Semi-supervised dynamic latent variable modeling: I/O probabilistic slow feature analysis approach

Modeling of high dimensional dynamic data is a challenging task. The high dimensionality problem in process data is usually accounted for using latent variable models. Probabilistic slow feature analysis (PSFA) is an example of such an approach that accounts for high dimensionality while simultaneously capturing the process dynamics. However, PSFA also suffers from a drawback that it cannot use output information when determining the latent slow features. To address this lacunae, extension of the PSFA by incorporating outputs, resulting in Input-Output PSFA (IOPSFA) is proposed. IOPSFA can use both input and output information for extracting latent variables. Hence, inferential models based on IOPSFA are expected to have better predictive ability. The efficacy of the proposed approach with an industrial and a laboratory scale soft sensing case studies that have both complete and incomplete output measurements is evaluated, respectively. © 2018 American Institute of Chemical Engineers AIChE J, 65: 964–979, 2019     

Nonlinear process identification in the presence of multiple correlated hidden scheduling variables with missing data

Identification of nonlinear processes in the presence of noise corrupted and correlated multiple scheduling variables with missing data is concerned. The dynamics of the hidden scheduling variables are represented by a state‐space model with unknown parameters. To assure generality, it is assumed that the multiple correlated scheduling variables are corrupted with unknown disturbances and the identification dataset is incomplete with missing data. A multiple model approach is proposed to formulate the identification problem of nonlinear systems under the framework of the expectation‐maximization algorithm. The parameters of the local process models and scheduling variable models as well as the hyperparameters of the weighting function are simultaneously estimated. The particle smoothing technique is adopted to handle the computation of expectation functions. The efficiency of the proposed method is demonstrated through several simulated examples. Through an experimental study on a pilot‐scale multitank system, the practical advantages are further illustrated. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3270–3287, 2015     

基于统计量模式分析的T-KPLS间歇过程故障监控

核函数的全影结构投影(total kernel projection to latent structures,T-KPLS)最近在故障监控领域取得了广泛应用, 其实质是对数据矩阵的协方差矩阵进行分解, 没有利用数据的高阶统计量等有用信息, 在进行特征提取时会造成数据有用信息的丢失, 导致故障识别效果差。为了解决此问题, 提出了统计量模式分析(statistics pattern analysis, SPA)与核函数的全影结构投影法(total kernel projection to latent structures, T-KPLS)相结合的多向统计量模式分析的核函数的全影结构投影法(multi-way statistics pattern analysis total kernel projection to latent structures, MSPAT-KPLS)。该方法首先构造样本的不同阶次统计量, 将数据从原始的数据空间映射到统计量样本空间, 然后利用核函数将统计量样本空间映射到高维核空间并在质量变量的引导下将特征空间分为过程变量与质量变量相关、过程变量与质量变量无关、过程变量与质量变量正交和残差4个子空间;最后针对与质量变量相关和残差空间建立联合监控模型, 当监控到有故障发生时进行故障变量追溯。最后将该方法应用到微生物发酵过程中, 并与传统方法进行比较, 发现该方法具有更好的监控性能。     

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     

An optimization framework to combine operable space maximization with design of experiments

The introduction of Quality by Design in the pharmaceutical industry stimulates practitioners to better understand the relationship of materials, processes and products. One way to achieve this is through the use of targeted experimentation. In this study, an optimization framework to design experiments that effectively leverage parameterized process models is presented to maximize the space covered in the output variables while also obtaining an orthogonal bracketing study in the process input factors. The framework considers both multi‐objective and bilevel optimization methods for relating the two maximization objectives. Results are presented for two case studies—a spray coating process and a continuously stirred reactor cascade—demonstrating the ability to generate and identify efficient designs with fit‐for‐purpose trade‐offs between bracketed orthogonality in the input factors and volume explored in the process output space. The proposed approach allows a more complete understanding of the process to emerge from a small set of experiments. © 2018 The Authors. AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers. AIChE J, 64: 3944–3957, 2018     

An efficient latent variable optimization approach with stochastic constraints for complex industrial process

For complex chemical processes, process optimization is usually performed on causalmodels fromfirst principle models. When the mechanism models cannot be obtained easily, restricted model built by process data is used for dynamic process optimization. A new strategy is proposed for complex process optimization, in which latent variables are used as decision variables and statistics is used to describe constraints. As the constraint condition will be more complex by projecting the original variable to latent space, Hotelling T² statistics is introduced for constraint formulation in latent space. In this way, the constraint is simplified when the optimization is solved in low-dimensional space of latent variable. The validity of the methodology is illustrated in pH-level optimal control process and practical polypropylene grade transition process.     

Tensor sequence component analysis for fault detection in dynamic process

For dynamic processes, using sequence information to augment the data can improve fault detection performance. Traditional approaches transform raw data into augmented vectors, which leads to losses in structural information in the variables and increases the data dimension. This paper proposes a novel data dimension reduction algorithm called tensor sequence component analysis (TSCA) and applies it to dynamic process fault detection. The algorithm extends each sample into a matrix comprising current and past process data, and simultaneously reduces the dimensions of time delay and the variables for feature extraction, solving the problem of the curse of dimensionality. For the dimension reduction of time delay, in order to extract similar information from the samples, each sample is reconstructed with time neighbourhoods. For the dimension reduction of the variables, considering the information of different variables variance information of the latent variables is maximized for feature extraction. Finally, a numerical example and the Tennessee Eastman process are used to demonstrate the efficacy of the proposed method.     

Industrial polyethylene melt index prediction using ensemble manifold learning–based local model

For online melt index prediction in multiple‐grade polyethylene polymerization processes, using only a fixed model is insufficient. Additionally, without enough process knowledge, it is difficult to select suitable input variables to accurately construct prediction models. A novel manifold learning based local probabilistic modeling method named ensemble just‐in‐time Gaussian process regression (EJGPR) is developed. By utilizing output variables, an optimization framework is proposed to preserve the local structure of both input and output variables. Then the output information is integrated into construction of a JGPR‐based local model. Additionally, some new extracted variables in the projection space can be obtained. Moreover, using the probabilistic prediction information, the uncertainty of each JGPR‐based local candidate model can be simply described. Consequently, using an efficient ensemble strategy, a more accurate EJGPR prediction model can be constructed online. The melt index prediction results in an industrial polyethylene process show it has better performance than conventional methods. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45094.     

深度融合特征提取网络及其在化工过程软测量中的应用

复杂化工过程的观测数据往往同时包含非线性和强动态特性,而传统的化工过程软测量方法无法准确提取观测数据的非线性动态特征,以至影响数据建模和质量预报的准确性。提出了一种基于变分自编码器的深度融合特征提取网络(deep fusion features extraction network, DFFEN)。在变分自编码器框架下,通过构建潜隐特征信息传递通道,提取非线性动态潜隐变量。并利用自注意力机制(self-attention)融合关键的隐层信息,优化因信息传递通道过长而导致的潜在特征被遗忘的问题。此外,在后端网络构建潜隐变量和关键质量变量之间的回归模型,以实现关键质量变量的预报。最后,通过数值案例和实际的合成氨过程验证了所提出的DFFEN模型的可行性和有效性。     

深度融合特征提取网络及其在化工过程软测量中的应用

复杂化工过程的观测数据往往同时包含非线性和强动态特性,而传统的化工过程软测量方法无法准确提取观测数据的非线性动态特征,以至影响数据建模和质量预报的准确性。提出了一种基于变分自编码器的深度融合特征提取网络(deep fusion features extraction network, DFFEN)。在变分自编码器框架下,通过构建潜隐特征信息传递通道,提取非线性动态潜隐变量。并利用自注意力机制(self-attention)融合关键的隐层信息,优化因信息传递通道过长而导致的潜在特征被遗忘的问题。此外,在后端网络构建潜隐变量和关键质量变量之间的回归模型,以实现关键质量变量的预报。最后,通过数值案例和实际的合成氨过程验证了所提出的DFFEN模型的可行性和有效性。     

Improved dynamic kernel PCA based on local preserving projections and its application for electric submersible pump fault diagnosis

Dynamic kernel principal component analysis (DKPCA) has been frequently implemented for nonlinear and dynamic process monitoring of complex industrial processes. However, traditional DKPCA focuses only on the global structural analysis of data sets and strongly neglects the local information, which is equally essential for process detection and identification. In this paper, an improved DKPCA, referred to as the local DKPCA (LDKPCA), is proposed based on local preserving projections (LPP) for nonlinear dynamic process fault diagnosis. The method combines the advantages of LPP and DKPCA by utilizing the local structure feature to maintain the geometric structure of the data in a unified framework. To achieve a highly comprehensive feature extraction, the local characteristics are fused in DKPCA to produce an optimization objective. The neighbouring points of the new objective function projection in the feature space are still maintained in proximity, and the variance information is retained simultaneously. For the purpose of fault detection, two statistics, known as the T² and squared prediction error (SPE) statistics, are constructed, based on the LDKPCA model, and used to monitor the latent variable space and the residual space, respectively. In addition, the sensitivity analysis is brought in for fault identification of the two statistics. Based on the experimental analysis using the shaft breakage data of an offshore oilfield electric submersible pump (ESP), the proposed method outperforms the conventional DKPCA in terms of fault monitoring performance. The experimental results demonstrate the potential of the method in nonlinear dynamic process fault diagnosis.     

Adaptive multiscale convolutional neural network model for chemical process fault diagnosis

Intelligent fault recognition techniques are essential to ensure the long-term reliability of manufacturing. Due to the variations in material, equipment and environment, the process variables monitored by sensors contain diverse data characteristics at different time scales or in multiple operating modes. Despite much progress in statistical learning and deep learning for fault recognition, most models are constrained by abundant diagnostic expertise, inefficient multiscale feature extraction and unruly multimode condition. To overcome the above issues, a novel fault diagnosis model called adaptive multiscale convolutional neural network (AMCNN) is developed in this paper. A new multiscale convolutional learning structure is designed to automatically mine multiple-scale features from time-series data, embedding the adaptive attention module to adjust the selection of relevant fault pattern information. The triplet loss optimization is adopted to increase the discrimination capability of the model under the multimode condition. The benchmarks CSTR simulation and Tennessee Eastman process are utilized to verify and illustrate the feasibility and efficiency of the proposed method. Compared with other common models, AMCNN shows its outstanding fault diagnosis performance and great generalization ability.     

Ensemble locally weighted partial least squares as a just‐in‐time modeling method

The predictive ability of soft sensors, which estimate values of an objective variable y online, decreases due to process changes in chemical plants. To reduce the decrease of predictive ability, adaptive soft sensors have been developed. We focused on just‐in‐time soft sensors, especially locally weighted partial least squares (LWPLS) regression. Since a set of hyperparameters in an LWPLS model has to be set beforehand and there is only onedataset, a traditional LWPLS model is difficult to accurately predict y‐values in multiple process states. In this study, we propose to combine LWPLS and ensemble learning, and predict y‐values with multiple LWPLS models, whose datasets and sets of hyperparameters are different. The weights of LWPLS models are determined based on Bayes’ theorem, considering their predictive ability. We confirmed that the proposed model has higher predictive accuracy than traditional models through numerical simulation data and two industrial data analyses. © 2015 American Institute of Chemical Engineers AIChE J, 62: 717–725, 2016     

A Kernel Time Structure Independent Component Analysis Method for Nonlinear Process Monitoring

Kernel independent component analysis (KICA) is a newly emerging nonlinear process monitoring method, which can extract mutually independent latent variables called independent components (ICs) from process variables. However, when more than one IC have Gaussian distribution, it cannot extract the IC feature effectively and thus its monitoring performance will be degraded drastically. To solve such a problem, a kernel time structure independent component analysis (KTSICA) method is proposed for monitoring nonlinear process in this paper. The original process data are mapped into a feature space nonlinearly and then the whitened data are calculated in the feature space by the kernel trick. Subsequently, a time structure independent component analysis algorithm, which has no requirement for the distribution of ICs, is proposed to extract the IC feature. Finally, two monitoring statistics are built to detect process faults. When some fault is detected, a nonlinear fault identification method is developed to identify fault variables based on sensitivity analysis. The proposed monitoring method is applied in the Tennessee Eastman benchmark process. Applications demonstrate the superiority of KTSICA over KICA.     

A quality relevant non‐Gaussian latent subspace projection method for chemical process monitoring and fault detection

Partial least‐squares (PLS) method has been widely used in multivariate statistical process monitoring field. The goal of traditional PLS is to find the multidimensional directions in the measurement‐variable and quality‐variable spaces that have the maximum covariances. Therefore, PLS method relies on the second‐order statistics of covariance only but does not takes into account the higher‐order statistics that may involve certain key features of non‐Gaussian processes. Moreover, the derivations of control limits for T² and squared prediction error (SPE) indices in PLS‐based monitoring method are based on the assumption that the process data follow a multivariate Gaussian distribution approximately. Meanwhile, independent component analysis (ICA) approach has recently been developed for process monitoring, where the goal is to find the independent components (ICs) that are assumed to be non‐Gaussian and mutually independent by means of maximizing the high‐order statistics such as negentropy instead of the second‐order statistics including variance and covariance. Nevertheless, the IC directions do not take into account the contributions from quality variables and, thus, ICA may not work well for process monitoring in the situations when the quality variables have strong influence on process operations. To capture the non‐Gaussian relationships between process measurement and quality variables, a novel projection‐based monitoring method termed as quality relevant non‐Gaussian latent subspace projection (QNGLSP) approach is proposed in this article. This new technique searches for the feature directions within the measurement‐variable and quality‐variable spaces concurrently so that the two sets of feature directions or subspaces have the maximized multidimensional mutual information. Further, the new monitoring indices including I² and SPE statistics are developed for quality relevant fault detection of non‐Gaussian processes. The proposed QNGLSP approach is applied to the Tennessee Eastman Chemical process and the process monitoring results of the present method are demonstrated to be superior to those of the PLS‐based monitoring method. © 2013 American Institute of Chemical Engineers AIChE J 60: 485–499, 2014     

ISOMAP-LDA方法用于化工过程故障诊断

针对化工连续生产过程的时序性及非线性等特征,提出一种新的基于数据驱动的化工过程故障诊断方法：ISOMAP-LDA。首先实行流形学习算法ISOMAP,在保持量测数据几何结构特性下完成非线性降维,然后基于提取的嵌入变量张成的低维空间,选用线性判别分析（LDA）构造故障模式类的判别函数,负责各采样个体故障类型的判定。将该方法用于仿真化工Tennessee Eastman 过程的故障诊断,结果表明,ISOMAP-LDA方法不仅拥有较高的故障诊断能力,而且取得采样在低维空间的可视化表示。     

Supervised sparse preserving projections model based on distributed principal component analysis for chemical process monitoring

For the monitoring of large-scale chemical processes, the distributed method is often used to extract local feature information and model the extracted local feature information to obtain a process monitoring model. But the distributed process monitoring model often contains more process variables, which makes the local information of the process data flooded. To make up for the insufficient extraction of local information in traditional distributed process monitoring, supervised sparse preserving projections model based on distributed principal component analysis (DPCA-SSPP) is proposed in this paper. First, the process data are decomposed by the PCA algorithm, and the principal component space and residual space are obtained. Second, the variables of each sub-block are selected according to the maximum correlation criterion, and the SSPP process monitoring model is established for each sub-block. Finally, the monitoring results of each sub-block are combined together to form a global monitoring result through the Bayesian information fusion strategy. The proposed scheme can be proved to be effective through the simulation on a nonlinear numerical example and the Tennessee Eastman benchmark (TE) process.     

Design and assessment of delay timer alarm systems for nonlinear chemical processes

In process and manufacturing industries, alarm systems play a critical role in ensuring safe and efficient operations. The objective of a standard industrial alarm system is to detect undesirable deviations in process variables as soon as they occur. Fault detection and diagnosis systems often need to be alerted by an industrial alarm system; however, poorly designed alarms often lead to alarm flooding and other undesirable events. In this article, we consider the problem of industrial alarm design for processes represented by stochastic nonlinear time‐series models. The alarm design for such complex processes faces three important challenges: (1) industrial processes exhibit highly nonlinear behavior; (2) state variables are not precisely known (modeling error); and (3) process signals are not necessarily Gaussian, stationary or uncorrelated. In this article, a procedure for designing a delay timer alarm configuration is proposed for the process states. The proposed design is based on minimization of the rate of false and missed alarm rates—two common performance measures for alarm systems. To ensure the alarm design is robust to any non‐stationary process behavior, an expected‐case and a worst‐case alarm designs are proposed. Finally, the efficacy of the proposed alarm design is illustrated on a non‐stationary chemical reactor problem. © 2017 American Institute of Chemical Engineers AIChE J, 63: 77–90, 2018     

Mathematical model of supercritical extraction applied to oil seed extraction by CO2+saturated alcohol — I. Desorption model

Supercritical fluid extraction of solutes from solid matrix is represented by the extraction curve, where cumulated extracted oil is plotted versus time. Experimental data obtained in laboratory scale and pilot plant is adjusted with different extraction models; in order to predict extraction curves for full-scale extractors. Sometimes, a shortcut method is useful to adjust experimental data; these correlations are typical in most of engineering processes. In this paper, three shortcut methods are reviewed. First, a model based on flux models considering residence time distribution curves for serially interconnected perfectly mixed tanks and plug flow in series or in parallel with them. It could be used to analyze extractor behavior taking into account bed distribution (preferential ways, dispersion). Second, fast adjusting or ‘t^n’ model considers a differential mass balance where mass transfer coefficient is an ‘nth^’ potential function of time; analytical solution gives an explicit equation. Third, it is presented a linear shortcut method by intervals based on Sovovà model; it predicts considering four extraction periods: delay, rapid extraction, slow extraction and depletion; delay time and solubility are evaluated using the ‘t^n’ model. This model gives a process transfer function (Laplace domain). Supercritical fluid extraction of sunflower seed oil with carbon dioxide was performed in a pilot plant at 30.0 MPa and 40°C, using different amounts of methanol, ethanol, butanol and hexanol as cosolvents. Experimental data are fitted with proposed shortcut methods. Fitting error is less than 5% except in linear shortcut method by intervals which is higher.     

Probabilistic slow feature analysis‐based representation learning from massive process data for soft sensor modeling

Latent variable (LV) models provide explicit representations of underlying driving forces of process variations and retain the dominant information of process data. In this study, slow features (SFs) as temporally correlated LVs are derived using probabilistic SF analysis. SFs evolving in a state‐space form effectively represent nominal variations of processes, some of which are potentially correlated to quality variables and hence help improving the prediction performance of soft sensors. An efficient expectation maximum algorithm is proposed to estimate parameters of the probabilistic model, which turns out to be suitable for analyzing massive process data. Two criteria are also proposed to select quality‐relevant SFs. The validity and advantages of the proposed method are demonstrated via two case studies. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4126–4139, 2015