Approximate solution of the problem of redundancy optimization of a complex technological system of ore grinding

Abstract

Relevance. The need to improve the reliability and efficiency of the technological ore grinding system by element-by-element optimal loaded redundancy of its elements. Aim. To substantiate the need to improve the efficiency of the ore grinding technological system functioning by optimal redundancy; to find out an approximate solution of the following problems: 1) to maximize the efficiency of the ore grinding complex system functioning by element-by-element loaded redundancy limited, superimposed on the technical and economic indicator of the system; 2) to minimize technical economic indicator of the ore grinding system at the set value of the efficiency indicator of its functioning. Object. Ore grinding technological system, considered as a system with many operable states (multi-state system), the elements of which have only two possible states. The system under consideration is reserved by the element-by-element loaded redundancy method. Methods. Method for evaluating the efficiency of functioning of the systems with many states, the method of indefinite Lagrange multipliers. Results. The authors have obtained an approximate value of the performance indicator of the ore grinding technological system with many workable states, the elements of which have only two possible states. The paper considers the problems of optimal redundancy of the ore grinding complex technological system. Approximate solutions of these problems are obtained by the method of indefinite Lagrange multipliers, which can be used in rough calculations at the stage of designing complex technological systems for grinding ore. The problem of optimal redundancy is also considered, when it is possible to reserve only m elements from the n elements of ore grinding complex system. Taking into account certain assumptions for the efficiency of the system functioning, reserved by the element-by-element loaded redundancy method, an approximate solution of this problem is obtained.