Quality-relevant and process-relevant fault monitoring based on GNPER and the fault quantification index for industrial processes

Traditional quality-relevant fault monitoring methods focus on extracting the relationship between the global structural features of the process and quality variables but ignore the local features. At the same time, they lack the quantification of quality-relevant faults. To solve these problems, a quality-relevant and process-relevant fault monitoring method and its fault quantification index based on global neighbourhood preserving embedding regression (GNPER) are proposed. First, by seeking the direction of maximum global variance, the global objective function is applied to neighbourhood preserving embedding algorithm, and the global neighbourhood preserving embedding (GNPE) model is established to fully extract the global and local information of process data. Second, on the basis of GNPE, through the idea of projection regression, the GNPER model is established to obtain mapping relationships among process variables and quality variables, and quality-relevant subspace and process-relevant subspace are extracted, the corresponding subspace statistics are established for fault monitoring. Finally, the fault quantification index is established for the faults in the two subspaces, which can provide more meaningful fault monitoring results. A numerical example, the hot rolling mill and the Tennessee Eastman (TE) process, verify the superiority and accuracy of the proposed method.     

基于全变量信息的子空间监控方法

实际化工过程采集得到的数据往往维度较高,直接建模比较复杂。主元分析(principal component analysis,PCA)方法可以提取原始数据主要特征,得到低维数据,但传统的PCA过程监控方法仅保留了方差较大的主元,会造成信息缺失,这将大大影响过程监控性能。针对这一问题,提出了一种新的基于全变量信息(full variable information,FVI)的子空间监控方法。首先,依据每个变量与主元空间(principal component subspace,PCS)和残差空间(residual subspace,RS)相似性的高低,将原始数据空间划分为3个维度较低的子空间,3个子空间保存了全部过程变量,可以更充分地利用过程信息。其次,在每个子空间中,分别建立监控模型,并利用贝叶斯推断整合子空间的监控结果。最后,通过数值仿真及Tennessee Eastman(TE)过程仿真研究验证FVI方法的有效性。     

Global optimization based on subspaces elimination: Applications to generalized pooling and water management problems

A global optimization strategy based on the partition of the feasible region in boxed subspaces defined by the partition of specific variables into intervals is described. Using a valid lower bound model, we create a master problem that determines several subspaces where the global optimum may exist, disregarding the others. Each subspace is then explored using a global optimization methodology of choice. The purpose of the method is to speed up the search for a global solution by taking advantage of the fact that tighter lower bounds can be generated within each subspace. We illustrate the method using the generalized pooling problem and a water management problem, which is a bilinear problem that has proven to be difficult to solve using other methods. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2336–2345, 2012     

独立元子空间算法及其在故障检测上的应用

针对高维数据建模问题,提出一种独立元子空间算法(ICSM),作为一种新的集成学习算法,ICSM利用独立元在不同变量上的贡献度来选取子空间,符合了集成学习的要求,具备了明确的物理意义,有效地克服了随机子空间算法(RSM)的主要缺点。在此基础上,进一步将ICSM应用于工业过程监控,提出了一种新的ICSM-PCA故障检测算法。首先在各个子空间内分别建立相应的PCA监测模型,然后根据T~2和SPE统计量的值计算出集成时各自的权重,最后构造两个集成统计量对工业过程进行监测。通过在Tennessee Eastman(TE)模型上的仿真研究,说明提出的算法具有较好的建模效果和故障检测能力。     

D-vine copulas混合模型及其在故障检测中的应用

过程监控技术是保证现代流程工业安全平稳运行及产品质量的有效手段。传统的过程监控方法大多采用维度约简方法提取数据特征,且要求过程数据必须服从高斯分布、线性等限制条件,对复杂工况条件下发生的故障难以取得较好的检测效果。因此,提出了混合D-vine copulas故障诊断模型,在不降维的情况下直接刻画数据中存在的复杂相关关系,构建过程变量的统计模型实现对存在非线性与非高斯性过程的精确描述。通过EM算法和伪极大似然估计优化混合模型参数,然后结合高密度区域（HDR）与密度分位数法等理论,构建广义贝叶斯概率（GBIP）指标实现对过程的实时监测。数值例子及在TE过程上的仿真结果说明了该混合模型的有效性及在故障检测中的良好性能。     

Multivariate probabilistic safety analysis of process facilities using the Copula Bayesian Network model

Integrated safety analysis of hazardous process facilities calls for an understanding of both stochastic and topological dependencies, going beyond traditional Bayesian Network (BN) analysis to study cause-effect relationships among major risk factors. This paper presents a novel model based on the Copula Bayesian Network (CBN) for multivariate safety analysis of process systems. The innovation of the proposed CBN model is in integrating the advantage of copula functions in modelling complex dependence structures with the cause-effect relationship reasoning of process variables using BNs. This offers a great flexibility in probabilistic analysis of individual risk factors while considering their uncertainty and stochastic dependence. Methods based on maximum likelihood evaluation and information theory are presented to learn the structure of CBN models. The superior performance of the CBN model and its advantages compared to traditional BN models are demonstrated by application to an offshore managed pressure drilling case study.     

Modeling and monitoring of multimode process based on subspace separation

In the paper, a new process monitoring approach is proposed for handling the multimode monitoring problem in the industrial batch processes. Compared to conventional method, the contributions are as follows: a new method of extracting the common subspace of different modes is proposed based on the subspace separation; after that the two different subspaces are separated, the kernel principal component models is built for the common and specific subspace respectively and the monitoring is carried out in subspace. The monitoring is carried out in the subspaces. The corresponding confidence regions are constructed according to their models respectively.     

基于IJB-PCA-ICA算法的故障检测

针对现代工业过程数据的高维性和分布复杂性等问题,提出了一种基于IJB-PCA-ICA（improved Jarque-Bera-principal component analysis-independent component analysis）的故障检测方法。首先采用改进的Jarque-Bera检测方法（J-B test）对原始数据划分高斯与非高斯核心部分,并对其中的高斯性与非高斯性均不明显的变量划分半高斯部分。将半高斯部分通过高斯分布置信概率加权与高斯核心部分和非高斯核心部分分别建立高斯子空间和分高斯子空间,然后对高斯子空间进行相关性划分后采用PCA方法得到高斯子空间的统计量;对非高斯子空间进行主元投影划分后采用ICA方法得到非高斯子空间的统计量,接着通过贝叶斯推断得到的联合统计量进行故障检测。最后通过Tenessee Eastman（TE）仿真实验,有效验证了所提出方法的有效性。     

Fault detection and identification using a Kullback-Leibler divergence based multi-block principal component analysis and bayesian inference

Considering the huge number of variables in plant-wide process monitoring and complex relationships (linear, nonlinear, partial correlation, or independence) among these variables, multivariate statistical process monitoring (MSPM) performance may be deteriorated especially by the independent variables. Meanwhile, whether related variables keep high concordance during the variation process is still a question. Under this circumstance, a multi-block technology based on mathematical statistics method, Kullback-Leibler Divergence, is proposed to put the variables having similar statistical characteristics into the same block, and then build principal component analysis (PCA) models in each low-dimensional subspace. Bayesian inference is also employed to combine the monitoring results from each sub-block into the final monitoring statistics. Additionally, a novel fault diagnosis approach is developed for fault identification. The superiority of the proposed method is demonstrated by applications on a simple simulated multivariate process and the Tennessee Eastman benchmark process.     

Quality‐relevant and process‐relevant fault monitoring with concurrent projection to latent structures

This paper proposes a new concurrent projection to latent structures is proposed in this paper for the monitoring of output‐relevant faults that affect the quality and input‐relevant process faults. The input and output data spaces are concurrently projected to five subspaces, a joint input‐output subspace that captures covariations between input and output, an output‐principal subspace, an output‐residual subspace, an input‐principal subspace, and an input‐residual subspace. Fault detection indices are developed based on these subspaces for various fault detection alarms. The proposed monitoring method offers complete monitoring of faults that happen in the predictable output subspace and the unpredictable output residual subspace, as well as faults that affect the input spaces only. Numerical simulation examples and the Tennessee Eastman challenge problem are used to illustrate the effectiveness of the proposed method. © 2012 American Institute of Chemical Engineers AIChE J, 59: 496–504, 2013     

A non-Gaussian pattern matching based dynamic process monitoring approach and its application to cryogenic air separation process

Principal component analysis (PCA) based pattern matching methods have been applied to process monitoring and fault detection. However, the conventional pattern matching approaches do not specifically take into account the non-Gaussian dynamic features in chemical processes. Furthermore, those techniques are more focused on fault detection instead of fault diagnosis. In this study, a non-Gaussian pattern matching based fault detection and diagnosis method is developed and applied to monitor cryogenic air separation process. First, independent component analysis (ICA) models are built on the normal benchmark and monitored data sets along sliding windows. The IC subspaces from the benchmark and monitored data are then extracted to evaluate the non-Gaussian patterns and detect process faults through a mutual information based dissimilarity index. Further, a difference subspace between the two IC subspaces is computed to characterize the divergence of the dynamic and non-Gaussian patterns between the benchmark and monitored data. Subsequently, the mutual information between the IC difference subspace and each process variable direction is defined as a new non-Gaussian contribution index for fault identification and diagnosis. The presented approach is applied to a simulated cryogenic air separation plant and the monitoring results are compared against those of PCA based pattern matching techniques and ICA based monitoring method. The application study demonstrates that the developed non-Gaussian pattern matching approach can effectively monitor the complex air separation process with superior fault detection and diagnosis capability.     

A transfer learning approach using improved copula subspace division for multi-mode fault detection

Multi-mode characteristics of industrial processes are prominent in the area of chemical production due to a diversified market demand. Despite mounting interests in predictive modelling for the optimization of operating conditions in chemical production processes, particularly in the petrochemical industry with multiple feeds and a range of cracking furnaces, targeted solutions that could hold wider applicability are typically hindered by the lack of available data. To overcome the limitation posed by data scarcity, an inductive approach based on transfer learning for fault detection is proposed utilizing copula subspace division (CSD), named TrAdaBoost CSD (TCSD). The proposed TCSD method is based on the probability view to transfer different most similar source samples to target samples. To select the optimal number of source samples, two adaptive indices were proposed and designed to adaptively assign the optimal model training iterations and sample number per iteration. Imbalance in data samples between the target and source datasets was addressed via the adaptive active vine copula-based probabilistic method. The effectiveness and superiority of the proposed TCSD approaches are validated via a numerical example (with the ranges of normalized fault detection and false alarm rates [FDR and FAR] between 0.82–0.94 and 0.01–0.04, respectively), the Tennessee Eastman process (~10% and 2.24% improvement for FDR and FAR, respectively), and the ethylene cracking furnace process (~15% and 8% improvement for FDR and FAR, respectively).     

Multi-layer features ensemble soft sensor regression model based on stacked autoencoder and vine copula

It is crucial in industrial processes to consider key variables to ensure safe operation and high product quality. Moreover, these variables are difficult to obtain using traditional measurement methods; hence, it makes sense to develop soft sensor regression models to process the variable prediction. However, there are numerous variables integrating noisy and redundant information in complex industrial processes. Using such variables in traditional regression models may result in reducing the model's efficiency and performance. Thus, this paper proposes a multi-layer feature ensemble soft sensor regression method using a stacked auto-encoder (SAE) and vine copula (ESAE–VCR) to address these problems. To do so, the number of neurons in the hidden layer of the SAE is determined by the principal component analysis (PCA). The multi-layer features of the process variables are extracted using a stacked AE, and the regression models are established for each feature layer. A linear regression ensemble method is used to combine the regression models with the multi-layer features to obtain the final predictive model that will estimate the values of the key variables. The effectiveness and practicality of the ESAE–VCR are validated by comparing them with several common soft measurement methods in two examples. In the numerical example, the ESAE–VCR yields an accuracy of prediction (R²) of 0.9898 and a root mean square error (RMSE) of 0.1804. In the industrial example, the ESAE–VCR yields an R² of 0.9908 and an RMSE of 0.1205.     

基于核T-PLS的化工过程故障检测算法

针对全潜结构投影法（T-PLS）在检测非线性过程故障时误报率和漏报率较高的缺点,提出了基于核函数的全潜结构投影法（KT-PLS）。该算法通过核函数将过程数据从低维输入空间非线性地映射到高维特征空间,实现非线性问题的线性化;然后在质量变量的引导下将特征空间分为与质量直接相关、与质量正交、与质量无关和残差四个子空间;最后分别构建D和Q统计量进行故障检测。将该算法应用到Tennessee Eastman process（TEP）,多种故障模式下的仿真结果表明,KT-PLS比T-PLS更适合监控具有强非线性的生产过程。     

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.     

Two-dimensional Bayesian monitoring method for nonlinear multimode processes

Nonlinear and multimode are two common behaviors in modern industrial processes, monitoring research studies have been carried out separately for these two natures in recent years. This paper proposes a two-dimensional Bayesian method for monitoring processes with both nonlinear and multimode characteristics. In this method, the concept of linear subspace is introduced, which can efficiently decompose the nonlinear process into several different linear subspaces. For construction of the linear subspace, a two-step variable selection strategy is proposed. A Bayesian inference and combination strategy is then introduced for result combination of different linear subspaces. Besides, through the direction of the operation mode, an additional Bayesian combination step is performed. As a result, a two-dimensional Bayesian monitoring approach is formulated. Feasibility and efficiency of the method are evaluated by the Tennessee Eastman (TE) process case study.     

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     

Vine Copula Specifications for Stationary Multivariate Markov Chains

Vine copulae provide a graphical framework in which multiple bivariate copulae may be combined in a consistent fashion to yield a more complex multivariate copula. In this article, we discuss the use of vine copulae to build flexible semiparametric models for stationary multivariate higher‐order Markov chains. We propose a new vine structure, the M‐vine, that is particularly well suited to this purpose. Stationarity may be imposed by requiring the equality of certain copulae in the M‐vine, while the Markov property may be imposed by requiring certain copulae to be independence copulae.     

基于多层优化PCC-SDG方法的化工过程故障诊断

化工过程的故障发生往往都是一个变量带动多个变量的连锁效应。本文基于变量的相关性变化特点,用符号有向图SDG（signed directed graph）描述系统因果影响关系,以皮尔逊相关系数PCC（Pearson correlation coefficient）计算网络统计指标,提出了一种基于多层优化PCC-SDG的故障诊断方法。该方法基于全工艺的网络拓扑结构,首先对选取的变量进行初步优化。然后,为有效提取工艺特征信息,运用PCA（principal component analysis）权重思想从多层相关系数集中选取了权重较大的关键变量,结合SDG建立最优PCC-SDG网络。最后,针对最优PCC-SDG网络变量的相关性规律重构聚集权重系数Q,进行过程故障检测与诊断。TE（Tennessee Eastman）仿真过程的应用结果表明,PCC-SDG建模及故障诊断步骤较为简洁,可以充分挖掘SDG深层次关联特性,定量简化SDG的故障诊断效果明显,具有较好的过程监控优势。     

Efficient structure synthesis of reactive distillation processes using the IDEAS approach

A new synthesis method for reactive distillation processes is proposed. At each stage of a column, vapor–liquid equilibrium (VLE) is assumed and kinetically controlled reaction in liquid phase is considered. First, the liquid composition space is divided into small subspaces. Then, for each subspace a representative liquid composition is decided and assigned to a module corresponding to a stage of a distillation column. Then, after the calculation of the VLE and the reaction rate, the distribution network (superstructure) connecting all modules by vapor and liquid flow paths is constructed. The feature of the proposed model is that all constraints are linear to the optimization variables: the liquid and vapor flow rate and the liquid hold-up. The developed method was applied to the metathesis reaction of 2-pentene, and a completely new process structure was obtained. The effectiveness of the implied structure was confirmed through a comparison with conventional structures.