2013/10/12 by Gerasimos Rigatos, Rigatos, Gerasimos G.
Computer Science · Engineering · #Advanced Control Systems Optimization #FOS: Electrical engineering #Fault Detection and Control Systems #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1310.3358
openalex publication_date 2013/10/12 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
The Derivative-free nonlinear Kalman Filter is proposed for state estimation\nand fault diagnosis in distributed parameter systems and particularly in\ndynamical systems described by partial differential equations of the nonlinear\nwave type. At a first stage, a nonlinear filtering approach for estimating the\ndynamics of a 1D nonlinear wave equation, from measurements provided from a\nsmall number of sensors is developed. It is shown that the numerical solution\nof the associated partial differential equation results into a set of nonlinear\nordinary differential equations. With the application of diffeomorphism that is\nbased on differential flatness theory it is shown that an equivalent\ndescription of the system is obtained in the linear canonical (Brunovsky) form.\nThis transformation enables to obtain local estimates about the state vector of\nthe system through the application of the standard Kalman Filter recursion. At\na second stage, the local statistical approach to fault diagnosis is used to\nperform fault diagnosis for the distributed parameters system by processing\nwith elaborated statistical tools the differences (residuals) between the\noutput of the Kalman Filter and the measurements obtained from the distributed\nparameter system. Optimal selection of the fault threshold is succeeded by\nusing the local statistical approach to fault diagnosis. The efficiency of the\nproposed filtering approach for performing fault diagnosis in distributed\nparameters systems is confirmed through simulation experiments.\n