ISIS project: Fault detection and diagnosis in process control systems

Selected publications

Background

This project is carried out by the Division of Automatic Control and the Division of Vehicular Systems in cooperation with ABB Automation Systems and ABB Corporate Research. Participant in the project from the Division of Automatic Control has been Anders Stenman, who is currently working at NIRA Automotive AB. Since autumn 2000 Anna Hagenblad works on this project together with Lennart Ljung, Inger Klein and Fredrik Gustafsson, and in autumn 2001 Mattias Krysander joined the project together with Mattias Nyberg The aim is to study and develop methods for detection and diagnosis in process control applications.

• Statistical methods for fault detection and diagnosis.
• Structural analysis for design and analysis of diagnosis systems

Statistical methods for fault detection and diagnosis.

ABB Corporate Research is interested in developing a model-based diagnostics system for a highly automated pulp and paper plant. By using models of different sections of the process and available sensors, we want to detect and isolate faults, primarily in sensors and actuators.

In [C4] the parity space approach to fault detection is compared to PCA. It is assumed that there are additive faults on input and output signals and stochastic unmeasurable disturbances.

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Structural analysis for design and analysis of diagnosis systems

Introduction

Today many technical processes are complex and highly integrated. When a process has failed, the complexity of the process makes it hard for humans to troubleshoot it. To facilitate troubleshooting a diagnostic system can supervise and alarm an operator when a fault is detected and also identify one, or several faults, that may have caused the alarm. It is a demanding and time-consuming task to design a diagnostic system. Therefore this project aims to develop algorithms and analysis methods that help and automate the design of diagnostic systems. 

In model-based diagnosis a model of the process is used to design a diagnostic system. This model describes the different behaviours of the behavioural modes of the process, which are chosen for the diagnosis task. Typical behavioural modes are the normally working mode and faulty working modes. The behavior is assumed to be described using differential algebraic equations.

In a diagnostic system a number of diagnostic tests validate different subset of equation in the model, i.e. sub-models, by using observations of the process. Each test is based on a residual, derived from the corresponding sub-model. The residual is designed such that it is small in the fault free case and large otherwise. If a sub-model is invalidated in a test, i.e. its residual is significantly large, the conclusion is that the present behavioural mode of the process belongs to a subset of considered behavioural modes. With properly chosen tests, different subsets of tests are sensitive to different subsets of faults. In this way identification, also called isolation, of different faults can be achieved.

To invalidate a sub-model, redundancy is needed. Overdetermined system of equations have redundancy and are therefore suitable to test in a diagnostic system. To decide which equations each test should validate, the structure of the model, i.e. which variables that are included in each equation, is used. The structure is used to find particular set of equations with more equations than unknowns called structurally overdetermined sub-models.

Results and Developments

The results and developments are partitioned into the four parts diagnosis framework, developing algorithms for finding structurally overdetermined models, predicting fault isolability properties using structural analysis, and residual generation of overdetermined sub-models. In the licentiate thesis [T1] the three first parts are thoroughly explained.

Diagnosis Framework

A new framework for model based diagnosis is presented in [C6] using ideas from AI, FDI, and statistical hypothesis testing. The isolation mechanism also studied in [MSc2] is based on AI methods, and the main advantage is that multiple faults are handled implicitly. Thus, no special care for isolation of multiple faults is needed. It is assumed that a set of overdetermined sub-models, that for example is computed using structural methods, is tested. The methods for residual generation, developed in the field of control theory (FDI), can within the framework be fully utilized. Since the framework is also based upon statistical hypothesis testing, it is suitable for problems including noise.

Developing Algorithms for Finding Structurally Overdetermined Models

The models are as said before assumed to consist of a set of nonlinear and linear differential-algebraic equations. To find tests by directly manipulating these equations is a computationally complex task, especially for large and nonlinear systems. To reduce the computational complexity of deriving tests, a two-step approach is proposed in [C1-3] and [R1]. In the first step, the model is analyzed structurally to find overdetermined sub-models. In the second, a residual for each of these submodels is derived as described in [C6]. The benefit with this two-step approach is that the sub-models obtained are typically much smaller than the whole model, and therefore the computational complexity of deriving a residual from each sub-model is substantially lower compared to directly manipulating the whole model.

A structural algorithm that finds all minimal structurally overdetermined sub-models in a model is given. It uses a new way of handling derivatives in structural models and a comparison with other approches is studied in [MSc3]. It is shown how the result of the structural algorithm can be used to analyze the isolation capability of a diagnostic system based on the computed sub-models. Thereby it is possible minimize the number of tests needed to obtain maximum isolability. This algorithm is implemented in Matlab and has been applied to a large non-linear example, a part of a paper mill studied in [MSc1]. In spite of the complexity of this process, a small set of tests with high isolability is successfully derived.

Predicting Fault Isolability Properties Using Structural Analysis

As said in the previous section, structural methods can be used to compute which sub-models to test in order to obtain a diagnostic system with high isolation capability. Since structural models are less detailed than analytical models, structural models can be obtained earlier in the design of a process. Since a structural model can be available earlier in the development of the process, the design of a diagnostic system can start earlier. This is advantageous because then it is possible to consider the isolability aspects of for example sensor placement. Furthermore a structural model is easier to obtain than an analytical model, and structural analysis is computationally less complex in many cases.

Efficient structural algorithms to compute isolabilty predictions are developed in [C9]. In [MSc4], these algorithms are applied to an unmanned aerial vehicle concept where isolability requirements have be derived from safety and maintenance requirements [C8]. In spite of only using structural models of the concept, the result of the analysis is that either a specified set of optional sensors needs to be added, or some computed isolability requirements cannot be fulfilled, or a new concept needs to be developed. In [C5] it is shown how different levels of knowledge about faults can be incorporated in a structural fault-isolability analysis and how they result in different isolability properties. The results are evaluated on the DAMADICS valve benchmark problem. It is also shown how to determine which faults in the benchmark that need further modelling to get desired isolability properties of the diagnostic system.

Residual Generation of Minimal Overdetermined Models

As mentioned earlier any method for residual generation, developed in the field of FDI, can be utilized for minimal overdetermined models. However in [C7] a new method that uses the minimallity property for finding residual generators is developed. Two approaches are considered, one which is based on the use of a dynamic numerical equation solver, and another which uses a static numerical equation solver. The approaches are demonstrated on a non-linear point-mass satellite system.

In [C10] minimal overdetermined differential algebraic systems are considered. By differentiating equations, a new set is formed, that is an overdetermined static algebraic system if derivatives of unknown signals are considered as separate independent variables. The task to derive analytical redundancy relations is thereby reduced to an algebraic problem. It is desirable to differentiate the equations as few times as possible and it is shown that there exists a unique minimally differentiated overdetermined system. 

Publications

Theses

Conference Papers

Technical Reports

Master Theses

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