Fault Detection and Isolation of Uncertain Nonlinear Parabolic PDE Systems

This paper proposes a novel fault detection and isolation (FDI) scheme for distributed parameter systems modeled by a class of parabolic partial differential equations (PDEs) with nonlinear uncertain dynamics. A key feature of the proposed FDI scheme is its capability of dealing with the effects of system uncertainties for accurate FDI. Specifically, an approximate ordinary differential equation (ODE) system is first derived to capture the dominant dynamics of the original PDE system. An adaptive dynamics identification approach using radial basis function neural network is then proposed based on this ODE system, so as to achieve locally-accurate identification of the uncertain system dynamics under normal and faulty modes. A bank of FDI estimators with associated adaptive thresholds are finally designed for real-time FDI decision making. Rigorous analysis on the FDI performance in terms of fault detectability and isolatability is provided. Simulation study on a representative transport-reaction process is conducted to demonstrate the effectiveness and advantage of the proposed approach.