Lytvynenko I. Methods of identification of segment and rhythmic structures of cyclic signals in systems of digital data processing

The dissertation is dedicated to the solution of the scientific problem which consists in the creation of new methods for identification of segment and rhythm structures of cyclic signals, which provide improved accuracy of cyclic signals processing and computer modeling in automated digital data processing systems. Considering the fact that there is a repetitive structure of cyclic signals, which is due to phase expansion in time or space of cyclic occurrences and processes - a methodology for constructing methods of segmentation (mathematical models of which are cyclic functions with segment structure) of different cyclic signals is created. The system of new methods of segmentation of cyclic signals was developed on the basis of the created methodology. It allows identifying their segment and discrete rhythm structures with increased accuracy at their automated processing within the framework of deterministic and stochastic mathematical models of cyclic functions with a variable or constant rhythm. There were improvements made in the method for identifying the rhythm structure of cyclic signals through the use of methods of interpolation by the means of a quadratic or cubic spline in comparison with the known method of identification of the rhythm structure on the basis of piecewise linear interpolation. The method of adaptive identification of the rhythm structure of cyclic signals was developed, which includes, as its components, the developed method of determining additional elements of the rhythm structure and the developed method of determining the optimal polynomial in the corresponding segment. Considering the greater number of elements of the rhythm structure, this allowed evaluating the type of optimal polynomial among the linear, quadratic and cubic ones in the investigated segment. This also allowed choosing a method of evaluating the rhythm structure in the investigated segment among the known method (based on piecewise linear interpolation) and the developed one in the process of work (based on quadratic and cubic splines). The achieved results gave a possibility to adaptively evaluate the investigated segment and improved accuracy of identifying the rhythm structure of cyclic signals. There was developed a method of verifying the models of the investigated signals which is based on testing the hypothesis of the relation of the investigated signal to the class of cyclic signals for the suitable, correct application of the methods developed in the process of this study (during the processing of cyclic signals). The mathematical model and methods of statistical development of the surface formation process on the metal’s outer layer, caused by the effect of mechanical or laser shock-wave force on it, in a form of a cyclic random process with a segment structure, was delineated. Mathematical tools were developed of identifying the segment and evaluating rhythm structures that increase the overall accuracy of methods of processing of cyclic signals, in particular, sampling methods, statistical processing and computer simulation of cyclic signals. These tools are suitable for use as components of specialized programs in both software and hardware digital processing systems (diagnostics or forecasting) of different cyclic signals: in cardiac diagnostics systems, in systems of technical diagnostics of the state of the surface of metals and in systems of analysis and forecasting of economic cyclic process.