Mathematical model of waste accumulation in Ukraine

Abstract

Purpose. Analysis and generalization of waste sources as factors that form the total volume of accumulated waste in Ukraine, which negatively affects the environment. Construction of a mathematical model of waste accumulation in Ukraine based on the results of the calculation of statistical indicators. Conducting research on the influence of selected factors on each other in order to avoid the phenomenon of non-collinearity or multicollinearity in the calculations. The methods. The application of multiple correlation-regression analysis methods for modeling, which allow, on the basis of the analysis of the studied statistical indicators, to single out the most statistically significant factor values, to assess the relationship between them and the relationship of these factor values with the resulting characteristic, which provides prerequisites for building a mathematical regression model. Findings. On the basis of descriptive statistics, an analysis of each of the studied factor values, such as generated, utilized, burned, removed waste, is presented, and the trends of their changes during 2010-2020 of years are established. The results of the correlation-regression analysis of statistical data are presented: the density of correlation relationships between the selected factor variables and the resulting variable; coefficient of linear determination; a measure of the quality of the regression equation. Those factor variables with weak correlation or multicollinearity were removed. A mathematical model based on regression-diffusion analysis was obtained and its adequacy was checked, the average relative error of the calculated data was 6 %, the maximum relative error was 10 %. The linear mathematical model was improved due to the introduction of non-linear variables, the average relative error of the calculated data was 3 %, the maximum relative error was 8 % Theoriginality. Dependencies and regularities have been established for the volumes of generated, utilized, incinerated and removed waste. A multifactorial mathematical model has been developed that establishes a relationship between different types of waste and the total amount of accumulated waste, which tends to increase, and this, in turn, increases the negative impact on the environment. Practical implementation. Mathematical apparatus for forecasting the total amount of accumulated waste due to the combined effect of generated, utilized, burned, removed waste and their combination, which is important when estimating the size of areas for accumulating waste and creating perspective plans for their disposal.