Diagnosis of Discrete Event Systems with Petri Nets and Coding Theory

Modern technological processes include complex and large scale systems, where faults in a single component have major effects on the availability and performances of the system as a whole. For example manufacturing systems consists of many different machines, robots and transportation tools all of which have to correctly satisfy their purpose in order to ensure and fulfil global objectives. In this context, a failure is any event that changes the behaviour of the system such that it does no longer satisfy its purpose. Failure events lead to fault states (Rausand et al., 2004). Faults can be due to internal events as to external ones, and are often classified into three subclasses : plant faults that change the dynamical input – output properties of the system, sensor faults that result in substantial errors during sensors reading, and actuator faults when the influence of the controller to the plant is disturbed (Blanke et al., 2003). In order to limit the effects of the faults on the system, diagnosis is used to detect and isolate the failures. Diagnosis is often associated with control reconfiguration, that adapts the controller to the faulty situation such that it continues to satisfy its goal. Fault diagnosis and controller reconfiguration are carried out by supervision systems. This chapter only consider problems related to the diagnosis of systems. Diagnosis includes distinct stages: 1. The fault detection decides whether or not a failure event has occurred. This stage also concerns the determination of the time at which the failure occurs. 2. The fault isolation find the component that is faulty. 3. The fault identification identifies the fault and estimates also its magnitude. Diagnosis is usually discussed according to the model type used, with component based analysis that uses architectural and structure graph models, with continuous variables systems described by differential or difference equations and transfer functions, with discrete event systems represented by automata or Petri nets and with hybrid dynamical systems that combine continuous and discrete event behaviours (Blanke et al., 2003). Component based methods uses qualitative methods (Rausand et al., 2004) as failure modes and effect analysis (Blanke, 1996) and bi-partite graphs to investigate the redundancies included in the set of constraints and measurements for diagnosis purposes (Cordier et al., 2000; Patton et al., 1999). Fault diagnosis of continuous variables systems is usually based on residual generation and evaluation with parity space approaches or observation,