The journal Scientific Bulletin "Modern Problems of Metallurgy" was founded in 1998 and is published once a year. According to the order of the Ministry of Education and Science of Ukraine No. 1643 dated December 28, 2019, the Scientific Bulletin "Modern Problems of Metallurgy" is included in the List of Scientific Professional Editions of Ukraine, category "Б". Knowledge area is technical sciences.
National metallurgical academy of Ukraine
PERCOLATION APPROACH TO THE DESCRIPTION OF INTERDENDRITIC FEEDING AT THE FINAL STAGE OF SOLIDIFICATION OF METALS AND ALLOYS
The paper examines the physical foundations of interdendritic feeding during the final stage of solidification of metals and alloys. It is shown that the efficiency of shrinkage compensation within the mushy zone is determined not only by the presence of residual liquid phase, but also by the conditions of its transport through the interdendritic space. Particular attention is paid to the role of permeability, local pressure gradients, morphology of liquid channels, and preservation of continuous feeding paths in ensuring the transport capacity of the liquid phase. The mechanisms of shrinkage and gas-shrinkage porosity formation are analyzed, and it is emphasized that the appearance of such defects is directly related to the degradation of the liquid feeding network at high solid fractions. The study summarizes the influence of increasing solid fraction on the narrowing of interdendritic channels, reduction in permeability, localization of liquid flow, and growth of local hydraulic resistance. It is shown that, as the dendritic skeleton evolves toward a coherent solid framework, the liquid phase gradually loses its ability to form a continuous transport network. Under such conditions, even if some amount of liquid remains in the mushy zone, it may no longer participate in real feeding because of topological isolation. This circumstance indicates the limitations of conventional continuum approaches, which mainly operate with averaged characteristics such as permeability, pressure, or liquid fraction, but do not fully capture the structural transformation of the liquid network at the final stage of solidification. To overcome these limitations, the applicability of the percolation approach is substantiated. Within this interpretation, the mushy zone is considered as a two-phase system in which the liquid phase acts as a transport network and the solid phase forms a constraining framework. It is argued that the loss of interdendritic feeding should be associated not with the complete disappearance of the liquid phase, but with the destruction of its global connectivity and the disappearance of a continuous feeding path. Thus, liquid-phase percolation is proposed as a physically meaningful criterion for feeding loss in the mushy zone. The obtained results confirm that the percolation-based interpretation provides a promising theoretical framework for further modeling of solidification processes, localization of feeding paths, and prediction of shrinkage-related defect formation in metallic castings.
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EFFICIENCY IMPROVEMENT OF CONCRETE MIX PREPARATION AND MORTAR DELIVERY PROCESSES IN CONSTRUCTION TECHNOLOGICAL COMPLEXES
The research relevance is determined by the need to improve construction production technological set operational efficiency ensuring concrete mix preparation and plastering mortar delivery under variable operating conditions. The study objective is to establish relationships between mixing equipment kinematic parameters, construction medium rheological characteristics, and conveying system geometric parameters and the technological set generalized efficiency indicator. The study uses mathematical modelling methods of construction mix mixing and transportation processes considering their structural-mechanical properties and equipment energy characteristics. An extremal dependence of the generalized efficiency indicator on mixer working body rotational speed was established, and the influence of mixture rheological parameters and pipeline system geometric characteristics on pressure loss and material delivery stability was determined. The obtained results enable substantiation of rational construction mix preparation and transportation technological set operating modes considering process energy and technological indicators.
CYBERSECURITY OF AUTOMATED INFORMATION SYSTEMS OF ELECTRIC POWER COMPLEXES IN THE MINING AND PROCESSING INDUSTRY
The implementation of digital manufacturing concepts and intelligent sensor networks in the mining and processing industry exponentially increases the risk of targeted cyberattacks on enterprises' electric power complexes, where interference with algorithms can cause technogenic disasters. To enhance the cyber resilience of automated information systems, a comprehensive architectural model based on the Defense-in-Depth concept has been developed. A multi-level infrastructure is proposed, featuring microsegmentation of industrial networks, Deep Packet Inspection for basic industrial protocols, hardening operating system configurations on engineering workstations, and the use of microkernel platforms for network gateways. It is demonstrated that combining international security standards with predictive hardware monitoring of programmable logic controller supply currents reliably prevents software-based control-logic spoofing, effectively mitigates intrusion vectors, and guarantees the continuity of energy-efficient control in raw-material processing operations.
DYNAMICS OF AN INTERNAL VIBRATOR CONSIDERING THE TRANSLATIONAL AND ANGULAR MOTION OF THE WORKING BODY
The article considers the dynamics of an internal vibrator for compacting concrete mixtures, taking into account the translational and angular motion of its working body. A calculation scheme of the internal vibrator is developed as a spatial oscillatory system in which the housing is assumed to be a rigid body with six degrees of freedom, while the action of the concrete mixture is considered through the added mass, elastic resistance, and inelastic resistance of the medium. The operation of an unbalanced vibration exciter with two unbalanced masses mounted on the shaft with corresponding eccentricities and a mutual phase angle is considered. Analytical dependencies are obtained for determining centrifugal forces, the resulting moment, the reduced mass of the system, the amplitude of translational oscillations of the center of mass, and the amplitude of angular oscillations of the housing. It is shown that the motion of the internal vibrator cannot be reduced only to horizontal oscillations, since the action of the unbalanced masses forms a rotating resultant force and a resulting moment, which cause complex spatial motion of the working body. It is established that the trajectory of an arbitrary point of the housing depends on its distance from the center of mass, the phase angle of the unbalanced masses, the moment of inertia, the shaft rotation frequency, and the added mass of the concrete mixture. It is proved that changing the phase angle of the unbalanced masses makes it possible to regulate the ratio between the translational and angular components of motion and, consequently, to influence the nature of vibration energy transmission into the concrete mixture. The obtained results can be used to substantiate the parameters of internal vibrators, select rational compaction modes, reduce the risk of mixture segregation, and further optimize the shape of the working body.
METHOD FOR CONSTRUCTING A CRISIS-CONTEXT DATASET FOR ADAPTIVE IRM VERIFICATION
Recent research in the field of crisis informatics is largely focused on the automatic processing of social media messages during emergency situations. Existing crisis corpora, including HumAID, CrisisBench, AIDR, TREC-IS, and CrisisMMD, provide an important foundation for message classification, informativeness detection, humanitarian categorization, prioritization, and multimodal annotation tasks. At the same time, most of these resources are oriented toward the analysis of individual messages or the identification of their class, rather than toward verifying the ability of a large language model to reconstruct hidden crisis context from an abstract query. With the development of large language models, there is a growing need for specialized datasets that make it possible to evaluate not only the general linguistic competence of a model, but also its ability to adapt a response to a context that is not explicitly specified in the user’s question. The purpose of this work is to develop a method for constructing a crisis-context dataset for the subsequent verification of Adaptive IRM in tasks of hidden contextual adaptation of large language model responses. To achieve this purpose, it is proposed to transform crisis messages from the HumAID corpus into pairs of the form “abstract query — crisis-dependent answer”, where the question does not contain direct markers of the disaster type but preserves a semantic connection with the original message. The paper proposes a generative dataset construction pipeline that includes primary generation, retry generation, and a fallback mechanism. For each crisis message, a locally deployed large language model generates a short WH-question to which the original tweet should provide a direct answer. After generation, the question undergoes automatic validation according to formal criteria: the presence of an interrogative structure, the absence of a yes/no form, ending with a question mark, compliance with the length limit, the absence of undesirable template-like formulations, and the absence of direct crisis markers such as earthquake, hurricane, flood, disaster, emergency, and others. If the initial question does not meet the specified requirements, a retry generation step is performed using a stricter instruction. In case of a repeated failure, a fallback question is applied, which makes it possible to preserve the completeness of the corpus. As a result, a dataset of 41,152 records was formed across five categories of crisis events: hurricanes, earthquakes, cyclones, wildfires, and floods. The fallback mechanism was used in 1,432 cases, which accounts for 3.48% of the corpus. The main result of the study is a method for transforming crisis messages into “abstract query — crisis-dependent answer” pairs and the dataset constructed on its basis for the future verification of hidden contextual adaptation in LLMs. The proposed approach differs from classical crisis datasets in that it models a situation in which the question does not directly indicate the type of disaster, while the correct answer requires taking into account the hidden context of the event. Future work includes formalized manual validation of the corpus, automatic retrieval-style verification of semantic consistency, construction of an event-disjoint split, implementation of Adaptive IRM, and comparison with LLM-baseline, RAG, and PEFT-baseline approaches.
THERMODYNAMIC ANALYSIS OF ENERGY OPTIMUM FORMATION IN COAL GASIFICATION
Equilibrium thermodynamic modeling was applied to analyze the energy efficiency of coal gasification as a function of the oxidizer consumption coefficient. The oxidizer consumption coefficient is considered as a continuous control parameter that determines the balance between reduction and oxidation processes, and the analysis is based on the coordinated evaluation of equilibrium temperature, producer gas composition, its heating value, and specific gas yield. It is shown that variation of the oxidizer consumption coefficient leads not to isolated changes of individual parameters, but to their interrelated transformation with a clearly pronounced structural character. It is established that within the studied range, a three-stage structure of the process is formed, including a region of incomplete conversion with the presence of unreacted carbon, a region of rational operating conditions, and a region of excessive oxidation accompanied by a decrease in the content of combustible gas components. It is shown that transitions between these regions are characterized by changes in the behavior of the main parameter dependencies, reflecting a shift in the balance between dominant thermochemical processes. It is established that within the region of rational operating conditions, an energy-optimal gasification regime is formed, corresponding to the maximum of the total combustible fraction of the producer gas and the minimum of oxidation products. It is shown that this regime is realized at an oxidizer consumption coefficient of approximately 0.3 and corresponds to the region of minimal oxidation losses. The introduction of the logarithmic indicator lg((CO+H₂)/CO₂) made it possible to obtain a stable criterion for evaluating the gasification regime, ensuring unambiguous identification of the optimum region. It is shown that the maximum of this indicator coincides with the maximum of the total combustible fraction and the minimum of oxidation products, confirming the realization of an optimal reduction–oxidation balance. It is established that the gasification temperature increases monotonically with increasing oxidizer consumption coefficient and does not determine the position of the energy optimum. It is shown that beyond a certain value of the oxidizer consumption coefficient, further increases in temperature and gas yield no longer compensate for the decrease in gas heating value, resulting in reduced energy efficiency. To generalize the obtained results, an integral energy indicator was proposed, which simultaneously accounts for the producer gas yield and its heating value. It is established that this indicator exhibits a well-defined maximum at an oxidizer consumption coefficient of approximately 0.3 for all investigated conditions, despite the opposite trends of its components. The obtained results show that the energy optimum of the gasification process is formed as a result of coordinated variation of process parameters and is determined by its internal thermodynamic structure. This makes it possible to move from the analysis of individual characteristics to a system-based identification of the rational gasification regime corresponding to minimal oxidation losses and maximum total energy output of the producer gas.
A SIMPLIFIED METHOD FOR CALCULATING INTEGRAL ENERGY INDICATORS OF METALLURGICAL PRODUCTS USING THROUGH CONSUMPTION COEFFICIENTS
The study considers the use of through consumption coefficients for the simplified calculation of energy performance indicators of metallurgical products in multi-stage production systems. It is shown that the conventional direct approach does not adequately account for internal relationships between technological stages, material flows, and secondary energy resources, which limits its applicability in predictive and comparative calculations. A simplified method is proposed in which through consumption coefficients are used as a generalized calculation basis for determining integral energy indicators of products without constructing a fully detailed model for each stage. The approach preserves high accuracy compared to the full calculation scheme while significantly simplifying the assessment of the effects of changes in production structure, product mix, and technological parameters. It is further demonstrated that the obtained energy indicators can be used for rapid calculation of related indicators associated with energy consumption, including fuel-equivalent values, primary energy equivalents, and carbon intensity, based on unified conversion factors. The proposed method can be applied in production planning, technical modernization of enterprises, and evaluation of the effectiveness of energy- and resource-saving measures.
IMPLEMENTATION OF RFID TECHNOLOGY FOR OBJECT IDENTIFICATION IN RETAIL: OPTIMIZATION OF AUTOMATED SORTING LINES
The problem of integrating UHF radio frequency identification systems into the hardware and software complexes of high-speed conveyor lines in retail warehouses is investigated. Architectural solutions to minimize the impact of multipath radio wave propagation and Doppler frequency shift on the probability of reading passive tags in dynamics are theoretically substantiated. The validation of the proposed hybrid mathematical model of collision processing, combining deterministic prefix tree segmentation (Query Tree) with the stochastic DFSA algorithm of the EPCglobal Gen2 standard, was carried out by developing a comprehensive digital twin in the MATLAB Simulink environment. Simulation modeling proved the architecture's ability to achieve an estimated identification reliability rate of 99.2% at a linear conveyor speed of 3.0 m/s. The architecture of distributed middleware based on the Edge Computing paradigm was virtualized for spatiotemporal filtration of raw radio frequency data and local caching of routing tables. Stochastic simulation results confirm that translating aggregated arrays into the Application Level Events format with subsequent asynchronous transmission via EPCIS interfaces to the Warehouse Management System reduces system latency to 42 ms. The overall estimated throughput of the optimized complex in the simulation environment is 10710 processed units per hour with an algorithmic mis-sort rate of less than 0.08%.
MATHEMATICAL MODELING FOR APPLICATIONS THE SELECTIVE LASER MELTING PROCESS IN 3D PRINTING
This paper provides an overview of the physical processes occurring during selective laser melting of metal powders, as well as an overview of methods for mathematically modeling these processes. The key physical processes that must be taken into account for an adequate modeling of selective laser melting of metal powders are identified. A general physical and mathematical model is formulated to solve the problem of selective laser melting of metal powders. The assumptions and constraints adopted for the formulated physical model are presented. The governing equations describing heat transfer processes, liquid metal dynamics, and the shape of the free surface are considered. The initial and boundary conditions are presented. Taking into account the requirements for mathematical models, a numerical algorithm for solving the governing equations has been developed, based on a three-layer implicit scheme with second-order accuracy in time integration, third-order counter-current approximation of convective terms, and second-order central difference approximation of diffusion terms. The pressure and velocity fields in the Navier-Stokes equations were coupled using the artificial compressibility method, modified for the calculation of unsteady problems. The system of initial equations was numerically integrated using the finite volume method. The system of linear algebraic equations of the implicit scheme was solved using the well-known generalized misfit minimization (GMRES) method with an incomplete LU decomposition of the total system matrix as preconditioning. Numerical simulations of the transient processes of selective laser melting of metal powders have yielded a temperature field distribution in the computational domain, highlighting the liquidus zone. Dependences of the width and depth of the molten pool on the laser velocity and the laser spot diameter have been plotted.
CONDITIONS FOR THE OPTIMAL RE-COMPACTION MODE OF A CONCRETE MIXTURE AND CRITERIA FOR VIBRATION EFFICIENCY
The article considers the conditions for the optimal re-compaction mode of a concrete mixture in a vibration machine with spatial excitation, in which the action of horizontal oscillations of the mould is combined with vertical oscillations of the surcharge device. The relevance of the study is обусловлена by the need to improve the efficiency of vibration compaction of concrete products, ensure intensive structural rearrangement of the mixture, and reduce energy consumption during the forming process. The aim of the study is to establish criteria for the efficiency of vibration re-compaction and to substantiate the parameters of the optimal operating mode of the installation based on an energy approach. The study uses methods of analytical modeling based on the energy balance over one oscillation cycle, determination of dissipated energy in the vertical and horizontal deformation channels, as well as formulation of threshold conditions for active compaction according to dynamic pressure and shear stresses. Relations were obtained that make it possible to assess the energy efficiency of the process, establish the conditions for coordinating excitation frequencies, and determine the synergy coefficient of the combined action of shear and compression mechanisms. It is shown that the optimal re-compaction mode is achieved under the condition of maximizing the energy dissipated in the mixture, fulfilling the threshold conditions for structural rearrangement of the medium, and maintaining a quasi-resonant mode while taking into account changes in the dynamic properties of the mixture during compaction. The practical significance of the obtained results lies in the possibility of using the proposed criteria to select the parameters of the surcharge device and the operating modes of vibration exciters in the design and improvement of vibration installations for forming concrete products.
ON THE FEASIBILITY OF PRETENTION REBAR IN UKRAINIAN CONDITIONS
Placing a part of industrial and social facilities underground, for a long time of operation and the influence of external sources of seismic energy of various origins has become an urgent problem of today. Frame-anchor fastening is the most common fastening system of underground workings, including for long-term operation of underground industrial structures. The fastening procedure begins with fastening the workings with metal-polymer anchors (AKM). Then, under the protection of the anchor fastening (AK), the workings are fastened with frames. The features of such a combination are that the anchor fastening counteracts any movement of rocks in the workings. At the same time, with minor movements of rocks in the working space, the frame fastening has not yet begun to counteract the rock pressure. With significant movements for the AKM, the frame fastening is forced to take on the load of the weight of the rocks of the volume of the compressed shell. This situation is not acceptable for fastening excavations with a long service life. Taking into account the factor of long-term operation of underground structures leads to a detailed analysis of the factors that may have an impact on it. One of the most important factors that has an impact on the load-bearing capacity of rocks in the vicinity of the excavation is the preload (PR) of AKM anchor rods. An analysis of literary sources showed the absence of a consistent opinion on its value and even on its feasibility in general. According to existing regulatory documents in Ukraine, it is accepted at the level of 5 tons. According to these documents, PR should be carried out by compressing rocks by tightening a nut on the tail section of the anchor rod. However, this method of creating PR has changed now. Given the technological complexity of the thread rolling operation, it was abandoned. Currently, the operation to create PR of anchor rods is carried out by tightening a cast nut on periodic protrusions on the surface of the anchor rod. As a result, the regulatory value of PR is not achievable. As calculations show, the maximum value of PN does not exceed 2t. The value of PN cannot be controlled, since it is determined by stopping the procedure for tightening the nut due to the impossibility of its further execution. Since the landings in the screw-nut pair are widely movable, that is, free, and as a result, the nut bites on periodic protrusions of the anchor rod. It is not worth talking about achieving the design values of PN. For fastening industrial facilities for a long period of operation, such a state of affairs is not permissible. To clarify the importance of fulfilling the PN regulatory values, it is necessary to conduct an experimental study in industrial conditions. Such a study was conducted and its results are presented in this article. Graphic images of the condition of the roof surface of the excavations that were subject to investigation are presented and conclusions are drawn.
DYNAMIC MODELING OF INDUCTION MOTOR PERFORMANCE UNDER POWER QUALITY DISTURBANCES
The paper presents a dynamic electromagnetic model of a three-phase squirrel-cage asynchronous motor developed to simulate its operation under real power quality disturbances. The relevance of this work is driven by the increasing impact of electromagnetic compatibility issues and energy losses in industrial systems exposed to voltage asymmetry and harmonic distortion–conditions typical for networks with nonlinear loads such as welding equipment, arc furnaces, and frequency converters. Traditional motor models, which assume ideal supply conditions, are not sufficient for accurately predicting performance degradation under such disturbances. To address this limitation, the proposed model is based on space-time complexes and an extended form of the Park–Gorev equations. A key feature of the model is the inclusion of magnetic core saturation, represented through a polynomial dependence of mutual inductance on magnetizing current, enabling more realistic simulation under high-load and unbalanced conditions. The model was tested on an MTKH 112-6 motor (5.3 kW) under two scenarios: ideal sinusoidal voltage and distorted asymmetric supply with harmonics up to the 10th order. The results showed that voltage distortion leads to increased losses in the stator (from 491.3 W to 498.3 W) and rotor (from 652.2 W to 661.5 W), a decrease in efficiency (from 81.4% to 81.2%), and a significant drop in power factor (from 0.98 to 0.90). Additionally, distorted current waveforms and torque pulsations confirmed higher electromagnetic stress. The model demonstrated strong agreement with experimental data (RMSE < 4%), confirming its reliability for applications in diagnostics, predictive maintenance, digital twins, and simulation environments. Unlike traditional Fourier-based approaches, the use of space-time complexes enables comprehensive modeling of both steady-state and transient processes without explicit harmonic decomposition. This research contributes to the development of energy-efficient and intelligent industrial systems. Future work will focus on incorporating stochastic elements to account for dynamic variations in power quality, supporting predictive control and advanced automation within Industry 4.0.
APPLICATION OF COMPUTER CONTROL SYSTEMS IN THE HIGH-PRESSURE DIE CASTING PROCESS OF ALUMINUM ALLOYS ON MODERNIZED EQUIPMENT
The article addresses the implementation of computer-based control systems in the high-pressure die casting process of aluminum alloys under conditions of equipment modernization. The necessity of ensuring high stability of technological parameters – melt velocity, compaction pressure, and mold temperature – under dynamic operational conditions is emphasized. The study presents a control architecture based on a two-level system: the upper level features a fanless industrial panel PC for visual supervision, while the lower level employs a programmable logic controller (Simatic S7-1200) for real-time signal processing and control of casting phases. The experiments were conducted on a renewed casting line equipped with adaptive control algorithms that monitor dynamic parameters every 10 milliseconds. The system enables precise coordination of the melt injection phase, cavity filling, and final compaction, minimizing hydraulic shock and improving mold filling uniformity. Data visualization modules capture casting temperature, piston velocity (up to 7 m/s), and pressure fluctuations during solidification, allowing predictive adjustments and optimization of process phases without operator intervention. The research results confirm a reduction in cycle time by 10–12%, energy consumption per 1,000 units by nearly 10%, and the share of defective castings (due to porosity or shrinkage cavities) by more than 50%. It is demonstrated that maintaining mold temperature within the range of 220–235 °C is critical for defect-free casting, and deviation from this range increases the occurrence of misruns and shrinkage defects. The proposed control system adapts in real time to alloy transitions and changes in mold geometry, supporting more robust, energy-efficient, and quality-stable casting operations. The integration of computer control technologies into die casting contributes to the advancement of digital manufacturing and supports the broader goal of increasing productivity and product reliability in the foundry industry.
INFLUENCE OF RUBBER VIBRATION MOUNT TEMPERATURE ON VIBRATING TABLE VERTICAL VIBRATION AMPLITUDE
The article examines and studies vibration equipment used for vibroforming concrete products with the application of elastic rubber vibration mounts. The relevance of this topic is confirmed by the widespread use of such equipment by industrial enterprises in the production of small-sized concrete products for paving streets and public areas. The aim of this work was to investigate the effect of the temperature of rubber vibration mounts on the amplitude of vertical oscillations of a vibrating table, maintaining the required value of which has a decisive impact on the quality of the manufactured products. General empirical and theoretical research methods were employed in the study. Initially, various designs of rubber vibration mounts used in vibroforming equipment were analyzed, with an assessment of their structural and operational features. Subsequently, experimental studies were carried out on operating vibration equipment to determine the temperature regimes of rubber vibration mounts and to measure the amplitude of vertical oscillations of the working element. The research revealed that at the initial stage the oscillation amplitude has minimal values; however, as the temperature increases, rubber loses stiffness due to increased mobility of macromolecules and a decrease in the modulus of elasticity, which leads to a gradual increase in amplitude. A detailed analysis of the experimental results was conducted to evaluate the influence of the studied parameters on the efficiency of the equipment operation. Practical recommendations for the operation and improvement of vibroforming equipment with elastic rubber vibration mounts are provided, taking into account the obtained results.
MULTI-AGENT ARCHITECTURE OF SOFT SENSORS BASED ON DEEP LEARNING FOR PROACTIVE ENERGY EFFICIENCY MANAGEMENT OF SUBMERGED ARC FURNACES
The relevance of this study is determined by the high energy intensity of ferroalloy production and the limited ability to directly monitor internal bath parameters in submerged arc furnaces (SAF), which significantly complicates effective process control under conditions of uncertainty and noisy industrial data. Existing automated control systems are predominantly based on reactive strategies that focus on correcting already occurred deviations, leading to increased energy consumption and higher operational risks. Therefore, there is a growing need to implement proactive approaches capable of predicting system states and generating control actions in advance. The aim of this study is to develop a concept of an intelligent control system based on a multi-agent architecture using soft sensors to improve energy efficiency and operational safety. The research employs deep learning methods, including recurrent neural networks (LSTM/GRU), physics-informed neural networks (PINN), as well as multi-agent coordination and decision-making approaches. The proposed system architecture includes specialized agents focused on energy balance, thermal state monitoring, and technological process parameters, whose interaction is coordinated by an orchestrator agent responsible for synthesizing optimal control actions. The results demonstrate the feasibility of transitioning to proactive control with a prediction horizon of 1–3 hours, enabling reduction of specific energy consumption and mitigation of operational risks. In addition, the proposed approach provides improved robustness to noisy industrial data and enhances the interpretability of model outputs through the integration of explainable artificial intelligence techniques. It is established that the combination of a multi-agent approach with hybrid neural network models improves prediction accuracy, consistency of control decisions, and overall stability and reliability of the technological process in energy-intensive industrial environments.
SYSTEM APPROACH TO DETERMINING THE EFFECT OF RARE-EARTH METALS ON THE STRUCTURE OF ROLL CAST IRONS
The article examines the effect of rare-earth metals on the microstructure of roll cast irons. An analysis of the current state of roll casting production and the issues within the selected research direction is presented. For many years, efforts have been made in roll casting to replace magnesium with alternative modifiers. The analysis of available studies and publications mainly focuses on individual components, while a comprehensive model of modification of roll cast irons using rare-earth metals still requires further investigation and generalization. The aim of the study is to determine the carbide-forming ability of various rare-earth metals in white roll cast irons. To achieve this goal, the following task was formulated: to establish the influence of chemical elements of the cerium and yttrium subgroups of rare-earth metals on the microstructure of roll cast iron, as well as to substantiate the selection of rare-earth metals for the treatment of white roll cast irons. Regularities of the influence of rare-earth elements of the cerium subgroup (samarium and cerium) and the yttrium subgroup (gadolinium and yttrium) on the structure formation processes of white cast irons for rolling rolls under cooling rates typical for roll casting molds have been established. It has been shown that the individual effects of the studied subgroups of rare-earth metals on the microstructure differ in terms of their residual content ranges. Modification of white cast iron with rare-earth metals leads to changes in the type of carbide eutectic and the dispersion of pearlite. It has been established that the carbide-forming ability of rare-earth metals of the yttrium subgroup is 5.2 times higher than that of the cerium subgroup. This made it possible to substantiate the composition of the base of a complex modifier to achieve the required properties of roll materials.
ANALYSIS OF EQUIPMENT FOR OBTAINING A HIGH-STRENGTH HEAT-RESISTANT ALLOY WITH REDUCED DENSITY IN LABORATORY CONDITIONS
The work presents a systematic analysis of modern electrothermal equipment used to obtain high-strength heat-resistant nickel-based alloys with reduced density in research laboratory conditions. The relevance of the study is due to the needs of the aviation and energy industries for materials capable of operating at high temperatures, cyclic loads and in aggressive environments while simultaneously reducing the mass characteristics of parts. A comparative assessment of electric arc furnaces, vacuum arc and electroslag remelting installations, vacuum induction and electron beam systems has been carried out from the standpoint of metal purity, chemical composition stability, the possibility of precise alloying and suitability for use in laboratory conditions. It has been established that laboratory arc furnaces are appropriate for the initial development of alloy compositions, while electron beam installations are effective for obtaining ultrapure materials, but have significant economic limitations. It is shown that vacuum induction melting provides an optimal balance between the depth of refining, the accuracy of the introduction of alloying elements, the homogeneity of the structure and energy efficiency. Criteria for selecting laboratory equipment for the synthesis of new generation heat-resistant alloys are formulated, taking into account technological and infrastructural limitations. The results obtained can be used in the creation of mobile laboratory complexes for the research and development of new heat-resistant materials.
INVESTIGATION OF THE WEAR RESISTANCE OF NITRIDED SHKH15 STEEL IN AN ABRASIVE ENVIRONMENT
The study investigates the wear resistance of nitrided ShKh15 steel in an abrasive environment after glow-discharge nitriding in hydrogen-free nitrogen–argon atmospheres. The influence of technological parameters, including pressure and argon content, on the thickness, hardness, phase composition, and hardness gradient of nitrided layers was analyzed using a two-factor rotatable design. Empirical mathematical models describing nitrided layer properties and wear behavior were developed. Experimental results showed that wear resistance, surface hardness, and layer thickness can be controlled and optimized by varying nitriding conditions. The highest wear resistance was achieved under optimal nitriding conditions, significantly exceeding that of quenched steel.
POSSIBILITIES OF REDISTRIBUTION OF AVAILABLE TUNGSTEN RESOURCES IN CIRCULATION BETWEEN INDUSTRIES OF USE
The purpose of this study is to identify the industries and forms of application of tungsten in which the largest amount of it is in circulation; to analyze the methods of processing materials containing tungsten, from the point of view of the possibility of redistributing the available resource between the areas of its application. The main research method in this work is the analysis of freely available data. The scientific novelty of this work is that it was established that the largest resource of tungsten in circulation is products made of hard alloys based on tungsten carbide. Based on the results of this study, the following conclusions can be drawn. The largest resource in terms of the possibility of redistributing the available amount of tungsten in circulation between different areas of use is products made of hard alloys based on tungsten carbide. Approximately one to two thousand tons of hard alloy products are in circulation in Ukraine annually, the basis of the vast majority of which is tungsten carbide. Methods of processing hard alloy waste that do not involve the recovery of tungsten from carbide are characterized by minimal energy consumption, but limited possibilities for redistributing the available tungsten resource between its areas of use. Methods of processing hard alloy waste that involve the recovery of tungsten create the widest possibilities for redistributing the available tungsten resource between its different areas of use.
BORON DIFFUSION SATURATION KINETICS OF TOOL STEEL U8
This article presents the results of a study on the effect of powder boriding parameters – temperature (850, 900, 950°C) and holding time (4, 6, 8 hours) – on the growth kinetics, microstructure, morphology, and microhardness of the boride diffusion layer on high-carbon tool steel U8. Boriding was carried out in sealed containers using a powder mixture of 85% B4C, 5% KBF4, and 10% Al2O3. Metallographic examination revealed a well-defined dual-phase FeB/Fe2B boride layer with a characteristic sawtooth interfacial morphology, which provides mechanical interlocking between the coating and the substrate, improving resistance to delamination. A cementite-enriched transition zone beneath the boride layer was observed, attributed to carbon redistribution during boron diffusion. Microhardness values reached approximately 20 GPa in the outer FeB zone and 16 GPa in the inner Fe2B zone, dropping sharply to base-metal values beyond 200–300 μm depth. The boride layer growth was found to follow a parabolic law, confirming diffusion-controlled kinetics. Arrhenius analysis yielded an activation energy Q = 199.6 kJ/mol and a pre-exponential factor D0 = 9.24×10-4 m2/s, consistent with literature data for carbon steels. Analysis of variance (ANOVA) confirmed that both factors are statistically significant (p < 0.05); the partial eta-squared values were η2 = 0.9897 for temperature and η2 = 0.8964 for time, establishing temperature as the dominant process variable. A second-order polynomial regression model based on response surface methodology was developed (R2adj = 0.9886), enabling reliable prediction of boride layer thickness without additional experiments. The results provide a quantitative basis for optimizing surface hardening of steel U8 components to improve their wear resistance and service life.
SOFTWARE IMPLEMENTATION OF AN IMPEDANCE PI CONTROLLER FOR AN ELECTRIC ARC FURNACE CONTROL SYSTEM USING THE GO PROGRAMMING LANGUAGE
Electrode control in electric arc furnace (EAF) operation represents one of the most technically demanding problems in steelmaking. The inherently unstable behaviour of the electric arc – its sensitivity to scrap composition, inter-electrode gap geometry, and thermal conditions – results in current and voltage fluctuations, increased specific energy consumption, and accelerated electrode wear. Despite a considerable body of research on mathematical modelling and controller design for EAFs, most published work relies on specialised software environments such as MATLAB/Simulink and does not address the direct deployment of control algorithms in industrial automation systems. The question of implementing control logic using general-purpose programming languages suitable for production environments remains insufficiently explored. The objective of this work is to develop an impedance-based PI control algorithm for the EAF electrode positioning system and to implement it in the Go programming language, followed by analysis of the closed-loop system's dynamic behaviour. The mathematical model is based on the Cassie-Mayr arc equations, which describe arc conductance dynamics under both transient and steady-state conditions. The controller is implemented in discrete time with a fixed integration step to ensure numerical stability. An anti-windup mechanism – clamping the accumulated error sum within defined bounds – is applied to prevent integrator saturation under control signal constraints. The software is structured as a modular Go application comprising dedicated components for control signal computation, simulation loop execution, and CSV-based result logging. The choice of Go is justified by its practical advantages for industrial automation: compilation to native executable code, absence of runtime dependencies, support for modular architecture, and high computational performance. Simulation results are visualised using Python/Matplotlib, ensuring reproducibility and clarity of the obtained data. Numerical simulation results show that the developed system achieves a stable transient response with a settling time of 0.15-0.2 s and overshoot within acceptable limits. A residual steady-state error of 2-3% is attributed to simplifications in the adopted arc model and can be reduced by introducing adaptive gain correction. The smooth control signal profile, free from abrupt changes, confirms the algorithm's suitability for real-world application with respect to mechanical loading on the electrode drive. The findings demonstrate the viability of Go as an implementation language for control algorithms within digital EAF automation systems, as well as for the development of digital twins of electrotechnological processes.
DETERMINATION OF DIAGNOSTIC INDICATORS OF THE TECHNICAL CONDITION OF IDLERS AND THEIR SERVICE LIFE IN A HEAVY BELT CONVEYOR
The article addresses the problem of determining diagnostic indicators of the technical condition of idlers of a heavy belt conveyor and estimating their service life under mining conditions. The relevance of the study is due to the fact that idler failures are among the most common causes of increased belt motion resistance, damage to the conveyor belt, overload of adjacent idler supports, and downtime of the transport system. The aim of the paper is to substantiate informative diagnostic parameters that make it possible to detect defective and jammed idlers in a timely manner and to assess the degree of their service life depletion with regard to actual operating loads. The study analyses the main factors influencing idler condition, namely linear load, mass and particle-size composition of the bulk material, conveying speed, belt tension, transverse belt oscillations, impact action of large lumps of material, and radial runout of the idler shell. Based on the derived relationships, it is shown that the least reliable element of the idler is the bearing assembly, whose service life is determined by the combined effect of static, dynamic, shock, and vibration loads. An approach to estimating the bearing damage measure over a time interval equal to one full revolution of the conveyor belt is proposed, as well as a method for detecting jammed idlers by comparing the amplitudes of informative frequencies in the vibration signal of a reference support and the monitored supports while taking into account oscillation attenuation and changes in belt speed. It is established that the most informative diagnostic indicators are vibration signal parameters, amplitude-frequency characteristics, amplitude growth at informative frequencies, increased rotation resistance, and thermal overheating indicators. The practical value of the results lies in the possibility of using the determined indicators to build automated condition monitoring systems for idlers of heavy belt conveyors and to predict the maintenance interval and service life of the equipment.
INTEGRATION OF COMPLIANCE MANAGEMENT FUNCTIONALITY INTO THE SYSTEM OF DECARBONIZED DEVELOPMENT OF METALLURGICAL PRODUCTION
The article identifies the main directions for integrating compliance functionality components into the technological development system of ferrous metallurgy, in line with modern concepts of decarbonization, circular economy, and ESG-oriented management. It examines mechanisms and methods for improving the environmental friendliness of key metallurgical processes through the use of secondary resources (slag, dust, dispersed waste from lime production), the physical heat of production gases, and the chemical energy of CO–H₂ mixtures. Relevance of the study. Given the high energy intensity and significant share of the metallurgical industry in global greenhouse gas emissions, reducing the carbon intensity of production is becoming one of the key factors in ensuring the competitiveness of metallurgical products on the world market, especially in the context of the introduction of carbon emission regulation mechanisms, in particular CBAM. In these conditions, the formation of effective management mechanisms becomes particularly important. One such mechanism capable of ensuring the integration of technological, environmental, and economic aspects of metallurgical production development is compliance management. Its functionality should be viewed as an integrated system for managing the decarbonized development of metallurgy, ensuring the alignment of innovative technological solutions with modern environmental standards, regulatory requirements, and sustainable development principles. The purpose of the work is to substantiate the conceptual foundations for integrating compliance management functionality into the system of decarbonized development of metallurgical production and to determine its role in improving energy and resource efficiency, environmental safety, and technological sustainability of iron and steel smelting processes. To achieve this goal, the following research methods were used: systematic analysis of current trends in the development of metallurgical technologies; methods of structural and functional analysis of production management systems; comparative analysis of energy and resource efficiency indicators and carbon intensity of metallurgical processes; generalization of scientific and technological approaches to the decarbonization of metallurgical production. Research objectives. The following tasks were solved in the work: Analysis of current technological and environmental challenges for the development of metallurgical enterprises in the context of industry decarbonization. Justification of a conceptual model for integrating compliance management into the sustainable development system of metallurgical production. Identification of the main directions for the use of compliance tools to improve energy and resource efficiency and reduce the carbon intensity of metallurgical processes. Assessment of the role of compliance functionality as an integration mechanism for coordinating technological, environmental, and economic parameters of production. The scientific novelty of the results obtained lies in the following. It is proposed to consider the mechanism of a functionally integrated system of compliance control and coordination of production processes, the main component of compliance – assurance as: a system-forming factor based on an institutional and technological platform for management/regulation of the mechanism for ensuring decarbonized development of production, combining technological, environmental, and management tools for ensuring the sustainability of metallurgical processes. Conceptual approaches to the integration of compliance tools into the energy and resource efficiency management system of metallurgical production have been substantiated, which allows for increased transparency of material and energy flows and control of the carbon intensity of the main stages of the end-to-end technological scheme of steel production. The system of key indicators for assessing the effectiveness of decarbonization of metallurgical processes, which combine technological, energy, and climate indicators of production, has been refined. The role of compliance management as an integration mechanism for harmonizing innovative technological solutions with modern environmental and regulatory requirements is revealed, which ensures the formation of prerequisites for the sustainable development of metallurgical enterprises. It is shown that the integration of compliance tools into decarbonization processes allows for carbon footprint control, minimization of man-made environmental impact, and increased economic stability of enterprises. The role of improving existing technologies in the implementation of the concept of sustainable and environmentally safe production is substantiated.
METHODOLOGY FOR ANALYZING GEOMETRY CHANGES AFTER IMPACT–ABRASIVE WEAR TESTING
The current stage of development in materials science is characterised by a high level of research into the structure and mechanical properties of materials. Further progress in this field is linked not only to the development of fundamentally new testing methods, but also to the refinement of existing approaches through the integration of modern digital technologies for data recording and analysis. This allows not only for increased measurement accuracy and a greater number of intermediate values, but also for the determination of additional material behaviour characteristics that were previously inaccessible to direct measurement. The aim of this work is to enhance the informative value of the impact-abrasive wear testing method through its digitalisation, in order to obtain a comprehensive assessment of a material’s resistance to dynamic impact. The paper presents an overview and examines aspects of improving the methodology for investigating impact-abrasive wear. Unlike classical approaches, which are limited to determining the mass loss of the specimen, the proposed methodology integrates 3D scanning to quantitatively assess changes in surface geometry following testing. The scientific novelty lies in the ability not only to record the integral wear index (mass loss), but also to directly measure the distribution and magnitude of plastic deformation accumulating in the metal under the dynamic impact of abrasive particles. The proposed approach allows a transition from a one-dimensional assessment of wear resistance to a two-dimensional one (mass loss + deformation relief). Based on the results of 3D scanning and subsequent processing of the obtained data, a graphical representation (depth map or profilogram) is generated, which quantitatively characterises the material’s resistance to plastic deformation under impact-abrasive conditions. This opens up new possibilities for the comparative analysis of materials, the prediction of their behaviour under operational conditions, and the verification of mathematical models of wear processes.
DEVELOPMENT OF A REFERENCE ARCHITECTURE FOR BUILDING DIGITAL TWINS IN AUTOMATED PRODUCTION FOR WASTEWATER TREATMENT PLANT CONTROL
Analysis of recent research and publications. Analysis of contemporary research on the integration of digital twins into production processes reveals the existence of numerous approaches aimed at improving modeling accuracy, enhancing equipment operational efficiency, and reducing development time and resource consumption. However, existing developments are predominantly oriented toward specific application tasks and do not provide a unified conceptual foundation for the phased implementation of digital twins in industrial environments. Issues related to interface standardization, interoperability between heterogeneous components, efficient data exchange, and a coherent architectural model that enables gradual scaling from pilot projects to the enterprise level require additional investigation. This justifies the relevance of developing a reference architecture for systems utilizing digital twins, particularly for such complex technological facilities as wastewater treatment plants. Research objective. The objective of the article is to develop a reference multi-layer architecture for building digital twins in automated production for wastewater treatment plant control, which ensures modularity, flexibility, and the capacity for gradual expansion without radical changes to the system structure. Presentation of the main research material. The article analyzes the key factors that must be considered prior to creating a digital twin: the scope and granularity of modeling (from a single asset to an entire production line), data sources (IoT devices, PLCs, SCADA, ERP/MES systems), modeling techniques (physics-based models, machine learning, or hybrid approaches), technology stack (off-the-shelf solutions, custom cloud-based developments, or combined variants), and intended purpose (prediction, optimization, quality control). The fundamental principles of architecture design are formulated: modularity, openness, scalability, simplicity of initial deployment, and incremental security implementation. Based on these principles, an architecture consisting of five layers is proposed: the Physical Layer, Data Ingestion Layer, Data Management Layer, Modeling and Simulation Layer, and Analytics and Application Layer. The first two layers are located directly at the production site, which minimizes network traffic through local data filtering and transformation, while the remaining layers are deployed in the cloud environment, providing flexibility, scalability, and cost efficiency through the pay-as-you-go model. For each layer, recommendations are provided regarding the selection of protocols (MQTT, OPC UA, HTTP), storage technologies (InfluxDB, PostgreSQL, AWS S3), and modeling tools (MATLAB, Simulink, Unity). Conclusions. The proposed reference multi-layer architecture allows the implementation of a digital twin to commence with the basic functionality of an individual asset and to be gradually scaled to cover the entire wastewater treatment facility or enterprise. A strategy for the phased development of a digital twin for wastewater treatment plants is defined: at the initial stage, the existing PLC- and SCADA-based infrastructure is used as the data source, and modeling is built upon deterministic physics-based models of biochemical and hydraulic processes. Subsequent stages involve transitioning to hybrid modeling techniques incorporating machine learning algorithms and introducing predictive maintenance and energy consumption optimization functions. This approach minimizes initial capital expenditures and ensures the systematic accumulation of historical data for the further development of the system.
THE CURRENT STATE OF SAWDUST PROCESSING OF CHIPBOARD AND IRON-CONTAINING METALLURGY WASTE
The object of the study is the metallurgical technology of chipboard dust processing and iron-containing waste from metallurgical production. The purpose of the work is the analysis of physical and chemical processes, experimental research and the development of innovative technological solutions and recommendations for chipboard dust and iron-containing metallurgical waste. Research methods – theoretical research is based on the basic principles of physical chemistry and the theory of metallurgical processes. Calculations of the thermodynamic equilibrium of oxide systems are based on the Gibbs theory and implemented using the computer program "FASTSage 6.0"; the chemical composition of the phase components of manganese ferroalloys was studied using a scanning electron microscope YSM-6300LA from JEOL, Japan. Scientific novelty. Effective removal of zinc from chipboard dust is already possible at moderate temperatures of 1000...1100oC, including when using substandard carbon materials as a carbon reducer. To obtain a liquid product, it is necessary to provide an excess amount of carburizing carbon to lower the temperature of the resulting melt. At temperatures of the order of 1000...1100°С, iron-containing dust and sludge undergo changes, which leads to a decrease in the content of Zn in the processed material, the transition of the original dust-like materials into a compact mass. Practical meaning. The joint processing of chipboard slag and dust by dosing in different proportions is not rational, because in this case the concentration of zinc collected in the gas cleaning processing unit is reduced. It will be more effective to organize alternate processing of chipboard dust and slag at different time periods (for example, monthly).
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ENERGY-SAVING TECHNOLOGIES IN PIPE PRODUCTION
Ukrainian metallurgical enterprises with a full cycle have fuel costs at the level of 1.4÷1.6 tons of conventional fuel per ton of produced products, while the share of energy costs in the cost of rolled products is approximately 40%. At the same time, at enterprises in Japan and the USA, these costs are 0.7÷1.0 tons of conventional fuel per ton of product. One of the current problems of Ukraine is the shortage of primary energy carriers, in particular natural gas, which limits the energy consumption of enterprises. The problem is exacerbated by the gradual increase in the cost of energy carriers (natural gas, electricity), as well as other reasons that reduce the competitiveness of Ukrainian metallurgical enterprises. The purpose of this work is to consider known technical solutions for energy saving in rolling production, mainly in the production of hot-rolled seamless pipes, for further improvement of pipe production. Based on the analysis of energy saving methods in the production of hot-rolled pipes, the main direction of energy saving in rolling production is noted - this is the construction of rolling mills near the continuous casting machine of the billet. This work considers such areas of energy consumption reduction as: hot rolling of billets in the heating furnaces of pipe rolling units; saving natural gas during heating and heat treatment; direct piercing of continuously cast billets on the slanting roll mill of the pilgrim unit; thermomechanical processing of pipes with rolling heating. The possibilities of hot-rolling of continuously cast billets entering the pipe rolling shop with a 5-12” pilgrim mill of PJSC “Interpipe Niko Tube” were analyzed. A new technology of using the heat of a pre-deformed billet for further rolling of pipes on the same mill was proposed on the pipe rolling shop 200 of PJSC “Interpipe Niko Tube”. The use of the technology of hot-rolling of continuously cast billets is also possible in other shops of PJSC “Interpipe Niko Tube”. To improve the organization of work on the development of the technology of hot-rolling of billets, it is possible to organize a metal preparation shop with wide technological capabilities. The introduction of such technologies as direct piercing of billets on the cross-rolling mill of the pipe rolling shop with a 5-12” pilgrim mill, thermomechanical processing of pipes with rolling heating on various pipe rolling shops will contribute to the reduction of energy consumption.
MODELING OF ELECTROMAGNETIC PROCESSES IN A NONLINEAR CIRCUIT OF AN ELECTROLYZER FOR PULSE DEPOSITION OF METAL COATINGS
The primary objective of this study is to construct a comprehensive analytical model describing the electromagnetic processes in a nonlinear electrical circuit of an electrolyzer operating under pulsed electrodeposition conditions. Special attention is given to the influence of reversed rectangular voltage pulse parameters on the near-cathode voltage drop, deposition current, and the general electrochemical behavior of the system. The goal is to identify optimal operation modes of the pulse power supply that ensure high-quality metal coatings while minimizing energy consumption and structural defects. Methodology. The research employs the method of variable transformation to develop a set of differential equations describing the dynamic behavior of voltage and current in a nonlinear electrolyzer circuit during pulsed operation. The model accounts for critical circuit components: resistive, capacitive, and inductive elements of the electrolyte, as well as nonlinear conductances reflecting electrochemical properties. Analytical expressions for voltage drop and deposition current are derived for both the forward and reverse pulse intervals. The model includes the influence of electrolyte inductance–an often-neglected factor–which significantly alters the current front shape and ultimately affects deposition kinetics and coating characteristics. Numerical simulations are performed to validate the analytical solutions. Results. Closed-form analytical expressions were obtained for the time-dependent near-cathode voltage drop and deposition current under pulsed conditions. It was shown that the electrolyte inductance leads to a rounding of the current front, influencing both the amplitude and stability of the electrochemical reactions. A parametric analysis identified that the optimal pulse duty cycle lies in the range of τ/T ≈ 0.73 to 0.78. Within this interval, the maximum near-cathode voltage drop does not exceed 0.6 V, while the peak voltage and total current remain within safe technological limits (up to 13 V and 150 A, respectively). The average partial discharge current at the cathode remains stable at approximately 70 A, ensuring consistent deposition rates. Scientific novelty. This work introduces a novel analytical approach to modeling pulsed electrodeposition that, for the first time, includes the effect of electrolyte inductance. Unlike existing models relying heavily on numerical simulations, the proposed model allows for direct computation of key process parameters. It enables the derivation of precise criteria for determining the optimal ranges of input pulse parameters–both in amplitude and duration–necessary to avoid the formation of crystalline defects and to achieve uniform, high-quality coatings. These innovations significantly advance the theoretical understanding of pulsed electrochemical processes. Practical significance. The developed model provides a valuable tool for industries that utilize electrochemical metal deposition, including microelectronics, galvanics, mechanical engineering, and power systems. It offers a foundation for designing advanced pulse power supplies with optimized operation modes and supports the development of automated control systems for deposition processes. Furthermore, the model can aid in adapting laboratory results for industrial implementation, improving coating quality, process efficiency, and operational reliability.
CALCULATION OF THE OPTIMAL HYDROPOWER UTILIZATION SYSTEM: A CASE STUDY OF A METALLURGICAL ENTERPRISE
This research is dedicated to the development, modeling, and optimization of a hydropower recovery system based on the reuse of secondary water resources within an industrial enterprise. The specific focus is on the graphitization workshop of PJSC "Ukrainian Graphite"–a metallurgical facility where substantial volumes of warm process water are discharged as a byproduct of production. The central objective of this study is to determine the optimal configuration of a water collection and energy conversion system that will enable efficient electricity generation at the lowest possible cost, while maintaining high energy performance. The task is conducted under the influence of strict technical and spatial constraints inherent to existing industrial infrastructure. Methodology. The study applies a set of engineering, mathematical, and economic methods. Hydraulic analysis is used to model water flow through both pressurized and gravity-fed pipelines, ensuring accurate determination of head losses and flow rates. A combinatorial optimization framework is employed to evaluate various topologies of system configurations, where water sources are matched with potential collection centers in the most effective way. A key feature of the methodology is the use of signature functions–a mathematical tool designed to define “prohibited zones” where placement of system elements is physically or operationally impossible due to safety, accessibility, or layout restrictions. These functions are integrated into the optimization model, enhancing the realism and applicability of the results. Additionally, a comprehensive techno-economic assessment is performed for each configuration, including calculations of capital expenditures, equipment cost, pipeline expenses, operational costs, and unit electricity production cost (LCOE). Results. The modeling process revealed that the most economically and technically viable system involves a single collection center–Center No. 2–into which water flows from four main technological sources: електрокальцинатори (electric calciners), барабани-охолоджувачі (cooling drums), формувальна машина (molding machine), and підшипники димососів (smoke exhauster bearings). These flows are collected via a pipeline network with a total length of approximately 200 meters. The selected micro-hydropower plant (type 10Пр) is of a modular design and includes a діагональна турбіна (diagonal turbine). According to the calculations, this system is capable of generating over 135,000 kWh of electricity annually. The levelized cost of electricity (LCOE) is just US$0.30 per kWh, which is substantially lower than the applicable industrial electricity tariff in Ukraine. The total capital investment, including the cost of the micro-HPP unit, pipelines, installation, and commissioning works, is approximately US$168,800. Maintenance costs are estimated at 5% of capital expenditures annually. Scientific novelty. The study introduces a new integrated methodology for assessing and designing hydropower recovery systems (HERS) at the local (workshop or facility) level, which takes into account technical parameters, hydraulic behavior, and spatial limitations. For the first time, the concept of signature functions is applied in this context to simulate constrained zones in system layout planning. This approach provides a flexible yet accurate mechanism for system designers to preclude impractical configurations early in the modeling phase, thereby saving resources and improving the efficiency of decision-making. Practical significance. The developed methodology and the results obtained offer a practical solution for the sustainable use of internal water resources in energy-intensive industries. By implementing optimized HERS configurations, industrial enterprises can reduce dependence on external electricity supplies, enhance operational energy efficiency, and decrease total electricity costs. The approach also contributes to improved environmental performance by reducing heat discharge and enhancing water recycling. Furthermore, the proposed system architecture is modular and adaptable, allowing for scaling and replication in other industrial enterprises with similar infrastructure. This makes it especially relevant in the context of global trends toward decarbonization, resource efficiency, and green transformation of heavy industry.
ALGORITHMS AND METHODS IN DYNAMIC PROBLEMS OF OPTIMAL PLACEMENT OF FIRE GROUPS
The work is devoted to the urgent task of deploying fire groups of air defense forces to cover the lines of air attacks. To solve the problem, modern methods of the theory of optimal set partitioning, mathematical modeling using differential equations and their systems, a specialized software package has been developed, which includes a mobile and browser application, is used. When developing the software package, modern programming languages and technologies were used, an overview and comparison with existing solutions in different countries was made. A retrospective analysis was carried out, criteria for the optimality of the solution being sought were developed, advantages and disadvantages of the approach were determined. The use of methods of the theory of optimal set partitioning allows you to analytically determine the criteria for the quality of the solution, conduct an analytical study of admissible solutions and determine the optimal one, and approbation of analytical results in practice and examples with practical input data increases the accuracy and relevance of the results obtained analytically. Nowadays, the issue of dynamic deployment of fire groups is very relevant for Ukraine. The decision to create and operate fire groups was made and implemented only from the beginning of the full-scale invasion of the aggressor country and became widely used during the massive use of attack drones by the aggressor country against civilian, military and energy facilities of Ukraine. The effectiveness of the use of fire groups has been proven in practice, but the method of their placement, as a rule, is heuristic, that is, not optimal.