A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> Fault detection and isolation is a crucial and challenging task in the automatic control of large complex systems. We propose a discrete-event system (DES) approach to the problem of failure diagnosis. We introduce two related notions of diagnosability of DES's in the framework of formal languages and compare diagnosability with the related notions of observability and invertibility. We present a systematic procedure for detection and isolation of failure events using diagnosers and provide necessary and sufficient conditions for a language to be diagnosable. The diagnoser performs diagnostics using online observations of the system behavior; it is also used to state and verify off-line the necessary and sufficient conditions for diagnosability. These conditions are stated on the diagnoser or variations thereof. The approach to failure diagnosis presented in this paper is applicable to systems that fall naturally in the class of DES's; moreover, for the purpose of diagnosis, most continuous variable dynamic systems can be viewed as DES's at a higher level of abstraction. > <s> BIB001 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> We address the problem of diagnosing large discrete event systems. Given a flow of observations from the system, the goal is to explain these observations on-line by identifying and localising possible failures and their consequences across the system. Model-based diagnosis approaches deal with this problem but, apart very recent proposals, either they require the computation of a global model of the system which is not possible with large discrete event systems, or they cannot perform on-line diagnosis. The contribution of this paper is the description and the implementation of a formal framework for the on-line decentralised diagnosis of such systems, framework which is based on the ''divide and conquer'' principle and does not require the global model computation. This paper finally describes the use of this framework in the monitoring of a real telecommunication network. <s> BIB002 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> In this paper we present an efficient approach for the fault detection of discrete event systems using Petri nets. We assume that some of the transitions of the net are unobservable, including all those transitions that model faulty behaviors. We prove that the set of all possible firing sequences corresponding to a given observation can be described as follows. First a set of basis markings corresponding to the observation are computed together with the minimal set of transitions firings that justify them. Any other marking consistent with the observation must be reachable from a basis marking by firing only unobservable transitions. For the computation of the set of basis markings we propose a simple tabular algorithm and use it to determine a basis reachability tree that can be used as a diagnoser. <s> BIB003 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> Many networked embedded sensing and control systems can be modeled as hybrid systems with interacting continuous and discrete dynamics. These systems present significant challenges for monitoring and diagnosis. Many existing model-based approaches focus on diagnostic reasoning assuming appropriate fault signatures have been generated. However, an important missing piece is the integration of model-based techniques with the acquisition and processing of sensor signals and the modeling of faults to support diagnostic reasoning. This paper addresses key modeling and computational problems at the interface between model-based diagnosis techniques and signature analysis to enable the efficient detection and isolation of incipient and abrupt faults in hybrid systems. A hybrid automata model that parameterizes abrupt and incipient faults is introduced. Based on this model, an approach for diagnoser design is presented. The paper also develops a novel mode estimation algorithm that uses model-based prediction to focus distributed processing signal algorithms. Finally, the paper describes a diagnostic system architecture that integrates the modeling, prediction, and diagnosis components. The implemented architecture is applied to fault diagnosis of a complex electro-mechanical machine, the Xerox DC265 printer, and the experimental results presented validate the approach. A number of design trade-offs that were made to support implementation of the algorithms for online applications are also described. <s> BIB004 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> The paper addresses the fault detection problem for discrete event systems in a Petri Net (PN) framework. Assuming that the structure of the PN model and the initial marking are known, faults are modelled by unobservable transitions. Moreover, we assume that there may be additional unobservable transitions associated with the system legal behaviour and that the marking reached after the firing of any transition is unknown. The proposed diagnoser works on-line: it waits for the firing of an observable transition and employs an algorithm based on the definition and solution of some integer linear programming problems to decide whether the system behaviour is normal or exhibits some possible faults. The results characterize the properties that the PN modelling the system fault behaviour has to fulfill in order to reduce the on-line computational effort. <s> BIB005 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> Fault diagnosis is crucial for ensuring the safe operation of complex engineering systems. Although discrete-event diagnosis methods are used extensively, they do not easily address parametric fault isolation in systems with complex continuous dynamics. This paper presents a novel event-based approach for diagnosis of abrupt parametric faults in continuous systems, based on a qualitative abstraction of measurement deviations from the nominal behavior. From a continuous model of the system, we systematically derive dynamic fault signatures expressed as event-based fault models, which are used, in turn, for designing an event-based diagnoser of the system and determining system diagnosability. The proposed approach is applied to a subset of the Advanced Diagnostics and Prognostics Testbed, which is representative of a spacecraft's electrical power system. We present experimental results from the actual testbed, as well as detailed simulation experiments that examine the performance of our diagnosis algorithms under different fault magnitudes and noise levels. <s> BIB006 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> In this brief, the problem of designing and developing a hybrid fault detection and isolation (FDI) scheme for a network of unmanned vehicles (NUVs) that is subject to large environmental disturbances is investigated. The proposed FDI algorithm is a hybrid architecture that is composed of a bank of continuous-time residual generators and a discrete-event system (DES) fault diagnoser. A novel set of residuals is generated so that the DES fault diagnoser empowered by incorporating appropriate combinations of the residuals and their sequential features will robustly detect and isolate faults in the NUVs. Our proposed hybrid FDI algorithm is then applied to actuator fault detection and isolation in a network of quad-rotors. Simulation results demonstrate and validate the performance capabilities of our proposed hybrid FDI algorithm. <s> BIB007 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> Recently, a bond-graph-based fault detection and isolation (FDI) framework has been developed with a new concept of global analytical redundancy relations (GARRs) (Low, Wang, Arogeti, and Luo, 2009, 2010; Low, Wang, Arogeti, and Zhang, 2010). This new concept allows the fault diagnosis for hybrid systems which consist of both continuous dynamics and discrete modes. A failure of a safety critical system such as the steering system of an automated guided vehicle may cause severe damage. Such failure can be avoided by an early detection and estimation of faults. In this paper, the newly developed FDI method is studied in details using an electrohydraulic steering system of an electric vehicle. The steering system and faults are modeled as a hybrid dynamic system by the hybrid bond graph (HBG) modeling technique. GARRs are then derived systematically from the HBG model with a specific causality assignment. Fault detection, isolation, and estimation are applied, experimental setup is described, and results are discussed. <s> BIB008 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> We consider the problem of diagnosing the occurrence of a certain unobservable event of interest, the fault event, in the operation of a partially-observed discrete-event system subject to permanent loss of observations modeled by a finite-state automaton. Specifically, it is assumed that certain sensors for events that would a priori be observable may fail at the outset, thereby resulting in a loss of observable events; the diagnostic engine is not directly aware of such sensor failures. We explore a previous definition of robust diagnosability of a given fault event despite the possibility of permanent (and unknown a priori) loss of observations and present a polynomial time verification algorithm to verify robust diagnosability and a methodology to perform online diagnosis in this scenario using a set of partial diagnosers. <s> BIB009 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> The diagnosis of a discrete-event system is the problem of computing possible behaviors of the system given observations of the actual behavior, and testing whether the behaviors are normal or faulty. We show how the diagnosis problems can be translated into the propositional satisfiability problem (SAT) and solved by algorithms for SAT. Our experiments demonstrate that current SAT algorithms can solve much bigger diagnosis problems than traditional diagnosis algorithms can. <s> BIB010 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> This technical note concerns fault detection and diagnosis for discrete event systems modeled with partially observed Petri nets. The proposed method provides diagnosis decisions via the analysis of observation sequences that include some observable events and the partial measurement of the successive states visited by the system. To this end, the observation sequences are decomposed into elementary observation sequences, linear matrix inequalities are used to compute the firing sequences consistent with each elementary observation sequence and an algorithm of linear complexity with respect to the length of the observation sequences is proposed to provide on-line diagnosis decisions. <s> BIB011 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> This paper presents a model-based fault diagnosis and prognosis scheme for a vehicle steering system. The steering system is modeled as a hybrid system with continuous dynamics and discrete modes using the hybrid bond graph tool. Multiple faults of different types, i.e., abrupt fault, incipient fault, and intermittent fault, are considered using the concept of Augmented Global Analytical Redundancy Relations (AGARRs). A fault discriminator is constructed to distinguish the type of faults once they are detected. After that, a fault identification scheme is proposed to estimate the magnitude of abrupt faults, the characteristic of intermittent faults, and the degradation behavior of incipient faults. The fault identification is realized by using a new adaptive hybrid differential evolution (AHDE) algorithm with less control parameters. Based on the identified degradation behavior of incipient faults, prognosis is carried out to predict the remaining useful life of faulty components. The proposed algorithm is verified experimentally on the steering system of a CyCab electric vehicle. <s> BIB012 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> In this paper, information from a hybrid bond graph (HBG) model and from discrete-event systems (DESs) is integrated into a fault diagnosis method for hybrid systems. In a pure-HBG framework, mode-change detection and isolation is handled by the mode-change signature and the mode-change signature matrix. In a DES approach, discrete states and faults are traced based on observable events (e.g., control signals) and diagnosers. Based on the two approaches, a new diagnoser that is driven by both observable events and consistency indicators generated by continuous residuals is presented. The proposed method allows not only to effectively trace the system mode but also to decide whether this mode is faulty or normal. The new method is presented and implemented on a testbed. The experimental results presented in this paper demonstrate the effectiveness of the method. <s> BIB013 </s> A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches <s> C. Fault Diagnosis for Discrete-Events and Hybrid Systems <s> Prognosis of hybrid systems is a challenging problem because multiple faults may happen simultaneously at a mode where these faults have different detectability. In other words, at the fault-initiating mode, some of the faults are detectable while others are nondetectable. As a result, decision making based on only one observation of abnormal behavior is not reliable under this condition. This paper focuses on the development of a model-based prognosis framework for hybrid systems where a dynamic fault isolation scheme is proposed to facilitate the prognostic tasks. The degradation behavior of each faulty component is mode dependent and can be estimated by a hybrid differential evolution algorithm. Thereafter, the remaining useful life of the faulty component that varies with different operating modes is calculated by using both the estimated degradation model and the user-selected failure threshold. Experiments are carried out to validate the key concepts of the developed methods, and results suggest the effectiveness. <s> BIB014
In industrial processes, the signals of some dynamic systems switch from one value to another rather than changing their values continuously. This kind of systems is called discreteevent systems. Fault diagnosis of discrete-event systems was initialized by BIB001 in the 1990s, and the underlying theory of fault diagnosis for discrete-event systems was proposed. The basic event-driven fault diagnosis problem is to perform model-based inferring at run time to determine whether a given unobservable fault event has occurred or not in the past by using sequences of observable events BIB009 . According to the model used, the fault diagnosis methods for discrete-event system can be roughly classified into automata-based fault method and Petri-net-based method. In order to overcome the complexity of the task, the automata-based fault diagnosis method has evolved into decentralized method BIB002 , symbolic method  , and the combination of decentralized and symbolic methods BIB010 . On the other hand, Petri net has intrinsically distributed nature, where the notions of state and action are local, which has been an asset to reduce the computational complexity of solving fault diagnosis problems BIB003 . Nevertheless, improved results were developed for avoiding complexity by either applying integer linear programming to Petri nets BIB005 or using partially observed Petri nets BIB011 . Recently, event-based approaches were applied to fault isolations for continuous dynamic processes, where a high-level discrete-event system fault diagnoser was employed to improve the robustness of the fault diagnosis against large environment disturbances BIB007 or isolate abrupt parameter faults BIB006 . Some complex industrial systems are both driven by timebased continuous dynamics and event-driven discrete dynamics, which are called hybrid systems, emerging from complex mechatronic systems, manufacturing systems, complex chemical processes, aerospace engineering systems, and automotive engine control and embedded control systems. Monitoring and fault diagnosis for hybrid systems entail challenges due to the fact that the continuous dynamics and discrete-event changes are mutually dependent and interacted. Hybrid automata are the most common models to represent hybrid systems, which can be utilized to design fault diagnosis algorithms to detect and isolate faults BIB004 ,  . Bond graph has become a powerful model to be used for fault diagnosis due to its capability of modeling complex systems in a unified way and the ease of obtaining analytical redundancy relation from the causalities on the graph. Recent results on Bond-graph-based fault diagnosis and their applications for hybrid systems can be found in BIB008 BIB012 BIB013 BIB014 .