Відновлення сигналів в системах спостереження та керування на основі розв'язування оберненої задачі з урізанням спектру ядра інтегрального оператора

• Datum: 2017
• Hauptverfasser: Верлань, Анатолій Федорович, Федорчук, Володимир Анатолійович
• Format: Artikel
• Sprache: Ukrainian
• Veröffentlicht: Kamianets-Podilskyi National Ivan Ohiienko University 2017
• Online Zugang: http://mcm-tech.kpnu.edu.ua/article/view/140000
• Назва журналу: Mathematical and computer modelling. Series: Technical sciences

In solving problems, control, monitoring and diagnostics, the reliability of the results of observations obtained with use the various measuring transducers is important. Improving the technical characteristics of such devices is an urgent task, as the growth rate of the requirements for the accuracy of surveillance systems outstrips the growth of technical capabilities, often limited not only by the existing technical and economic conditions, but also by the physical capabilities of the equipment for direct measurements. One of the ways to increase the resolution of measuring converters is to obtain the dependencies characterizing the processes and objects under study, based on the results of indirect measurements by solving the problem of inversion of operators describing objects and observation systems.An approach to constructing mathematical models of dynamic objects and systems based on the use of mathematical models, described in integral form is proposed. The questions of application of integral models for solving the problems of signal reconstruction registered at the output of measuring converters of the monitoring system are considered. A new method is proposed that makes it possible to improve the accuracy in solving inverse problems, which are described by integral Fredholm equations of the first kind, by truncating the spectrum of the kernel of the integral operator. Numerical experiments on the effect of the inversion error of the integral kernel on the accuracy and stability of the solution of integral equation of convolution of the first kind in the spectral domain are was performed.The proposed methods of describing mathematical models, algorithmic and software tools for their realization on computer, allow to increase the efficiency of development and designing of controlled dynamic objects and systems by expanding the spectrum of mathematical descriptions of dynamic objects, which allows more fully and adequately to display the properties of real systems, and also apply a greater number of methods of numerical realization of models, by adapting algorithms to certain classes of tasks.