Statistical process monitoring with independent component analysis

In this paper we propose a new statistical method for process monitoring that uses independent component analysis (ICA). ICA is a recently developed method in which the goal is to decompose observed data into linear combinations of statistically independent components [1 and 2]. Such a representation has been shown to capture the essential structure of the data in many applications, including signal separation and feature extraction. The basic idea of our approach is to use ICA to extract the essential independent components that drive a process and to combine them with process monitoring techniques. I², I_e² and SPE charts are proposed as on-line monitoring charts and contribution plots of these statistical quantities are also considered for fault identification. The proposed monitoring method was applied to fault detection and identification in both a simple multivariate process and the simulation benchmark of the biological wastewater treatment process, which is characterized by a variety of fault sources with non-Gaussian characteristics. The simulation results clearly show the power and advantages of ICA monitoring in comparison to PCA monitoring.     

Ensemble modified independent component analysis for enhanced non-Gaussian process monitoring

As a multivariate statistical tool, the modified independent component analysis (MICA) has drawn considerable attention within the non-Gaussian process monitoring circle since it can solve two main problems in the original ICA method. Despite the diversity in applications, the determination logic for non-quadratic functions involved in the iterative procedures of MICA algorithm has always been empirical. Given that the MICA is an unsupervised modeling method, a direct rational study that can conclusively demonstrate which non-quadratic function is optimal for the general purpose of fault detection is inaccessible. The selection of non-quadratic functions is still a challenge that has rarely been attempted. Recognition of this issue and motivated by the superiority of ensemble learning strategy, a novel ensemble MICA (EMICA) modeling approach is presented for enhancing non-Gaussian process monitoring performance. Instead of focusing on a single non-quadratic function, the proposed method combines multiple base MICA models derived from different non-quadratic functions into an ensemble one, and the Bayesian inference is employed as a decision fusion method to form a unique monitoring index for fault detection. The enhanced fault detectability of the EMICA method is also illustrated on two industrial processes.     

Integrating independent component analysis and local outlier factor for plant-wide process monitoring

We propose a novel process monitoring method integrating independent component analysis (ICA) and local outlier factor (LOF). LOF is a recently developed outlier detection technique which is a density-based outlierness calculation method. In the proposed monitoring scheme, ICA transformation is performed and the control limit of LOF value is obtained based on the normal operating condition (NOC) dataset. Then, at the monitoring phase, the LOF value of current observation is computed at each monitoring time, which determines whether the current process is a fault or not. The comparison experiments are conducted with existing ICA-based monitoring schemes on widely used benchmark processes, a simple multivariate process and the Tennessee Eastman process. The proposed scheme shows the improved accuracy over existing schemes. By adopting LOF, the monitoring statistic is computed regardless of data distribution. Therefore, the proposed scheme integrating ICA and LOF is more suitable for real industry where the monitoring variables are the mixture of Gaussian and non-Gaussian variables, whereas existing ICA-based schemes assume only non-Gaussian distribution.     

基于ICA-PCA的化工流程仪表故障诊断

传统的多元统计过程控制(MSPC)的故障诊断方法要求观测变量数据服从高斯分布,然而实际化工流程中的仪表数据中难以满足这一要求。针对这一问题,提出在仪表数据中提取分离出非高斯信息和高斯信息,并分别利用独立元分析法和主元分析法建立不同的故障诊断模型。在检测到发生故障后,通过改进的贡献度算法定位出发生故障的仪表。通过对Tennessee Eastman(TE)过程数据进行仿真研究,验证了ICA-PCA故障诊断法在化工流程仪表不同故障诊断中的有效性。     

Robust multi-scale principal components analysis with applications to process monitoring

Robust multi-scale principal component analysis (RMSPCA) improves multi-scale principal components analysis (MSPCA) techniques by incorporating the uncertainty of signal noise distributions and eliminating/down-weighting the effects of abnormal data in the training set. The novelty of the approach is to integrate MSPCA with the robustness to the typical normality assumption of noisy data. By using an M-estimator based on the generalized T distribution, RMSPCA adaptively transforms the data in the score space at each scale in order to eliminate/down-weight the effects of the outliers in the original data. The robust estimation of the covariance or correlation matrix at each scale is obtained by the proposed approach so that accurate MSPCA models can be obtained for process monitoring purposes. The performance of the proposed approach in process fault detection is illustrated and compared with that of the conventional MSPCA approach through a pilot-scale setting.     

A probabilistic principal component analysis-based approach in process monitoring and fault diagnosis with application in wastewater treatment plant

Probabilistic principal component analysis (PPCA) based approaches have been widely used in the field of process monitoring. However, the traditional PPCA approach is still limited to linear dimensionality reduction. Although the nonlinear projection model of PPCA can be obtained by Gaussian process mapping, the model still lacks robustness and is susceptible to process noise. Therefore, this paper proposes a new nonlinear process monitoring and fault diagnosis approach based on the Bayesian Gaussian latent variable model (Bay-GPLVM). Bay-GPLVM can obtain the posterior distribution rather than point estimation for latent variables, so the model is more robust. Two monitoring statistics corresponding to latent space and residual space are constructed for PM-FD purpose. Further, the cause of fault is analyzed by calculating the gradient value of the variable at the fault point. Compared with several PPCA-based monitoring approaches in theory and practical application, the Bay-GPLVM-based process monitoring approach can better deal with nonlinear processes and show high efficiency in process monitoring.     

Detecting and isolating multiple plant-wide oscillations via spectral independent component analysis

Disturbances that propagate throughout a plant can have an impact on product quality and running costs. There is thus a motivation for the automated detection of plant-wide disturbances and for the isolation of the sources. A new application of independent component analysis (ICA), multi-resolution spectral ICA, is proposed to detect and isolate the sources of multiple oscillations in a chemical process. Its key feature is that it extracts dominant spectrum-like independent components each of which has a narrow-band peak that captures the behaviour of one of the oscillation sources. Additionally, a significance index is presented that links the sources to specific plant measurements in order to facilitate the isolation of the sources of the oscillations. A case study is presented that demonstrates the ability of spectral ICA to detect and isolate multiple dominant oscillations in different frequency ranges in a large data set from an industrial chemical process.     

Integrating independent component analysis and support vector machine for multivariate process monitoring

This study aims to develop an intelligent algorithm by integrating the independent component analysis (ICA) and support vector machine (SVM) for monitoring multivariate processes. For developing a successful SVM-based fault detector, the first step is feature extraction. In real industrial processes, process variables are rarely Gaussian distributed. Thus, this study proposes the application of ICA to extract the hidden information of a non-Gaussian process before conducting SVM. The proposed fault detector will be implemented via two simulated processes and a case study of the Tennessee Eastman process. Results demonstrate that the proposed method possesses superior fault detection when compared to conventional monitoring methods, including PCA, ICA, modified ICA, ICA–PCA and PCA–SVM.     

Laplacian regularized robust principal component analysis for process monitoring

Principal component analysis (PCA) is one of the most widely used techniques for process monitoring. However, it is highly sensitive to sparse errors because of the assumption that data only contains an underlying low-rank structure. To improve classical PCA in this regard, a novel Laplacian regularized robust principal component analysis (LRPCA) framework is proposed, where the “robust” comes from the introduction of a sparse term. By taking advantage of the hypergraph Laplacian, LRPCA not only can represent the global low-dimensional structures, but also capture the intrinsic non-linear geometric information. An efficient alternating direction method of multipliers is designed with convergence guarantee. The resulting subproblems either have closed-form solutions or can be solved by fast solvers. Numerical experiments, including a simulation example and the Tennessee Eastman process, are conducted to illustrate the improved process monitoring performance of the proposed LRPCA.     

参考独立分量分析固定点算法

参考独立分量分析将源信号的先验信息以参考信号的形式引入到算法中,仅实现期望源信号的抽取,消除了传统独立分量分析中抽取信号的不确定性;以期望信号和参考信号的接近性度量作为目标函数提出了一个固定点算法,避免了人为选取步长,同时通过优选初值进一步提高算法的收敛速率。针对合成数据和实际的心电图数据仿真实验,证明了算法的有效性和更好的收敛性。     

An adaptive multimode process monitoring strategy based on mode clustering and mode unfolding

A comprehensive monitoring framework is proposed for multimode processes in which mode clustering and mode unfolding are integrated within an adaptive strategy. To start, an aggregated k-means algorithm produces an optimal ensemble clustering solution for a multimode process dataset. Next, a mode unfolding (MU) scheme enables the development of a single principal component analysis (PCA) model for processes operating under multiple desired steady-states (modes). Finally, adaptive strategies for online mode identification and model updating are presented to address the challenges in fault detection in the presence of multiple operating modes. The validity and usefulness of the adaptive MU-PCA based monitoring framework is demonstrated through a study of the Tennessee Eastman benchmark process.     

基于判别式的核独立元分析*

核独立元分析（KICA）法是近年来发展起来的核化算法,但难以将其用于故障诊断问题。为了解决该问题,对两种核独立元分析算法——基于受限协方差测度的方法KICA2和基于核互信息测度的方法KICA3进行变形得到适用于分类或故障诊断的形式。进一步分析了KICA2与一种核偏最小二乘（KPLS）方法的等价性以及KICA3与核主元分析（KPCA）的等价性。最后对Tennessee Eastman过程进行仿真,说明了方法的有效性。     

Process monitoring of iron-making process in a blast furnace with PCA-based methods

Incidents happening in the blast furnace will strongly affect the stability and smoothness of the iron-making process. Thus far, diagnosis of abnormalities in furnaces still mainly relies on the personal experiences of individual workers in many iron works. In this paper, principal component analysis (PCA)-based algorithms are developed to monitor the iron-making process and achieve early abnormality detection. Because the process exhibits a non-normal distribution and a time-varying nature in the measurement data, a static convex hull-based PCA algorithm (SCHPCA) which replaces the traditional T²-based abnormality detection logic with the convex hull-based abnormality detection logic, and its moving window version, called the moving window convex hull-based PCA algorithm (MWCHPCA) are proposed, respectively. These two algorithms are tested on the real process data to verify their effectiveness in the early abnormality detection of iron-making process.     

基于加权核独立成分分析的故障检测方法

针对核独立成分分析故障检测时忽略各独立成分分量对系统故障贡献度的差异, 提出一种基于加权核独立成分分析的故障检测方法. 使用核独立成分分析提取过程变量的独立成分, 根据核密度估计衡量各独立成分分量对系统故障的贡献度, 对各独立成分分量赋予不同权重, 突出包含有用信息的独立成分分量, 引入局部离群因子在特征空间构造统计量进行故障检测. 基于数值仿真和Tennessee Eastman 数据集的仿真结果表明了所提出方法的优越性.

     

改进的ICA算法及其在特征捆绑中的应用

针对fM RI数据信噪比低、数据量大的特点,将Pearson分布族应用于独立成分分析算法中,提出基于Pearson系统的独立成分分析算法。增加非线性函数生成器,改进调整步长的方法,能根据观测数据自适应地估计非线性函数。改进的算法与原ICA算法相比,运行速度时间缩短,在fM RI信号分离中取得了较好的效果。将该算法应用于颜色和形状的特征捆绑认知中,得出参与捆绑认知的各大脑区域的主要作用,为建立视觉特征捆绑的认知模型提供理论基础。     

改进的快速独立分量分析方法研究

快速独立分量分析算法硬件实现困难,基于Huber M估计函数的独立分量算法硬件实现容易,但是该算法稳健性有待提高。针对这一问题,提出了一种硬件实现容易,而且具有很好稳健性的改进的快速独立分量分析算法。该算法硬件实现容易,且具有很好稳健性的Tukey双权函数作为原算法代价函数中的非线性函数,通过牛顿迭代方法对代价函数进行优化,得到改进的快速独立分量分析算法。仿真实验证明,该算法是有效的,且稳健性较好。     

Concurrent quality and process monitoring with canonical correlation analysis

Canonical correlation analysis (CCA) is a well-known data analysis technique that extracts multidimensional correlation structure between two sets of variables. CCA focuses on maximizing the correlation between quality and process data, which leads to the efficient use of latent dimensions. However, CCA does not focus on exploiting the variance or the magnitude of variations in the data, making it rarely used for quality and process monitoring. In addition, it suffers from collinearity problems that often exist in the process data. To overcome this shortcoming of CCA, a modified CCA method with regularization is developed to extract correlation between process variables and quality variables. Next, to handle the issue that CCA focuses only on correlation but ignores variance information, a new concurrent CCA (CCCA) modeling method with regularization is proposed to exploit the variance and covariance in the process-specific and quality-specific spaces. The CCCA method retains the CCA's efficiency in predicting the quality while exploiting the variance structure for quality and process monitoring using subsequent principal component decompositions. The corresponding monitoring statistics and control limits are then developed in the decomposed subspaces. Numerical simulation examples and the Tennessee Eastman process are used to demonstrate the effectiveness of the CCCA-based monitoring method.     

Increasing mapping based hidden Markov model for dynamic process monitoring and diagnosis

Hidden Markov models (HMMs) perform parameter estimation based on the forward–backward (FB) procedure and the Baum–Welch (BW) algorithm. The two algorithms together may increase the computational complexity and the difficulty to understand the algorithm structure of HMMs clearly. In this study, an increasing mapping based hidden Markov model (IMHMM) is proposed. Between the observation sequence and possible state sequence an increasing mapping is established. The re-estimation formulas for the model parameters are derived straightforwardly based on these mappings instead of FB variables. The IMHMM has simpler algorithm structure and lower storage requirement than the HMM. Based on IMHMM, an expandable process monitoring and fault diagnosis framework for large-scale dynamical process is developed. To characterize the dynamic process, a novel index considering serial correlation is used to evaluate process state. The presented methodology is carried out in Tennessee Eastman process (TEP). The results show improvement over HMM in terms of memory complexity and training time of the model. Also, the power of IMHMM can be observed compared with principal component analysis (PCA) based methods.     

时段划分的多向主元分析间歇过程监测及故障变量追溯

针对间歇过程的多时段特性,提出一种生产过程操作时段划分方法.该方法利用反映过程特性变化的负载矩阵以及主成份矩阵的变化实现了间歇过程子时段的两步划分.提出了基于加权负载向量夹角余弦的负载矩阵相似性度量以及基于加权奇异值变化的奇异值矩阵相似性度量方法,以更客观的反映负载矩阵以及奇异值矩阵的相似性,进而更准确的判断过程特性的变化.根据同一操作子时段的过程特性,其负载矩阵和奇异值矩阵相似性较大的特点,实现了生产过程的子时段划分.将基于子时段划分的多向主元分析(MPCA)建模应用于三水箱系统的在线监测和故障变量追溯,实验结果验证了该方法的有效性.