  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.
