Optimization of Identification, Recognition and Prediction of Non-Stationary Objects Based on Tools for Monitoring and Correcting Distorted Information

Scientific and methodological foundations have been developed for optimal identification, recognition, and forecasting of random time series of non-stationary objects based on tools for detecting and correcting distorted information. Mechanisms for optimizing identification are proposed, involving the use of tools for extracting and using textural, specific characteristics of information. A wide range of mechanisms for tracking, identifying characteristic areas, detecting and correcting distorted information based on the tools of basis functions of Fourier transform and filtering under the condition of internal and external influences, the presence of noise (interference), blurring of points, various defects, a priori limitations and uncertainty have been studied. A mechanism based on graph embedding in vector space and the Young-Householder transformation method have been developed. Mechanisms that represent random time series by vectors of numerical characteristics, spectral characteristics, a search graph, and use decompositions of the normalized Laplace matrix have been studied and implemented. Solutions of the thermal kernel equations are obtained using the eigenvalues and vectors of the Laplace matrix. The effectiveness of identifying a non-stationary object has been studied on the basis of mechanisms using parabolic, orthogonal algebraic polynomial, linear autoregressive model, Daubechies 4 interpolation polynomial, cubic interpolation spline function, and three-layer neural network. A software package was implemented, the modules of which were created in the C++ language in the parallel computing environment “CUDA”.