The article considers the problems of coolant flow computational diagnostics in a closed circulation loop. The mathematical models of acoustic waves in two-phase flow are developed. Indirect diagnostic information, contained in the flow vibrational spectra recorded by regular systems is used. The inverse eigenvalue problem is formulated. Solving it the optimization approach is implemented. It is supposed that partial criteria are presented by continuous, Lipschitz, not everywhere differentiable, multi-extremal functions. Search of global solutions was performed using a new hybrid algorithms integrating stochastic algorithm of variable space viewing and deterministic methods of local search. A numerical example of model diagnosing the phase composition of the coolant in the circulation loop of nuclear reactor plant is presented.
Sulimov V., Shkapov P. Hybrid methods of computer diagnosis of two-phase flow in the circulation loop. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 68-88
The study examines extremum problems for eigen spectra components of Lagrangian dynamical systems. Mathematical models of the systems studied are described by the matrices depending on the parameters. The eigenproblems defined for such systems, in general, are characterized by a spectrum, which can contain multiple eigenvalues. Subtests in extremum problems are assumed to be continuous, Lipschitzian, multiextremum and maybe not everywhere differentiable functions. The search for global solutions is conducted using new hybrid algorithms that combine a stochastic algorithm for scanning the variables space and deterministic local search methods. The study gives numerical examples of solving the problems of global nondifferentiable minimization of the maximum systems eigenvalues.
Sulimov V., Shkapov P., Goncharov D. Use of hybrid algorithms in extremum eigenproblems of Lagrangian dynamical systems. Маthematical Modeling and Coтputational Methods, 2016, №4 (12), pp. 84-102