A Reconstruction Algorithm for a Dynamic System Phase Space and its Application for Development of Predictive Models
Keywords:
Dynamic System, Predictive Model, Phase Space, Attractor, Telemetric InformationAbstract
Purpose: Development of a predictive model of state of a non-linear dynamic system on the basis of reconstruction of its phase space. Results: There has been formulated general problem definition of predicting a state of a dynamic system on the basis of attractor reconstruction (a limit set of points) of its phase space using a system of discrete mapping of observed parameters. There has been developed a reconstruction algorithm of phase space of a dynamic system according to time series of one of its parameters which includes splitting initial time sampling in training and test samples as well as their preliminary processing; assessment of phase space dimension; definition of an amount of time series points required for attractor reconstruction; the analysis of attractor sections; determination of dimension and creation of a predictive model in a form of a system of discrete displays; optimization of model and its testing. There has been given an example of a predictive model of a telemetric parameter of the spacecraft onboard dynamic system. For the given example time of prediction anticipation has been defined and possibilities of preliminary processing of analyzed time series have been shown using algorithms of exception of abnormal values and smoothing. Practical significance: Reconstruction of phase space of a dynamic system allows to evaluate parameters of a synthesized predictive model and to accelerate the solution of the problem of optimization of its characteristics. The obtained algorithms and the model have been used in a software complex for processing of telemetric information.