FAULT DETECTION AND ESTIMATION IN A CLASS OF DISTRIBUTED PARAMETER SYSTEMS

摘要

In this paper, the problem of fault detection and isolation in a class of distributedrnparameter systems (DPS) will be investigated. The behavior of distributed parameterrnsystems is best described by partial differential equation (PDE) models. However, due torncomplex nature of DPS, a PDE model is traditionally transformed into a finite set ofrnordinary differential equations (ODE) prior to the design of control or fault detectionrnschemes by using significant approximations thus reducing the accuracy and reliability ofrnthe overall system. By contrast, in this paper, the PDE representation of the system isrndirectly utilized to design the fault diagnosis scheme for DPS. Faults that can occurrnanywhere in the domain of the DPS (referred to as state faults) are considered, rather thanrnonly actuator and sensor faults. State faults are significantly more complicated to deal withrnin the case of DPS since they can be initiated anywhere within a continuous range of space,rnwhile in practice sensors are only available at limited locations which in many cases onlyrninclude the input and/or output sides of the DPS. This problem is tackled by using anrnobserver structure, which includes input, and output filters directly based on the PDE modelrnof the system. A fault is detected by comparing the detection residual, which is therndifference between measured and estimated outputs, with a predefined detection threshold.rnOnce the fault is detected, an online approximator is activated to learn the fault function.rnAn update law is introduced for updating the unknown parameters of the onlinernapproximator. The stability of the observer along with the online approximator will berndiscussed analytically in the paper. It is shown that one sensor is satisfactory for faultrndetection and approximation if the fault function has only one unknown parameter or canrnbe expressed as linear in the unknown parameters. However, additional sensors arernrequired for fault approximation or isolation in the general case. For example, a leakagernfault in a pipeline has magnitude and location as unknown parameters and these parametersrncannot be approximated by using one sensor. An algorithm is designed to approximate thernlocation of a state fault with unknown magnitude by using multiple sensors. The distributedrnparameter systems considered in this paper are modelled by parabolic partial differentialrnequations with Neumann or Dirichlet boundary conditions. Heat transfer systems and fluidrnpipelines are examples of systems in this class of DPS. The scheme is verified inrnsimulations on the aforementioned systems.