Computational Diagnostics of Jacobi Unstable Dynamical Systems with the Use of Hybrid Algorithms of Global Optimization

The study focuses on the problems of restoration and analysis of free parameters of dynamical systems from indirect, approximately given information. In the context of the Kosambi --- Cartan --- Chern theory, a geometric description of the time-evolution of the system is introduced. Five geometric invariants are determined for the system under study. The eigenvalues of the second invariant estimate the Jacobi stability of the system. Such a study is of interest in practical applications, where it is required to identify the regions in which both Lyapunov stability and Jacobi stability occur simultaneously. The inverse problem of computational diagnostics of the system is formulated for approximately given eigenvalues of the second invariant. The solution to the regularized inverse problem is determined using an optimization approach. Scalar criterion functions are assumed to be continuous, multidimensional, locally Lipschitzian, and not necessarily everywhere differentiable. When searching for global solutions, we used new hybrid algorithms that integrate stochastic algorithms for scanning the space of variables and a deterministic local minimization procedure. The numerical scanning procedure is implemented with the use of two modified versions: quasi-opposition-based and rotation-based learning mechanisms. In the phase of local search, two-parameter smoothing approximations of criterion functions are introduced. Examples of solving problems of computational diagnostics of Jacobi unstable dynamical systems are given: the Lorentz system and a controllable elliptical pendulum

BASIC POSITIONS OF THE ENTHALPY-ENTROPY METHODOLOGY OF THERMODYNAMIC ANALYSIS OF GAS TURBINE POWER PLANTS

The basic positions of the enthalpy-entropy methodology of thermodynamic modeling of processes in gas turbine units (GTUs) and combined power plants on basis GTUs are presented. The main requirements and conditions of this methodology are formulated, they allows the construction of a sequential (without iterations) algorithm for the computational diagnostics of the thermodynamic parameters of the GTU cycle, which includes the calculation blocks for the compressor, combustion chamber, turbine, and exhaust tube of the GTU. The obtained regression equations are presented. The use of these equations simplifies of the procedure for evaluating the thermodynamic parameters of the components at the nodal points of the cycle. The advantages of the proposed methodology in comparison with the traditional thermal-entropy methodology are indicated.