INPUT MATERIAL FLOW VALUES GENERATOR OF A CONVEYOR WITH A GIVEN CORRELATION FUNCTION AND DISTRIBUTION LAW
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Abstract
The object of this study is a stationary stochastic input flow of material arriving at the input of an industrial conveyor transport system. The goal of this research is to develop a universal, statistically mathematical model of the input flow of materials, fully identifiable from a single long-term experimental implementation, as well as to create a multi-level system of dimensionless stochastic similarity criteria, enabling the objective classification and comparison of heterogeneous flows with similar structural properties. The results obtained. A simplified canonical decomposition of a stationary ergodic process with a minimum number of random coefficients is proposed, reproducing the specified mathematical expectation, variance, correlation function, and one-dimensional probability density of flow values. Analytical expressions are derived for approximating the distribution density of random coefficients with guaranteed fulfillment of the conditions of centering, normalization, and non-negativity. A multilevel system of stochastic similarity criteria is developed, including aggregated dimensionless criteria, a functional similarity criterion based on a normalized autocorrelation function, and a functional criterion based on quantile-quantile diagrams. A dimensionless flow normalization method is proposed, ensuring model transferability between conveyor systems differing by orders of magnitude in throughput and time scales. Using six independent long-term implementations of real conveyor systems in the mining and processing industries, the accuracy of the developed stochastic input flow generator using an analytical approximation of random coefficients is demonstrated. Conclusion. The developed methodology enables the classification and comparison of material input flows in transport systems and serves as the basis for a universal approach to constructing mathematical models and flow control algorithms under stochastic uncertainty.
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