The Determination of Instants of the Change of Modes of a Dynamic System Using the Indicator Function of the Number of States

When operating and testing technical devices, including turbines of rocket and aviation engines, there can be a need for diagnostics of the process of change of their dynamic modes, for the determination of the current type of the dynamic mode and the instants or the time interval of the event onset. Along with the spectral methods, a method based on the analysis of conditions of the dynamic system in a discrete phase space can be applied to solve this problem. The authors examine a method and an algorithm that describes the behavior of the dynamic system based on the analysis of the evolution of the indicator function of the number of states, determined in a temporary window and summing up the quantity of the differing conditions of the system in a discrete phase space. A model of the two-dimensional phase space is constructed, in which discrete conditions of the analyzed dynamic process are determined. A method to build a basic discrete set of states of the dynamic system and the indicator function behaviour are described while creating a basic set of states and subsequently identifying discrete conditions of the dynamic process. It is shown that an increase in the indicator function occurs when changing the dynamic mode, leading to the emergence of new states in relation to the conditions of the window of a given width, which is displaced along a time axis. As an example, by analyzing the acoustic signal, the authors examine a change in the dynamic behavior of the system represented by a rotating shaft onto which a thrust force containing constant and pulse components is applied.

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