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1

A graph theory-based approach to the description of the process and the diagnostic system

Kościelny Jan Maciej, Bartyś Michał, Syfert Michał, Sztyber Anna

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 2

213--227

EN

The paper proposes an original, comprehensive, and methodically consistent graph theory-based approach to the description of the diagnosed process and the diagnosing system. The main baseline of the presented approach is in the dichotomous approach to diagnosing. It involves a separate description of both the process and the diagnostic system. This approach reflects the practice of designing implementable diagnostic systems. Thus, it can be seen as a proposal of a new, alternative, and, at the same time, flexible design procedure with great potential for applications. The primary motivation behind it was an attempt to circumvent the numerous limitations of well-known and well-established diagnosis approaches proposed by the communities working on fault detection and isolation (FDI) and artificial intelligence theories for diagnosis (DX). Accordingly, the paper identifies and provides an extensive discussion and a critical analysis of the existing limitations. Numerous examples and references to practical applications of the approach are indicated.

2

A data driven fault isolation method based on reference faulty situations with application to a nonlinear chemical process

Ragot José, Mourot Gilles, Kallas Maya

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 4

635--655

EN

The diagnosis of systems is one of the major steps in their control and its purpose is to determine the possible presence of dysfunctions, which affect the sensors and actuators associated with a system but also the internal components of the system itself. On the one hand, the diagnosis must therefore focus on the detection of a dysfunction and, on the other hand, on the physical localization of the dysfunction by specifying the component in a faulty situation, and then on its temporal localization. In this contribution, the emphasis is on the use of software redundancy applied to the detection of anomalies within the measurements collected in the system. The systems considered here are characterized by non-linear behaviours whose model is not known a priori. The proposed strategy therefore focuses on processing the data acquired on the system for which it is assumed that a healthy operating regime is known. Diagnostic procedures usually use this data corresponding to good operating regimes by comparing them with new situations that may contain faults. Our approach is fundamentally different in that the good functioning data allow us, by means of a non-linear prediction technique, to generate a lot of data that reflect all the faults under different excitation situations of the system. The database thus created characterizes the dysfunctions and then serves as a reference to be compared with real situations. This comparison, which then makes it possible to recognize the faulty situation, is based on a technique for evaluating the main angle between subspaces of system dysfunction situations. An important point of the discussion concerns the robustness and sensitivity of fault indicators. In particular, it is shown how, by non-linear combinations, it is possible to increase the size of these indicators in such a way as to facilitate the location of faults.

3

Fault tolerant control of wind turbine via identified fuzzy models prototypes

Djoudi Habib Chaouki Ben, Hafaifa Ahmed, Djoudi Dalila, Guemana Mouloud

Diagnostyka

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2020

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Vol. 21, No. 3

3--13

EN

The main purpose of this study is the comparison of two control strategies of wind turbine 4.8 MW, using fuzzy control and proportional integral control, taking into account eight kinds of faults that can occur in a wind turbine model. A technique based on fault diagnosis has been used to detect and isolate faults actuators and sensors in this system, it's about an observer applied to the benchmark model. The obtained results are presented to validate the effectiveness of this diagnostic method and present the results of the proposed control strategies.

4

Robust MPC for actuator-fault tolerance using set-based passive fault detection and active fault isolation

Xu F., Puig V., Ocampo-Martinez C., Olaru S., Niculescu S. I.

International Journal of Applied Mathematics and Computer Science

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2017

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Vol. 27, no. 1

43--61

EN

In this paper, a fault-tolerant control (FTC) scheme is proposed for actuator faults, which is built upon tube-based model predictive control (MPC) as well as set-based fault detection and isolation (FDI). In the class of MPC techniques, tube-based MPC can effectively deal with system constraints and uncertainties with relatively low computational complexity compared with other robust MPC techniques such as min-max MPC. Set-based FDI, generally considering the worst case of uncertainties, can robustly detect and isolate actuator faults. In the proposed FTC scheme, fault detection (FD) is passive by using invariant sets, while fault isolation (FI) is active by means of MPC and tubes. The active FI method proposed in this paper is implemented by making use of the constraint-handling ability of MPC to manipulate the bounds of inputs. After the system has been detected to become faulty, the input-constraint set of the MPC controller is adjusted to actively excite the system for achieving FI guarantees on-line, where an active FI-oriented input set is designed off-line. In this way, the system can be excited in order to obtain more extra system-operating information for FI than passive FI approaches. Overall, the objective of this paper is to propose an actuator MPC scheme with as little as possible of FI conservatism and computational complexity by combining tube-based MPC and set theory within the framework of MPC, respectively. Finally, a case study is used to show the effectiveness of the proposed FTC scheme.

5

Switching time estimation and active mode recognition using a data projection method

Hakem A., Cocquempot V., Pekpe K. M.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 4

827--840

EN

This paper proposes a data projection method (DPM) to detect a mode switching and recognize the current mode in a switching system. The main feature of this method is that the precise knowledge of the system model, i.e., the parameter values, is not needed. One direct application of this technique is fault detection and identification (FDI) when a fault produces a change in the system dynamics. Mode detection and recognition correspond to fault detection and identification, and switching time estimation to fault occurrence time estimation. The general principle of the DPM is to generate mode indicators, namely, residuals, using matrix projection techniques, where matrices are composed of input and output measured data. The DPM is presented in detail, and properties of switching detectability (fault detectability) and discernability between modes (fault identifiability) are characterized and discussed. The great advantage of this method, compared with other techniques in the literature, is that it does not need the model parameter values and thus can be applied to systems of the same type without identifying their parameters. This is particularly interesting in the design of generic embedded fault diagnosis algorithms.

6

Fault isolability with different forms of the faults–symptoms relation

Kościelny J. M., Syfert M., Rostek K., Sztyber A.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 4

815--826

EN

The definitions and conditions for fault isolability of single faults for various forms of the diagnostic relation are reviewed. Fault isolability and unisolability on the basis of a binary diagnostic matrix are analyzed. Definitions for conditional and unconditional isolability and unisolability on the basis of a fault information system (FIS), symptom sequences and directional residuals are formulated. General definitions for conditional and unconditional isolability and unisolability in the cases of simultaneous evaluation of diagnostic signal values and a sequence of symptoms are provided. A comprehensive example is discussed.

7

A double window state observer for detection and isolation of abrupt changes in parameters

Byrski J., Byrski W.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 3

585--602

EN

The paper presents a new method for diagnosis of a process fault which takes the form of an abrupt change in some real parameter of a time-continuous linear system. The abrupt fault in the process real parameter is reflected in step changes in many parameters of the input/output model as well as in step changes in canonical state variables of the system. Detection of these state changes will enable localization of the faulty parameter in the system. For detecting state changes, a special type of exact state observer will be used. The canonical state will be represented by the derivatives of the measured output signal. Hence the exact state observer will play the role of virtual sensors for reconstruction of the derivatives of the output signal. For designing the exact state observer, the model parameters before and after the moment of fault occurrence must be known. To this end, a special identification method with modulating functions will be used. A novel concept presented in this paper concerns the structure of the observer. It will take the form of a double moving window observer which consists of two signal processing windows, each of width T . These windows are coupled to each other with a common edge. The right-hand side edge of the left-side moving window in the interval [t − 2T, t − T ] is connected to the left-hand side edge of the right-side window which operates in the interval [t − T, t]. The double observer uses different measurements of input/output signals in both the windows, and for each current time t simultaneously reconstructs two values of the state—the final value of the state in the left-side window zT (t − T ) and the initial value of the state z0(t − T ) in the right-side window. If the process parameters are constant, the values of both the states on the common joint edge are the same. If an abrupt change (fault) in some parameter at the moment tA = t − T occurs in the system, then step changes in some variables of the canonical state vector will also occur and the difference between the states will be detected. This will enable localization of the faulty parameter in the system.

8

Performance optimization of model-free fault diagnosis schemes

Kalisch M., Przystałka P., Katunin A., Timofiejczuk A.

Diagnostyka

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2016

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Vol. 17, No. 1

51--58

EN

This paper describes the method of model-free fault detection and isolation. The main purpose of the research is to present one possibility of the development of diagnostic schemes for which the component structure and behavioural parameters are tuned automatically in order to obtain the maximal efficiency of the fault detection and isolation system. The proposed approach can be viewed as the intersection of elementary methods (classic and soft computing) such as discrete wavelet analysis, machine learning (using decision trees or artificial neural networks), and evolutionary algorithms. The fundamental verification of the method was conducted for data made available within the benchmark problem involving a wind turbine. The achieved results confirm the effectiveness of the proposed approach while also showing its limitations.

PL

Artykuł opisuje metodę detekcji i izolacji uszkodzeń bez użycia modelu. Głównym celem badań jest pokazanie możliwości opracowania schematów diagnostycznych, których struktura oraz parametry są dostrajane automatycznie w celu osiągnięcia najwyższej możliwej sprawności detekcji i izolacji uszkodzeń. Zaproponowane podejście może być postrzegane jako połączenie elementarnych metod (klasyczne metody oraz obliczenia miękkie) jak np. analiza falkowa, metody uczenia maszynowego (drzewa decyzyjne i sztuczne sieci neuronowe) oraz algorytmy ewolucyjne. Weryfikacja metody została przeprowadzona na danych symulacyjnych wygenerowanych za pomocą modelu turbiny wiatrowej. Uzyskane wyniki potwierdziły wysoką skuteczność metody oraz pokazały jej ograniczenia.

9

SMAC-FDI: A single model active fault detection and isolation system for unmanned aircraft

Ducard G. J. J.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 1

189--201

EN

This article presents a single model active fault detection and isolation system (SMAC-FDI) which is designed to efficiently detect and isolate a faulty actuator in a system, such as a small (unmanned) aircraft. This FDI system is based on a single and simple aerodynamic model of an aircraft in order to generate some residuals, as soon as an actuator fault occurs. These residuals are used to trigger an active strategy based on artificial exciting signals that searches within the residuals for the signature of an actuator fault. Fault isolation is carried out through an innovative mechanism that does not use the previous residuals but the actuator control signals directly. In addition, the paper presents a complete parameter-tuning strategy for this FDI system. The novel concepts are backed-up by simulations of a small unmanned aircraft experiencing successive actuator failures. The robustness of the SMAC-FDI method is tested in the presence of model uncertainties, realistic sensor noise and wind gusts. Finally, the paper concludes with a discussion on the computational efficiency of the method and its ability to run on small microcontrollers.

10

Modelowanie testów diagnostycznych za pomocą metod uczenia maszynowego

Kalisch M.

Modelowanie Inżynierskie

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2014

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T. 22, nr 53

70--77

PL

W pracy zaprezentowano metodykę tworzenia testów diagnostycznych służących do detekcji i izolacji uszkodzeń za pomocą algorytmów uczenia maszynowego z wykorzystaniem darmowego oprogramowania RapidMiner. Porównano różne metody łączenia klasyfikatorów na przykładzie danych symulacyjnych wygenerowanych za pomocą modelu numerycznego zaworu elektro-pneumatycznego opracowanego w ramach projektu DAMADICS. Przedstawione wyniki badań potwierdzają poprawność proponowanego podejścia.

EN

The papers deals with the methodology of designing diagnostics tests that can be used for fault detection and isolation using machine learning algorithms implemented in open source RapidMiner application. In the paper there were compared different methods of combining classifiers using the benchmark data generated by means of the simulator of electro-pneumatic valve that has been developed within the DAMADICS project. The results of the research study confirm the effectiveness of the proposed approach.

11

Residual generator fuzzy identification for automotive diesel engine fault diagnosis

Simani S.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 2

419--438

EN

Safety in dynamic processes is a concern of rising importance, especially if people would be endangered by serious system failure. Moreover, as the control devices which are now exploited to improve the overall performance of processes include both sophisticated control strategies and complex hardware (input-output sensors, actuators, components and processing units), there is an increased probability of faults. As a direct consequence of this, automatic supervision systems should be taken into account to diagnose malfunctions as early as possible. One of the most promising methods for solving this problem relies on the analytical redundancy approach, in which residual signals are generated. If a fault occurs, these residual signals are used to diagnose the malfunction. This paper is focused on fuzzy identification oriented to the design of a bank of fuzzy estimators for fault detection and isolation. The problem is treated in its different aspects covering the model structure, the parameter identification method, the residual generation technique, and the fault diagnosis strategy. The case study of a real diesel engine is considered in order to demonstrate the effectiveness the proposed methodology.

12

Generalized reasoning about faults based on the diagnostic matrix

Bartyś M.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 2

407--417

EN

This paper introduces a set of comprehensive general reasoning rules about single faults based on a diagnostic matrix. The reasoning scheme unifies inference about faults based on a conventional binary diagnostic matrix, a two- and three-valued fault isolation system as well as on their fuzzy counterparts. There are introduced and defined notions of alternative and dominant fault signatures, fuzzy fault signatures as well as a matrix of alternative signatures. This matrix is supposed to be used instead of the classic diagnostic one. It is also shown that dominant fault signatures are transformable into alternative ones. Finally, three variants of concise general reasoning rules of faults are given. Three examples illustrate key point issues of the paper. The first example refers to a medical diagnostic case. It shows an instance of dominant fault signatures and, in fact, proposes a rational approach for planning diagnostic tests. The other examples describe the fuzzy reasoning approach employing a matrix of fuzzy alternative signatures applicable for use with multi-valued fuzzy diagnostic signals. Future works are outlined in the summary section.

13

Double fault distinguishability in linear systems

Kościelny J. M., Łabęda-Grudziak Z. M.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 2

395--406

EN

This paper develops a new approach to double fault isolation in linear systems with the aid of directional residuals. The method of residual generation for computational as well as internal forms is applied. Isolation of double faults is based on the investigation of the coplanarity of the residual vector with the planes defined by the individual pairs of directional fault vectors. Additionally, the method of designing secondary residuals, which are structured and directional, is proposed. These transformations allow achieving various isolation properties. It is shown that double fault distinguishability can be improved by decomposing the observed residual vector along the response directions. The described methods are illustrated with a simple computational example.

14

Automatyzacja sieci rozdzielczych jako podstawowy element sieci inteligentnych

Babś A.

Automatyka, Elektryka, Zakłócenia

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2013

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Vol. 4, Nr 2(12)

22-29

PL

W artykule przedstawiono podstawowe cechy sieci inteligentnych oraz te cechy które powodują, że tradycyjna sieć rozdzielcza może mieć charakter sieci inteligentnej. Szczegółowo przedstawiono dwie funkcje inteligentnych sieci rozdzielczych tj. wykrywanie zwarć, ich izolacja i przywracanie zasilania oraz funkcję regulacji napięcia wykorzystującą pomiary napięć w głębi sieci. Opisano również wymagania jakie powinna spełniać infrastruktura telekomunikacyjna, aby umożliwić realizacje funkcji sieci inteligentnych. Przedstawiono przykład wdrożenia sieci inteligentnej na Półwyspie Helskim opisując wdrożone w 2012 roku funkcje.

EN

Paper presents the basic features of the distribution smart grid. Fault detection, isolation and restoration function is described along with integrated volt/var control function based on the low voltage network measurements. Some requirements related with telecommunication infrastructure utilized for smart grid automation are specified. Practical example of the smart grid functions deployment is described.

15

Supervisory fault tolerant control with integrated fault detection and isolation: a switched system approach

Yang H., Jiang B., Cocquempot V., Lu L.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 1

87-97

EN

This paper focuses on supervisory fault tolerant control design for a class of systems with faults ranging over a finite cover. The proposed framework is based on a switched system approach, and relies on a supervisory switching within a family of pre-computed candidate controllers without individual fault detection and isolation schemes. Each fault set can be accommodated either by one candidate controller or by a set of controllers under an appropriate switching law. Two aircraft examples are included to illustrate the efficiency of the proposed method.

16

Uogólniona metoda wnioskowania o uszkodzeniach na podstawie binarnej macierzy diagnostycznej

Bartyś M.

Pomiary Automatyka Kontrola

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2011

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R. 57, nr 7

779-783

PL

W artykule wprowadzono i zdefiniowano pojęcia sygnatur alternatywnych i dominujących. Wprowadzenie tych pojęć pozwoliło na sformalizowanie i uogólnienie schematu wnioskowania o uszkodzeniach obejmującego zarówno podejścia bazujące na binarnej macierzy diagnostycznej jak i podejścia bazujące na podstawie dwuwartościowego systemu informacyjnego FIS. Przedstawiono przykład ilustrujący uogólniony schemat wnioskowania. W podsumowaniu przedstawiono kierunki dalszych prac.

EN

A brief survey of diagnostic fault isolation methods based on a binary diagnostic matrix and bi-valued FIS [3] information system is presented in the introductory part (Section 1) of the paper. It is shown on an example of carcinoma renis disease (Tab.2), that the classic reasoning scheme about single faults based on a binary diagnostic matrix is insufficient and should be revised. It is also shown that the problems of proper reasoning remain unsolved even if the Fault Information System - FIS will be applied. In both cases, there is possible to reject true diagnosis as well as generate a false one. To solve the problem, there were introduced and defined the so called: alternative (10) and dominant signatures (11). Introduction of these signatures enables formal generalisation and extension of the inference scheme about faults (16) including approaches based on a binary diagnostic matrix as well as bi-valued FIS. The advantages of introducing the dominant signatures are described in Section 5. Also, some hints for implementation of the general reasoning scheme are formulated in Section 5. The proposed general reasoning method is useful for applications to system with embedded diagnostics, particularly to those making use of on-line serial and parallel diagnostics [6]. The future works are outlined in the summary (Section 6), including generalization of the inference scheme based on multi-valued FIS and fuzzy evaluation of diagnostic signals.

17

Fault Diagnosis Basing on the Information of the Interval Delays of Symptoms

Kościelny J. M., Syfert M.

Pomiary Automatyka Kontrola

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2011

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R. 57, nr 5

463-466

EN

The paper presents the formal conditions for fault isolability in the case of reasoning based on binary diagnostics matrix and the intervals of delays for each fault-symptom pair. It is shown that the higher fault isolability can be achieved while taking into account the knowledge about the symptoms delays. Finally, the new isolation algorithm utilising such knowledge is proposed. The presented approaches are illustrated with the example of fault isolability analysis for three tank system.

PL

W artykule przedstawiono formalne warunki rozróżnialności uszkodzeń w przypadku wnioskowania wykorzystującego binarną macierz diagnostyczna oraz przedziały opóźnień zdefiniowane dla każdej pary uszkodzenie - symptom. Wykazano iż możliwe jest uzyskanie wyższej rozróżnialności uszkodzeń gdy wykorzystywana jest wiedza o opóźnieniach symptomów. Przedstawiono także nowy algorytm lokalizacji wykorzystujący tego typu wiedzę.

18

Diagnostyka złożonych procesów przemysłowych - ograniczenia, wymagania, problemy

Kościelny J. M., Syfert M., Bartyś M.

Pomiary Automatyka Kontrola

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2011

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R. 57, nr 7

801-805

PL

W artykule omówiono uwarunkowania i ograniczenia występujące w diagnostyce złożonych instalacji w przemyśle chemicznym, petrochemicznym, energetycznym itp. Określono wymagania stawiane systemom diagnostycznym dla takich instalacji oraz scharakteryzowano problemy istotne w procesie projektowania systemów diagnostycznych. Do problemów tych zaliczyć należy: zmienność struktury obiektu w trakcie eksploatacji, opóźnienia powstawania symptomów prowadzące do fałszywych diagnoz oraz występowanie uszkodzeń wielokrotnych. Podano sposoby rozwiązania tych problemów. Zostały one zastosowane przy realizacji systemów modelowania, diagnostyki i nadrzędnego sterowania procesów AMandD oraz DiaSter.

EN

Limitations, requirements and problems of diagnostics of complex industrial systems is discussed in this paper. Brief discussion given in Section 1 is particularly relevant to issues typical for chemical, petrochemical, power, food etc. large scale industrial installations. Section 2 of the paper lists and discusses main limitations and restrictions that should be taken into account in design phase of industrial diagnostic system. Basic issues are connected with variations in the diagnosed system structure, delays of fault symptoms causing false diagnoses, and necessity of isolation of multiple faults. Three applicable approaches of solving the issues stated in Section 2 are described in Section 3. Here, in Subsection 3.1, a novel and robust inference scheme against system structure variation is proposed (2) and Dynamic Decomposition of the Diagnosed System is briefly described. The problems of generation of false diagnoses caused by delays of fault symptoms are discussed in Subsection 3.2. As a remedy, a simple and robust algorithm on fault delays is presented. The discussion of applicable approach allowing handling multiple faults [9] is given in Subsection 3.3. The industrial pilot applications with use of advanced diagnostic and monitoring systems AMandD [16] and DiaSter [19] are presented in the summary part (Section 4). These systems make use, among others, from approaches presented in this paper.

19

Active fault tolerant control of nonlinear systems: the cart-pole example

Bonfe M., Castaldi P., Mimmo N., Simani S.

International Journal of Applied Mathematics and Computer Science

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2011

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Vol. 21, no 3

441-455

EN

This paper describes the design of fault diagnosis and active fault tolerant control schemes that can be developed for nonlinear systems. The methodology is based on a fault detection and diagnosis procedure relying on adaptive filters designed via the nonlinear geometric approach, which allows obtaining the disturbance de-coupling property. The controller reconfiguration exploits directly the on-line estimate of the fault signal. The classical model of an inverted pendulum on a cart is considered as an application example, in order to highlight the complete design procedure, including the mathematical aspects of the nonlinear disturbance de-coupling method based on the nonlinear differential geometry, as well as the feasibility and efficiency of the proposed approach. Extensive simulations of the benchmark process and Monte Carlo analysis are practical tools for assessing experimentally the robustness and stability properties of the developed fault tolerant control scheme, in the presence of modelling and measurement errors. The fault tolerant control method is also compared with a different approach relying on sliding mode control, in order to evaluate benefits and drawbacks of both techniques. This comparison highlights that the proposed design methodology can constitute a reliable and robust approach for application to real nonlinear processes.

20

Zaawansowana diagnostyka procesów i układy regulacji tolerujące uszkodzenia

Kościelny J.

Przegląd Elektrotechniczny

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2009

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R. 85, nr 9

207-214

PL

Omówiono cele i zadania bieżącej diagnostyki procesów przemysłowych. Przedstawiono różnice między klasycznymi systemami alarmowymi a systemami diagnostycznymi. Scharakteryzowano stosowane metody detekcji i lokalizacji uszkodzeń oraz problemy praktyczne występujące przy diagnozowaniu złożonych instalacji technologicznych. Omówiono system diagnostyczny AMandD oraz jego pilotowe wdrożenia. Przedstawiono koncepcją budowy układów regulacji tolerujących uszkodzenia oraz przykłady takich rozwiazań.

EN

The aims and tasks of on-line diagnostics of industrial processes have been discussed. Differences between classic alarm systems and diagnostics systems have been shown. Applicable detection methods as well as practical problems of diagnostics of the complex technological installations have been characterized. The diagnostic system AMandD and its pilot implementations have been described. The concepts and examples of fault tolerant control systems have been presented.