Machine Learning Framework for Causal Modeling for Process Fault Diagnosis and Mechanistic Explanation Generation

Machine learning models, typically deep learning models, often come at the cost of explainability. To generate explanations of such systems, models need to be rooted in first-principles, at least mechanistically. In this work we look at a gamete of machine learning models based on different levels of process knowledge for process fault diagnosis and generating mechanistic explanations of processes. In chapter 1, we introduce the thesis using a range of problems from causality, explainability, aiming towards the goal of generating mechanistic explanations of process systems. Chapter 2 looks at an approach for generating causal models purely through data-centric approach, with minimal process knowledge with respect to equipment connectivity and identifying causality in the domains. These causal models generated can be utilized for process fault diagnosis. Chapter 3 and chapter 4 show how deep learning models can be used for both classification for process fault diagnosis and regression. We see that depending on the hyperparameters, i.e., purely the breadth and depth of a neural network, the learned hidden representations vary from a simple set of features, to more complex sets of features. While these hidden representations may be exploited to aid in classification and regression problems, the true explanations of these representations do not correlate with mechanisms in the system of interest. There is thus a requirement to add more mechanistic information about the features generated to aid in explainability. Chapter 5 shows how incorporating process knowledge can aid in generating such mechanistic explanations based on automated variable transformations. In this chapter we show how process knowledge can be used to generate features, or model forms to generate explainable models. These models have the ability of extracting the true models of the system from the model knowledge provided

Qualitative Fault Detection and Hazard Analysis Based on Signed Directed Graphs for Large-Scale Complex Systems

Nowadays in modern industries, the scale and complexity of process systems are increased continuously. These systems are subject to low productivity, system faults or even hazards because of various conditions such as mis-operation, equipment quality change, externa

Minimising the kullback-leibler divergence for model selection in distributed nonlinear systems

© 2018 by the authors. The Kullback-Leibler (KL) divergence is a fundamental measure of information geometry that is used in a variety of contexts in artificial intelligence. We show that, when system dynamics are given by distributed nonlinear systems, this measure can be decomposed as a function of two information-theoretic measures, transfer entropy and stochastic interaction. More specifically, these measures are applicable when selecting a candidate model for a distributed system, where individual subsystems are coupled via latent variables and observed through a filter. We represent this model as a directed acyclic graph (DAG) that characterises the unidirectional coupling between subsystems. Standard approaches to structure learning are not applicable in this framework due to the hidden variables; however, we can exploit the properties of certain dynamical systems to formulate exact methods based on differential topology. We approach the problem by using reconstruction theorems to derive an analytical expression for the KL divergence of a candidate DAG from the observed dataset. Using this result, we present a scoring function based on transfer entropy to be used as a subroutine in a structure learning algorithm. We then demonstrate its use in recovering the structure of coupled Lorenz and Rössler systems

Plant-Wide Diagnosis: Cause-and-Effect Analysis Using Process Connectivity and Directionality Information

Production plants used in modern process industry must produce products that meet stringent environmental, quality and profitability constraints. In such integrated plants, non-linearity and strong process dynamic interactions among process units complicate root-cause diagnosis of plant-wide disturbances because disturbances may propagate to units at some distance away from the primary source of the upset. Similarly, implemented advanced process control strategies, backup and recovery systems, use of recycle streams and heat integration may hamper detection and diagnostic efforts. It is important to track down the root-cause of a plant-wide disturbance because once corrective action is taken at the source, secondary propagated effects can be quickly eliminated with minimum effort and reduced down time with the resultant positive impact on process efficiency, productivity and profitability. In order to diagnose the root-cause of disturbances that manifest plant-wide, it is crucial to incorporate and utilize knowledge about the overall process topology or interrelated physical structure of the plant, such as is contained in Piping and Instrumentation Diagrams (P&IDs). Traditionally, process control engineers have intuitively referred to the physical structure of the plant by visual inspection and manual tracing of fault propagation paths within the process structures, such as the process drawings on printed P&IDs, in order to make logical conclusions based on the results from data-driven analysis. This manual approach, however, is prone to various sources of errors and can quickly become complicated in real processes. The aim of this thesis, therefore, is to establish innovative techniques for the electronic capture and manipulation of process schematic information from large plants such as refineries in order to provide an automated means of diagnosing plant-wide performance problems. This report also describes the design and implementation of a computer application program that integrates: (i) process connectivity and directionality information from intelligent P&IDs (ii) results from data-driven cause-and-effect analysis of process measurements and (iii) process know-how to aid process control engineers and plant operators gain process insight. This work explored process intelligent P&IDs, created with AVEVA® P&ID, a Computer Aided Design (CAD) tool, and exported as an ISO 15926 compliant platform and vendor independent text-based XML description of the plant. The XML output was processed by a software tool developed in Microsoft® .NET environment in this research project to computationally generate connectivity matrix that shows plant items and their connections. The connectivity matrix produced can be exported to Excel® spreadsheet application as a basis for other application and has served as precursor to other research work. The final version of the developed software tool links statistical results of cause-and-effect analysis of process data with the connectivity matrix to simplify and gain insights into the cause and effect analysis using the connectivity information. Process knowhow and understanding is incorporated to generate logical conclusions. The thesis presents a case study in an atmospheric crude heating unit as an illustrative example to drive home key concepts and also describes an industrial case study involving refinery operations. In the industrial case study, in addition to confirming the root-cause candidate, the developed software tool was set the task to determine the physical sequence of fault propagation path within the plant. This was then compared with the hypothesis about disturbance propagation sequence generated by pure data-driven method. The results show a high degree of overlap which helps to validate statistical data-driven technique and easily identify any spurious results from the data-driven multivariable analysis. This significantly increase control engineers confidence in data-driven method being used for root-cause diagnosis. The thesis concludes with a discussion of the approach and presents ideas for further development of the methods

Industrial fault detection and diagnosis using Bayesian belief network

Rapid development in industry have contributed to more complex systems that are prone to failure. In applications where the presence of faults may lead to premature failure, fault detection and diagnostics tools are often implemented. The goal of this research is to improve the diagnostic ability of existing FDD methods. Kernel Principal Component Analysis has good fault detection capability, however it can only detect the fault and identify few variables that have contribution on occurrence of fault and thus not precise in diagnosing. Hence, KPCA was used to detect abnormal events and the most contributed variables were taken out for more analysis in diagnosis phase. The diagnosis phase was done in both qualitative and quantitative manner. In qualitative mode, a networked-base causality analysis method was developed to show the causal effect between the most contributing variables in occurrence of the fault. In order to have more quantitative diagnosis, a Bayesian network was constructed to analyze the problem in probabilistic perspective

A Review of Kernel Methods for Feature Extraction in Nonlinear Process Monitoring

Kernel methods are a class of learning machines for the fast recognition of nonlinear patterns in any data set. In this paper, the applications of kernel methods for feature extraction in industrial process monitoring are systematically reviewed. First, we describe the reasons for using kernel methods and contextualize them among other machine learning tools. Second, by reviewing a total of 230 papers, this work has identified 12 major issues surrounding the use of kernel methods for nonlinear feature extraction. Each issue was discussed as to why they are important and how they were addressed through the years by many researchers. We also present a breakdown of the commonly used kernel functions, parameter selection routes, and case studies. Lastly, this review provides an outlook into the future of kernel-based process monitoring, which can hopefully instigate more advanced yet practical solutions in the process industries

Visualization of fault propagation paths in process monitoring systems

Modern industrial processes typically have complex interconnections among process equipment and units. A fault can easily propagate far beyond its origin, making it difficult to locate the root cause and to identify its propagation paths. Thus, the latest approach for identifying fault propagation paths uses qualitative models, e.g., topology-based models, for improving the results acquired from the data-driven methods of causal analysis. However, the current approach includes no display of the fault propagation paths in process monitoring systems, which could enable the visualisation of the spread of fault effects. In this thesis, the aim is to develop and to test a new technique which enables a process monitoring system to display fault propagation paths, based on the causality matrix obtained from a process. A causality matrix is created using the Granger causality method, which contains the details of the fault propagation path. Subsequently, the causality matrix is refined using a connectivity matrix, which was obtained from a piping and instrumentation diagram (P&ID). Furthermore, the process monitoring system and the refined causality matrix are linked together, to transfer the fault propagation paths details to the process monitoring interface. A number of algorithms in the automation system are developed and implemented to accomplish the link. A flotation pilot process is the case study in this thesis, used for testing this technique. The experiment data acquired from the flotation pilot was analysed to generate a causality matrix, which is subsequently refined and stored in the database of the automation system. Hence, the fault propagation paths is visualised in the process monitoring system. Finally, this procedure confirmed that the propagation of the effects of a fault is better understood if the propagation path is visualised in the process monitoring system

Improving the interpretability of causality maps for fault identification

Thesis (MEng)--Stellenbosch University, 2020.ENGLISH ABSTRACT: Worldwide competition forces modern mineral processing plants to operate at high productivity. This high productivity is achieved by implementing process monitoring to maintain the desired operating conditions. However, a fault originating in one section of a plant can propagate throughout the plant and so obscure its root cause. Causality analysis is a method that identifies the cause-effect relationships between process variables and presents these in a causality map which can be used to track the propagation path of a fault back to its root cause. A major obstacle to the wide acceptance of causality analysis as a tool for fault diagnosis in industry is the poor interpretability of causality maps. This study identified, proposed and assessed ways to improve the interpretability of causality maps for fault identification. All approaches were tested on a simulated case study and the resulting maps compared to a standard causality map or its transitive reduction. The ideal causality map was defined and all comparisons were performed based on its characteristics. Causality maps were produced using conditional Granger causality (GC), with a novel heuristic approach for selecting sampling period and time window. Conditional GC was found to be ill-suited to plant-wide causality analysis, due to large data requirements, poor model order selection using AIC, and inaccuracy in the presence of multiple different residence times and time delays. Methods to incorporate process knowledge to constrain connections and potential root causes were investigated and found to remove all spurious connections and decrease the pool of potential root cause variables respectively. Tools such as visually displaying node rankings on the causality map and incorporating sliders to manipulate connections and variables were also investigated. Furthermore, a novel hierarchical approach for plant-wide causality analysis was proposed, where causality maps were constructed in two subsequent stages. In the first stage, a less-detailed plant-wide map was constructed using representatives for groups of variables, and used to localise the fault to one of those groups of variables. Variables were grouped according to plant sections or modules identified in the data, and the first principal component (PC1) was used to represent each group (PS-PC1 and Mod-PC1 respectively). PS-PC1 was found to be the most promising approach, as its plant-wide map clearly identified the true root cause location, and the stage-wise application of conditional GC significantly reduced the required number of samples from 13 562 to 602. Lastly, a usability study in the form of a survey was performed to investigate the potential for industrial application of the tools and approaches presented in this study. Twenty responses were obtained, with participants consisting of Stellenbosch University final-year/postgraduate students, employees of an industrial IoT firm, and Anglo American Platinum employees. Main findings include that process knowledge is vital; grouping variables improves interpretability by decreasing the number of nodes; accuracy must be maintained during causality map simplification; and sliders add confusion by causing significant changes in the causality map. In addition, survey results found PS-PC1 to be the most user-friendly approach, further emphasizing its potential for application in industry.AFRIKAANSE OPSOMMING: Wêreldwye kompetisie forseer moderne mineraalprosesseringaanlegte om by hoë produktiwiteit bedryf te word. Hierdie hoë produktiwiteit word bereik deur prosesmonitering te implementeer om die gewenste bedryfskondisies te handhaaf. ’n Fout wat in een deel van ’n aanleg ontstaan kan egter regdeur die aanleg voortplant en so die grondoorsaak verberg. Oorsaaklikheidanalise is ’n metode wat die oorsaak-en-gevolg-verhouding tussen prosesveranderlikes identifiseer en hierdie in ’n oorsaaklikheidskaart toon wat gebruik kan word om die voortplantings roete van ’n fout terug na sy grondoorsaak te volg. ’n Groot hindernis vir die wye aanvaarding van oorsaaklikheidanalise as instrument vir foutdiagnose in industrie, is die swak interpreteerbaarheid van oorsaaklikheidskaarte. Hierdie studie het maniere om die interpreteerbaarheid van oorsaaklikheidskaarte vir foutidentifikasie te verbeter, geïdentifiseer, voorgestel en geassesseer. Alle benaderings is getoets op ’n gesimuleerde gevallestudie en die resulterende kaarte is vergelyk met ’n standaard oorsaaklikheidskaart of sy transitiewe inkrimping. Die ideale oorsaaklikheidskaart is gedefinieer en alle vergelykings is uitgevoer gebaseer op sy karakteristieke. Oorsaaklikheidskaarte is geproduseer deur kondisionele Granger-oorsaaklikheid (GC) te gebruik, met ’n nuwe heuristiese benadering om steekproefperiode en tydgleuf te selekteer. Kondisionele GC is gevind om nie gepas te wees vir aanlegwye oorsaaklikheidanalise nie, as gevolg van groot datavereistes, swak seleksie van modelorde as AIC gebruik word, en onakkuraatheid in die teenwoordigheid van veelvoudige, verskillende verblyftye en tydvertraging. Metodes om proseskennis te inkorporeer om konneksies en potensiële grondoorsake te bedwing, is ondersoek en gevind om alle konneksies wat vals is te verwyder en die groep van potensiële grondoorsaakveranderlikes te verminder, onderskeidelik. Instrumente soos om node-ordes op die oorsaaklikheidskaart visueel te vertoon en skuiwers te inkorporeer om konneksies en veranderlikes te manipuleer is ook ondersoek. Verder is ’n nuwe hiërargiese benadering vir aanlegwye oorsaaklikheidanalise voorgestel, waar oorsaaklikheidskaarte in twee opeenvolgende fases gebou is. In die eerste fase is ’n minder gedetaileerde aanlegwye kaart gebou deur verteenwoordigers vir groepe veranderlikes te gebruik, en is gebruik om die fout na een van daardie groepe van veranderlikes te lokaliseer. Veranderlikes is gegroepeer volgens aanlegdele of modules geïdentifiseer in die data, en die eerste hoof komponent (PC1) is gebruik om elke groep te verteenwoordig (PS-PC1 en Mod-PC1 onderskeidelik). PS-PC1 is gevind om die mees belowende benadering te wees, want sy aanlegwye kaart het duidelik die ware grondoorsaakligging geïdentifiseer, en die stap-gewyse toepassing van kondisionele GC het die vereisde aantal steekproewe beduidend verminder van 13 562 tot 602. Laastens, ’n bruikbaarheidstudie in die vorm van ’n opname is uitgevoer om die potensiaal vir industriële toepassing van die instrumente en benaderinge voorgestel in hierdie studie, te ondersoek. Twintig antwoorde is verkry, met deelnemers wat bestaan het uit Universiteit van Stellenbosch se finale jaar/nagraadse studente, werknemers van ’n industriële IoT-firma, en Anglo American Platinum werknemers. Hoofbevindinge het ingehou dat proseskennis noodsaaklik is; om veranderlikes te groepeer verbeter interpreteerbaarheid deur die aantal nodes te verminder; akkuraatheid moet gehandhaaf word gedurende vereenvoudiging van oorsaaklikheidskaarte; en skuiwers dra by tot verwarring deur beduidende veranderinge in die oorsaaklikheidskaart te maak. Daarmee saam het die opname se resultate gevind dat PS-PC1 die meer gebruiksvriendelike benadering was, wat sy potensiaal vir toepassing verder beklemtoon.Master

마르코프 랜덤 필드 학습 및 추론과 그래프 라쏘를 활용한 공정 이상 감지 및 진단 방법론

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 화학생물공학부, 2019. 2. 이원보.Fault detection and diagnosis (FDD) is an essential part of safe plant operation. Fault detection refers to the process of detecting the occurrence of a fault quickly and accurately, and representative methods include the use of principal component analysis (PCA), and autoencoders (AE). Fault diagnosis is the process of isolating the root cause node of the fault, then determining the fault propagation path to identify the characteristic of the fault. Among the various methods, data-driven methods are the most widely-used, due to their applicability and good performance compared to analytical and knowledge-based methods. Although many studies have been conducted regarding FDD, no methodology for conducting every step of FDD exists, where the fault is effectively detected and diagnosed. Moreover, existing methods have limited applicability and show limited performance. Previous fault detection methods show loss of variable characteristics in dimensionality reduction methods and have large computational loads, leading to poor performance for complex faults. Likewise, preceding fault diagnosis methods show inaccurate fault isolation results, and biased fault propagation path analysis as a consequence of implementing knowledge-based characteristics for construction of digraphs of process variable relationships. Thus a comprehensive methodology for FDD which shows good performance for complex faults and variable relationships, is required. In this study, an efficient and effective comprehensive FDD methodology based on Markov random fields (MRF) modelling is proposed. MRFs provide an effective means for modelling complex variable relationships, and allows efficient computation of marginal probability of the process variables, leading to good performance regarding FDD. First, a fault detection framework for process variables, integrating the MRF modelling and structure learning with iterative graphical lasso is proposed. Graphical lasso is an algorithm for learning the structure of MRFs, and is applicable to large variable sets since it approximates the MRF structure by assuming the relationships between variables to be Gaussian. By iteratively applying the graphical lasso to monitored variables, the variable set is subdivided into smaller groups, and consequently the computational cost of MRF inference is mitigated allowing efficient fault detection. After variable groups are obtained through iterative graphical lasso, they are subject to the MRF monitoring framework that is proposed in this work. The framework obtains the monitoring statistics by calculating the probability density of the variable groups through kernel density estimation, and the monitoring limits are obtained separately for each group by using a false alarm rate of 5%. Second, a fault isolation and propagation path analysis methodology is proposed, where the conditional marginal probability of each variable is computed via inference, then is used to calculate the conditional contribution of individual variables during the occurrence of a fault. Using the kernel belief propagation (KBP) algorithm, which is an algorithm for learning and inferencing MRFs comprising continuous variables, the parameters of MRF are trained using normal process data, then the individual conditional contribution of each variable is calculated for every sample of the fault process data. By analyzing the magnitude and reaction speed of the conditional contribution of individual variables, the root fault node can be isolated and the fault propagation path can be determined effectively. Finally, the proposed methodology is verified by applying it to the well-known Tennessee Eastman process (TEP) model. Since the TEP has been used as a benchmark process over the past years for verifying various FDD methods, it serves the purpose of performance comparison. Also, since it consists of multiple units and has complex variable relationships such as recycle loops, it is suitable for verifying the performance of the proposed methodology. Application results show that the proposed methodology performs better compared to state-of-the-art FDD algorithms, in terms of both fault detection and diagnosis. Fault detection results showed that all 28 faults designed inside the TEP model were detected with a fault detection accuracy of over 95%, which is higher than any other previously proposed fault detection method. Also, the method showed good fault isolation and propagation path analysis results, where the root-cause node for every fault was detected correctly, and the characteristics of the initiated faults were identified through fault propagation path analysis.공정 이상의 감지 및 진단 시스템은 안전한 공정 운영에 필수적인 부분이다. 이상 감지는 이상이 발생했을 경우 즉각적으로 이를 정확하게 감지하는 프로세스를 의미하며, 대표적인 방법으로는 주성분 분석 및 오토인코더를 활용한 감지 방법론이 있다. 이상 진단은 결함의 근본 원인이 되는 노드를 격리하고, 이상의 전파 경로를 탐지하여 이상의 특성을 식별하는 프로세스이다. 공정 이상의 감지 및 진단 방법론에는 모델 분석 방법론, 지식 기반 방법론 등의 다양한 방법론이 있지만, 공정에 대한 적용 가능성과 성능 측면에서 가장 유용하다고 알려져 있는 데이터 기반 방법론이 널리 활용되고 있다. 공정 이상의 감지 및 진단에 대한 데이터 기반 방법론은 다방면으로 연구되어 왔지만, 이상 감지 및 진단을 모두 효과적으로 수행할 수 있는 방법론은 소수에 불과하며, 존재하고 있는 방법론들 역시 두 분야 모두에서 좋은 성능을 보여주고 있는 경우는 없다. 이는 기존 방법론들의 적용 가능성이 제한되어 있으며 공정에 적용시 제한된 성능을 보여주기 때문이다. 이상 감지의 경우, 대용량의 데이터를 처리할 때 발생하는 과부하로 인한 감지 능력의 저하, 차원 축소 방법론들을 사용할 시 이에 따른 변수 특성 반영의 부정확성, 그리고 축소된 차원에서의 계산으로 인하여 복합적인 형태의 이상을 감지해 내지 못하는 문제 등이 있다. 이상 진단의 경우 이상의 원인이 되는 노드의 격리 및 이상 전파 경로에 대한 분석이 부정확한 경우가 많은데, 이는 차원 축소로 인하여 공정 변수의 특성이 소실되는 성질이 있고, 방향성 그래프를 활용할 시 공정에 대한 선행 지식을 적용함으로써 편향된 이상 진단 결과가 나타나는 경우들이 발생하기 때문이다. 기존 방법론들에 대한 이러한 한계점들을 고려해 봤을때, 변수 각각의 특성이 소실되지 않도록하여 효과적으로 이상에 대한 감지와 진단을 모두 수행해 낼 수 있으면서도, 계산상의 효율성을 갖춘, 이상 감지 및 진단에 대한 통합된 방법론의 개발이 시급하다고 할 수 있다. 본 연구에서는 마르코프 랜덤 필드 모델링과 그래프 라쏘를 기반으로하여, 이상에 대한 감지 및 진단을 모두 수행해 낼 수 있는 통합적인 공정 모니터링 방법론을 제안한다. 마르코프 랜덤 필드는 비선형적이고 비정규적인 변수 관계를 효과적으로 모델링할 수 있게 해주고, 이상 발생 상황에서의 모니터링 통계값 계산시에 각 변수의 특성을 반영하여 확률 계산을 해 낼 수 있기 때문에 효과적인 이상 감지 및 진단 수단이 된다. 기본적으로 마르코프 랜덤 필드는 확률값 계산시의 부하가 크지만, 본 연구에서는 그래프 라쏘 방법론을 추가적으로 함께 활용하여 계산 상의 부하를 줄이고 효율적으로 이상 감지 및 진단을 해낼 수 있도록 하였다. 본 연구에서 제안된 내용들은 다음과 같다. 첫째, 공정 변수를 마르코프 랜덤 필드 형태로 모델링하고, 그래프 라쏘를 활용해 마르코프 랜덤 필드의 구조를 얻을 수 있는 방법론을 제시하였다. 그래프 라쏘는 마르코프 랜덤 필드의 구조를 파악하기 위한 방법론인데, 변수 간의 관계를 가우스 함수의 형태로 가정하기 때문에 다변수 시스템에서도 효율적으로 그래프 구조를 파악할 수 있도록 해준다. 본 연구에서는 반복적 그래프 라쏘를 제안하여 모든 공정 변수들이 상관관계가 높은 변수 집단으로 묶일 수 있도록 하였다. 이를 활용하면 전체 공정 변수 집단을 다수의 소집단으로 분류하고 각각에 대한 그래프 구조를 파악할 수 있게 되는데, 크게 두 가지의 효과를 얻을 수 있다. 우선적으로 마르코프 랜덤 필드 확률 계산의 대상이 되는 변수의 개수를 줄여줌으로써 계산 부하를 줄이고 효율적인 이상 감지가 이루어질 수 있도록 한다. 또한 상관관계가 높은 집단끼리 묶여서 모델링 된 그래프를 활용하여 이상의 진단 과정에서 공정 변수 간의 관계 파악 및 전파 경로 분석을 용이하도록 해준다. 두 번째로, 마르코프 랜덤 필드의 확률 추론을 기반으로 하여 효과적으로 이상 감지가 이루어질 수 있도록 하는 방법론을 제안하였다. 반복적 그래프 라쏘를 통해 얻어진 다수의 변수 소집단에 대하여 각각 확률 추론을 적용하여 이상 감지를 진행하게 되는데, 제안된 방법론에서는 커널 밀도 추정 방법론을 활용하였다. 정상 데이터를 활용하여 각 변수들에 대한 커널 밀도의 대역폭을 학습하고, 이상 데이터가 발생할 시 이를 활용한 커널 밀도 추정법을 사용하여 이상감시 통계치를 계산하게 된다. 이때 허위 진단율을 5%로 가정하여 각각의 소집단에 대한 공정 감지 기준선을 설정하였고, 이상감시 통계치가 공정 감시 기준선보다 낮게 될 경우 이상이 감지된다. 세 번째로, 이상 발생 시 원인이 되는 변수의 격리 및 이상 전파 경로 분석을 효과적으로 수행할 수 있는 방법론을 제시하였다. 제시된 방법론에서는 마르코프 랜덤 필드의 확률 추론 과정을 활용하여 이상 발생 시 각 변수의 조건부 한계 확률을 계산하고, 이를 활용해 새롭게 정의된 조건부 기여도 값을 계산하여, 이상에 대한 각 변수의 기여도를 파악할 수 있도록 한다. 이 과정에서는 커널 신뢰도 전파 방법론이 사용되는데, 이는 연속 변수를 가지는 마르코프 랜덤 필드에 대하여 확률 추론을 수행할 수 있도록 하는 방법론이다. 커널 신뢰도 전파법을 사용하면 정상 상태의 공정 데이터를 활용하여 마르코프 랜덤 필드를 구성하는 파라미터 값들을 학습하고, 이상 발생시 이상 데이터에 대하여 각 변수의 조건부 기여도 값을 계산할 수 있게 된다. 이 때 계산된 조건부 기여도 값의 크기와, 이상 발생 이후 각 변수의 조건부 기여도 값의 변화 반응 속도를 종합적으로 판단하여, 이상의 원인 변수에 대한 격리와 이상 전파 경로 분석을 효과적으로 수행할 수 있게 된다. 본 연구에서는 제안된 이상 감지 및 진단 방법론의 성능을 검증하기 위하여 테네시 이스트만 공정 모델에 이를 적용하고 결과를 분석하였다. 테네시 이스트만 공정은 수년간 공정 감시 방법론을 검증하기 위한 벤치마크 공정으로 널리 사용되어 왔기 때문에, 제시된 방법론을 이에 적용해 봄으로써 다른 공정 감시 방법론들과의 성능을 비교해 볼 수 있었다. 또한 다수의 단위 공정을 포함하고 있고, 순환적인 변수 관계 역시 포함하고 있기 때문에 제시된 방법론의 성능을 시험해 보기에 적합했다. 테네시 이스트만 공정 내부에는 28개 종류의 이상이 프로그램 상에 내장되어 있는데, 제시된 공정 감지 방법론을 적용한 결과 모든 이상에 대하여 96% 이상의 높은 이상 감지율을 나타내었다. 이는 기존에 제시된 공정 감시 방법론들에 비하여 월등히 높은 수치였다. 또한 이상 진단 성능을 분석해 본 결과, 모든 이상에 대하여 원인이 되는 노드를 효과적으로 파악할 수 있었고, 이상 전파 경로 역시 정확하게 탐지하여 기존 방법론들과는 차별화된 성능을 나타내었다. 제시된 방법론을 테네시 이스트만 공정에 적용해 봄으로써, 본 연구 내용이 공정 이상의 감지 및 진단에 대한 통합적인 방법론 중에서 가장 우수한 성능을 나타내는 것을 확인할 수 있었다.Contents Abstract i Contents iv List of Tables vii List of Figures ix 1 Introduction 1 1.1 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Markov Random Fields Modelling, Graphical Lasso, and Optimal Structure Learning 10 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Markov Random Fields . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Graphical Lasso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 MRF Modelling & Structure Learning . . . . . . . . . . . . . . . . . 19 2.4.1 MRF modelling in process systems . . . . . . . . . . . . . . 19 2.4.2 Structure learning using iterative graphical lasso . . . . . . . 20 2.5 Application of Iterative Graphical Lasso on the TEP . . . . . . . . . . 24 3 Efficient Process Monitoring via the Integrated Use of Markov Random Fields Learning and the Graphical Lasso 31 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 MRF Monitoring Integrated with Graphical Lasso . . . . . . . . . . . 35 3.2.1 Step 1: Iterative graphical lasso . . . . . . . . . . . . . . . . 36 3.2.2 Step 2: MRF monitoring . . . . . . . . . . . . . . . . . . . . 36 3.3 Implementation of Glasso-MRF monitoring to the Tennessee Eastman process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.3.1 Tennessee Eastman process . . . . . . . . . . . . . . . . . . 41 3.3.2 Glasso-MRF monitoring on TEP . . . . . . . . . . . . . . . . 48 3.3.3 Fault detection accuracy comparison with other monitoring techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.3.4 Fault detection speed & fault propagation . . . . . . . . . . . 95 4 Process Fault Diagnosis via Markov Random Fields Learning and Inference 101 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.2.1 Probabilistic graphical models & Markov random fields . . . 106 4.2.2 Kernel belief propagation . . . . . . . . . . . . . . . . . . . . 107 4.3 Fault Diagnosis via MRF Modeling . . . . . . . . . . . . . . . . . . 113 4.3.1 MRF structure learning via graphical lasso . . . . . . . . . . 116 4.3.2 Kernel belief propagation - bandwidth selection . . . . . . . . 116 4.3.3 Conditional contribution evaluation . . . . . . . . . . . . . . 117 4.4 Application Results & Discussion . . . . . . . . . . . . . . . . . . . 118 4.4.1 Two tank process . . . . . . . . . . . . . . . . . . . . . . . . 119 4.4.2 Tennessee Eastman process . . . . . . . . . . . . . . . . . . 137 5 Concluding Remarks 152 Bibliography 157 Nomenclature 169 Abstract (In Korean) 170Docto