Research On Data Filtering Based Identification Methods And Applications Of Nonlinear Systems

Nonlinear systems are widely used in real industry, such as energy and power generation, electronic communication and industrial manufacturing field. Recently, an increasing number of researchers focus on the parameter estimation problem of nonlinear systems constantly. This thesis studies the Hammerstein, Wiener and Hammerstein-Wiener Errors-in-Variables nonlinear systems gradually by adopting the filtering identification theory and derives the recursive least squares algorithm, the stochastic gradient algorithm, the iterative least squares algorithm and the asymptotically unbiased two-stage least squares algorithm. The simulations illustrate the e?ectiveness of the proposed algorithms theoretically and their applications on wind power research field show the practicality of the derived methods, which gives their theoretical significance and application value for enriching and developing the identification theory.The main contributions of this thesis are listed as follows:1. For single input single output Hammerstein finite impulse response moving average systems, a filtering based recursive least squares algorithm is derived to raise the estimation accuracy. Besides, to decrease the calculation load, a decomposition based filtering recursive least squares algorithm is proposed. By decomposing the filtered Hammerstein system into two subsystems, one containing the parameter vector of the linear subsystem and the other containing the parameter vector of the nonlinear part, the calculation load is much lower than the recursive least squares algorithm.2. The filtering theory and iterative method are combined to derive a filtering based gradient identification algorithm and a filtering based least squares iterative algorithm for single input single output Hammerstein finite impulse response moving average systems. By expanding the scalar innovations to innovation vectors, a filtering based multi-innovation extended stochastic gradient algorithm is presented and numerical simulations are also provided to show its e?ectiveness.3. Construct the identification model of the single input single output Wiener nonlinear finite impulse response moving average system before that the filtering idea is used to reform the feedback Wiener model. A filtering based decomposition recursive least squares algorithm is proposed by decomposing the feedback system into two subsystems.4. For multi-input multi-output Hammerstein nonlinear finite impulse response moving average systems, the Kronecker product is used to reconstruct the parameter vectors of the nonlinear model that leads to a easier modeling of the multivariable system.The filtering theory is adopted to propose a filtering based recursive least squares algorithm and a filtering based stochastic gradient algorithm.5. By adopting the singular value decomposition method to extract the parameters from the coupling matrices without parameter redundancy, a two-stage least squares algorithm is presented for the Hammerstein-Wiener Errors-in-Variables system. In view of unknown covariance of measurement noise, an asymptotically unbiased twostage least squares algorithm is derived to estimate the parameters of the Errorsin-Variables model and the asymptotical property is strictly proved.6. Based on the proposed identification methods, some actual engineering problems are discussed, such as the wind speed forecasting and wind power prediction problem.Firstly, the iterative identification theory is adopted in deriving the wind speed prediction algorithm based on the gray model. After going through the step of wind speed prediction, the filtering theory is used to model the nonlinear wind power output-wind speed characteristics for short-term wind power prediction that shows its application value in actual engineering field.In conclusion, this thesis mainly studies the identification algorithms based on filtering method for nonlinear systems, including Hammerstein, Wiener and HammersteinWiener models. The numerical simulations and their applications on wind power prediction verify the effectiveness of the proposed algorithms, which illustrate that the proposed algorithms have high effectiveness and wide practicability.