Mirgorod V. Mathematical models of processes of controlled change of the state of power plants

Thesis is devoted to solving the important scientific and technical problem of creation of real time mathematical models set, that intended for computer realization directly as a part of on-board and ground tools for control, state monitoring and diag-nostics of power plants. The developed mathematical models provide the obtaining of estimations of variables, that are inaccessible for the direct measuring. On the basis of analysis of requirements to the on-board model the approach for solving the problem of creation of new mathematical models class of processes of the controlled change of power plants states is offered. Approach is implemented using the developed methods of equivalent and approximation transformations of models in the form of nonlinear differential equations of state space to the mathematical model in Hammerstein form with linear part as a multidimensional follow-up system. The offered mathematical model allows to take into account a priori information about nonlinear static characteristics and dynamics of deviations from them and due to it to decrease the modelling errors. The mathematical models of processes of state control changing in the form of Volterra integral equations of the second kind are offered, the solutions of integral equation concerning to resolvent are found, the new method of equivalent transformations of mathematical models in the form of linear differential equations to the models in the form of integral equations is offered and substantiated. The approach to creating the mathematical models of technical state control, that provides the consecutive stages of forming of polynomial regression mathematical models of static and multidimensional trend models of operational dynamics, that allows to determine the operating conditions changing of object life cycle is offered and substantiated. The new methods of trend analysis of time series of registration of power plants states on the basis of forming the multidimensional arrays from trajectory matrices and their singular decomposition, allowing to separate the samples on trend, cyclical (seasonal) and noise components at given confidence level are offered. The solutions a number of the applied tasks of modelling and estimation of power plants states are obtained.