A Game-Theoretic approach to Fault Diagnosis of Hybrid Systems

Physical systems can fail. For this reason the problem of identifying and reacting to faults has received a large attention in the control and computer science communities. In this paper we study the fault diagnosis problem for hybrid systems from a game-theoretical point of view. A hybrid system is a system mixing continuous and discrete behaviours that cannot be faithfully modeled neither by using a formalism with continuous dynamics only nor by a formalism including only discrete dynamics. We use the well known framework of hybrid automata for modeling hybrid systems, and we define a Fault Diagnosis Game on them, using two players: the environment and the diagnoser. The environment controls the evolution of the system and chooses whether and when a fault occurs. The diagnoser observes the external behaviour of the system and announces whether a fault has occurred or not. Existence of a winning strategy for the diagnoser implies that faults can be detected correctly, while computing such a winning strategy corresponds to implement a diagnoser for the system. We will show how to determine the existence of a winning strategy, and how to compute it, for some decidable classes of hybrid automata like o-minimal hybrid automata.Comment: In Proceedings GandALF 2011, arXiv:1106.081

Discrete and hybrid methods for the diagnosis of distributed systems

Many important activities of modern society rely on the proper functioning of complex systems such as electricity networks, telecommunication networks, manufacturing plants and aircrafts. The supervision of such systems must include strong diagnosis capability to be able to effectively detect the occurrence of faults and ensure appropriate corrective measures can be taken in order to recover from the faults or prevent total failure. This thesis addresses issues in the diagnosis of large complex systems. Such systems are usually distributed in nature, i.e. they consist of many interconnected components each having their own local behaviour. These components interact together to produce an emergent global behaviour that is complex. As those systems increase in complexity and size, their diagnosis becomes increasingly challenging. In the first part of this thesis, a method is proposed for diagnosis on distributed systems that avoids a monolithic global computation. The method, based on converting the graph of the system into a junction tree, takes into account the topology of the system in choosing how to merge local diagnoses on the components while still obtaining a globally consistent result. The method is shown to work well for systems with tree or near-tree structures. This method is further extended to handle systems with high clustering by selectively ignoring some connections that would still allow an accurate diagnosis to be obtained. A hybrid system approach is explored in the second part of the thesis, where continuous dynamics information on the system is also retained to help better isolate or identify faults. A hybrid system framework is presented that models both continuous dynamics and discrete evolution in dynamical systems, based on detecting changes in the fundamental governing dynamics of the system rather than on residual estimation. This makes it possible to handle systems that might not be well characterised and where parameter drift is present. The discrete aspect of the hybrid system model is used to derive diagnosability conditions using indicator functions for the detection and isolation of multiple, arbitrary sequential or simultaneous events in hybrid dynamical networks. Issues with diagnosis in the presence of uncertainty in measurements due sensor or actuator noise are addressed. Faults may generate symptoms that are in the same order of magnitude as the latter. The use of statistical techniques,within a hybrid system framework, is proposed to detect these elusive fault symptoms and translate this information into probabilities for the actual operational mode and possibility of transition between modes which makes it possible to apply probabilistic analysis on the system to handle the underlying uncertainty present

Fault diagnosis of hybrid systems with applications to gas turbine engines

Stringent reliability and maintainability requirements for modern complex systems demand the development of systematic methods for fault detection and isolation. Many of such complex systems can be modeled as hybrid automata. In this thesis, a novel framework for fault diagnosis of hybrid automata is presented. Generally, in a hybrid system, two types of sensors may be available, namely: continuous sensors supplying continuous-time readings (i.e., real numbers) and threshold sensitive (discrete) sensors supplying discrete outputs (e.g., level high and pressure low). It is assumed that a bank of residual generators (detection filters) designed based on the continuous model of the plant is available. In the proposed framework, each residual generator is modeled by a Discrete-Event System (DES). Then, these DES models are integrated with the DES model of the hybrid system to build an Extended DES model. A "hybrid" diagnoser is then constructed based on the extended DES model. The "hybrid" diagnoser effectively combines the readings of discrete sensors and the information supplied by residual generators (which is based on continuous sensors) to determine the health status of the hybrid system. The problem of diagnosability of failure modes in hybrid automata is also studied here. A notion of failure diagnosability in hybrid automata is introduced and it is shown that for the diagnosability of a failure mode in a hybrid automaton, it is sufficient that the failure mode be diagnosable in the extended DES model developed for representing the hybrid automaton and residual generators. The diagnosability of failure modes in the case that some residual generators produce unreliable outputs in the form of false alarm or false silence signals is also investigated. Moreover, the problem of isolator (residual generator) selection is examined and approaches are developed for computing a minimal set of isolators to ensure the diagnosability of failure modes. The proposed hybrid diagnosis approach is employed for investigating faults in the fuel supply system and the nozzle actuator of a single-spool turbojet engine with an afterburner. A hybrid automaton model is obtained for the engine. A bank of residual generators is also designed, and an extended DES is constructed for the engine. Based on the extended DES model, a hybrid diagnoser is constructed and developed. The faults diagnosable by a purely DES diagnoser or by methods based on residual generators alone are also diagnosable by the hybrid diagnoser. Moreover, we have shown that there are faults (or groups of faults) in the fuel supply system and the nozzle actuator that can be isolated neither by a purely DES diagnoser nor by methods based on residual generators alone. However, these faults (or groups of faults) can be isolated if the hybrid diagnoser is used

RULES BASED MODELING OF DISCRETE EVENT SYSTEMS WITH FAULTS AND THEIR DIAGNOSIS

Failure diagnosis in large and complex systems is a critical task. In the realm of discrete event systems, Sampath et al. proposed a language based failure diagnosis approach. They introduced the diagnosability for discrete event systems and gave a method for testing the diagnosability by first constructing a diagnoser for the system. The complexity of this method of testing diagnosability is exponential in the number of states of the system and doubly exponential in the number of failure types. In this thesis, we give an algorithm for testing diagnosability that does not construct a diagnoser for the system, and its complexity is of 4th order in the number of states of the system and linear in the number of the failure types. In this dissertation we also study diagnosis of discrete event systems (DESs) modeled in the rule-based modeling formalism introduced in [12] to model failure-prone systems. The results have been represented in [43]. An attractive feature of rule-based model is it\u27s compactness (size is polynomial in number of signals). A motivation for the work presented is to develop failure diagnosis techniques that are able to exploit this compactness. In this regard, we develop symbolic techniques for testing diagnosability and computing a diagnoser. Diagnosability test is shown to be an instance of 1st order temporal logic model-checking. An on-line algorithm for diagnosersynthesis is obtained by using predicates and predicate transformers. We demonstrate our approach by applying it to modeling and diagnosis of a part of the assembly-line. When the system is found to be not diagnosable, we use sensor refinement and sensor augmentation to make the system diagnosable. In this dissertation, a controller is also extracted from the maximally permissive supervisor for the purpose of implementing the control by selecting, when possible, only one controllable event from among the ones allowed by the supervisor for the assembly line in automaton models