Dmytrotsa L. Models, methods and information technology for analysis of processes with variable period

The thesis deals with the solution of the important scientific and practical problem of increasing the completeness degree of information about processes with a variable period and the level of these processes analysis automation by developing the model, methods and information technology for reasonable decision-making in various practical applications, particularly, in cardiology problems while evaluating heart rate variability after exercise stress effect on the patient body. While developing the information technology for the analysis of processes with a variable period in operation, an approach, the essence of which is concentrated in the triad "model-algorithm-program", is offered. In the first stage, the model of processes in the form of periodic functions with a variable period (PFVP) is chosen. In the second stage, on base of the model, methods including construction of Fourier series of PFVP are developed. In the third stage, appropriate software and information technology for determination the electrocardiogram variability obtained after exercise stress effect on the human body as a process with a variable period are developed. In the first stage of the triad, the simplest examples of periodic functions with the variable period – trigonometric functions with the variable period are investigated, the analytical expressions of their periods are recorded and graphs of certain functions and their periods are presented. Methods of analytical representation of functions with the variable period are developed and systematized; their variable periods allowing to verify the correctness of the theoretical positions of the series theory for periodic functions with the variable period are recorded in this paper. The developed methods of the analytical PFVP specifying and their variable periods have their independent significance since they generalize and thus considerably extend the set of analytically given periodic functions with the constant period. On the basis of elementary trigonometric functions with the variable period, the system of trigonometric functions with the variable period is constructed and it is shown that the system is orthogonal with weight function, moreover the orthogonality interval is variable. The method of constructing Fourier series of periodic functions with the variable period is developed. Formulas for determining the coefficients of the Fourier series of such functions are obtained. Using the formula for distance estimation between the PFVP and its Fourier series, it is established that, with the growth of coefficients amount, PFVP Fourier series approximates to the function itself proving the correctness of the model and algorithms for Fourier series construction. Information technology including developed algorithms and created software "Fourier-analysis of functions with the variable period" makes it possible to carry out spectral analysis of processes with the variable period. In cases where the variable period is unknown, the method of its estimation is offered. Due to additional parameters obtaining this method enables to increase the degree of automation of analysis of processes with the variable period. On the basis of the algorithm of the variable period evaluation the information technology for evaluation of heart rate variability after exercise stress effect on the human body is developed. The main component of this information technology is "Analysis of R-R intervals and evaluation of heart rate variability" software. The developed IT allows to automate ECG analysis after exercise stress and, due to new informative parameters, to submit the information about the state of the cardiovascular system of a person while testing the cardiac rate variability after physical activity more completely. By means of developed methods and software, the effectiveness of the offered information technology of process analysis with the variable period allowing to submit information about such processes more completely due to the additional parameters determination and to automate their analysis for the purpose of supporting decision-making is proved.