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In this paper we investigate the uniqueness of potential recovery in the inverse Borg–Levinson problem, and our study deals with a model of its recovery. The article applies the theory of elliptic equations. Using the resolvent method, in fact, we obtain uniqueness conditions for potential recovery in the inverse Borg–Levinson problem with Newton's boundary condition considered on a multidimensional parallelepiped if the nature of the asymptotic decomposition of eigenvalues is known. The inverse Borg–Levinson problem with Dirichlet's boundary condition was investigated in Sadovnichii et al. (Dokl Math 61(1):67–69, 2000). It was proved that the lack of knowledge about a finite number of spectral data does not affect the uniqueness of the potential recovery, and we can also exclude some infinite sequences of eigenvalues that have certain properties, which will not affect the uniqueness of the potential recovery. Here the authors consider a problem with more general Newton's boundary condition. The study convinces that with a certain asymptotic behavior of the eigenvalues, which is valid on a two-dimensional and three-dimensional cube and cannot be considered on it as an additional requirement, with the eigenfunctions bounded at the boundary and some other conditions, a uniqueness result for the potential restoration holds true. This result is also valid for a problem with Neumann's boundary condition. A potential recovery model was formulated. If the potential of one of their tasks is known, and the difference between the spectral characteristics of the other problem with an unknown potential and the spectral characteristics of the initial one satisfies the presented conditions, then the potentials of these problems coincide. [ABSTRACT FROM AUTHOR]

The research is aimed at increasing the quality of a concast billet macrostructure by limiting static and dynamic longitudinal forces created in billets by electrical drives of withdrawal rolls during wear and bending of the withdrawal roll body and random and periodic slips of drives. The paper analyzes process requirements for electrical drives of withdrawal rolls: contains a procedure for calculating dynamic longitudinal forces created in billets by drives of withdrawal rolls, determines whether influence of operating modes of the said drives on changes in billet withdrawal force is relevant, contains developed techniques and algorithms of withdrawal roll drive automated control limiting static and dynamic longitudinal forces in billets, and includes the experimental analysis of efficiency of methods and technical solutions on operating drives. Research was carried out at the Russian large iron and steel works. When performing the research, the authors applied analytical and numerical methods of solving algebraic and differential equations and systems, methods for structural modeling. As a result of the research, the authors developed and experimentally confirmed methods for "soft" restoring of the contact between the withdrawal roll and the billet and adjusting phases of fluctuating changes in load currents of motor groups. The obtained results are transferred as technical specifications and taken for introduction, when revamping electrical equipment of existing continuous casting machines. Results of mathematical simulation and experimental research are used to design automated electrical drives of withdrawal rolls in the secondary cooling zone of the bow-type continuous casting machine. Impact dynamic loads were decreased by 3 times, resulting in an average increase of 8% in the quality of the billet center with regard to all types of defects. [ABSTRACT FROM AUTHOR]

The aim of the research is to develop the theory of mathematical modelling for describing the processes occurring during metal forming. The research was carried out in several stages: experimental study of the backup roll wear, finding a dependence to describe the shape of the roll generatrix allowing for the roll wear, refinement of the Meltzer-Salganik model taking into account the backup roll wear, development of algorithmic solutions and software for carrying out the computational experiment. The methods of system analysis were used to study the uneven wear of the roll barrel, the methods of statistical analysis to identify cause-effect relationships, the methods of building deterministic models to describe the strip profile, object-oriented programming to develop the basic modules and the software interface. On the basis of algorithmic solutions, software products have been developed to perform the computational experiment to determine the nature of the roll barrel wear. The results of the computational experiment showed a discrepancy with production measurements of no more than 3% and allowed working out recommendations on changing the values of technological parameters that compensated for the negative effect of wear of the backup rolls in the production of hot-rolled steel. [ABSTRACT FROM AUTHOR]

The aim of this research is to help reduce the share of cast slabs with extensive macrostructural defects by changing the structure and the control system of the straightener drive. The article describes the results of a passive experiment. On the basis of these results, requirements have been formulated to the structure and the control system of the straightener drive, a control philosophy developed and a new functional block diagram proposed. The study has been carried out for the curve-type continuous caster operated by one of the major Russian steel producers. The experimental study involved a statistical analysis of the pinch roll drive load sharing data registered by the current monitoring system, as well as the data provided by the sample testing laboratory on the main internal defects found in slabs. The theoretical study included the application of analytical and numerical solutions to algebraic equations, as well as structural modelling. The results of this research were tested on a prototype electric drive for the continuous caster pinch rolls. The authors offer some recommendations on the design of the automatic drive for the pinch rolls installed in the horizontal section of the secondary cooling zone, which also include a technique for calculating the load torques on the straightener pinch rolls, a functional block diagram and a control algorithm for the pinch roll drive installed in the horizontal section of the secondary cooling zone. An average of 50% improvement has been seen in load sharing between the pinch roll drives of the secondary cooling zone. The maximum axial stresses in the slab have reduced four times. There has been an average of 16% improvement in the slab macrostructure for all types of defects and a 13% improvement in terms of axial defects. [ABSTRACT FROM AUTHOR]

The paper presents the results of the study aimed at solving the problem of rational distribution of electric drives of pulling rollers along the technological line of a continuous casting machine and selecting a minimum number of pulling rollers in different areas of the secondary cooling zone. The research includes construction and ranking the criteria for distribution of drive rollers along the production line of the continuous casting machine; development of methods and algorithms for calculating the required distribution of load moments on pulling rollers and distribution of electric drives of pulling rollers along the secondary cooling zone in threemodes of the electric drive operation of the pulling-straightening device: containment of the dummy bar in the preparatory casting mode of the continuous casting machine; pulling the dummy bar with the head of the ingot at the initial stage of pouring the metal; withdrawal of the ingot in the working mode of casting. Theoretical studies were carried out with the use of analytical and numerical methods for solving algebraic equations, methods of structural modeling. Experimental studies were carried out in the conditions of a large metallurgical enterprize with subsequent processing of the obtained data by statistical methods. The technical and economic analysis of the options of the electric drive execution of the pulling-straightening device showed that due to a significant reduction in the number of electric drives of pulling rollers, the payback period of replacement of a group scheme of power supply of electric motors to an individual one in new continuous casting machines decreases from 5.8 to 7.8 years with the traditional distribution of pulling rollers along the secondary cooling zone to 2.8-3 years with their rational distribution, calculated by the developed methods. The results of the work were used in the design of a slab machine for continuous casting of curvilinear strands intended for casting wide slabs up to 2.5 m. According to the proposed method, the number of electric drives pulling the rollers was reduced to 56. [ABSTRACT FROM AUTHOR]

A structure is proposed for the automated system used in batch preparation for arc furnaces at steel plants. Structural and set-theory analysis of such automated systems is employed. The introduction of the new automated control system eliminates the deficiencies of the traditional technology. The new system is universal and ergodic, with formalization of the decision-making process. [ABSTRACT FROM AUTHOR]

The authors of this paper look at the aspect of engineering information systems for planning and scheduling operations of an industrial plant. The authors propose to introduce new steps to the engineering process which include functional modelling, elaboration of an initial request for proposal (or RFP) for a functional model, development of functional models and algorithms, and elaboration of a software specification. The engineering step-by-step process is presented as an entity set model. The authors introduce a system functionality design formula which includes business rules, business logic, project roles, and visualization. An example of a machining shop with repeated machining operations is used to demonstrate the effect of introduction of new design stages. The simulation software AnyLogic was chosen as a visualization tool to demonstrate all the functionalities of the new system. AnyLogic enabled to implement all the roles of the information system. Elaboration of the functional model took place along with development of an RFP for implementation of an information system as part of an automation package of an industrial plant. As a result of the functional model demonstration, certain drawbacks were identified in the project, and recommendations were provided on how to eliminate them. [ABSTRACT FROM AUTHOR]

This paper describes a solution to the problem of energy-saving optimal control over heating of continuous cast billets in a transient operation of high-performance hot rolling mills. We set forth a technique for forecasting a total time of heating by the moment of charging billets into a furnace and suggested a technique for prompt calculation and optimal control following the surface temperature of heated billets subject to generation of set points for temperature controllers in heating areas and objective control of a thermal state of every heated billet before its discharge from the furnace and forecast of expected temperature of the feedstock after roughing mills. All studied techniques focus on software implementation entailing insignificant economic costs and guaranteed success. [ABSTRACT FROM AUTHOR]

The development of an automatic system for the intelligent support of continuous cast billet production control processes is described. The motivation for the development of the system is that it should improve the efficiency of production facilities and minimize the possibility of producing inferior and unacceptable quality products. A theoretical analysis of the information relating to the quality control of the processes and the finished products is presented, enabling the identification of the sources of information, methods of information acquisition, and techniques for processing it to ensure improved product quality. The development of mathematical support is described for a program analyzer that automatically and reliably identifies the defects and quality of the continuously cast billets. The application of graphic information acquisition and processing techniques concerning the quality of the metal products is also presented. The development of mathematical and software support is described for the set point adjustment module operating in the automatic system for the intelligent support of the multistage continuous cast billet production control facility. This module makes use of adaptive fuzzy trees with dynamic structures to provide scientifically grounded analysis of factors causing billet defects. The introduction of the developed systems, including practical issues, into the operation of a production facility is explained. The study identifies the general lack of automatic systems that encompass and control the whole production chain on the basis of product quality. Typical savings resulting from quality improvements in a continuous cast billet production facility can approach a million rubles. [ABSTRACT FROM AUTHOR]

Results are presented from the use of alternative charge materials to make steel in an AC EAF. The authors formulate and solve an optimization problem aimed at minimizing the cost of the charge materials and limiting the steel's residual contents of such elements as chromium, nickel, and copper. Specific results are presented from studies of steel 08Yu made in accordance with the standard GOST 9045, cord, wire rod, and a grade of steel governed by the standard GOST 380. [ABSTRACT FROM AUTHOR]

Monitoring of the energy consumption in an arc smelting furnace when using various materials permits the optimization of the batch composition. To this end, the corresponding multicriterial optimization problem is analyzed, and a method is proposed for determining the energy-saving batch composition. This method consists of six main steps, including the following: collection and organization of the technological information; plotting of cause-and-effect diagrams; and description of the electrical consumption by means of a multicriterial optimization problem containing a system of constraints with empirical coefficients. [ABSTRACT FROM AUTHOR]

A strategy for optimization of the batch composition in steel-smelting arc furnaces is considered. In this approach, the optimization problem is divided into two parts: the first step is to optimize the ratio of metal scrap and hot metal; the second is to optimize the chemical composition of the scrap in terms of the chromium, nickel, and copper content. As an example, this approach is applied to OAO Magnitogorskii Metallurgicheskii Kombinat (MMK), in terms of the requirements for each grade of steel. A generalized protocol for application of the optimization strategy is presented. [ABSTRACT FROM AUTHOR]