Mathematical Description of Harmful Industrial Factors for Assessing the Quarry Workers' Occupational Risk

Abstract

Mining industry is highly important in the economy of each country. At the same time, the mining industry is an industry with a high level of morbidity among workers. Quarry workers are often exposed to hazardous environments, while at the same time a low level of process safety organization. This study aims to develop a mathematical description of modelling the values of harmful factors in the production environment at the workplaces of quarry workers, which will help ensure high-quality engineering control during the work shift. The initial statistical data for the development of mathematical models were obtained directly by the authors through personal observations of the technological process and measurements of the level of harmful factors in the working environment. Measurements were taken using portable digital devices. To develop mathematical description based on accumulated statistical data, polynomial regression was used. The construction of models using polynomial regression is based on the property of functional dependencies, which can be formulated as follows: with a gradual increase in the complexity of the model (polynomial degree), the magnitude of errors (approximation error, forecast error) monotonically decreases. As a result, fourth-order polynomial equations were obtained to model the values of dust concentration and noise level at certain time intervals of the work shift. The correlation coefficient of these models is R = 0.98 and R = 0.99, and the relative error is 9.76% and 6.11% of dust concentration and noise level respectively, which indicates sufficient accuracy of the model. It was established that the studied harmful factors during a normal production process, have a level of impact at which early forms of occupational diseases develop. The proposed mathematical description of modelling the values of these factors makes it possible for high-quality engineering control over current technology processes in order to avoid abnormal excesses of the values. Further research, according to the authors, should be aimed at identifying and mathematically describing other potentially harmful and dangerous factors in the working environment. The originality of the current study lies in the fact that an attempt was made to propose a non-classical approach to quickly identify deteriorating working conditions directly in the work process using mathematical modelling.