Lomovoy V. Methods and Tools of Nonparametric Identification for Nonlinear Dynamical Systems Based on Volterra Models in Frequency Domain

The dissertation is devoted to the solution of important scientific and practical problems. The first one is to increase the accuracy and computational stability of deterministic identification methods for nonlinear dynamic systems in the form of Volterra models in frequency domain based on experimental data from «input-output» observations, taking into account computational errors. The second one is to create, based on conducted theoretical studies, effective computational and software tools for estimating multidimensional frequency characteristics in the context of incomplete a priori information on the system under study. The aim of the thesis research is to improve the efficiency of deterministic identification methods for non-linear dynamic systems based on Volterra models in the form of multifrequencys characteristics by creating new and developing current computational methods and software tools for their estimation according to the data of «input-output» experiments that are resistant to external noise and errors measurements. Efficiency refers to the accuracy and computational robustness of frequency characteristics. The object of the study is the process of nonparametric identification of nonlinear dynamic systems based on Volterra models in the frequency domain. The subject of the study are methods, algorithmic and software tools for the deterministic identification of non-linear dynamic systems based on Volterra series and polynomials in the form of multidimensional amplitude and phase characteristics. The paper presents a number of new scientific findings and results. For the first time was developed method for constructing of an approximation model for a nonlinear dynamic system in the form of Volterra polynomial in frequency domain using polyharmonic test signals of different amplitudes. In proposed method, unlike in known ones, for decomposing responses to partial components regularized least squares method is used and optimal amplitude of the test signal selected. This improves the accuracy and computational stability of the identification procedure and enables the simulation of systems in a given range of input amplitudes, beyond the radius of convergence of the Volterra series. For the first time was, developed a method of deterministic identification of nonlinear dynamical systems based on a model in the form of Volterra series in the frequency domain. Method differs from the existing ones by using regularized compensatory method of identification, which use amplitudes of test signal as regularization parameters for decom-posing responses to partial components. It allows to improve accuracy and computational stability of identification procedure and at the same time to reduce its numerical complexity. The method for constructing an approximation model of a nonlinear dynamical system in the form of Volterra polynomial in the frequency domain was improved. The method differs by use of wavelet filtration for smoothing the estimates of obtained multifrequency characteristics in conditions of a real experiment, taking into account measurement errors. This improves accuracy and ensures the smoothness of identification results. The method for constructing a model of a nonlinear dynamic system in the form of Volterra series in the frequency domain was further developed. The method is aries by determining the optimal amplitudes of the test polyharmonic signals and the corresponding scaling factors in the linear combination of response signals identifiable system. At that minimized methodological errors evaluating multifrequency characteristics. The scientific results of the dissertation work extend variety of methods of identification for nonlinear dynamic systems and their mathematical models. The practical importance of the work lies in creation of software tools that implement computational algorithms for deterministic identification of nonlinear dynamical systems based on Volterra series and polynomials in the form of multidimensional amplitude and phase characteristics, and their implementation in scientific research and educational process. Based on developed methods and algorithms, as well as efficient use of the Matlab system platform, there were developed hardware and software tools for constructing Volterra models in the frequency domain with automatic identification process control functions. These tools were used to determine the multidimensional amplitude and phase characteristics of the telecommunication system's communication channel in VHF range, according to «input-output» experiments using polyharmonic test signals. Keywords: nonlinear dynamical systems, nonparametric models, Volterra series, Volterra polynomial, multidimensional frequency characteristics, polyharmonic signals, computing identification, numerical algorithms, identification tools.