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     

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.     

Robust model predictive control and fault handling of batch processes

This work considers the control of batch processes subject to input constraints and model uncertainty with the objective of achieving a desired product quality. First, a computationally efficient nonlinear robust Model Predictive Control (MPC) is designed. The robust MPC scheme uses robust reverse‐time reachability regions (RTRRs), which we define as the set of process states that can be driven to a desired neighborhood of the target end‐point subject to input constraints and model uncertainty. A multilevel optimization‐based algorithm to generate robust RTRRs for specified uncertainty bounds is presented. We then consider the problem of uncertain batch processes subject to finite duration faults in the control actuators. Using the robust RTRR‐based MPC as the main tool, a robust safe‐steering framework is developed to address the problem of how to operate the functioning inputs during the fault repair period to ensure that the desired end‐point neighborhood can be reached upon recovery of the full control effort. The applicability of the proposed robust RTRR‐based controller and safe‐steering framework subject to limited availability of measurements and sensor noise are illustrated using a fed‐batch reactor system. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

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.     

Active fault isolation of nonlinear process systems

This work considers the problem of designing an active fault‐isolation scheme for nonlinear process systems subject to uncertainty. The faults under consideration include bounded actuator faults and process disturbances. The key idea of the proposed method is to exploit the nonlinear way that faults affect the process evolution through supervisory feedback control. To this end, a dedicated fault‐isolation residual and its time‐varying threshold are generated for each fault by treating other faults as disturbances. A fault is isolated when the corresponding residual breaches its threshold. These residuals, however, may not be sensitive to faults in the operating region under nominal operation. To make these residuals sensitive to faults, a switching rule is designed to drive the process states, upon detection of a fault, to move toward an operating point that, for any given fault, results in the reduction of the effect of other faults on the evolution of the same process state. This idea is then generalized to sequentially operate the process at multiple operating points that facilitate isolation of different faults for the case where the residuals are not simultaneously sensitive to faults at a single operating point. The effectiveness of the proposed active fault‐isolation scheme is illustrated using a chemical reactor example and demonstrated through application to a solution copolymerization of methyl methacrylate and vinyl acetate. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2435–2453, 2013     

Sequential and iterative architectures for distributed model predictive control of nonlinear process systems

In this work, we focus on distributed model predictive control of large scale nonlinear process systems in which several distinct sets of manipulated inputs are used to regulate the process. For each set of manipulated inputs, a different model predictive controller is used to compute the control actions, which is able to communicate with the rest of the controllers in making its decisions. Under the assumption that feedback of the state of the process is available to all the distributed controllers at each sampling time and a model of the plant is available, we propose two different distributed model predictive control architectures. In the first architecture, the distributed controllers use a one‐directional communication strategy, are evaluated in sequence and each controller is evaluated only once at each sampling time; in the second architecture, the distributed controllers utilize a bi‐directional communication strategy, are evaluated in parallel and iterate to improve closed‐loop performance. In the design of the distributed model predictive controllers, Lyapunov‐based model predictive control techniques are used. To ensure the stability of the closed‐loop system, each model predictive controller in both architectures incorporates a stability constraint which is based on a suitable Lyapunov‐based controller. We prove that the proposed distributed model predictive control architectures enforce practical stability in the closed‐loop system and optimal performance. The theoretical results are illustrated through a catalytic alkylation of benzene process example. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

On-line process fault detection and diagnosis in plants with recycle

A process fault detection and diagnosis system is performed for the complex case of plant-wide control in processes with recycle in which the control system is the inventory control. It is considered an artificial neural network based supplement of a fuzzy system in a block oriented configuration. A methodology to design the system is described. As a case study, a chemical plant with a recycle stream is considered. Faults in supply of raw materials and in controllers are simulated. Performance of the system to handle simultaneous faults is also analysed. A comparison is made against a classification method (artificial neural networks) and an inference method (knowledge — based system).     

基于WPRKPCA的非线性化工过程微小故障检测

传统核主元分析法（KPCA）是一种广泛应用的非线性化工过程故障检测方法,但是其未充分利用过程数据的概率分布信息,往往难以有效检测过程中的微小故障。针对传统KPCA方法的局限性,本文提出了一种基于加权概率相关核主元分析（WPRKPCA）的非线性化工过程微小故障检测方法。与传统KPCA方法监控核成分的变化不同,该方法利用Kullback Leibler散度（KLD）度量核成分的概率分布变化,进而建立基于KLD成分的统计监控模型,以充分挖掘过程数据所包含的概率信息。进一步考虑到不同KLD成分承载故障信息的差异性,该方法设计了一种基于核密度估计的指数加权策略,根据KLD成分描述故障信息程度的差异分配相应的权值,以加强监控模型对微小故障检测的灵敏性。在一个数值例子和连续搅拌反应器（CSTR）系统上的仿真结果表明,本文所提方法具有比传统KPCA方法更好的微小故障检测性能。     

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.     

基于KECA的非线性工业过程故障检测与诊断新方法

提出了一种基于核熵成分分析（kernel entropy component analysis，KECA）的非线性过程故障检测与诊断新方法。该方法首先利用KECA获取过程数据的得分向量及非线性特征子空间；然后鉴于KECA可以以角结构的方式揭示数据中潜在的集群结构，设计了基于角度的监测指标VoA。该指标通过各得分向量之间的角度方差来描述变换后数据间的结构差异,并根据角度方差的变化情况实现故障检测；接着，为了在检测到故障后有效地进行故障识别，构建了KECA相似度因子来度量特征子空间的相似程度以识别故障模式；最后，以非线性数值案例及Tennessee Eastman过程进行仿真测试研究，结果验证了所提方法的可行性及有效性。     

基于主元分析法的冷水机组传感器故障检测效率分析

冷水机组是一个高度非线性的复杂系统,其自控系统传感器故障会导致冷水机组的运行偏离正常状态和能耗浪费。采用冷水机组正常运行数据,通过多元统计方法中的主元分析法建立训练矩阵,利用平方预测误差进行故障分析工作。引入不同程度故障,分析主元分析法的检测效率。结果表明,主元分析法故障检测效果明显,但对于不同传感器的不同程度故障,故障检测的误判率存在一定的差异。     

Reconstruction in integrating fault spaces for fault identification with kernel independent component analysis

In the original fault identification methods, contribution plots are popular. However, it is not accurate because of the smearing effect. In addition, traditional contribution plots cannot be applied to nonlinear process because there seems no way to accurately calculate variable contributions. As a comparison, the reconstruction method is widely used in fault identification for finding the root causes of the fault. For fault detection and identification of actual industrial process with nonlinear and non-Gaussian features, a new reconstruction-based fault identification method with kernel independent component analysis (KICA) is developed in this article. The proposed method, reconstruction in integrating fault spaces (RIFSs), extends the classic reconstruction-based fault identification approach to KICA for the first time, and develops the reconstruction method from unidimensional faults to multidimensional ones for nonlinear cases. Furthermore, the number of reconstruction is effectively reduced on the basis of the integrating fault spaces (IFSs) which are composed of fault subspaces satisfying orthogonal to each other from the known fault set. In addition, fault magnitude, indicating the adjustment magnitude of a fault sample back to normal range, is used as index to identify faults, and it makes the fault identification problem become more straightforward than with the existing fault identification index, such as ratio (index I) or the reconstructed statistics (index II). Finally, the proposed method is applied to the fault detection and identification on cyanide leaching of gold, which shows its feasibility and efficiency for both sensor faults and complex process faults.     

基于加权深度支持向量数据描述的工业过程故障检测

传统支持向量数据描述（SVDD）方法本质上采用浅层学习框架,难以有效监控非线性工业过程的复杂故障。针对此问题,提出一种基于加权深度支持向量数据描述（WDSVDD）的故障检测方法。该方法一方面在深度学习框架下重新定义SVDD优化目标函数,构建基于深度特征的深度SVDD监控模型（DSVDD）,并利用核密度估计法计算监控指标的统计控制限;另一方面,考虑到深度特征的故障敏感度差异特性,在DSVDD监控模型中设计特征加权层,分别从静态和动态信息分析角度给出权重因子的计算方法,利用权重因子突出故障敏感特征的影响以提高故障检测率。应用于一个典型化工过程的测试结果表明,所研究的方法能够比传统SVDD方法更有效地监控过程中复杂故障的发生。     

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。     

基于T-S模糊模型的间歇过程的迭代学习容错控制

间歇过程不仅具有强非线性,同时还会受到诸如执行器等故障影响,研究非线性间歇过程在具有故障的情况下依然稳定运行至关重要。针对执行器增益故障及系统所具有的强非线性,提出一种新的基于间歇过程的T-S模糊模型的复合迭代学习容错控制方法。首先根据间歇过程的非线性模型,利用扇区非线性方法建立其T-S模糊故障模型,再利用间歇过程的二维特性与重复特性,在2D系统理论框架内,设计2D复合ILC容错控制器,进而构建此T-S模糊模型的等价二维Rosser模型,接着利用Lyapunov方法给出系统稳定充分条件并求解控制器增益。针对强非线性的连续搅拌釜进行仿真,结果表明所提出方法具有可行性与有效性。     

基于加权概率CVDA的动态化工系统微小故障检测

典型变量差异度分析（CVDA）是近年来提出的一种新型动态过程监控方法,已在微小故障检测领域获得成功应用。针对传统CVDA方法忽视了特征量的概率信息挖掘问题,提出一种基于加权概率CVDA（WPCVDA）的动态化工系统微小故障检测方法。一方面,该方法在基本CVDA模型特征基础上引入Wasserstein距离（WD）度量特征量概率分布的变化,构造概率化的WD特征提高CVDA模型对微小故障的灵敏度;另一方面,进一步考虑不同的WD特征成分携带故障信息的差异性,设计一种自适应权值计算策略,为关键的故障敏感特征成分设置大的权值,突出其在监控统计量中的作用。在一个标准化工过程的验证结果说明,所提出的WPCVDA方法比传统CVDA方法具有更好的微小故障检测性能。     

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.     

Multi-linear model-based fault detection during process transitions

Process transitions due to startup, shutdown, product slate changes, and feedstock changes are frequent in the process industry. Experienced operators usually execute transitions in the manual mode as transitions may involve unusual conditions and nonlinear process behavior. Processes are therefore more prone to faults as well as inadvertent operator errors during transitions. Fault detection during transition is critical as faults can lead to abnormal situations and even cause accidents. This paper proposes a model-based fault detection scheme that involves decomposition of nonlinear transient systems into multiple linear modeling regimes. Kalman filters and open-loop observers are used for state estimation and residual generation based on the resulting linear models. Analysis of residuals using thresholds, faults tags, and logic charts enables on-line detection and isolation of faults. The multi-linear model-based fault detection technique has been implemented using Matlab and successfully tested to detect process faults and operator errors during the startup transition of highly nonlinear pH neutralization reactor in the laboratory.     

一类不匹配不确定动态系统的鲁棒执行器故障检测与重构

针对一类不匹配不确定性动态系统,将不匹配不确定性的滑模控制方法与线性矩阵不等式（LMI）方法结合,设计一种新的鲁棒滑模观测器,提出了不匹配不确定动态系统滑模观测器稳定的充分必要条件以及LMI的存在定理,并证明了对系统不确定性以及外界干扰具有鲁棒性。无须对动态系统进行规范化处理,直接利用LMI方法求解鲁棒观测器增益矩阵,简化了滑模观测器设计过程。根据上述设计的鲁棒滑模观测器,应用等价输出误差介入原理和LMI方法,设计重构执行器故障的优化策略,提出在线获取故障信息的鲁棒执行器故障检测与重构方法,实现执行器故障的检测与重构。数字仿真验证了执行器故障重构方法的可靠性。     

Distributed output‐feedback fault detection and isolation of cascade process networks

Distributed output‐feedback fault detection and isolation (FDI) of nonlinear cascade process networks that can be divided into subsystems is considered. Based on the assumption that an exponentially convergent estimator exists for each subsystem, a distributed state estimation system is developed. In the distributed state estimation system, a compensator is designed for each subsystem to compensate for subsystem interaction and the estimators for subsystems communicate to exchange information. It is shown that when there is no fault, the estimation error of the distributed estimation system converges to zero in the absence of system disturbances and measurement noise. For each subsystem, a state predictor is also designed to provide subsystem state predictions. A residual generator is designed for each subsystem based on subsystem state estimates given by the distributed state estimation system and subsystem state predictions given by the predictor. A subsystem residual generator generates two residual sequences, which act as references for FDI. A distributed FDI mechanism is proposed based on residuals. The proposed approach is able to handle both actuator faults and sensor faults by evaluating the residual signals. A chemical process example is introduced to demonstrate the effectiveness of the distributed FDI mechanism. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4329–4342, 2017