A Kalman Filtering approach of improved precision for fault diagnosis in distributed parameter systems

Abstract—The Derivative-free nonlinear Kalman Filter is proposed for state estimation and fault diagnosis in distributed parameter systems and particularly in dynamical systems described by partial differential equations of the nonlinear wave type. At a first stage, a nonlinear filtering approach for estimating the dynamics of a 1D nonlinear wave equation, from measurements provided from a small number of sensors is developed. It is shown that the numerical solution of the associated partial differential equation results into a set of nonlinear ordinary differential equations. With the application of diffeomorphism that is based on differential flatness theory it is shown that an equivalent description of the system is obtained in the linear canonical (Brunovsky) form. This transformation enables to obtain local estimates about the state vector of the system through the application of the standard Kalman Filter recursion. At a second stage, the local statistical approach to fault diagnosis is used to perform fault diagnosis for the distributed parameters system by processing with elaborated statistical tools the differences (residuals) between the output of the Kalman Filter and the measurements obtained from the distributed parameter system. Optimal selection of the fault threshold is succeeded by using the local statistical approach to fault diagnosis. The efficiency of the proposed filtering approach for performing fault diagnosis in distributed parameters systems is confirmed through simulation experiments.