Mathematical model of waste accumulation in Ukraine

T. Rusakova
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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.
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乌克兰废物堆积的数学模型
目的。分析和概括废物来源,作为构成乌克兰累积废物总量的因素,对环境产生负面影响。根据统计指标的计算结果,构建了乌克兰垃圾堆积的数学模型。研究所选因素之间的相互影响,避免计算中出现非共线性或多重共线性的现象。的方法。运用多元相关回归分析方法进行建模,在对所研究的统计指标进行分析的基础上,筛选出最具统计显著性的因子值,评估它们之间的关系以及这些因子值与所得到的特征之间的关系,为建立数学回归模型提供前提条件。发现。在描述性统计的基础上,对研究的废弃物产生量、利用量、燃烧量、清除量等各因子值进行了分析,并建立了2010-2020年各因子值的变化趋势。统计数据的相关回归分析结果如下:所选因子变量与结果变量之间的相关关系密度;线性确定系数;对回归方程质量的度量。剔除弱相关或多重共线性的因子变量。建立了基于回归-扩散分析的数学模型,并对其充分性进行了检验,计算数据的平均相对误差为6%,最大相对误差为10%。由于引入了非线性变量,对线性数学模型进行了改进,计算数据的平均相对误差为3%,最大相对误差为8%。垃圾产生量、利用量、焚化量和清除量的依赖关系和规律已经确立。已经发展了一个多因素数学模型,建立了不同类型的废物与积累的废物总量之间的关系,废物总量趋于增加,而这反过来又增加了对环境的负面影响。实际的实现。用于预测由于产生、利用、燃烧、清除废物及其组合的综合影响而累积的废物总量的数学装置,这在估计废物积累区域的大小和制定废物处置的远景计划时很重要。
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