APPLICATION OF MARKOV’S CHAIN THEORY TO PREDICT PROPERTIES OF HOT ROLLED STEEL SHEET

Abstract

The multivariance and multistage nature of manufacturing technological processes of a wide range metal products of different purposes requires the use of special approaches for their formalization in order to find optimal solutions to ensure obtaining the products with the required level of properties. Under conditions of wide variability of the raw materials used, possibility to change the technological modes of processing, use of technological operations of various physical nature, possibility to provide the given level of metal products properties has the probabilistic nature. The theory of Markov processes is used to determine the probability of an object to appear in one of the process states for a certain time or time interval. In the example of the hot rolling process, a graph of the states of rolled steel properties, which are possible during the operation of this technological system, is constructed. It is shown that in this system there is a probability of transition from one state to the next in a finite number of steps, which means the existence of limiting probabilities. Matrices have been constructed to calculate the transition probabilities of the technological system “hot rolled steel sheet” for possible states: compliance of rolled metal with specified properties, partial compliance with specified properties, partial non-compliance with specified properties, and non-compliance with specified properties. Based on the calculations performed, it can be concluded that it is possible to ensure the probability to form the properties of hot rolled steel sheet. The obtained results can be used to improve existing technological processes for the production of hot rolled steel sheet with the required level of properties.