Robust modeling of mixture probabilistic principal component analysis and process monitoring application

In this article, a robust modeling strategy for mixture probabilistic principal component analysis (PPCA) is proposed. Different from the traditional Gaussian distribution driven model such as PPCA, the multivariate student t‐distribution is adopted for probabilistic modeling to reduce the negative effect of outliers, which is very common in the process industry. Furthermore, for handling the missing data problem, a partially updating algorithm is developed for parameter learning in the robust mixture PPCA model. Therefore, the new robust model can simultaneously deal with outliers and missing data. For process monitoring, a Bayesian soft decision fusion strategy is developed which is combined with the robust local monitoring models under different operating conditions. Two case studies demonstrate that the new robust model shows enhanced modeling and monitoring performance in both outlier and missing data cases, compared to the mixture probabilistic principal analysis model. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2143–2157, 2014     

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.     

鲁棒PPLS模型及其在过程监控中的应用

概率偏最小二乘（PPLS）模型建立的条件是主元和误差都服从高斯分布,但是高斯分布的期望和方差容易受到离群点的影响,导致模型的鲁棒性较差。针对PPLS模型的不足,提出一种鲁棒概率偏最小二乘（RPPLS）方法,用拖尾更宽的T分布代替高斯分布,通过调整自由度参数,使模型对含离群点数据的拟合效果更好。更进一步,将RPPLS引入过程监控中,提出GT²和GSPE两个监控指标,分别监控过程的受控状态以及模型关系的变化。PPLS和RPPLS在TE过程监控的应用结果表明RPPLS不仅能更准确检测故障的产生,而且能更有效降低故障的漏报率。     

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.     

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.     

A Bayesian approach to robust process identification with ARX models

In the context of process industries, outlying observations mostly represent a large random error resulting from irregular process disturbances, instrument failures, or transmission problems. Statistical analysis of process data contaminated with outliers may lead to biased parameter estimation and plant‐model mismatch. The problem of process identification in the presence of outliers has received great attention and a wide variety of outlier identification approaches have been proposed. However, there is a great need to seek for more general solutions and a robust framework to deal with different types of outliers. The main objective of this work is to formulate and solve the robust process identification problem under a Bayesian framework. The proposed solution strategy not only yields maximum a posteriori estimates of model parameters but also provides hyperparameters that determine data quality as well as prior distribution of model parameters. Identification of a simulated continuous fermentation reactor is considered to show the effectiveness and robustness of the proposed Bayesian framework. The advantages of the method are further illustrated through an experimental case study of a pilot‐scale continuous stirred tank heater. © 2012 American Institute of Chemical Engineers AIChE J, 59: 845–859, 2013     

A sparse PCA for nonlinear fault diagnosis and robust feature discovery of industrial processes

Pearson's correlation measure is only able to model linear dependence between random variables. Hence, conventional principal component analysis (PCA) based on Pearson's correlation measure is not suitable for application to modern industrial processes where process variables are often nonlinearly related. To address this problem, a nonparametric PCA model is proposed based on nonlinear correlation measures, including Spearman's and Kendall tau's rank correlation. These two correlation measures are also less sensitive to outliers comparing to Pearson's correlation, making the proposed PCA a robust feature extraction technique. To reveal meaningful patterns from process data, a generalized iterative deflation method is applied to the robust correlation matrix of the process data to sequentially extract a set of leading sparse pseudoeigenvectors. For online fault diagnosis, the T² and SPE statistics are computed and analyzed with respect to the subspace spanned by the extracted pseudoeigenvectors. The proposed method is applied to two industrial case studies. Its process monitoring performance is demonstrated to be superior to that of the conventional PCA and is comparable to those of Kernel PCA and kernel independent component analysis at a lower computational cost. The proposed PCA is also more robust in sparse feature extraction from contaminated process data. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1494–1513, 2016     

浮选工艺指标KPCA-ELM软测量模型及应用

精矿品位和尾矿品位是浮选过程重要的工艺技术指标,其难以实现在线检测,且与过程控制变量具有强非线性、不确定性等综合复杂特性,难以直接采用精确的数学模型描述,主要依靠人工化验分析。人工采样化验周期较长,难以满足控制要求,使得浮选精矿品位偏低,尾矿品位偏高,因此建立浮选品位指标的软测量方法受到工业界广泛关注。在分析浮选过程工艺指标相关影响因素的基础上,建立一种基于主元分析KPCA(kernel principal component analysis)和极限学习机ELM(extreme learning machine)的软测量模型。为了消除离群点对软测量模型精度的影响,采用基于稳健位置估计的方法识别离群点,利用核主元分析对软测量模型的输入数据进行降维,提取非线性主元,然后用极限学习机进行建模。该建模方法已成功应用于中国西北某选矿厂浮选车间,工业应用结果表明该方法有很高的预报精度,对生产有一定的指导意义。     

基于贝叶斯推理的PKPCAM的非线性多模态过程故障检测与诊断方法

针对一类非线性多模态的化工过程,提出一种基于概率核主元的混合模型(PKPCAM),并利用贝叶斯推理策略进行过程监控与故障诊断.在提出的模型中, 每个操作模态由一个局部化的概率核主元分量描述,从而构建的一系列分量对应了不同的操作模态.首先,将过程数据从原始的度量空间投影到高维特征空间;其次,在该特征空间建立概率主元混合模型,从概率角度刻画数据集的多个局部分量特征;最后,在提取的核主元分量内获得测试样本的后验概率,结合模态内的马氏距离贡献度,提出基于贝叶斯推理的全局概率指标进行故障检测,同时利用模态内变量的相对贡献度,基于全局贡献度指标进行故障诊断.利用TEP仿真平台,与基于k均值聚类的次级主元分析和核主元分析的方法进行了对比分析,验证了提出的贝叶斯推理的PKPCAM方法对非线性多模态过程进行故障检测与诊断的可行性和有效性.     

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     

On robust spectral analysis by least absolute deviations

The method of least absolute deviations has been successfully used in construction of robust tools for spectral analysis under the conditions of outliers and heavy‐tailed statistical distributions. This article compares two such spectral analyzers, called the Laplace periodograms of the first and second kind, which can be viewed as robust alternatives to the ordinary periodogram. The article proves that the Laplace periodogram of the second kind has a similar asymptotic distribution to the Laplace periodogram of the first kind which established its association with the zero‐crossing spectrum in a recent publication. The article also demonstrates that the Laplace periodogram of the second kind has a smoother sample path which is more suitable for visualization, identification, and estimation of arbitrarily located narrowband components. Extensions of the results to complex time series are discussed.     

基于过采样结构的贝叶斯鲁棒辨识方法

在实际工业过程中，异常值的干扰是不可避免的，现有的处理异常值方法会导致模型估计有偏差，并且没有考虑潜在异常值的影响。针对上述缺点，利用学生分布噪声来处理潜在异常值，提出一种适用于学生分布噪声情况的贝叶斯鲁棒辨识方法，并且将其与过采样结构相结合，推出了基于过采样结构的贝叶斯鲁棒辨识方法。仿真实验表明：本文提出的算法，随着异常值影响的增加，仍然保持较小的辨识误差，而传统辨识方法已不再适用，同时，还克服了传统结构需添加额外测试信号所带来的巨额成本。因此，本文的算法更适合于实际工业过程辨识。     

一种新的多工况过程在线监测方法

针对复杂工业过程中的多工况和非高斯信息问题,提出一种基于外部分析的ICA-PCA（independent component analysis and principal component analysis）在线统计监测新方法。首先把过程变量分为外部变量和主要变量,通过偏最小二乘（PLS）回归方法分离外部变量对主要变量的影响,然后利用ICA-PCA两步信息提取策略,完整地提取过程的信息,最后用3个统计量对过程进行监测,建立了一种具有非高斯特性的多工况过程在线监测算法。通过对一个数值例子和连续搅拌槽（CSTR）过程的仿真研究,说明提出的方法是可行、有效的。     

A novel robust dynamic method for NOx emissions prediction in a thermal power plant

NOx is a harmful by-product of coal-fired boilers, and accurate prediction of NOx emissions in the outlet of a boiler is essential for environmental protection. In recent years, data-driven models have been widely studied and applied in this area. However, dynamic characteristics are ignored by many existing models, leading to sub-optimal performance. Besides, outliers that occur in the operation data have adverse effects on the efficacy of these prediction models. To address these issues, this paper presents a novel method for predicting NOx concentration via integrating a robust dynamic probabilistic approach and the long short-term memory (LSTM). First, mutual information (MI) is applied to determine the input variables. Subsequently, a robust probabilistic method is proposed to extract dynamic latent features considering outliers. On this basis, the generated latent variables are further utilized to train the LSTM-based model, with which the intrinsic relation between inputs and NOx values are obtained. Based on the application to a 660 MW thermal power plant, the superiority of the proposed method is demonstrated in terms of high prediction accuracy.     

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     

基于主元提取的鲁棒极限学习机研究及其化工建模应用

化工生产过程日益复杂，传统极限学习机(extreme learning machine, ELM)无法有效地对化工过程数据建模。针对该问题，提出一种基于主元提取(principal components extraction, PCE)的鲁棒极限学习机(PCE-RELM)。通过对ELM隐含层进行主元分析，提取数据的主元特征，去除变量间的线性相关性，简化研究问题。可以减小隐含层节点数对模型精度的影响，实现对ELM隐含层节点数的快速随机选取，同时使ELM具有鲁棒性。为验证提出方法的有效性，将PCE-RELM模型应用于精对苯二甲酸(purified terephthalic acid,PTA)生产过程建模。仿真结果显示，相比传统的ELM，PCE-RELM模型具有设计简单、鲁棒性好、精度高等优势，可以对化工过程控制、分析起到指导作用。     

一种鲁棒半监督建模方法及其在化工过程故障检测中的应用

复杂化工过程的观测样本往往包含着测量噪声与少量的离群点数据,而这些受污染的数据会影响数据驱动的过程建模与故障检测方法的准确性。本文考虑了化工过程测量样本的这一实际情况,提出了一种鲁棒半监督PLVR模型（RSSPLVR）,并利用核方法将其扩展为非线性的形式（K-RSSPLVR）。此类算法利用基于样本相似度的加权系数作为概率模型的先验参数,能有效消除离群点对建模的影响。利用加权后的建模样本,本文通过EM算法训练了RSSPLVR和K-RSSPLVR的模型参数,并提出了相应的故障检测算法。最后,通过TE过程仿真实验验证了所提出方法的有效性。     

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     

Probabilistic combination of local independent component regression model for multimode quality prediction in chemical processes

In this paper, a probabilistic combination form of the local independent component regression (ICR) model is proposed for quality prediction of chemical processes with multiple operation modes. Through the introduction of the Bayesian inference strategy, the posterior probabilities of the data sample in different operation modes are calculated upon two monitoring statistics of the independent component analysis (ICA) model. Then, based on the combination of local ICR models in different operation modes, a probabilistic multiple ICR (MICR) model is developed. Meanwhile, the operation mode information of the data sample is located through posterior analysis of the new model. To evaluate the multimode quality prediction performance of the proposed method, two case studies are provided.     

基于M估计器的支持向量机算法及其应用

训练样本的准确性对回归分析模型有很大的影响,然而训练样本中难免会出现一些造成分析模型失效的奇异点。 为克服奇异点对回归模型的影响,本文提出了一种基于M估计器的支持向量机（M-SVM）。它采用M估计器的目标函数代替最小二乘支持向量机（LS-SVM）目标函数中的残差平方和,同时提出了M-SVM的迭代求解算法,并将该算法应用于含有奇异点的低维仿真数据回归和汽油近红外光谱定量分析中。实验结果证明,相比于其他的支持向量机,M-SVM具有更好的稳健性和分析精度。