Probability of traumatic situations in mechanized processes in agriculture using mathematical apparatus of Markov chain method
2019
Voinalovych, O., National Univ. of Life and Environmental Sciences of Ukraine, Kiev (Ukraine) | Hnatiuk, O., National Univ. of Life and Environmental Sciences of Ukraine, Kiev (Ukraine) | Rogovskii, I., National Univ. of Life and Environmental Sciences of Ukraine, Kiev (Ukraine) | Pokutnii, O., National Academy of Sciences of Ukraine, Kiev (Ukraine). Inst. of Mathematics
In this paper for exploring the mechanisms of formation of traumatic situations, the conditions and circumstances that contribute to them, and the study of the course of events leading to dangers in mechanized processes in agriculture the mathematical apparatus was used developed by the probability theory for Markov random processes with discrete states and continuous time, when the transition of a system from one state to another is possible at any unknown random time. It has been established that the processes of traumatic situations and their consequences can be represented by graph structures, using four states of the “man-machineindustrial environment” system: working and defective conditions of the tractor (machinery), hit of the machine operator into a dangerous and emergency condition (situation). A system of Kolmogorov differential equations was made, in which unknown functions are the probabilities of states of the system as functions of time with the normative condition that the sum of these probabilities will be equal to 1. Introducing the matrix of the intensity of events, the Laplace transform was used to solve the system of differential equations, which allowed the system to be transformed into a linear algebraic system. Elements of the matrix of intensities of the flows of events that bind separate states of the graph were given taking into account the probabilities of accidents with mechanics, established on the basis of the statistics of occupational injuries and data of accumulation of cracks in the array of tractor parts, were determined as a result of defectoscopic control. The results of the research allow in the medium and long term perspective to predict the probable states of the “human-machine-industrial environment” system in the risks of professional injury of agricultural machine operators.
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