立简单快捷的质量评价方法。结果:主成分(PCA)分析的结果表明,存在样品质量差别的最明显原因可能是由化合物2、6、9、14、17、21、22、24、29、33、37、39、44等造成。结论:蜂蜡质量标准应该控制总烷酸类含量的同时也控制烷烃及游离烷酸的含量。     

Mixture Bayesian regularization method of PPCA for multimode process monitoring

This article intends to address two drawbacks of the traditional principal component analysis (PCA)‐based monitoring method: (1) nonprobabilistic; (2) single operation mode assumption. On the basis of the monitoring framework of probabilistic PCA (PPCA), a Bayesian regularization method is introduced for performance improvement, through which the effective dimensionality of the latent variable can be determined automatically. For monitoring processes with multiple operation modes, the Bayesian regularization method is extended to its mixture form, thus a mixture Bayesian regularization method of PPCA has been developed. To enhance the monitoring performance, a novel probabilistic strategy has been proposed for result combination in different operation modes. In addition, a new mode localization approach has also been developed, which can provide additional information and improve process comprehension for the operation engineer. A numerical example and a real industrial application case study have been used to evaluate the efficiency of the proposed method. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Analysis of rat haunch odor using dynamic solvent effect and principal component analysis

We used the dynamic solvent effect to sample rat haunch odor, which we then analyzed using principal component analysis. PCA, based on 22 volatile components, indicated that one axis clearly separated rat haunch odor samples according to sex and female reproductive condition (estrus and diestrus), explaining 79.5% of the variation in proportional peak area. We have therefore been able to separate odors along biologically meaningful lines.     

Detection of olive oil adulteration using principal component analysis applied on total and regio FA content

Principal component analysis (PCA) has been used to establish a new method for the detection of olive oil adulteration. The data set, composed of values obtained from the determination of the mole percentage of total FA and their regiospecific distribution in positions 1 and 3 in TG of oils (pure or mixtures) by GC analysis, was subjected to PCA. 3-D scatter plots showed clearly that it is possible to distinguish the pure oils from the mixtures. Moreover it is possible to discriminate the different types of seed oil used for the adulteration.     

Functional unfold principal component regression methodology for analysis of industrial batch process data

This work proposes a methodology utilizing functional unfold principal component regression (FUPCR), for application to industrial batch process data as a process modeling and optimization tool. The methodology is applied to an industrial fermentation dataset, containing 30 batches of a production process operating at Novozymes A/S. Following the FUPCR methodology, the final product concentration could be predicted with an average prediction error of 7.4%. Multiple iterations of preprocessing were applied by implementing the methodology to identify the best data handling methods for the model. It is shown that application of functional data analysis and the choice of variance scaling method have the greatest impact on the prediction accuracy. Considering the vast amount of batch process data continuously generated in industry, this methodology can potentially contribute as a tool to identify desirable process operating conditions from complex industrial datasets. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1986–1994, 2016     

Multivariate statistical monitoring of process operating performance

Process computers routinely collect hundreds to thousands of pieces of data from a multitude of plant sensors every few seconds. This has caused a “data overload” and due to the lack of appropriate analyses very little is currently being done to utilize this wealth of information. Operating personnel typically use only a few variables to monitor the plant's performance. However, multivariate statistical methods such as PLS (Partial Least Squares or Projection to Latent Structures) and PCA (Principal Component Analysis) are capable of compressing the information down into low dimensional spaces which retain most of the information. Using this method of statistical data compression a multivariate monitoring procedure analogous to the univariate Shewart Chart has been developed to efficiently monitor the performance of large processes, and to rapidly detect and identify important process changes. This procedure is demonstrated using simulations of two processes, a fluidized bed reactor and an extractive distillation column.     

Localized Fisher discriminant analysis based complex chemical process monitoring

Complex chemical process is often corrupted with various types of faults and the fault‐free training data may not be available to build the normal operation model. Therefore, the supervised monitoring methods such as principal component analysis (PCA), partial least squares (PLS), and independent component analysis (ICA) are not applicable in such situations. On the other hand, the traditional unsupervised algorithms like Fisher discriminant analysis (FDA) may not take into account the multimodality within the abnormal data and thus their capability of fault detection and classification can be significantly degraded. In this study, a novel localized Fisher discriminant analysis (LFDA) based process monitoring approach is proposed to monitor the processes containing multiple types of steady‐state or dynamic faults. The stationary testing and Gaussian mixture model are integrated with LFDA to remove any nonstationarity and isolate the normal and multiple faulty clusters during the preprocessing steps. Then the localized between‐class and within‐class scatter mattress are computed for the generalized eigenvalue decomposition to extract the localized Fisher discriminant directions that can not only separate the normal and faulty data with maximized margin but also preserve the multimodality within the multiple faulty clusters. In this way, different types of process faults can be well classified using the discriminant function index. The proposed LFDA monitoring approach is applied to the Tennessee Eastman process and compared with the traditional FDA method. The monitoring results in three different test scenarios demonstrate the superiority of the LFDA approach in detecting and classifying multiple types of faults with high accuracy and sensitivity. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Modeling and performance monitoring of multivariate multimodal processes

A multimodal modeling and monitoring approach based on maximum likelihood principal component analysis and a component‐wise identification of operating modes are presented. Analyzing each principal component individually allows separating components describing the variation within the individual modes from those capturing variation which the modes commonly share. On the basis of the former set, a Gaussian mixture model produces a statistical fingerprint that describes the production modes. The advantage of the component‐wise analysis is a simple identification of the mixture model parameters, which does not rely on the computationally cumbersome expectation maximization. The proposed method diagnoses abnormal process conditions by defining statistics relating to the components describing (1) between‐cluster variation, (2) within cluster variation, and (3) model residuals. The article demonstrates the benefits of this approach over existing work by an application to a continuous stirred tank reactor (CSTR) simulator and the analysis of recorded data from a furnace and a chemical reaction process. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1557–1569, 2013     

应重视数理统计方法在成分分析中的应用

从7个方面阐述了数理统计在成分分析中的重要性和必要性。例举了标准偏差、灵敏度、检出限、定量限和加标回收试验等概念的定义及其计算式,以及应用中常见的问题和错误。     

Multiway independent component analysis mixture model and mutual information based fault detection and diagnosis approach of multiphase batch processes

Batch process monitoring is a challenging task, because conventional methods are not well suited to handle the inherent multiphase operation. In this study, a novel multiway independent component analysis (MICA) mixture model and mutual information based fault detection and diagnosis approach is proposed. The multiple operating phases in batch processes are characterized by non‐Gaussian independent component mixture models. Then, the posterior probability of the monitored sample is maximized to identify the operating phase that the sample belongs to, and, thus, the localized MICA model is developed for process fault detection. Moreover, the detected faulty samples are projected onto the residual subspace, and the mutual information based non‐Gaussian contribution index is established to evaluate the statistical dependency between the projection and the measurement along each process variable. Such contribution index is used to diagnose the major faulty variables responsible for process abnormalities. The effectiveness of the proposed approach is demonstrated using the fed‐batch penicillin fermentation process, and the results are compared to those of the multiway principal component analysis mixture model and regular MICA method. The case study demonstrates that the proposed approach is able to detect the abnormal events over different phases as well as diagnose the faulty variables with high accuracy. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2761–2779, 2013