Browsing by Author "Svinarenko, Andrey"

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Analysis and forecast of the environmental radioactivity dynamics based on the methods of chaos theory: general conceptions
(Publishing House of Lviv Polytechnic National University, 2016) Glushkov, Alexander; Safranov, Timur; Khetselius, Olga; Ignatenko, Anna; Buyadzhi, Vasily; Svinarenko, Andrey
For the first time, we present a completely new technique of analysis, processing and forecasting of any time series of the environmental radioactivity dynamics, which schematically is as follows: a) general qualitative analysis of a dynamical problem, typical environmental radioactivity dynamics (including a qualitative analysis from the viewpoint of ordinary differential equations, the “Arnold-analysis”); b) checking for the presence of chaotic (stochastic) features and regimes (the Gottwald-Melbourne’s test; the correlation dimension method); c) reducing the phase space (the choice of time delay, the definition of the embedding space by the correlation dimension methods and false nearest neighbours algorithms); d) determination of the dynamic invariants of a chaotic system (computation of the global Lyapunov dimension la; determination of the Kaplan-Yorke dimension dL and average limits of predictability Prmax on the basis of the advanced algorithms; e) a nonlinear prediction (forecasting) of any dynamical system evolution. The last block really includes new (in the theory of environmental radioactivity dynamics and environmental protection) methods and algorithms of nonlinear prediction such as methods of predicted trajectories, stochastic propagators and neural networks modeling, renormanalysis with blocks of polynomial approximations, wavelet-expansions etc.
Damage analysis and detection under varying environmental and operational conditions using a chaos theory methods
(Lviv Politechnic Publishing House, 2017-09-08) Buyadzhi, Vasily; Ternovsky, Valentin; Glushkov, Alexander; Khetselius, Olga; Svinarenko, Andrey; Bakunina, Elena; Odessa State Environmental University
The paper is devoted to problem of analysis, identification and prediction of the presence of damages, which above a certain level may present a serious threat to the engineering (vibrating) structures such as different technical systems (hydrotechnical equipment, hydroelectrical station engines, atomic reactors ones etc). Usually change of structural dynamic properties due to environmental, operational and other effects allows to determine the existence, location and size of damages. We present and apply an effective computational approach to modelling, analysis of chaotic behaviour of structural dynamic properties of the engineering structures. The approach includes a combined group of non-linear analysis and chaos theory methods such as a correlation integral approach, average mutual information, surrogate data, false nearest neighbours algorithms, the Lyapunov’s exponents and Kolmogorov entropy analysis, nonlinear prediction models etc. As illustration we present the results of the numerical investigation of a chaotic elements in dynamical parameter time series for the experimental cantilever beam (environmental conditions are imitated by damaged structure, variating temperature, availability of a pinknoise force). For the first time we list the numerical data on topological and dynamical invariants, i.e., correlation, embedding, Kaplan-Yorke dimensions, Lyapunov’s exponents and Kolmogorov entropy etc.
Modeling evolutionary dynamics of complex ecosystems using combined chaos theory and neural networks methods: I. Formal theoretical basis for application to environmental radioactivity dynamics
(Lviv Politechnic Publishing House, 2017-09-08) Glushkov, Alexander; Khetselius, Olga; Safranov, Tamerlan; Buyadzhi, Vasily; Ignatenko, Anna; Svinarenko, Andrey; Odessa State Environmental University
We present elements of the formal mathematical approach to the analysis, modeling and further prediction of the nonlinear dynamics of chaotic systems based on the methods of nonlinear analysis and neural networks. As the object of studing is the environmental radioactivity dynamics. Using such a combined method is proposed for the first time in the environmental radioactivity dynamnics studying. Use of the information about the phase space in the simulation of the evolution of the physical process in time can be considered as a major innovation in the modeling of chaotic processes in the complex systems. This concept can be achieved by constructing a parameterized nonlinear function F (x, a), which transform y (n) to y(n+1) = = F[y(n),a], and then use different criteria for determining the parameters a . Firstly to build the desired functions it is offered using the wavelet expansions. Further, since there is the notion of local neighborhoods, we can create a model of the process occurring in the neighborhood, at the neighborhood and by combining together these local models to construct a global non-linear model to describe most of the structure of the attractor.