Sterten J. Methods and tools of mathematical modelling of the measuring converters’ structural dynamic correction processes based on integral equations

In the dissertation the scientific and engineering task of developing methods for mathematical modelling of measuring systems’ dynamic correction processes based on application of integral dynamic models in the form of Volterra type operators and equations and construction of effective algorithms and programs of their numerical implementation is solved. The expediency of application of the inverse (algorithmic) approach, which is based on the use of methods of mathematical processing of measuring signals with the help of appropriate computer means that provides cost-effectiveness and mobility of technical developments, in modern technical means’ developments of dynamic correction, is substantiated. As the dynamic models of measurement processes, the Volterra-type integral operators and equations pertained to the class of nonparametric models of dynamics problems are used, which allows them to be directly derived by known dynamic characteristics of measuring instruments and develop a wide range of algorithms for numerical implementation of models in accordance with the requirements for the modelling process. Regularization of the task of restoring the input signal by solving the Volterra equation of the 1st kind is performed based on the modular experiment method. Computer experiments for the study of the proposed integral models of the measuring systems’ dynamics in comparison with other equivalent forms of models have indicated their high performance and quality. Numerical realization of integral dynamic models is carried out by applying the quadrature formulas, while their wide selection provides the necessary indicators of accuracy and complexity of the computational process, which must meet the requirements of the computer-integrated systems. At the same time the obtained recurring computational algorithms provide the necessary performance. The proposed integral method allows to receive productive algorithms of numerical differentiation of signals. The algorithms of signal recovery at the input of distributed parameters systems are developed. An applied software complex for modelling the processes of measuring systems’ dynamic correction with the implementation of linear and nonlinear integral macro models in MATLAB environment is developed. Level of implementation: Pukhov Institute for Modelling in Energy Engineering, National Academy of Sciences of Ukraine (Kyiv), National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” (Kyiv).