Апроксимаційно-марківські моделі зміни параметрів технічного стану силових та енергетичних установок у довготривалій експлуатації

Abstract

The design and implementation of systems for automatic control of changes in the coordinates of the state and the output variables of power and energy installations consist of several successive stages, which implementation is widely used mathematical modeling. One of the most important such stages is the development of the created system (regulator) on a semi-natural stand. Such a stand usually contains a sample of a system with physically implemented measuring channels, and the control object and actuators are made in the form of a real-time computer mathematical model (stand-simulator). The problem is to resolve the contradiction between the requirements of the adequacy of the computer experiment to the real operating conditions and the capabilities of the simulator stand because the mathematical model of the control object is deterministic. In real conditions, there are random disturbances, which determine the random nature of the original-measuring coordinates of the control object. The use of known statistical modeling techniques is limited by the stationary requirements because the controlled objects are multi-mode. A solution to this contradiction is proposed by applying new information technology, which consists of the consistent implementation of the stages of preliminary approximation of time series of deviations of such variables from the formed approximation model, and the stage of statistical modeling. As a statistical model of random processes of deviations of such variables from the formed approximation model, the Markov process model is proposed, which considers the possible correlation of the initial data. The application of the approximation model provides the conditions of stationary and correctness of the proposed model. The applied problem of modeling the change of parameters of the technical conditions of a multi-mode technical object in long-term operation on the basis of the proposed model and experimental data is solved.