Voronova O. Operational methods for modeling and signal processing for dynamical systems monitoring within software environment of Mathematica and LabVIEW

Dissertation work is devoted to generalization and development of operational methods for dynamical systems modeling and signal processing, oriented to development of monitoring complexes. Some elements of nonlinear algebra of approximating impulse spectra (AIS) are developed. Rules for operational fractional integration matrices are obtained in case of extended local-impulse basis. Results earned were applied in developing and modifying of algorithms for simulation of integro-differential equations of following type: fractional equations, equations systems and equations with variable coefficients. A method for grid adapting in signals approximation and resolving of differential equations using operational methods of AIS is proposed. An algorithm for multiresolutional analysis in extended local-impulse basis is developed. A method of discrete approximating impulse spectra for discrete signals and functions approximation is proposed. All methods and algorithms proposed were implemented in Mathematica and LabVIEW software. Applications of obtained results in arc welding monitoring complex is considered. Basic results of the dissertation were used in research work of Department of Hybrid Modeling and Control Systems in Power Engineering of G.E. Pukhov's ISPP of NAS of Ukraine and in projects of Science and Technology Center in Ukraine.