Robust probabilistic principal component analysis for process modeling subject to scaled mixture Gaussian noise

Conventionally, for probabilistic principal component analysis (PPCA) based regression models, noise with a Gaussian distribution is assumed for both input and output observations. This assumption makes the model to be vulnerable to large random errors, known as outliers. In this article, unlike the conventional noise assumption, a mixture noise model with a contaminated Gaussian distribution is adopted for probabilistic modeling to diminish the adverse effect of outliers, which usually occur due to irregular process disturbances, instrumentation failures or transmission problems. This is done by downweighing the effect of the noise component which accounts for contamination on output prediction. Outliers are common in process industries; therefore, handling this issue is of practical importance. In comparison with conventional PPCA based regression model, prediction performance of the developed robust probabilistic regression model is improved in presence of data contamination. To evaluate the model performance two case studies were carried out. A simulated set of data with specific characteristics to highlight the presence of outliers was used to demonstrate the robustness of the developed model. The advantages of this robust model are further illustrated via a set of real industrial process data.     

Mixture robust L1 probabilistic principal component regression and soft sensor application

In this paper, the multivariate Laplace distribution (also called L1 distribution) is adopted to construct a robust probabilistic principal component regression model (MRPPCR-L1) under multiple operating modes. In the practical industrial chemistry process, outliers exist due to incorrect recording, disturbances, and process noises and might result in modelling distortion. To address this problem, Laplace distribution, instead of the Gaussian distribution in traditional methods, is introduced to reduce the negative influence of outliers. Moreover, probabilistic principal component regression is employed for dealing with the mixture modelling problem owing to its probabilistic property to determine the operating modes. The formulation of this approach is derived with the expectation maximum algorithm and the soft sensing model is also developed for prediction. Compared to the conventional method, a numerical example and the Tennessee Eastman process are used to demonstrate the robust modelling performance of the proposed method.     

基于稀疏核主元分析的在线非线性过程监控

核主元分析(KPCA)适合非线性过程的监控,但存在计算量大、实时性差等缺点。提出一种基于稀疏KPCA(SKPCA)的过程监控方法,先使用SKPCA对正常建模数据进行加权,少数权值大的数据基本能代表全部正常数据的信息,因此稀化了建模数据,然后根据稀化后的正常数据建立过程的KPCA模型,并提出监控指标,大大减少了计算量,提高了监控的实时性,最后以化工分离过程为对象,就KPCA与SKPCA的监控效果和实时性进行了详细的对比研究,结果表明了基于SKPCA监控方法的优越性。     

一种基于改进MPCA的间歇过程监控与故障诊断方法

针对基于不同展开方式的多向主元分析(MPCA)方法在线应用时各自存在的缺陷,提出一种改进的基于变量展开的MPCA方法,实现间歇过程的在线监控与故障诊断。该方法采用随时间更新的主元协方差代替固定的主元协方差进行T²统计量的计算,充分考虑了主元得分向量的动态特性;同时引入主元显著相关变量残差统计量,避免SPE统计量的保守性,且该统计量能提供更详细的过程变化信息,对正常工况改变或过程故障引起的T²监控图变化有一定的识别能力;最后提出一种随时间变化的贡献图计算方法用于在线故障诊断。该方法和MPCA方法的监控性能在一个青霉素发酵仿真系统上进行了比较。仿真结果表明：该方法具有较好的监控性能,能及时检测出过程存在的故障,且具有一定的故障识别和诊断能力。     

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     

Local component based principal component analysis model for multimode process monitoring

For plant-wide processes with multiple operating conditions,the multimode feature imposes some chal-lenges to conventional monitoring techniques.Hence,to solve this problem,this paper provides a novel local component based principal component analysis(LCPCA)approach for monitoring the status of a multimode process.In LCPCA,the process prior knowledge of mode division is not required and it purely based on the process data.Firstly,LCPCA divides the processes data into multiple local components using finite Gaussian mixture model mixture(FGMM).Then,calculating the posterior probability is applied to determine each sample belonging to which local component.After that,the local component information(such as mean and standard deviation)is used to standardize each sample of local component.Finally,the standardized samples of each local component are combined to train PCA monitoring model.Based on the PCA monitoring model,two monitoring statistics T2 and SPE are used for monitoring multimode pro-cesses.Through a numerical example and the Tennessee Eastman(TE)process,the monitoring result demonstrates that LCPCA outperformed conventional PCA and LNS-PCA in the fault detection rate.     

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     

变量加权型主元分析算法及其在故障检测中的应用

传统主成分分析（PCA）算法旨在挖掘训练数据各变量间的相关性特征,已在数据驱动的故障检测领域得到了广泛的研究与应用。然而,传统PCA方法在建模过程中通常认为各个测量变量的重要性是一致的,因此不能有效而全面地描述出变量间相关性的差异。为此,提出一种变量加权型PCA（VWPCA）算法并将之应用于故障检测。首先,通过对训练数据进行加权处理,使处理后的数据能够充分体现出变量间相关性的差异。然后,在此基础上建立分布式的PCA故障检测模型。在线实施故障检测时,则通过贝叶斯准则将多组监测结果融合为一组概率指标。VWPCA方法通过相关性大小为各变量赋予不同的权值,从而将相关性差异考虑进了PCA的建模过程中,相应模型对训练数据特征的描述也就更全面。最后,通过在TE过程上的测试验证VWPCA方法用于故障检测的优越性。     

因子分析及其在过程监控中的应用

概率主元分析（PPCA）模型是因子分析（FA）模型的一种特殊形式，而主元分析（PCA）模型是PPCA模型的一种特例。PPCA和PCA已经在过程监控中得到了成功的应用，但是这两种方法的约束条件较多，而FA约束条件少，因此更能反映数据的本质特征。本文将FA引入工业过程监控，通过期望最大化（EM）算法建立FA模型，然后提出基于FA的监控指标，并讨论了因子个数的选择方案。在田纳西-伊斯曼（TE）过程中的应用结果以及与PCA、PPCA监控结果的对比表明了该方法的优越性。     

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.     

Online process monitoring for complex systems with dynamic weighted principal component analysis☆

Conventional multivariate statistical methods for process monitoring may not be suitable for dynamic processes since they usually rely on assumptions such as time invariance or uncorrelation. We are therefore motivated to propose a new monitoring method by compensating the principal component analysis with a weight approach. The proposed monitor consists of two tiers. The first tier uses the principal component analysis method to extract cross-correlation structure among process data, expressed by independent components. The second tier estimates auto-correlation structure among the extracted components as auto-regressive models. It is therefore named a dynamic weighted principal component analysis with hybrid correlation structure. The essential of the proposed method is to incorporate a weight approach into principal component analysis to construct two new subspaces, namely the important component subspace and the residual subspace, and two new statistics are de-fined to monitor them respectively. Through computing the weight values upon a new observation, the proposed method increases the weights along directions of components that have large estimation errors while reduces the influences of other directions. The rationale behind comes from the observations that the fault information is associated with online estimation errors of auto-regressive models. The proposed monitoring method is exem-plified by the Tennessee Eastman process. The monitoring results show that the proposed method outperforms conventional principal component analysis, dynamic principal component analysis and dynamic latent variable. ? 2016 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. Al rights reserved.     

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.     

Two‐step principal component analysis for dynamic processes monitoring

In this study, a two‐step principal component analysis (TS‐PCA) is proposed to handle the dynamic characteristics of chemical industrial processes in both steady state and unsteady state. Differently from the traditional dynamic PCA (DPCA) dealing with the static cross‐correlation structure and dynamic auto‐correlation structure in process data simultaneously, TS‐PCA handles them in two steps: it first identifies the dynamic structure by using the least squares algorithm, and then monitors the innovation component by using PCA. The innovation component is time uncorrelated and independent of the initial state of the process. As a result, TS‐PCA can monitor the process in both steady state and unsteady state, whereas all other reported dynamic approaches are limited to only processes in steady state. Even tested in steady state, TS‐PCA still can achieve better performance than the existing dynamic approaches.     

基于主元子空间富信息重构的过程监测方法

作为一种经典的多元投影方法,主元分析（PCA）已在多变量统计过程监测领域得到了广泛应用。然而,传统的主元挑选方法往往选择方差较大的主元以表征建模样本中包含的较大信息量,但当过程信息发生变化时,方差较小的主元所表现出来的变异性可能更为明显,即包含的信息量更为丰富,也更有利于故障检出。为此,提出一种基于主元子空间富信息重构的过程监测方法（informative PCA,Info-PCA）。该方法通过计算过程数据在各主元方向上累积T²统计量的变化率,选择变化较为明显的主元以重构主元子空间。在此基础上,建立相应的统计监测模型。最后,通过实例验证该方法用于过程监测的可行性与有效性。     

间歇生产过程鲁棒统计监控及其应用

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.     

基于ReliefF的主元挑选算法在过程监控中的应用

传统的主成分分析（principal component analysis,PCA（算法选取包含大部分方差信息的成分作为主元,并将其应用到过程监控中。但是故障信息不一定会投影到方差较大的成分上,使用方差贡献度挑选主元会导致严重的信息丢失和监控效果的恶化。因此使用ReliefF-PCA算法,其中ReliefF算法从故障角度出发,挑选出在区分正常样本和故障样本上权重更高,效果相对更好的成分作为主元。这样挑选出的主元避免了传统PCA算法在主元挑选过程中出现的主观性、盲目性以及重要信息的丢失。ReliefF-PCA算法在过程监控中主要有两个优势,第1,监控效果更好;第2,对原始数据降维效果更好。随后,基于ReliefF-PCA算法,提出一种加权的故障变量贡献图方法。最后,通过Tennessee Eastman（TE（仿真实验测试,ReliefF-PCA算法达到了预期效果。     

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.