Detection of parametric changes in the Peyrard-Bishop- Dauxois model of DNA using nonlinear Kalman filtering.

The derivative-free nonlinear Kalman filter is proposed for state estimation and fault diagnosis in distributed parameter systems of the wave-type and particularly in the Peyrard-Bishop-Dauxois model of DNA dynamics. At a first stage, a nonlinear filtering approach is introduced for estimating the dynamics of the Peyrard-Bishop-Dauxois 1D nonlinear wave equation, through the processing of a small number of measurements. It is shown that the numerical solution of the associated partial differential equation results in a set of nonlinear ordinary differential equations. With the application of a 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 DNA model through the application us of the standard Kalman filter recursion. At a second stage, the local statistical approach to fault diagnosis is used to perform fault diagnosis for this distributed parameter system by processing with 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 in the problem of fault diagnosis for parametric change detection, in nonlinear wave-type models of DNA dynamics, is confirmed through simulation experiments.