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The method of forecasting based on spectral component dynamics analysis


E. S. Sokolova, D. A. Lyakhmanov

At present one of the main methods to optimize the process of the complex object control is its technical state prediction. Such prediction may be understood here as a posteriori estimate of some property of a phenomenon under investigation based on a priori data on the past and present. A priori information is the only evidence to determine a model of such phenomenon under investigation. The available methods of prediction do not possess adequate flexibility. They are time-taking and do not always produce acceptable result from the point of view of the prediction accuracy and long-term character. On this basis they are mostly applied as auxiliary methods to reduce the dimension of the prediction object description and to prepare data for other methods. To solve prediction problems under conditions of high indeterminacy, it is suggested to use a method based on the analysis of spectral component dynamics (ASCD). It is based on the principle of the identity of spectra of time series crossed regions and the change of the multistep prediction of complex process by one-step extrapolation of its several simpler constituents such as harmonic fractions. The process of prediction consists in finding spectral representations of unknown parts of time series and comes to multiple operations of extrapolating series, which characterize the spectral component dynamics. This method has a number of advantages as compared to conventional extrapolation methods. The latter give in most cases such prediction which accuracy exponentially decreases with the increase of its depth. The described method based on the analysis of spectral components lacks similar disadvantages and with retaining tendencies enables to make prediction for several readings with similar probability of expressions as the prediction procedure for several readings is changed by a set of operations consisting of one-step extrapolation of reference signal spectral components. The ASCD method requires no a priori information on the process logic and physics. Therefore, it is a universal method for process extrapolation with a trend curve of composite form and expressed noise term. The possibility to determine prediction errors may be also referred to ad-vantages of this method as it allows to make the local correction of prediction values.

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