Fault Detection of a Class of Nonlinear Uncertain Parabolic PDE Systems

Abstract

This letter investigates the fault detection (FD) problem of a class of uncertain distributed parameter systems modeled by nonlinear parabolic partial differential equations (PDEs). A novel FD scheme is proposed with a neural network-based adaptive dynamics learning approach. Specifically, based on the Galerkin method, a finite dimensional ordinary differential equation (ODE) system is first derived to capture the dominant dynamics of the PDE system. An adaptive dynamics learning approach using radial basis function neural networks (RBF NN) is then developed to achieve locally accurate identification of the associated uncertain system dynamics. The learned knowledge can be obtained and stored in a bank of constant RBF NN models, which can be used to further construct a bank of FD estimators. A threshold is finally designed for real-time FD decision making. One important feature of the proposed FD scheme is that the spatio-temporal uncertain dominant dynamics of the parabolic PDE system can be locally accurately identified, such that occurring faults can be effectively distinguished from system uncertainties for accurate FD. Extensive simulation studies are conducted to verify the effectiveness and advantages of the proposed FD scheme.