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The Derivative-free nonlinear Kalman Filter is proposed for state estimationand fault diagnosis in distributed parameter systems and particularly indynamical systems described by partial differential equations of the nonlinearwave type. At a first stage, a nonlinear filtering approach for estimating thedynamics of a 1D nonlinear wave equation, from measurements provided from asmall number of sensors is developed. It is shown that the numerical solutionof the associated partial differential equation results into a set of nonlinearordinary differential equations. With the application of diffeomorphism that isbased on differential flatness theory it is shown that an equivalentdescription of the system is obtained in the linear canonical (Brunovsky) form.This transformation enables to obtain local estimates about the state vector ofthe system through the application of the standard Kalman Filter recursion. Ata second stage, the local statistical approach to fault diagnosis is used toperform fault diagnosis for the distributed parameters system by processingwith elaborated statistical tools the differences (residuals) between theoutput of the Kalman Filter and the measurements obtained from the distributedparameter system. Optimal selection of the fault threshold is succeeded byusing the local statistical approach to fault diagnosis. The efficiency of theproposed filtering approach for performing fault diagnosis in distributedparameters systems is confirmed through simulation experiments.

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