Decentralized Fault Isolation by a Combination of Transfer Entropy and Classification Methods

Early fault detection and isolation in industrial systems is vitally necessary to prevent any potential product damage. The paper proposes a new decentralized multi-unit fault isolation methodology in which all the known process faults with similar time signatures are grouped into appropriate categories. An innovative genetic algorithm-based method is introduced to explore for optimum plant zones in a large-scale plant wide search to appropriately configure each architectural unit, having less reliance on excess process variables with redundant and uncorrelated diagnostic information. The methodology employs a set of Bayes and radial basis function neural network classifiers to properly isolate the most usual known faults. A new idea based on transfer entropy algorithm has been integrated in the decentralized configuration to be triggered for isolation of novel faults which have been left unrecognized by the set of maintained classifiers. Experimental results clearly demonstrate that the proposed methods are considerably superior to the conventional centralized methods.     

A fault magnitude based strategy for effective fault classification

A common approach in fault diagnosis is monitoring the deviations of measured variables from the values at normal operations to identify the root causes of faults. When the number of conceivable faults is larger than that of predictive variables, conventional approaches can yield ambiguous diagnosis results including multiple fault candidates. To address the issue, this work proposes a fault magnitude based strategy. Signed digraph is first used to identify qualitative relationships between process variables and faults. Empirical models for predicting process variables under assumed faults are then constructed with support vector regression (SVR). Fault magnitude data are projected onto principal components subspace, and the mapping from scores to fault magnitudes is learned via SVR. This model can estimate fault magnitudes and discriminate a true fault among multiple candidates when different fault magnitudes yield distinguishable responses in the monitored variables. The efficacy of the proposed approach is illustrated on an actuator benchmark problem.     

Detection and management of actuator faults in controlled particulate processes using population balance models

This paper presents a methodology for the design of an integrated fault detection and fault-tolerant control (FD-FTC) architecture for particulate processes described by population balance models (PBMs) with control constraints, actuator faults and a limited number of process measurements. The architecture integrates model-based fault detection, state estimation, nonlinear feedback and supervisory control on the basis of an appropriate reduced-order model that captures the dominant dynamics of the process and is obtained through application of the method of weighted residuals. The architecture comprises a family of control configurations together with a fault detection filter and a supervisor. For each configuration, a stabilizing output feedback controller with well-characterized stability properties is designed through the combination of a state feedback controller and a state observer that uses the available measurements of principal moments of the particle size distribution (PSD) and the continuous-phase variables to provide appropriate state estimates. A fault detection filter that simulates the behavior of the fault-free, reduced-order model is designed, and its discrepancy from the behavior of the actual process state estimates is used as a residual for fault detection. Finally, a switching law based on the stability regions of the constituent control configurations is derived to reconfigure the control system in a way that preserves closed-loop stability in the event of fault detection. Appropriate fault detection thresholds and control reconfiguration criteria that account for model reduction and state estimation errors are derived for the implementation of the FD-FTC architecture on the particulate process. Finally, the methodology is applied to the problem of constrained, actuator fault-tolerant stabilization of an unstable steady-state of a continuous crystallizer.     

基于约翰逊转换的鲁棒化工过程监控方法

化工厂中一个小故障可能导致大事故,从而造成生命财产损失和环境破坏。为了防止小故障演变成大事故,化学工业需要有效的过程监控来及时检测故障和诊断故障原因。传统化工过程监控方法主元分析法(Principal Component Analysis, PCA)假设数据服从高斯分布,实践中有时并不满足该条件。此外,其使用方差、协方差捕捉数据非线性变化时,鲁棒性较差。本工作提出一种改进的主元分析法—基于约翰逊转换的鲁棒过程监控方法。首先引入约翰逊正态转换(Johnson Transformation)使过程数据服从高斯分布;其次使用鲁棒性强的斯皮尔曼相关系数(Spearman Correlation Coefficient)矩阵代替传统主元分析法的协方差矩阵提取特征向量,构造特征空间;最后将过程数据投影到特征空间,使用T2和SPE统计量实施过程监控。将此方法应用于TE过程故障案例,并与PCA和核主元分析法(Kernel Principal Component Analysis, KPCA)对比,验证了此方法的有效性。     

基于加权互信息主元分析算法的质量相关故障检测

质量相关的故障检测已成为近几年研究热点,它的目标是在过程监测中,对质量相关的故障检测率更高,对质量无关的故障少报警或不报警。传统主元分析算法的故障检测会对所有故障均报警,不能达到上述要求。另外,在实际工业生产中,质量变量通常难以实时获得,需要后续分析或延时得到。为此,提出一种融合贝叶斯推断与互信息的加权互信息主元分析算法。首先利用贝叶斯推断的加权方法将度量过程变量和质量变量之间相关关系的互信息进行融合,选出包含质量变量信息量最大的一组过程变量。然后对过程变量利用主元分析（principal component analysis,PCA）进行统计建模,再次根据加权互信息选出包含质量变量信息量最大的主元,建立统计量进行故障检测。最后,通过实验验证该方法的可行性和有效性。     

Uncertainty quantification and global sensitivity analysis of complex chemical process using a generalized polynomial chaos approach

Uncertainties are ubiquitous and unavoidable in process design and modeling. Because they can significantly affect the safety, reliability and economic decisions, it is important to quantify these uncertainties and reflect their propagation effect to process design. This paper proposes the application of generalized polynomial chaos (gPC)-based approach for uncertainty quantification and sensitivity analysis of complex chemical processes. The gPC approach approximates the dependence of a process state or output on the process inputs and parameters through expansion on an orthogonal polynomial basis. All statistical information of the interested quantity (output) can be obtained from the surrogate gPC model. The proposed methodology was compared with the traditional Monte-Carlo and Quasi Monte-Carlo sampling-based approaches to illustrate its advantages in terms of the computational efficiency. The result showed that the gPC method reduces computational effort for uncertainty quantification of complex chemical processes with an acceptable accuracy. Furthermore, Sobol’s sensitivity indices to identify influential random inputs can be obtained directly from the surrogated gPC model, which in turn further reduces the required simulations remarkably. The framework developed in this study can be usefully applied to the robust design of complex processes under uncertainties.     

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。     

Enhanced statistical analysis of nonlinear processes using KPCA, KICA and SVM

In this paper, some drawbacks of original kernel independent component analysis (KICA) and support vector machine (SVM) algorithms are analyzed for the purpose of multivariate statistical process monitoring (MSPM). When the measured variables follow non-Gaussian distribution, KICA provides more meaningful knowledge by extracting higher-order statistics compared with PCA and kernel principal component analysis (KPCA). However, in real industrial processes, process variables are complex and are not absolutely Gaussian or non-Gaussian distributed. Any single technique is not sufficient to extract the hidden information. Hence, both KICA (non-Gaussion part) and KPCA (Gaussion part) are used for fault detection in this paper, which combine the advantages of KPCA and KICA to develop a nonlinear dynamic approach to detect fault online compared to other nonlinear approaches. Because SVM is available for classifying faults, it is used to diagnose fault in this paper.For above mentioned kernel methods, the calculation of eigenvectors and support vectors will be time consuming when the sample number becomes large. Hence, some dissimilar data are analyzed in the input and feature space.The proposed approach is applied to the fault detection and diagnosis in the Tennessee Eastman process. Application of the proposed approach indicates that proposed method effectively captures the nonlinear dynamics in the process variables.     

基于双层局部KPCA的非线性过程微小故障检测方法

针对传统核主元分析（KPCA）方法难以有效检测微小故障的问题,提出一种基于双层局部核主元分析（double-level local kernel principal component analysis,DLKPCA）的非线性过程微小故障检测方法。该方法从变量和样本两个角度来挖掘数据内部的局部信息,以提高故障检测能力。首先,利用变量分块思想,基于不同变量与核主元之间互信息相关度的相似性,将所有过程变量划分多个局部变量块。然后,构建基于得分向量和特征值的残差函数以挖掘样本局部信息。最后利用贝叶斯融合策略对各块的结果进行融合。在田纳西-伊斯曼基准过程的仿真结果表明,在微小故障检测方面,本文所提方法具有比传统KPCA方法更好的故障检测性能。     

Multiway discrete hidden Markov model‐based approach for dynamic batch process monitoring and fault classification

A new multiway discrete hidden Markov model (MDHMM)‐based approach is proposed in this article for fault detection and classification in complex batch or semibatch process with inherent dynamics and system uncertainty. The probabilistic inference along the state transitions in MDHMM can effectively extract the dynamic and stochastic patterns in the process operation. Furthermore, the used multiway analysis is able to transform the three‐dimensional (3‐D) data matrices into 2‐D measurement‐state data sets for hidden Markov model estimation and state path optimization. The proposed MDHMM approach is applied to fed‐batch penicillin fermentation process and compared to the conventional multiway principal component analysis (MPCA) and multiway dynamic principal component analysis (MDPCA) methods in three faulty scenarios. The monitoring results demonstrate that the MDHMM approach is superior to both the MPCA and MDPCA methods in terms of fault detection and false alarm rates. In addition, the supervised MDHMM approach is able to classify different types of process faults with high fidelity. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Nonlinear multiscale modelling for fault detection and identification

In order to detect abnormal events at different scales, a number of multiscale multivariate statistical process control (MSPC) approaches which combine a multivariate linear projection model with multiresolution analysis have been suggested. In this paper, a new nonlinear multiscale-MSPC method is proposed to address multivariate process performance monitoring and in particular fault diagnostics in nonlinear processes. A kernel principal component analysis (KPCA) model, which not only captures nonlinear relationships between variables but also reduces the dimensionality of the data, is built with the reconstructed data obtained by performing wavelet transform and inverse wavelet transform sequentially on measured data. A guideline is given for both off-line and on-line implementations of the approach. Two monitoring statistics used in multiscale KPCA-based process monitoring are used for fault detection. Furthermore, variable contributions to monitoring statistics are also derived by calculating the derivative of the monitoring statistics with respect to the variables. An intensive simulation study on a continuous stirred tank reactor process and a comparison of the proposed approach with several existing methods in terms of false alarm rate, missed alarm rate and detection delay, demonstrate that the proposed method for detecting and identifying faults outperforms current approaches.     

Hierarchical monitoring of industrial processes for fault detection,fault grade evaluation,and fault diagnosis

Traditional process monitoring methods cannot evaluate and grade the degree of harm that faults can cause to an industrial process. Consequently, a process could be shut down inadvertently when harmless faults occur. To overcome such problems, we propose a hierarchical process monitoring method for fault detection, fault grade evaluation, and fault diagnosis. First, we propose fault grade classification principles for subdividing faults into three grades: harmless, mild, and severe, according to the harm the fault can cause to the process. Second, two‐level indices are constructed for fault detection and evaluation, with the first‐level indices used to detect the occurrence of faults while the second‐level indices are used to determine the fault grade. Finally, to identify the root cause of the fault, we propose a new online fault diagnosis method based on the square deviation magnitude. The effectiveness and advantages of the proposed methods are illustrated with an industrial case study. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2781–2795, 2017     

A unified framework for detection, isolation and compensation of actuator faults in uncertain particulate processes

This paper presents a methodology for the robust detection, isolation and compensation of control actuator faults in particulate processes described by population balance models with control constraints and time-varying uncertain variables. The main idea is to shape the fault-free closed-loop process response via robust feedback control in a way that enables the derivation of performance-based fault detection and isolation (FDI) rules that are less sensitive to the uncertainty. Initially, an approximate finite-dimensional system that captures the dominant process dynamics is derived and decomposed into interconnected subsystems with each subsystem directly influenced by a single manipulated input. The decomposition is facilitated by the specific structure of the process input operator. A robustly stabilizing bounded feedback controller is then designed for each subsystem to enforce an arbitrary degree of asymptotic attenuation of the effect of the uncertainty in the absence of faults. The synthesis leads to (1) an explicit characterization of the fault-free behavior of each subsystem in terms of a time-varying bound on an appropriate Lyapunov function and (2) an explicit characterization of the robust stability region in terms of the control constraints and the size of the uncertainty. Using the fault-free Lyapunov dissipation bounds as thresholds for FDI in each subsystem, the detection and isolation of faults in a given actuator is accomplished by monitoring the evolution of the system within the stability region and declaring a fault if the threshold is breached. The thresholds are linked to the achievable degree of asymptotic uncertainty attenuation and can therefore be properly tuned by proper tuning of the controllers, thus making the FDI criteria less sensitive to the uncertainty. The robust FDI scheme is integrated with a robust stability-based controller reconfiguration strategy that preserves closed-loop stability following FDI. Finally, the implementation of the fault-tolerant control architecture on the particulate process is discussed and the proposed methodology is applied to the problem of robust fault-tolerant control of a continuous crystallizer with a fines trap.     

变量加权型主元分析算法及其在故障检测中的应用

传统主成分分析（PCA）算法旨在挖掘训练数据各变量间的相关性特征,已在数据驱动的故障检测领域得到了广泛的研究与应用。然而,传统PCA方法在建模过程中通常认为各个测量变量的重要性是一致的,因此不能有效而全面地描述出变量间相关性的差异。为此,提出一种变量加权型PCA（VWPCA）算法并将之应用于故障检测。首先,通过对训练数据进行加权处理,使处理后的数据能够充分体现出变量间相关性的差异。然后,在此基础上建立分布式的PCA故障检测模型。在线实施故障检测时,则通过贝叶斯准则将多组监测结果融合为一组概率指标。VWPCA方法通过相关性大小为各变量赋予不同的权值,从而将相关性差异考虑进了PCA的建模过程中,相应模型对训练数据特征的描述也就更全面。最后,通过在TE过程上的测试验证VWPCA方法用于故障检测的优越性。     

Robust fault detection and monitoring of hybrid process systems with uncertain mode transitions

A methodology for fault detection and monitoring of a class of hybrid process systems modeled by switched nonlinear systems with control actuator faults, uncertain continuous dynamics, and uncertain mode transitions is presented. A robust hybrid monitoring scheme that distinguishes reliably between faults, mode transitions, and uncertainty is developed using tools from unknown input observer theory and results from Lyapunov stability theory. The monitoring scheme consists of (1) a family of dedicated mode observers that locate the active operating mode at any given time and detect mode switches, (2) a family of robust Lyapunov‐based fault detection schemes that detect the faults within the continuous modes, and (3) a supervisor that synchronizes the switching between different controllers and different fault detectors as the process transitions from one mode to another. A key idea of the developed framework is to design the mode observers in a way that facilitates the identification of the active mode without information from the controllers and renders the residuals insensitive to the faults and uncertainties in the constituent subsystems. The implementation of the developed monitoring scheme is demonstrated using a simulated model of a chemical reactor that switches between multiple operating modes. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

基于PCA混合模型的多工况过程监控

针对传统多元统计故障检测方法大多假设测量数据服从单一高斯分布的不足,提出了一种基于PCA(principal component analysis)混合模型的多工况过程监测方法。首先通过直接对混合模型的各高斯成分的协方差进行PCA降维变换,使得协方差阵对角化,既减少了运算量又避免了变量相关而导致的奇异性问题;同时采用BYY增量EM算法自动获取混合模型的最佳混合分量数目,避免了常规EM算法的不足。所得的混合模型,除包括均值、协方差和先验概率等参数外,还包括了PCA载荷阵,即对每个混合元建立了PCA模型。然后给出了统计量定义,实现对多工况过程的故障检测。数值例子和TE过程的应用表明,本文提出的方法无需过程先验知识,能自动获取工况数目、精确估计各个工况的统计特性,并更准确及时地检测出多工况过程的各种故障。     

An embedded fault detection, isolation and accommodation system in a model predictive controller for an industrial benchmark process

Fault detection and isolation (FDI) for industrial processes has been actively studied during the last decades. Traditionally, the most widely implemented FDI methods have been based on model-based approaches. In modern process industry, however, there is a demand for data-based methods due to the complexity and limited availability of the mechanistic models. The aim of this paper is to present a data-based, fault tolerant control (FTC) system for a simulated industrial benchmark process, Shell control problem. Data-based FDI systems, employing principal component analysis (PCA), partial least squares (PLS) and subspace model identification (SMI) are presented for achieving fault tolerance in co-operation with controllers. The effectiveness of the methods is tested by introducing faults in simulated process measurements. The process is controlled by using model predictive control (MPC). To compare the effectiveness of the MPC, the FTC system is also tested with a control strategy based on a set of PI controllers.     

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。     

基于MAF的传感器故障检测与诊断

针对工业控制系统中变量之间既存在线性相关性,且在时间结构上呈现自相关的特点,提出了一种基于最小/最大自相关因子(min/max autocorrelation factors, MAF)分析的传感器故障检测与诊断方法。首先,利用正常工况下的历史数据进行自相关因子分析,获得强自相关因子和弱自相关因子;在此基础上构造故障检测统计量,由核密度估计方法获得故障检测控制限,根据贡献图进行传感器故障定位。将所提出的方法应用于连续反应釜仿真过程的传感器故障检测与诊断,与经典的多变量统计方法——主元分析方法相比,所提出的方法能避免虚警,更快地检测缓变故障,并能更好地诊断和解释复杂故障。     

Integrated nonlinear model predictive fault tolerant control and multiple model based fault detection and diagnosis

In this paper, a new fault-tolerant control approach is presented for a class of nonlinear systems, which preserves system stability despite a time delay in fault detection. The faults are assumed to occur in the actuators and are modeled for the general form of affine nonlinear systems. A fault detection and diagnosis (FDD) block is designed based on the multiple model method. The bank of extended Kalman filters (EKF) is used to detect predefined actuator faults and to estimate the unknown parameters of actuator position. The estimated parameters are then used to correct the model of the faulty system and to reconfigure the controller. The reconfigurable controller is designed based on the stabilizing nonlinear model predictive control (NMPC) scheme. On the other hand, in the duration between fault occurrence and fault detection, because of the mismatch between the process and the model, the system states may go off the attraction region. The proposed method is based on designing multiple local controllers for individual predefined faults. Depending on the value of a system variable at the moment of fault detection, one of these controllers will operate. This leads to a stability region of a set of auxiliary equilibrium points (AEPs), which is larger than the attraction region. Moreover, a framework for preserving system stability is presented. Finally, a practical chemical process example is presented to illustrate the effectiveness of this method.