The combined algorithm to estimate the dynamics of chaotic state statistics in time series

To improve the performance of machine learning algorithms in monitoring dynamic and unstable processes, it is necessary to carefully analyze the data structure forming the training sample. This stage is especially important in artificial intelligence systems, where the control object interacts with changing external conditions. Algorithms for analyzing the dynamics of randomness statistics and their application in monitoring dynamic systems are considered: the Hurst criterion is considered as a measure of the randomness of a series; The emergence score is an information indicator that is used to measure the degree to which the properties of a system cannot be fully explained or predicted based on the properties of its individual components; the fractal dimension score describes the complexity and self–similarity of an object's structure; the senior Lyapunov exponent is a key concept in the theory of dynamical systems that allows analyzing their sensitivity to initial conditions. The indicator helps to understand how the system reacts to the slightest changes in the source data. The Helder exponent evaluates a local measure of the regularity of a function. A new approach with averaging within each window is proposed, which increases the efficiency of the analysis and reduces the risk of false periodic components. An example of the application of the described methods for estimating the uncertainties that arise when determining the state of complex technical systems is given (based on fragments of time series from an open database). Numerical results of a study of time series nonlinearity and randomness statistics using a sliding window are presented. The presented combined estimation algorithm allows us to consider the evaluation system as a generalized representation of a segment of a series of observations, which creates the basis for solving one of the key tasks of machine learning – the creation of generalized models of the dynamics of state vectors. These models are used in clustering and use case analysis tasks. To process multidimensional time series, it is proposed to use a specialized method based on their singular value decomposition.