Информационная система "Конференции"

Abstracts

Numerical solution of differential and integral equations

One of major problems of preparation of an aluminum cell to operation is the determination condition of a preheating, which would ensure maximal quality of a preheating at minimum expenditures. The model of an aluminum cell is circumscribed by classic one-dimensional problem of a thermal conduction with boundary requirements of 3-rd kind. The behaviour of flue gases is circumscribed by the ordinary linear differential equation of the first order. The passage from a classic one-dimensional problem of a thermal conduction to a system of the ordinary differential equations is realized with the purpose of further usage in methods of searching of optimum control. The mathematical model of voltages originating in cathode of an aluminum cell during a preheating on the basis of the theory of a strength of materials surveyed. The choice of criteria of an optimality surveyed and matching different criteria of an optimality is carried out. The kinds of criteria, founded on monitoring of thermal voltages originating in cathode during a preheating are offered. The application of a method of a maxima to an offered problem surveyed, the method of a solution of a boundary value problem originating by usage of a method of a maxima is offered. On the basis of a method of a maxima is rotined, that the optimum process control of a preheating of an aluminum cell in some cases looks like switching function. The passage from a problem of searching of optimum control to a problem of conditional optimization of function many variable is realized on the basis of knowledge of character of optimum control (switching function), obtained from a maximum principle. The procedure of a solution of the obtained problem by a method of genetic programming and method of a coordinate descent surveyed. The search algorithm of optimum process control of a preheating of an aluminum cell designed on the basis of a method of discrete optimization. The global convergence of the obtained algorithm is proved. The estimated computational expenditures on searching of optimum control are obtained for the given algorithm, the character of convergence of the given algorithm to a point of an optimum surveyed. The procedure of the human-machine procedure of a select of optimum process control of a preheating of cathode of an aluminum cell is offered. The circumscribed complex of mathematical models and methods of searching of optimum control is implemented of program complex in Matlab v. 5.2.

Note. Abstracts are published in author's edition

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