Diagnosis and Fault-tolerant Control 1 E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 409

Veröffentlichungsjahr: 2021

Beschreibung

This book presents recent advances in fault diagnosis strategies for complex dynamic systems. Its impetus derives from the need for an overview of the challenges of the fault diagnosis technique, especially for those demanding systems that require reliability, availability, maintainability and safety to ensure efficient operations. Moreover, the need for a high degree of tolerance with respect to possible faults represents a further key point, primarily for complex systems, as modeling and control are inherently challenging, and maintenance is both expensive and safety-critical. Diagnosis and Fault-tolerant Control 1 also presents and compares different diagnosis schemes using established case studies that are widely used in related literature. The main features of this book regard the analysis, design and implementation of proper solutions for the problems of fault diagnosis in safety critical systems. The design of the considered solutions involves robust data-driven, model-based approaches.

Leseprobe

Table of Contents

Cover

Title page

Copyright

Introduction

1 Mathematical Modeling and Fault Description

1.1. Introduction

1.2. Model-based FDI techniques

1.3. Modeling of faulty systems

1.4. Residual generation

1.5. Residual generation techniques

1.6. Change detection and symptom evaluation

1.7. Residual generation robustness problem

1.8. Fault diagnosis technique integration

1.9. Conclusion

1.10. References

2 Structural Analysis

2.1. Introduction

2.2. Background

2.3. Fault isolability analysis

2.4. Testable submodels

2.5. Sensor placement

2.6. Summary and discussion

2.7. References

3 Set-based Fault Detection and Isolation

3.1. Introduction

3.2. Notations, definitions and properties

3.3. Problem statement

3.4. Proposed techniques

3.5. Design methods

3.6. Fault detection and isolation procedures

3.7. Application example: quadruple-tank system

3.8. Conclusion

3.9. References

4 Diagnosis of Stochastic Systems

4.1. Introduction

4.2. Stochastic diagnosis task

4.3. Inference methods for diagnosis task

4.4. Model-based approach

4.5. Data-driven approaches

4.6. Hybrid approaches: surrogate methods

4.7. Comparative analysis of approaches

4.8. Summary and conclusions

4.9. References

5 Data-Driven Methods for Fault Diagnosis

5.1. Introduction

5.2. Models for linear system fault diagnosis

5.3. Parameter estimation methods for fault diagnosis

5.4. Nonlinear dynamic system identification

5.5. Fuzzy data-driven approach to fault diagnosis

5.6. Fuzzy model identification

5.7. Conclusion

5.8. References

6 The Artificial Intelligence Approach to Model-based Diagnosis

6.1. Introduction

6.2. Case studies

6.3. Knowledge-based diagnosis systems

6.4. Model-based diagnosis

6.5. CBD for dynamic systems

6.6. Conclusion

6.7. References

List of Authors

Index

Summary of Volume 2

End User License Agreement

List of Illustrations

Introduction

Figure I.1. Comparison between hardware and analytical redundancy schemes

Figure I.2. Scheme for the model-based fault diagnosis

Figure I.3. Fault estimation scheme FTC

Chapter 1

Figure 1.1. Structure of the model-based FDI system

Figure 1.2. Closed-loop FDI system

Figure 1.3. The rearranged FDI scheme

Figure 1.4. Monitored system and fault topology

Figure 1.5. The monitored system and fault typology

Figure 1.6. The structure of the plant sensors

Figure 1.7. Fault topology with actuator input signal measurement

Figure 1.8. Residual generator general structure

Figure 1.9. System simulator or output estimator for residual generation

Figure 1.10. Transfer function residual generator

Figure 1.11. Parameter estimation Equation Error (EE)

Figure 1.12. Parameter estimation Output Error (OE)

Figure 1.13. State and output dynamic observer

Figure 1.14. MIMO process with faults and noises

Figure 1.15. Process and output observer

Figure 1.16. Parity equation methods: (a) EE and (b) OE

Figure 1.17. Parity EE methods for a MIMO model

Figure 1.18. Neuro-fuzzy-based FDI scheme

Figure 1.19. TSK NF-based FDI scheme

Chapter 2

Figure 2.1. A circuit view of the electric motor that will be used as a running ...

Figure 2.2. Structural model of the electric motor

Figure 2.3. Dulmage–Mendelsohn decomposition with over- and underdetermined part...

Figure 2.4. Dulmage–Mendelsohn’s decomposition applied to variants of the electr...

Figure 2.5. Diagnosis analysis results for the model in Figure 2.2. For a color ...

Figure 2.6. Canonical decomposition of the overdetermined part of a model

Figure 2.7. Computational graphs for MSO set M3 with different residual equation...

Figure 2.8. Model structure and Hasse diagram of the block partial order over th...

Figure 2.9. Block structure of the example in section 2.5.1 extended with measur...

Chapter 3

Figure 3.1. Set-membership state estimation

Figure 3.2. Interval observer

Figure 3.3. The quadruple-tank system

Figure 3.4. Closed-loop data. For a color version of this figure, see www.iste.c...

Figure 3.5. Residual intervals with the set-membership approach. For a color ver...

Figure 3.6. Residual intervals with zonotopic Kalman observer. For a color versi...

Figure 3.7. Residual intervals with zonotopic observer considering only robustne...

Figure 3.8. Residual intervals with zonotopic observer considering both robustne...

Chapter 4

Figure 4.1. Hierarchy of methods examined. For a color version of this figure, s...

Figure 4.2. Architecture of observer-based approach. For a color version of this...

Chapter 5

Figure 5.1. PPCRE criterion for different ARX model orders k

Figure 5.2. Mean square error criterion for different ARX model orders k

Figure 5.3. Noise space and singularity surfaces

Figure 5.4. Two–dimensional space partition example

Figure 5.5. Prism triangulation example

Figure 5.6. Singularity curve example

Figure 5.7. Singularity curve example

Figure 5.8. Singularity curves example

Figure 5.9. Fuzzy model diagram

Figure 5.10. Fuzzy clustering phases

Chapter 6

Figure 6.1. The full adder (source: Reiter 1987)

Figure 6.2. The three-tank system (source: Escobet et al. 2019)

Figure 6.3. Simple KBS architecture

Figure 6.4. Example of a MYCIN production rule rewritten in the form of natural ...

Figure 6.5. Heuristic classification (from Clancey 1985)

Figure 6.6. Heuristic classification in MYCIN (adapted from Clancey 1985)

Figure 6.7. MYCIN production rule for the heuristic model of Figure 6.6

List of Tables

Introduction

Table I.1. FDI applications and number of contributions

Table I.2. Fault type and number of contributions

Table I.3. FDI methods and number of contributions

Table I.4. Residual evaluation methods and number of contributions

Table I.5. Reasoning strategies and number of contributions

Table I.6. Applications of model-based fault detection

Chapter 4

Table 4.1. Notation used in the chapter

Chapter 6

Table 6.1. Set of Minimal Evaluable Chains for the three-tank system. Only three...

Guide

Cover

Table of Contents

Title page

Copyright

Introduction

Begin Reading

Index

End User License Agreement

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SCIENCES

Systems and Industrial Engineering, Field Director – Jean-Paul Bourrières

Reliability, Diagnosis, Safety and Maintenance of Systems, Subject Head – Jean-Marie Flaus

Diagnosis and Fault-tolerant Control 1

Data-driven and Model-based Fault Diagnosis Techniques

Coordinated by

Vicenç Puig

Silvio Simani

First published 2021 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd

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John Wiley & Sons, Inc.

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USA

www.wiley.com

© ISTE Ltd 2021

The rights of Vicenç Puig and Silvio Simani to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2021943898

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-78945-058-3

ERC Code:

PE7 Systems and Communication Engineering

 PE7_1 Control engineering

Introduction

Vicenç PUIG1 and Silvio SIMANI2

1Institute for Robotics and Industrial Informatics, Polytechnic University of Catalonia, Barcelona, Spain

2Department of Engineering, University of Ferrara, Emilia-Romagna, Italy

I.1. Introduction

There is an increasing interest in the theory and applications of model-based fault detection and fault diagnosis methods, because of economical and safety-related matters. In particular, well-established theoretical developments can be seen in many contributions published in the IFAC (International Federation of Automatic Control) Congresses and IFAC Symposium SAFEPROCESS (Fault Detection, Supervision and Safety of Technical Processes) since the seminal editions (Isermann and Ballé 1997; Isermann 1997; Patton 1999; Frank et al. 2000).

The developments began at various places in the early 1970s. Beard (1971) and Jones (1973) reported, for example, the well-known “failure detection filter” approach for linear systems.

A summary of this early development is given by Willsky (1976). Then, Rault et al. (1971) considered the application of identification methods to the fault detection of jet engines. Correlation methods were applied to leak detection (Siebert and Isermann 1976).

The first book on model-based methods for fault detection and diagnosis with specific application to chemical processes was published by Himmelblau (1978). Sensor failure detection based on the inherent analytical redundancy of multiple observers was shown by Clark (1978).

The use of parameter estimation techniques for fault detection of technical systems was demonstrated by Hohmann (1977), Bakiotis et al. (1979), Geiger (1982) and Filbert and Metzger (1982).

The development of process fault detection methods based on modeling, parameter and state estimation was then summarized by Isermann (1984, 1997).

Parity equation-based methods were developed initially by Chow and Willsky (1984) and then further developed by Patton and Chen (1994), Gertler (1991) and Höfling and Pfeufer (1994).

Frequency domain methods are typically applied when the effects of faults as well as disturbances have frequency characteristics that differ from each other and thus the frequency spectra serve as criterion to distinguish the faults (Massoumnia et al. 1989; Ding and Frank 1990; Ding et al. 2000; Frank et al. 2000).

The developments of fault detection and isolation (FDI) methods to the present time are summarized in books by Pau (1981), Patton et al. (2000), Basseville and Nikiforov (1993), Chen and Patton (1999), Gertler (1998) and Isermann (1994b) as well as in survey papers by Gertler (1988), Frank (1990) and Isermann (1994a).

Within IFAC, the increasing interest in this field was taken into account by creating first in 1991 a SAFEPROCESS (Fault Detection Supervision and Safety for Technical Processes) Steering Committee, which then became a Technical Committee in 1993. The first IFAC SAFEPROCESS Symposium was held in Baden–Baden (Germany) in 1991 (Isermann and Freyermuth 1992). The last edition was organized in 2018 in Warsaw (Poland). Another triennial series of IFAC workshops exist for “Fault detection and supervision in the chemical process industries”. Many other thematic workshops have been organized between 1992 and 2020.

Most contributions in fault diagnosis rely on the analytical redundancy principle. The basic idea consists of using an accurate model of the system to mimic the real process behavior. If a fault occurs, the residual signal (i.e. the difference between the real system and model behavior) can be used to diagnose and isolate the malfunction.

Model-based method reliability, which also includes false alarm rejection, is strictly related to the “quality” of the model and measurements exploited for fault diagnosis, as model uncertainty and noisy data can prevent an effective application of analytical redundancy methods.

This is not a simple problem, because model-based fault diagnosis methods are designed to detect any discrepancy between the real system and model behaviors. It is assumed that this discrepancy signal is related to (has a response from) a fault. However, the same difference signal can respond to model mismatch or noise in real measurements, which are erroneously detected as a fault. These considerations have led to research in the field of “robust” methods, in which particular attention is paid to the discrimination between actual faults and errors due to model mismatch.

However, the availability of a “good” model of the monitored system can significantly improve the performance of diagnostic tools, minimizing the probability of false alarms.

This book explains what a good model is, one that is suitable for robust diagnosis of system performance and operation. The book also explains how robust models can be obtained from real data. A large amount of attention is paid to the “real system modeling problem”, with reference to either linear or nonlinear model structures. Special treatment is given to the case in which noise affects the acquired data. The mathematical description of the monitored system is obtained by means of a system identification scheme based on equation error and errors-in-variables models. This is an identification approach that leads to a reliable model of the plant under investigation, as well as the estimation of the variances of the input–output noises affecting the data.

The purpose of this book is also to provide guidelines for the modeling and identification of real processes for fault diagnosis and fault-tolerant control (FTC). Hence, significant attention is paid to the practical application of the methods describing real system studies, as reported in the last chapters of Volume 2.

In particular, this introduction of the book outlines a new common terminology in the fault diagnosis framework and provides some discussion and a summary of developments in the field of fault detection and diagnosis as well as FTC based on papers selected during 1991–2020.

I.2. Nomenclature

By going through the literature, one immediately recognizes that the terminology in this field is not consistent. This makes it difficult to understand the goals of the contributions and to compare the different approaches.

The IFAC SAFEPROCESS Technical Committee therefore discussed this matter and tried to find commonly accepted definitions. Some basic definitions can be found, for example, in the RAM (Reliability, Availability and Maintainability) dictionary (Omdahl 1988) and in contributions to the IFIP (International Federation for Information Processing) (IFI 1983).

Some of the terminology used in this book is given below. These are based on information obtained from the IFAC SAFEPROCESS Technical Committee and are considered “on-going” in the sense that new definitions and updates are still being made.

1)

States and signals

-

Fault

: an unpermitted deviation of at least one characteristic property or parameter of the system from the acceptable, usual or standard condition.

-

Failure

: a permanent interruption of a system’s ability to perform a required function under specified operating conditions.

-

Malfunction

: an intermittent irregularity in the fulfillment of a system’s desired function.

-

Error

: a deviation between a measured or computed value of an output variable and its true or theoretically correct value.

-

Disturbance

: an unknown and uncontrolled input acting on a system.

-

Residual

: a fault indicator based on a deviation between measurements and model-equation-based computations.

-

Symptom

: a change of an observable quantity from normal behavior.

2)

Functions

-

Fault detection

: determination of faults present in a system and the time of detection.

-

Fault isolation

: determination of the kind, location and time of detection of a fault. It follows fault detection.

-

Fault identification

: determination of the size and time-variant behavior of a fault. It follows fault isolation.

-

Fault diagnosis

: determination of the kind, size, location and time of detection of a fault. It follows that fault diagnosis includes fault detection and identification.

-

Monitoring

: a continuous real-time task of determining the conditions of a physical system by recording information, recognizing and indicating anomalies in the behavior.

-

Supervision

: monitoring a physical system and taking appropriate actions to maintain the operation in the case of a fault.

3)

Models

-

Quantitative model

: use of static and dynamic relationships among system variables and parameters in order to describe a system’s behavior in quantitative mathematical terms.

-

Qualitative model

: use of static and dynamic relationships among system variables in order to describe a system’s behavior in qualitative terms such as causalities and IF–THEN rules.

-

Diagnostic model

: a set of static or dynamic relationships that link specific input variables, the

symptoms

, to specific output variables, the

faults

.

-

Analytical redundancy

: use of more (not necessarily identical) ways to determine a variable, where one way uses a mathematical process model in an analytical form.

4)

System properties

-

Reliability

: ability of a system to perform a required function under stated conditions, within a given scope, during a given period of time.

-

Safety

: ability of a system to operate without causing danger to persons, equipment or the environment.

-

Availability

: probability that a system or equipment will operate satisfactorily and effectively at any point of time.

5)

Time dependency of faults

-

Abrupt fault

: fault modeled as step-wise function. It represents bias in the monitored signal.

-

Incipient fault

: fault modeled by using ramp signals. It represents drift of the monitored signal.

-

Intermittent fault

: combination of impulses with different amplitudes.

6)

Fault terminology

-

Additive fault

: it influences a variable by an addition of the fault itself. It may represent, for example, offsets of sensors.

-

Multiplicative fault

: it is represented by the product of a variable with the fault itself. It can appear as parameter changes within a process.

I.3. Fault diagnosis methods based on analytical redundancy

A traditional approach to fault diagnosis in the wider application context is based on hardware or physical redundancy methods, which use multiple sensors, actuators and components to measure and control a particular variable. Typically, a voting technique is applied to the hardware redundant system to decide if a fault has occurred and its location among all the redundant system components. The major problems encountered with hardware redundancy are the extra equipment and maintenance costs, as well as the additional space required to accommodate the equipment (Isermann 1997; Isermann and Ballé 1997).

In view of the conflict between reliability and the cost of adding more hardware, it is possible to use the dissimilar measured values together to cross-compare with each other rather than replicating each hardware individually. This is the meaning of analytical or functional redundancy. It exploits redundant analytical relationships among various measured variables of the monitored process (Patton et al. 1989; Chen and Patton 1999). Figure I.1 illustrates the concepts of hardware and analytical redundancy.

In the analytical redundancy scheme, the resulting difference generated from the comparison of different variables is called a residual or symptom signal. The residual should be zero when the system is in normal operation and should be different from zero when a fault has occurred. This property of the residual is used to determine whether faults have occurred (Patton et al. 1989; Chen and Patton 1999).

Consistency checking in analytical redundancy is normally achieved through a comparison between a measured signal and estimated values. The estimation is generated by a mathematical model of the plant considered. The comparison is done using the residual quantities that are computed as differences between the measured signals and the corresponding signals generated by the mathematical model (Patton et al. 1989; Chen and Patton 1999).

Figure I.1.Comparison between hardware and analytical redundancy schemes

In practice, the most frequently used diagnosis method is to monitor the level (or trend) of the residual and take action when the signal reaches a given threshold. This method of geometrical analysis, while simple to implement, has a few drawbacks. The most important is that, in the presence of noise, input variations and change of operating point of the monitored process, false alarms are possible.

The major advantage of the model-based approach is that no additional hardware components are required to implement an FDI algorithm as well as FTC. A model-based FDI algorithm can be implemented via software on a process control computer. In many cases, the measurements necessary to control the process are also sufficient for the FDI algorithm, so no additional sensors have to be installed (Patton et al. 1989; Basseville and Nikiforov 1993; Chen and Patton 1999).

Analytical redundancy uses a mathematical model of the system under investigation and therefore it is often referred to as the model-based approach to fault diagnosis.

I.4. Model-based fault diagnosis

This diagnosis task detects faults in the technical process, including actuators, components and sensors by measuring the available input and output variables u(t) and y(t). The principle of model-based fault diagnosis is depicted in Figure I.2.

Figure I.2.Scheme for the model-based fault diagnosis

Basic process model-based FDI methods have been described by Patton et al. (1989, 2000), Basseville and Nikiforov (1993), Gertler (1998) and Chen and Patton (1999), which include the following steps:

1) output observers (OO, estimators, filters);

2) parity equations;

3) identification and parameter estimation.

These methods generate residuals for output variables with fixed parametric models using step 1, fixed parametric or non-parametric models using step 2 and adaptive non-parametric or parametric models using step 3.

An important aspect of these methods is the kind of fault to be detected. As noted above, one can distinguish between additive faults, which influence the variables of the process by summation, and multiplicative faults, which are products of the process variables. The basic methods show different results, depending on the type of fault.

If only output signals y(t) can be measured, signal model-based methods can be applied, for example, vibrations can be detected, which are related to rotating machinery or electrical circuits. Typical signal model-based methods of fault detection are as follows:

1) bandpass filters;

2) spectral analysis (FFT);

3) maximum-entropy estimation.

The characteristic quantities or features from fault detection methods show stochastic behavior with mean values and variances. Deviations from the normal behavior must then be detected by methods of change detection (residual analysis, Figure I.2), such as:

1) mean and variance estimation;

2) likelihood-ratio test, Bayes decision;

3) run-sum test.

I.5. Model uncertainty and fault detection

Model-based FDI makes use of mathematical models of the system. However, a perfectly accurate mathematical model of a physical system is not possible. Usually, the parameters of the system may vary with time, and the characteristics of the disturbances and noises are unknown, so they cannot be modeled accurately. Hence, there is always a mismatch between the actual process and its mathematical model, even under no fault conditions. Such discrepancies cause difficulties in FDI applications, in particular, since they act as sources of false alarms and missed alarms. Therefore, the effect of modeling uncertainties, disturbances and noise is the most crucial point in the model-based FDI concept, and the solution to this problem is the key for its practical applicability (Chen and Patton 1999).

To overcome these problems, a model-based FDI scheme has to be insensitive to modeling uncertainty. Sometimes, a reduction of the sensitivity to modeling uncertainty does not solve the problem, because the sensitivity reduction may be associated with a reduction of the sensitivity to faults (Gertler 1998; Chen and Patton 1999). A more meaningful formulation of the FDI problem is to increase the insensitivity to modeling uncertainty in order to provide increasing fault sensitivity.

The difficulties introduced by model uncertainties, disturbances and noises in model-based FDI have been widely considered during the last 10 years by both academia and industry (Gertler 1998). A number of methods have been proposed to tackle this problem, for example, the Unknown Input Observer (UIO), eigenstructure assignment and parity relation methods.

An important task of the model-based FDI scheme is to be able to diagnose incipient faults in a system. With respect to abrupt faults, incipient faults may have a small effect on residuals and can be hidden by disturbances. On the other hand, hard faults can be detected more easily because their effects are usually larger than modeling uncertainties and a simple fixed threshold is usually enough to diagnose their occurrence by residual analysis.

The presence of incipient faults may not necessarily degrade the performance of the plant, however, they may indicate that the component should be replaced before the probability of more serious malfunctions increases. The successful detection and diagnosis of incipient faults can therefore be considered a challenge for the design and evaluation of FDI algorithms.

I.6. Robust fault diagnosis

In the context of automatic control, the term robustness is used to describe the insensitivity or invariance of the performance of control systems with respect to disturbances, model–plant mismatches or parameter variations. Fault diagnosis schemes, on the other hand, must, of course, also be robust to the mentioned disturbances, but, in contrast to automatic control systems, they must not be robust to actual faults. On the contrary, while generating robustness to disturbances, the designer must maintain or even enhance the sensitivity of fault diagnosis schemes to faults. Furthermore, the robustness, as well as the sensitivity properties, must be independent of the particular fault and disturbance mode. Generally, the problem of robust FDI can be divided into the tasks of robust residual generation followed by robust residual evaluation.

In many cases, the disturbances and model–plant mismatches to which robustness must be generated are due to the use of linear models for describing dynamic behavior of nonlinear processes. Modeling errors can be avoided from the very beginning by focusing on robust residual generation methods using linear and nonlinear process models. This, in turn, simplifies the problem of residual evaluation without reducing the sensitivity to actual faults.

Effective tools for robust residual generation and even complete decoupling from external disturbances and unknown system parameters can be provided, for example, by UIOs, which are introduced and applied to industrial processes. It is shown that the proposed solution to the disturbance decoupling problem also provides the solution to both the fault detection and fault isolation problems.

On the other hand, many dynamic processes can only be described effectively using nonlinear mathematical models. However, most of the existing observer-based FDI techniques are limited to the use of linear process models. The methods that can be found in the literature are based on the assumption that the system under supervision stays, during normal operation, in a neighborhood of a certain known operating point (Chen and Patton 1999; Patton et al. 2000)

It is clear that, as almost every process system is nonlinear, the modeling errors almost always reduce the accuracy of the linear model and therefore the performance of the FDI algorithm is compromised. Various methods for generating robustness to linearization have been proposed in the literature and the reader is referred to (Patton et al. 2000, Chapter 7) for a comprehensive treatment of this subject.

This book also surveys the state of the art of robustness methods and presents some important ideas concerning the development of the use of nonlinear models and predictors for FDI. For example, observer-based approaches to robust FDI and FTC for dynamic systems are considered in more detail. The available model-based approaches are generalized, and thus extended to a wider class of dynamic systems.

In order to accommodate the application of robust FDI concepts, disturbances and parameter uncertainties of the monitored plants, as well as faults, are modeled in the form of unknown input signals. It is shown that, provided certain conditions can be met, complete decoupling of the residual from disturbances as well as from the parameter uncertainties of the process model can be achieved, while the sensitivity of the residual to faults is maintained. As the faults are also modeled in the form of external signals, this method additionally provides tools for the purpose of fault isolation. Fault isolation requires the decoupling of the effects of different faults from the residual (Chen and Patton 1999) and this, in turn, allows for decisions on which fault or faults out of a given set of possible faults has actually occurred.

These residual properties must be completely independent of the magnitude or frequency of the unknown inputs and the faults. This is crucial in cases where no a priori knowledge about these properties is available. For systems where the complete decoupling of the remaining unknown inputs or faults from the residual proves impossible, a threshold selection method, employing functional analytic methods and appropriate vector and operator norms, can be exploited. This technique provides a tool for the robust evaluation of the residuals, which have been generated by UIOs. Using the same functional analysis methods as employed for threshold selection, a performance index can be defined that allows for performance evaluation and, to a certain degree, also allows for optimal residual generator design (Patton et al. 2000).

I.7. Data–driven approaches to robust FDI

In previous sections, we have seen that model-based FDI methods formally require a high accuracy mathematical model of the monitored system. The better the model is as a representation of the dynamic behavior of the system, the better the FDI performance will be. It is difficult to develop a highly accurate model of a complex system and hence the interesting question is: “what is a reasonable model to enable good performance in FDI to be guaranteed?”.

It would be attractive to develop a robust FDI technique which is insensitive to modeling uncertainty, that is, so that a highly accurate mathematical model is no longer required. However, in order to design a robust FDI scheme, we should have a description (i.e. some information) about the uncertainty, for example, its distribution matrix and spectral bandwidth, and so on. Furthermore, this description should provide assistance for a robust FDI design, that is, it can be handled in a systematic manner. This book will show how a typical uncertainty description makes use of the concept of “unknown inputs” acting upon a nominal linear model of the system. These unknown disturbances describe the uncertainties acting upon the system but disturbance distribution matrices are assumed to be known since they can be estimated by identification schemes.

It is clear that disturbances and faults act on the system in the same way, and thus we cannot easily discriminate between these excitation signals unless we know the structure of the disturbance distribution matrix. Once the disturbance distribution matrix is known, we can generate the residual with the disturbance decoupling (robust) property, that is, the residual is decoupled from the disturbance (uncertainty). The robust residual can then be used to achieve reliable FDI and FTC.

The theories underlying robust FDI approaches have been very well developed, but for real applications the following problems remain unsolved:

– estimation of the reliable model for the monitored process;

– modeling accuracy of the real uncertainty by means of identified disturbance terms when no knowledge of the uncertainty is available;

– estimation of the disturbance terms and the structure of distribution matrices.

This book addresses these unsolved problems. Some simulation and real examples are given to test some of the theoretical results. These problems have to be addressed, otherwise the application domain of the disturbance decoupling approach for robust FDI is very limited. In fact, few researchers and contributions have presented the application results of robust fault diagnosis to real processes.

As mentioned above, a primary requirement for model-based and disturbance decoupling approaches to robust FDI is that both the system model and disturbance distribution matrices must be known. It is interesting that, within the framework of international research on this subject, there have been few attempts to address the problem by means of the identification approach. This lack of information has obstructed the application of robust FDI in real engineering systems. Therefore, we present the research developments surrounding the joint estimation of system and disturbance matrices in order to solve the robust fault diagnosis problem.

Concerning the data-driven schemes developed and exploited throughout the book, when all observed variables of a dynamic process are affected by uncertainties, the parameter estimation task can be performed by the so-called errors-in-variables methods. On the other hand, equation error methods can be developed in the case of exactly known plant variables (Simani et al. 2000). It is worthwhile noting that less attention has been paid to errors-in-variables schemes.

Under these considerations, this book presents the robust FDI results concerning the description of monitored plants by means of equation error and error-in-variables identified models in the presence of variable uncertainties. Moreover, for the examples presented, estimates obtained by the proposed data-driven approaches and parameter estimates will be computed and compared.

I.8. Data-driven methods for fault diagnosis

If several symptoms change differently for certain faults, an initial way of determining them is to use classification methods which indicate changes of symptom vectors.

Some classification methods are as follows (Patton et al. 1989; Basseville and Nikiforov 1993; Babuška 1998; Gertler 1998; Chen and Patton 1999):

1) geometrical distance and probabilistic methods;

2) artificial neural networks;

3) fuzzy clustering.

When more information about the relations between symptoms and faults is available in the form of diagnostic models, methods of reasoning can be applied. Diagnostic models then exist in the form of symptom–fault causalities, for example, in the form of symptom–fault trees. The causalities can be expressed as IF–THEN rules. Then analytical as well as heuristic symptoms (from operators) can be processed. By considering these symptoms as vague facts, probabilistic or fuzzy set descriptions lead to a unified symptom representation. By using forward and backward reasoning, probabilities or possibilities of faults are obtained as a result of diagnosis. Typical approximate reasoning methods are as follows (Basseville and Nikiforov 1993; Chen and Patton 1999):

1) probabilistic reasoning;

2) possibilistic reasoning with fuzzy logic;

3) reasoning with artificial neural networks.

This very short consideration shows that many different methods have been developed over the last 30 years. It is also clear that many combinations of them are possible.

On the basis of different contributions during the last 30 years, it can be stated that parameter estimation and observer-based methods are the most frequently applied techniques for fault detection, especially for the detection of sensor and process faults. Nevertheless, the importance of neural network-based and combined methods for fault detection is steadily growing. In most applications, fault detection is supported by simple threshold logic or hypothesis testing. Fault isolation is often carried out using classification methods. For this task, neural networks are being more and more widely used.

The number of applications using nonlinear models is growing, while the trend of using linearized models is diminishing. It seems that analytical redundancy-based methods have their best application areas in mechanical systems where the models of the processes are relatively precise. Most nonlinear processes under investigation belong to the group of thermal and fluid dynamic processes. The field of applications to chemical processes has few developments, but the number of applications is growing. The favorite linear process under investigation is the DC motor. In general, the trend is changing from applications to safety-related processes with many measurements, as in nuclear reactors or aerospace systems, to applications in common technical processes with only a few sensors. For diagnosis, classification and rule-based reasoning methods are the most important, and the use of neural network classification as well as fuzzy logic-based reasoning is growing.

I.9. FDI application report

Because of the many publications and increasing number of applications (IFAC Congress and IFAC Symposia SAFEPROCESS) between 1991 and 2018, it is of interest to show some trends (Patton et al. 1989; Basseville and Nikiforov 1993; Gertler 1998; Chen and Patton 1999; Frank et al. 2000). Therefore, a literature study is briefly presented as follows. Contributions taking into account the applications reported in Table I.1 were considered. The type of faults considered is distinguished according to Table I.2. Among all contributions, the fault detection methods were classified as in Table I.3. The change detection and fault classification methods are indicated in Table I.4. The reasoning strategies for fault diagnosis are reported in Table I.5. The contributions considered are summarized in Table I.6. The evaluation has been limited to the fault detection and diagnosis (FDD) of laboratory, pilot and industrial processes.

Table I.1.FDI applications and number of contributions

Application

Number of contributions

Simulation of real processes

105

Large-scale pilot processes

94

Small-scale laboratory processes

68

Full-scale industrial processes

98

Table I.2.Fault type and number of contributions

Fault type

Number of contributions

Sensor faults

129

Actuator faults

111

Process faults

123

Control loop or controller faults

48

Table I.3.FDI methods and number of contributions

Method type

Number of contributions

Observer

123

Parity space

74

Parameter estimation

101

Frequency spectral analysis

57

Neural networks

79

Table I.4.Residual evaluation methods and number of contributions

Evaluation method

Number of contributions

Neural networks

89

Fuzzy logic

65

Bayes classification

54

Hypothesis testing

48

Table I.5.Reasoning strategies and number of contributions

Reasoning strategy

Number of contributions

Rule based

40

Sign directed graph

33

Fault symptom tree

32

Fuzzy logic

66

Table I.6.Applications of model-based fault detection

FDD

Number of contributions

Milling and grinding processes

91

Power plants and thermal processes

106

Fluid dynamic processes

67

Combustion engine and turbines

96

Automotive

68

Inverted pendulum

63

Miscellaneous

102

DC motors

121

Stirred tank reactor

77

Navigation system

75

Nuclear process

50

Table I.6 shows that among mechanical and electrical processes, DC motor applications are mostly investigated. Parameter estimation and observer-based methods are used in the majority of applications in these kind of processes, followed by parity space and combined methods. Thermal and chemical processes are investigated less frequently.

Table I.3 shows that parameter estimation and observer-based methods are used in nearly 70% of all applications considered. Neural networks, parity space and combined methods are applied notably less often.

More than 50% of sensor faults are detected using observer-based methods, while parameter estimation, parity space and combined methods play a less important role. For the detection of actuator faults, observer-based methods are mostly used, followed by parameter estimation and neural network methods.

Parity space and combined methods are rarely applied. In general, there are fewer applications for actuator faults than for sensor or process faults. The detection of process faults is mostly carried out with parameter estimation methods. Nearly 50% of all the applications considered use parameter estimation-based methods for detection of process faults. Observer-based, parity space and neural network-based methods are used less often for this class of faults.

Among all the described processes, linear models have been used much more than nonlinear models. In processes with nonlinear models, observer-based methods are mostly applied, but parity equations and neural networks also play an important role. In processes with linear or linearized models, parameter estimation and observer-based methods are mostly used. Parity space and combined methods are also used in several applications but not to the same extent as observer-based and parameter estimation methods.

Taking into account the system considered, the number of nonlinear process applications using nonlinear models is decreasing. For linear processes, no significant change can be stated. The applications of fault-detection methods for nonlinear processes used mostly observer-based and parameter estimation, more than parity space methods. Also, the use of neural networks and combinations are important.

Concerning the fault diagnosis methods, in recent years, the field of classification approaches, especially with neural networks and fuzzy logic, has steadily been growing. Also, rule-based reasoning methods are increasingly being based on fault diagnosis. A growing application of fuzzy rule-based reasoning can be stated. Applications using neural networks for classification are increasing and the trends are analogous to the increasing number of nonlinear process investigations. Nevertheless, the classification of generated residuals seems to remain the most important application area for neural networks.

I.10. From FDI to FTC

A conventional feedback control design for complex systems may result in unsatisfactory performance in the event of malfunction in input–output sensors, actuators and system components. A fault-tolerant closed-loop control system is very attractive because it can tolerate faults while also maintaining desirable performance.

The conventional approach to the design of an FTC includes different steps and separate modules: modeling or identification of the controlled system, design of the controller, FDI scheme and a method for re-configuring the control system. Identification and design of the controller can be performed separately or using combined methods. Hence, the FDI and controller are linked through the reconfiguration module. The fundamental problem with such a system lies in the identification stage in the independent design of the control and FDI modules. Significant interactions occurring among these modules can be neglected. There is therefore a need for a research study into the interactions between system identification, control design, the FDI stage and the FTC design strategy.

Fault identification is the most important of all the fault diagnosis tasks. When a fault is estimated, detection and isolation can be easily achieved since the fault nature can improve the diagnosis process. However, the fault identification problem itself has not gained enough research attention.

Most fault diagnosis techniques, such as parameter identification, parity space and observer-based methods, cannot be directly used to identify faults in sensors and actuators. Very little research has been done to overcome the fault identification problem. The Kalman filter for statistical testing and fault identification was proposed in Chen and Patton (1999). However, the statistical testing methods can impose a high computational demand. A fault identification scheme solving a system inversion problem was proposed in Chen and Patton (1999); Simani et al. (2003) and Simani and Farsoni (2018).

In the scheme, depicted in Figure I.3, fault identification is performed by estimating the nonlinear relationship between residuals and fault magnitudes. This is possible because robust residuals should only contain fault information.

Figure I.3.Fault estimation scheme FTC

Such a nonlinear function approximation and estimation can be performed by using fuzzy systems, neural networks or an inversion of the transfer matrix between residuals and faults (Simani et al. 2003; Simani and Farsoni 2018). The central task in model-based fault detection is the residual generation. Most residual generation techniques are based on linear system models. For nonlinear systems, the traditional approach is to linearize the model around the system operating point. However, for systems with high nonlinearity and a wide dynamic operating range, the linearized approach fails to give satisfactory results.

One solution is to use a large number of linearized models corresponding to a range of operating points. This means that a large number of FDI schemes corresponding to each of the operating points is needed. Hence, it is important to study residual generation techniques that tackle nonlinear dynamic systems directly. There are some research studies on the residual generation of nonlinear dynamic systems, for example using nonlinear observers (Chen and Patton 1999; De Persis and Isidori 2001). There have been some attempts to use nonlinear observers to solve nonlinear system FDI problems, (Chen and Patton 1999; De Persis and Isidori 2001), for example, nonlinear UIOs, including adaptive observers and sliding mode observers. If the class of nonlinearities can be restricted, observers for bilinear systems were also proposed (Chen and Patton 1999).

On the other hand, the analytical models that the nonlinear observer approaches are based on are not easy to obtain in practice. Sometimes, it is impossible to model the system using an explicit mathematical model. To overcome this problem, it is desirable to find a universal approximate model that can be used to represent the real system with an arbitrary degree of accuracy. Different approaches were proposed and they are currently under investigation: neural networks, fuzzy models and hybrid models.

As shown in Simani et al. (2003) and Simani and Farsoni (2018), fuzzy systems and neural networks are a powerful tool for handling nonlinear problems. One of the most important advantages of neural networks is their ability to implement nonlinear transformations for functional approximation problems. Therefore, neural networks can be used in a number of ways to tackle fault diagnosis problems for nonlinear dynamic systems. In existing publications, they were mainly exploited as fault classifier with steady-state processes, whereas neural networks have been used as residual generators and for modeling nonlinear dynamic systems for FDI purposes (Chen and Patton 1999).

Fuzzy models can be used both as a residual classifier and as a nonlinear system parametric model (Chen and Patton 1999). In the second case, the main idea is to build an FDI scheme based on fuzzy observers. Estimated outputs and residuals are computed as fuzzy fusion of local observer output and residuals. The main problem of this approach concerns the stability of the global observer. A linear matrix inequality method was proposed in Chen and Patton (1999) using Lyapunov theorem, but this solution can be quite conservative.

Hybrid models can describe the behavior of any nonlinear dynamic process if they are described as a composition of several local affine models, selected according to the process operating conditions (Chen and Patton 1999; Simani et al. 2003). Instead of exploiting complicated nonlinear models obtained by modeling techniques, it is possible to describe the plant by a collection of affine models. Such a compound system requires the identification of the local models from data. Several works (Chen and Patton 1999; Simani et al. 2003) addressed a method for the identification and the optimal selection of the local affine models from a sequence of noisy measurements acquired from the process. Application of these results to model-based fault diagnosis for safety critical systems is another research area worthy of mention.

I.11. Structure of the book

To detect and isolate faults in a dynamic system, based on the use of an analytical model, a residual signal has to be used. It is derived from a comparison between real measurements and the relative estimates (generated by the model). The modeling uncertainty problem can be tackled by designing FDI and FTC schemes, whose residuals are insensitive to uncertainties while sensitive to faults. On the other hand, a model with satisfactory accuracy can be estimated using identification procedures (Norton 1986; Söderström and Stoica 1987; Ljung 1999).

The aim of the design of FDI and FTC schemes is to reduce the effects of uncertainties on the residuals and to enhance the effects of faults acting on the residuals. The main aim of this book is to develop a residual generator for model-based fault diagnosis and to design an effective FTC strategy for a dynamic process by means of input and output signals. An accurate model of the process under investigation will be estimated using identification procedures from data affected by noises and acquired from simulated and/or actual plants. The book consists of an Introduction and six chapters in Volume 1 and eight chapters in Volume 2 and the main contributions are summarized in the following.

The Introduction, provides a brief overview and critical discussion of the state of the art of the most recent literature from 2015 to 2020, thereby introducing the field of fault detection, fault diagnosis and fault-tolerant systems with methods, which have proven their significance in practical applications.

Chapter 1 addresses the mathematical modeling and description of the faults most commonly exploited for providing a proper description of the process under diagnosis, in connection with the strategy proposed for the diagnosis and FTC designs.

By taking into account these aspects, Chapter 2 is focused on structural analysis issues. In particular, this chapter addresses the standard tool used to identify submodels that can be used to design model-based and data-driven diagnostic modules. Structural approaches typically operate on models described by a set of equations, which can also be obtained from model-free approaches.

With reference to FDI, Chapter 3 considers set-based methods. The set-membership and interval observer approaches are introduced to deal with the robustness problem in fault detection. The design conditions to guarantee robustness, and at the same time fault sensitivity, are presented. Next, the extension to fault isolation using unknown-input observer schemes is described.

Chapter 4 describes stochastic methods for FDI. In particular, the chapter revises the existing methods for FDI using stochastic modeling of uncertainty, using both models and data.

As an alternative to analytical approaches, Chapter 5