The article presents the results of modeling in a dynamic format of one of the most important parameters of any research object – the efficiency of its work. As the object of investigation, a blast furnace with a volume of 2014 m3 was chosen. The main parameters of the efficiency of this object are traditionally used daily productivity and specific consumption of coke; these two parameters were generalized in this paper. In this case, various algebraic signs of the influence of these parameters were taken into account in the generalized efficiency index. Taking into account the variation of each of these parameters at 3 levels, the number of levels of the generalized efficiency index was determined as 32 = 9, therefore it was rational to take a 9-point scale with the measuring scale of profitability from the efficient operation of the blast furnace. The two-dimensional array of primary data of the volume N = 177 was transformed into a 9×9 transitional matrix for processing of random transitions of the efficiency index from one state to another by the Markov chain method with discrete states and time. The set of parameters of the random process is calculated: for the long-term forecast – the stationary vector of state probabilities, the average time of recurrence (reversal) for each efficiency state, the evaluation of the blast furnace efficiency in points; for a short-term forecast – the first time of transition from each state to any other state, the step number for a “burst” of probability for each reliable state at the initial moment of time, and the components of the efficiency index are obtained. It was established that the average level of the analyzed efficiency of the blast furnace (daily output 3702 tons and specific coke consumption 470 kg/ton) is achieved mainly due to short-term transitions of low-efficiency states to high-efficiency states and vice versa. The transfer of the system to more efficient and prolonged conditions is possible, and as practice has shown on the same blast furnace after repair works to eliminate the distortion of the furnace profile, the daily productivity has increased to 5048 tons with a specific coke consumption of 445 kg/t, but the structure of the transition matrix and the calculated indicators of the Markov chain have fundamentally changed in the direction of increasing the probabilities of stay and transitions of the system in more efficient states. The use of the Markov chain method with discrete states and time makes it possible to estimate the probable value of the change in the parameters of the operation of a blast furnace in a given time interval with constant levels of parameters characterizing the conditions of its operation.
APPLICATION OF MARKOV CHAINS TO THE ANALYSIS OF BLAST FURNACE OPERATION EFFICIENCY
