Simplicial analysis of the water resource distribution system of an enrichment plant

Yevhen Tymokhin*, Vadym Kharlamenko

eugene.t@knu.edu.ua

Received 31.10.2025, Revised 13.02.2026, Accepted 28.04.2026, Published 29.05.2026
Abstract

Water management in modern ore enrichment plants requires the application of advanced topological analysis methods to optimise their complex information and control architecture prior to implementing intelligent control systems based on machine learning algorithms. Consequently, the main aim of the work was to comprehensively investigate structural connectivity and determine the exact control hierarchy of a water resource distribution system within an enrichment plant section using the methodology of simplicial analysis to further minimise specific energy consumption. The research was based on the fundamental principles of algebraic topology. The primary object was a topological graph model of the water supply system, which was systematically decomposed into thirteen key concepts, including technological mechanisms, sensor arrays, and control modules at both local and upper levels. The study yielded significant results, confirming the high effectiveness of the proposed mathematical approach. For the developed system, an adjacency matrix was constructed, and the structural redundancy index was calculated, resulting in a positive value of Rk ≈ 0.31. This strictly mathematically confirmed the presence of high connectivity, the absence of structural breaks, and robust internal reservation of the technological network. Furthermore, a step-by-step multidimensional analysis was performed: the topological dimension of each individual simplex was determined, the corresponding equivalence classes were formed, and the first structural vector of the topological complex  was generated. The calculation of the uniform distribution index of directed graph links (ϵ2 = 4,77) proved the existence of a rigid hierarchical structure with pronounced centres of influence, completely refuting the hypothesis of network homogeneity. It was established that the adaptive optimisation module and integrated actuators formed the highest topological dimensions (q = 1 and q = 2). The practical value of the obtained results lies in forming a reliable topological basis for the future deployment of graph neural networks. Identifying the simplices of the highest dimension allows for optimising the hardware placement of sensors, significantly increasing the reliability of local control loops, and reducing the specific consumption of electrical energy and fresh water through targeted management of hydraulic flows under conditions of dynamically changing physical characteristics of the input ore

Keywords:
water supply; algebraic topology; graph theory; adjacency matrix; automation; recycled water; mineral processing

Retrieved from Volume 24, No. 1, 2026

Pages 54–62

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Tymokhin, Ye., & Kharlamenko, V. (2026). Simplicial analysis of the water resource distribution system of an enrichment plant. Journal of Kryvyi Rih National University, 24(1), 54-62. https://doi.org/10.31721/2306-5451-2026-1-24-54-62
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