Process data modeling using modified kernel partial least squares

In this paper, a multivariate data modeling approach is proposed based on modified kernel partial least squares (MKPLS) with the signal filtering method. Then it is applied to quality prediction of industrial processes. In the original KPLS, several disadvantages are: (1) Has to iteratively calculate until convergence of score vectors to extract one principal component. Thus, this situation will affect the computing speed and waste lots of time. (2) Has to give a limited number of iterative steps and a precision limit which will reduce the accuracy of original KPLS, when the score vectors are not convergent. (3) Contains unwanted dinal KPLS is not able to remove undesirable systematic variation in X that is unrelated to Y. For the above problems, a modified KPLS regression model with orthogonal-kernel projections to latent structures (O-KPLS) is proposed, which is called OKPLS-KPLS. Advantages of the proposed OKPLS-KPLS are: (1) gets score vectors directly by using the corresponded eigenvector to the largest eigenvalue instead of the iterative calculation, it will improve the computing speed, (2) does not involve the limited number of iterative steps and the precision limit, hence, it will increase the accuracy compared to that of original KPLS, and (3) removes unwanted disturbed variation through the use of data preprocessing method (O-KPLS). O-KPLS is proposed here as a nonlinear data preprocessing method that removes from X information not correlated to Y. Furthermore, O-KPLS solves the issue of data nonlinearity compared to orthogonal projections to latent structures (O-PLS). In this paper, the prediction performance of the proposed approach (OKPLS-KPLS) is compared to those of original KPLS and OPLS using two examples. Of the three methods, OKPLS-KPLS shows the best performance in terms of regression fitting capacity and predicting future observations of the response variable(s).     

基于LTSA和MICA与PCA联合指标的过程监控方法及应用

独立成分分析(ICA)方法主要被用来对线性非高斯过程进行监控,为了提高对非高斯过程的监控效果,则利用过程数据信息对ICA的监控指标进行了改进,提出了一种改进的独立成分分析(MICA)方法。许多实际工业过程数据都具有非线性、非高斯与高斯混合分布的特点,为此提出了一种基于LTSA和MICA与PCA联合指标的过程监控的方法。首先采用局部切空间排列(LTSA)算法对样本数据进行非线性降维,然后分别用MICA和PCA方法得到非高斯与高斯统计量,对其进行加权得到新的统计量,并被用于过程监控。最后将该方法应用在田纳西-伊斯曼(TE)过程和乙烯裂解炉的过程监控中,证明了该方法的有效性。     

Fault detection and diagnosis in a non-Gaussian process with modified kernel independent component regression

Quality-related fault detection and diagnosis are crucial in the data-driven process monitoring field. Most existing methods are based on principal component analysis (PCA) or partial least squares (PLS), which will miss high-order statistical information when the industrial process does not satisfy a Gaussian distribution. Meanwhile, the traditional contribution plot is difficult to directly apply to nonlinear processes in some cases due to its limitation of convergence. As such, a modified kernel independent component regression (MKICR) model, which considers high-order statistical information, is proposed for quality-related fault detection and faulty variable identification. First, the relationship between the independent components and quality variables is established by kernel independent component regression, and the correlation matrix is obtained. Then, the kernel independent components can be suitably divided into quality-related and quality-unrelated parts. Finally, an analysis of the contribution of each variable to the statistics based on Lagrange's mean value theorem is presented. In addition, a numerical case and the Tennessee Eastman process (TEP) demonstrate the efficacy and superiority of the proposed method.     

Improved Kernel PLS-based Fault Detection Approach for Nonlinear Chemical Processes

In this paper, an improved nonlinear process fault detection method is proposed based on modified ker-nel partial least squares （KPLS）. By integrating the statistical local approach （SLA） into the KPLS framework, two new statistics are established to monitor changes in the underlying model. The new modeling strategy can avoid the Gaussian distribution assumption of KPLS. Besides, advantage of the proposed method is that the kernel latent variables can be obtained directly through the eigen value decomposition instead of the iterative calculation, which can improve the computing speed. The new method is applied to fault detection in the simulation benchmark of the Tennessee Eastman process. The simulation results show superiority on detection sensitivity and accuracy in com-parison to KPLS monitoring.     

A nonlinear kernel Gaussian mixture model based inferential monitoring approach for fault detection and diagnosis of chemical processes

A nonlinear kernel Gaussian mixture model (NKGMM) based inferential monitoring method is proposed in this article for chemical process fault detection and diagnosis. Aimed at the multimode non-Gaussian process with within-mode nonlinearity, the developed NKGMM approach projects the operating data from the raw measurement space into the high-dimensional kernel feature space. Thus the Gaussian mixture model can be estimated in the feature space with each component satisfying multivariate Gaussianity. As a comparison, the conventional independent component analysis (ICA) searches for the non-Gaussian subspace with maximized negentropy, which is not equivalent to the multi-Gaussianity in multimode process. The regular Gaussian mixture model (GMM) method, on the other hand, assumes the Gaussianity of each cluster in the original data space and thus cannot effectively handle the within-mode nonlinearity. With the extracted kernel Gaussian components, the geometric distance driven inferential index is further derived to monitor the process operation and detect the faulty events. Moreover, the kernel Gaussian mixture based inferential index is decomposed into variable contributions for fault diagnosis. For the simulated multimode wastewater treatment process, the proposed NKGMM approach outperforms the ICA and GMM methods in early detection of process faults, minimization of false alarms, and isolation of faulty variables of nonlinear and non-Gaussian multimode processes.     

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.     

Multivariate statistical process monitoring using an improved independent component analysis

An approach for multivariate statistical monitoring based on kernel independent component analysis (Kernel ICA) is presented. Different from the recently developed KICA which means kernel principal component analysis (KPCA) plus independent component analysis (ICA), Kernel ICA is an improvement of ICA and uses contrast functions based on canonical correlations in a reproducing kernel Hilbert space. The basic idea is to use Kernel ICA to extract independent components and later to provide enhanced monitoring of multivariate processes. I² (the sum of the squared independent scores) and squared prediction error (SPE) are adopted as statistical quantities. Besides, kernel density estimation (KDE) is described to calculate the confidence limits. The proposed monitoring method is applied to fault detection in the simulation benchmark of the wastewater treatment process and the Tennessee Eastman process, the simulation results clearly show the advantages of Kernel ICA monitoring in comparison to ICA and KICA monitoring.     

基于加权统计特征KICA的故障检测与诊断方法

针对核独立元分析（kernel independent component analysis, KICA）在非线性动态过程中对微小故障检测率低的问题,提出一种基于加权统计特征KICA（weighted statistical feature KICA, WSFKICA）的故障检测与诊断方法。首先,利用KICA从原始数据中捕获独立元数据和残差数据;然后,通过加权统计特征和滑动窗口获取改进统计特征数据集,并由此数据集构建统计量进行故障检测;最后,利用基于变量贡献图的方法进行过程故障诊断。与传统KICA统计量相比,所提方法的统计量对非线性动态过程中的微小故障具有更高的故障检测性能。应用该方法对一个数值例子和田纳西-伊斯曼（Tennessee-Eastman, TE）过程进行仿真测试,仿真结果显示出所提方法相对于独立元分析（ICA）、KICA、核主成分分析（kernel principal component analysis, KPCA）和统计局部核主成分分析（statistical local kernel principal component analysis, SLKPCA）检测的优势。     

Statistical monitoring of dynamic processes based on dynamic independent component analysis

Most multivariate statistical monitoring methods based on principal component analysis (PCA) assume implicitly that the observations at one time are statistically independent of observations at past time and the latent variables follow a Gaussian distribution. However, in real chemical and biological processes, these assumptions are invalid because of their dynamic and nonlinear characteristics. Therefore, monitoring charts based on conventional PCA tend to show many false alarms and bad detectability. In this paper, a new statistical process monitoring method using dynamic independent component analysis (DICA) is proposed to overcome these disadvantages. ICA is a recently developed technique for revealing hidden factors that underlies sets of measurements followed on a non-Gaussian distribution. Its goal is to decompose a set of multivariate data into a base of statistically independent components without a loss of information. The proposed DICA monitoring method is applying ICA to the augmenting matrix with time-lagged variables. DICA can show more powerful monitoring performance in the case of a dynamic process since it can extract source signals which are independent of the auto- and cross-correlation of variables. It is applied to fault detection in both a simple multivariate dynamic process and the Tennessee Eastman process. The simulation results clearly show that the method effectively detects faults in a multivariate dynamic process.     

Fault detection of non-Gaussian processes based on modified independent component analysis

In this paper, some drawbacks of both the original independent component analysis (ICA) algorithm and the FastICA algorithm are analyzed as follows: the order of the independent components is difficult to be determined; because of using the Newtonian iteration, FastICA method often leads to local minimum solution, and the suitable source signals are not isolated. To solve these problems, a modified ICA algorithm based on particle swarm optimization (PSO) called PSO-ICA is proposed for the purpose of multivariate statistical process monitoring (MSPM). The basic idea of the approach is to use the PSO-ICA algorithm to extract some dominant independent components from normal operating process data. The order of independent components is determined according to the role of resumption of the original signal. The proposed monitoring method is applied to fault detection and diagnosis in the Tennessee Eastman process. Applications indicate that PSO-ICA effectively captures the independent components.     

基于主元分析和核密度估计的多变量统计过程监控及在工厂聚丙烯催化剂反应器的应用

Abstract Data-driven tools, such as principal component analysis （PCA） and independent component analysis （ICA） have been applied to different benchmarks as process monitoring methods. The difference between the two methods is that the components of PCA are still dependent while ICA has no orthogonality constraint and its latentvariables are independent. Process monitoring with PCA often supposes that process data or principal components is Gaussian distribution. However, this kind of constraint cannot be satisfied by several practical processes. To ex-tend the use of PCA, a nonparametric method is added to PCA to overcome the difficulty, and kernel density estimation （KDE） is rather a good choice. Though ICA is based on non-Gaussian distribution intormation, .KDE can help in the close monitoring of the data. Methods, such as PCA, ICA, PCA.with .KDE（KPCA）, and ICA with KDE,（KICA）, are demonstrated and. compared by applying them to a practical industnal Spheripol craft polypropylene catalyzer reactor instead of a laboratory emulator.     

基于KPLS模型的间歇过程产品质量控制

针对间歇过程所具有的非线性特性,提出了一种基于核偏最小二乘(KPLS)模型的最终产品质量控制策略。利用初始条件、批次展开后的过程数据以及最终产品质量建立了间歇过程的KPLS模型;采用基于主成分分析(PCA)映射的预估方法对未知的过程数据进行补充,实现了最终产品质量的在线预测。为了解决最终产品质量的控制,利用T2统计量确定KPLS模型的适用范围,并作为约束引入产品质量控制问题,提高控制策略的可行性;采用粒子群优化(PSO)算法实现了优化问题的高效求解。仿真结果表明,与基于偏最小二乘(PLS)模型的控制策略相比,所提出的方法具有更高的预测精度,且能有效解决产品质量控制中出现的各种问题。     

基于MKECA的非高斯性和非线性共存的间歇过程监测

多向核独立成分分析（multiway kernel independent component analysis,MKICA）在监测间歇过程非高斯性和非线性方面取得了广泛应用,其仅仅是将线性独立成分分析（independent component analysis,ICA）方法利用核主成分分析（kernel principal component analysis,KPCA）白化扩展到非线性领域,但数据经KPCA白化后只考虑数据信息最大化未考虑数据簇结构信息的不足,为解决此问题,采用核熵成分分析（kernel entropy component analysis,KECA）代替KPCA白化的过程监测方法。该方法首先利用AT展开方法将过程三维数据变为二维数据;其次用KECA进行白化处理的同时解决数据的非线性;然后建立ICA监测模型用于非高斯生产过程监测;最后将该方法应用到青霉素发酵仿真和实际的工业过程并与MKICA方法进行对比,验证该方法的有效性。     

基于主元独立性分析与混合核RVM的复杂过程区间预测方法研究及应用

近年来,随着化工过程日趋复杂,对过程监控及关键变量预测提出了更高的要求。传统意义上的点预测已不能满足化工过程上的实际需求,且点预测无法描述过程上的不确定性问题,因此不能很好地把握预测变量的趋势。由此,提出了一种基于主元独立性分析（principal component independent analysis,PCIA）与混合核相关向量机（RVM）的区间预测方法。首先,结合核主元成分分析（KPCA）和独立元分析（ICA）对复杂过程原始变量进行主元成分提取和独立性分析,形成独立主元;其次,将高斯核函数与多项式核函数相结合形成混合核,与RVM结合对得到的独立主元进行回归建模预测,并运用T分布对预测值进行区间估计;然后,构造区间评价综合函数对区间估计结果进行优劣分析,在分析预测区间覆盖率（PICP）及预测区间宽度（NMPIW）的基础上,引入累积偏差（AD）提高区间评判的合理性。最后,将所提方法应用到TE仿真过程进行区间预测分析,仿真结果表明,提出的区间预测方法对实际生产过程具有较高的预测精度和区间估计质量,可以有效地预测关键变量的趋势。     

Application of fault monitoring and diagnosis in process industry based on fourth order moment and singular value decomposition

Principal component analysis (PCA) and partial least squares (PLS) have been frequently used for process industry monitoring; however, their application on industrial sites is limited because they cannot be used to process data with non-Gaussian distribution. Independent component analysis (ICA) has become a powerful modelling method for non-Gaussian process monitoring. However, the ICA-based modelling method has been found to contribute to double the amount of data loss in feature extraction. There are two reasons for this. First, when the PCA algorithm is used to whiten the original data, the smaller principal component is discarded. Second, when selecting independent components, some smaller independent components will be discarded according to the evaluation index. The abovementioned two data feature extraction methods may discard useful information for fault monitoring, which will inevitably lead to inaccurate fault monitoring. To solve this problem, a fault monitoring and diagnosis method based on fourth order moment (FOM) analysis and singular value decomposition (SVD) is proposed. First, the fourth order moments of each process variable were constructed separately. Then, the data space of the fourth order moments was decomposed by singular value decomposition to establish the global monitoring statistics. Finally, the contribution diagram was drawn and the fault diagnosis was performed based on the global monitoring results. The proposed method was applied to the Tennessee Eastman (TE) simulation platform, and its effectiveness and feasibility were verified by a comparison with PCA and ICA.     

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.     

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     

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。     

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。     

Multiphase batch process monitoring based on higher-order cumulant analysis

In this paper, a two-step phase partitioning strategy is proposed. Firstly, the number of phases is automatically determined according to the intra-class and inter-class similarity of feature space data, thus avoiding excessive manual intervention. Secondly, the phases are partitioned by step-wise adding the kernel entropy extended load matrix (KEELM), avoiding the wrong division of phases caused by unstable state of working condition conversion. A process monitoring model based on multiway kernel entropy independent component analysis (MKEICA) is constructed in each sub-phase to deal with complex batch processes with nonlinear and non-Gaussian properties. A new statistics index based on the idea of high order cumulant analysis (HCA) is constructed in each sub-phase for process monitoring. Compared with the traditional second-order statistics, it can obtain high-order statistical information. Finally, the proposed method is applied to the penicillin simulation platform process and compared with the traditional multiway kernel independent components analysis (MKICA) and HCA methods to verify the effectiveness of the method that is mentioned above.