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- Dzgoev A., Lagunova A., Karatsev S., Konushok I., Komarov I., Huzmiev I., Gladushev O. System data analysis and modeling of electricity consumption behavior for every hour of the day using machine learning methods
Electricity consumption is a key driver of sustainable development in the energy industry, and accurately predicting its changes is essential for the efficient management of large electric power systems and resources. The aim of this study is to develop a mathematical (regression) model for predicting the behavior of electricity consumption for each hour of the next day for energy supply companies using modern methods of machine learning and artificial intelligence. This article discusses various artificial intelligence methods used to model and predict electricity consumption. These methods include a linear model, a random forest, and two implementations of gradient boosting over decision trees. A scientific approach based on Boosting artificial intelligence technology allows to minimize the error in forecasting electricity consumption in large energy companies. The authors have developed a new, useful and high-quality regression model that adequately describes experimental data on electricity consumption for each hour of the day. The developed regression model was tested on real production data of an energy company. The conducted research and the obtained results allow the authors to conclude that the mathematical model developed using the machine learning method – LightGBM, can be used by energy supply companies for hourly planning of electricity consumption when submitting applications to the wholesale electricity and capacity market (WECM) for several days in advance. The research was carried out in the Python programming language.
- Zhukov P. Dynamic restoration of continuum coefficients in modeling of non-stationary processes
When modeling nonstationary processes in continuous media by means of parabolic differential equations, we often encounter situations when the coefficient providing the connection between the left and right parts of the equation is described as a function of a set of variables, including the states of the medium under study. The recovery of this dependence, as a rule, requires the solution of inverse coefficient problems based on known states of the medium. In practice, this means that the inverse problem is solved relying, among other things, on some discrepancy between model data and known observations. Nevertheless, there are cases when such observations are critically small in time, for example, measurements of the state of the medium occur with a certain very large time step or only at the end of a nonstationary process. In such cases, retrospective observations contain time moments when the state of the medium is unknown, which makes it impossible to determine the error gradient for them and to restore the desired functional dependence with acceptable accuracy. In this paper, we propose an alternative view of the problem of restoring continuum coefficients for situations when the known states of the medium are much smaller than the unknown ones. A continuous nonstationary process was considered as a discrete process evolving in time, and a recurrent function of discrete state change was proposed. Based on this function, a numerical method for interpolating the error gradient between the expected and actual states of the medium within any two known states was proposed. The process of recovery of discrete values of coefficients at separate moments of time by means of the stochastic gradient descent method was demonstrated on the basis of a numerical model of a generalized parabolic equation with an arbitrary external influence on the boundary.
- Tkacheva O. Behavior of trajectories of the development model of a cellular population system
The paper studies a mathematical model of the development of an "in vitro" cellular population system that includes two types of cells, healthy and diseased, such as cancer cells. The model allows one to describe various scenarios of cell behavior, including the degeneration of healthy cells into cancer cells. The model is represented by a second-order ODE system. The phase space of this system is a non-negative orthant, which must be taken into account when analyzing the behavior of this system. An analysis of constraints on the parameters of the system is presented. The paper completes the analysis of equilibrium positions, which was started in earlier works. Conditions are given for the parameters when the system has one, two, three or four equilibrium positions in a non-negative orthant. The condition for the transition of an equilibrium position from a state located inside the positive region to the coordinate axis is described. The conditions for the stability of equilibrium positions in some cases are considered. Phase portraits of the system are constructed for various parameters, illustrating cases of different numbers of equilibrium positions. For the system, using the method of localization of invariant compacts, boundaries for limited trajectories are found, conditions are determined when there is no cycle in the obtained localizing set.
- Imangazieva A. Control of a network of time-varying agents under conditions of parametric uncertainty and external disturbances
The structure of the control system for synchronisation of a network of identical agents under conditions of nonstationarity and parametric uncertainty of agent models is proposed. During synchronisation, it is required to ensure time-consistent behaviour of identical agents of the network taking into account external perturbations acting on each agent. In subsystems the scalar output of the leading agent is monitored, the agents are independent. Scalar inputs and outputs of agents are available for measurement. To solve the set network problem, controlling laws are built in each agent based on the auxiliary loop method, which is based on the principle of dynamic compensation. Signals carrying information negatively affecting the regulation of the subsystem are formed in advance, and then their compensation is carried out. In each agent, information about the derivatives of the intermediate signals is required, for which Khalil observers are used. To illustrate the performance of the proposed synchronisation system, we consider a numerical example of controlling a network object consisting of four agents, each of which is subject to external disturbances of different amplitude. Modelling in MATLAB Simulink has been carried out. The simulation results confirmed the theoretical conclusions and showed good performance of the synchronisation system under conditions of uncertainty and non-stationarity of the network agents' models.
- Khliustov D. Modelling induced polarization effect in frequency domain aem data
Airborne electromagnetics is one of the most widespread methods of geophyysical survey. In the process of exploration airplane obtains data on electromagnetic response of the medium to the signal of controlled electromagnetic source. Often it is possible to create a simple model of the medium, havin real-valued apparent resistivities. However, sometimes data are significantly impacted by the induced polarizzation effect. It manifests itself in dependence of apparent resistivity on signal frequency. The classical approach to modelling IP consists in using a frequency dependent resistivity model for each layer of the medium. However, the number of parameters in this approach increases rapidly with resolution, hence the inversion problem becomes incorrect. The lack of unique solution of inverse problem leads to the final result of data interpretation being dependent on starting model and prior information.In this work authors suggest an approach to solving this problem, which is applied for inversion of real data. It is shown that sometimes the starting model may be chosen based on analysis of responses obtained for a part of data close to the one containing IP.
- Pechnikov A. Journal intersection graph: definition, modifications and a meaningful example
Bibliometric networks are defined by the relationships between publications and/or their authors, implemented on the basis of lists of co-authors and bibliographic lists. The mathematical models of such networks, which allow us to explore the communities of scientists and the connections between their works, are the corresponding bibliographic graphs. The paper defines a new type of bibliographic graph, the graph of journal intersections, based on the well–known binary operation of intersection of sets. The sets here are the sets of authors: the author belongs to the set of authors of the journal, if he has publications in this journal. The vertices of the intersection graph are journals, and connections between them arise if the intersections of the corresponding sets of authors are non-empty. Two modifications of the graph of journal intersections are proposed, taking into account the power of a subset of intersections and the similarity of sets of authors determined using the Jacquard coefficient. Data from 20 leading Russian mathematical journals are used as an example of the construction and study of the journal intersection graph and its modifications. As a result of the analysis, some results were obtained (the "closeness" or "openness" of the communities of authors and journals; a high correlation between the PageRank of graph vertices and the SCIENCE INDEX of journals in eLibrary), allowing a slightly different look at traditional approaches to ranking scientific journals used to assess scientific performance. The directions of further experimental and theoretical research are determined.
- Khomutov D. Latent consensus protocol with weak background links and time-delay
Coordination in multiagent system with information influences and time-delay is considered. In particular, the case when consensus is not achieved for any vector of initial values was considered. Such a problem may arise in a multi-agent system with a weakly coupled structure, that is, when there are several leading agents or groups of agents. To achieve consensus, a latent consensus protocol with weak background links and time-delay was used. Using the Nyquist criterion applied by Tsypkin, a boundary value of time-delay was established, depending on the spectral properties of the Laplace matrix, and a condition for the independence of convergence from time-delay. With a decrease in the weights of background links, the boundary value of time-delay of the protocol under consideration approaches the one of the required protocol. It was found that in the case of convergence, the latent consensus protocol with background links converges to consensus for any vector of initial values, while the weights of background links can be arbitrarily small. Thus, the use of this protocol solves the above problem, and this study allows adapting other previously considered latent consensus protocols for multiagent systems with time-delay.
- Volkov A., Roslyakova N. Assessment of the effectiveness of regulatory instruments for the development of the Russian Arctic regions: experience of sociological research
The article is devoted to the study of aspects of the elaboration and effectiveness of business support measures in the territories of the Arctic zone of Russia. The specifics of the work are determined by unique data obtained as a result of expeditionary research in 2024 and the use of a semi-structured interview technique. The study sample included 18 business representatives and 18 representatives of local administrations – 3 experts from each Arctic district or region of the Komi Republic and the Nenets Autonomous Okrug. Analytical processing of the data was carried out using a methodological approach based on statistical (comparative and average estimates) and non-parametric (rating, Kendall concordance coefficient, Mann-Whitney criterion, Spearman rank correlation coefficient) analysis. The approach allows us to consistently identify the consistency of expert opinions on the assessment of individual aspects and problems, substantiate the significance of differences in assessments between government and business representatives, and measure their consistency in the case of solidarity of opinions. The aspects of the development of support measures according to the criteria of completeness of available information, simplicity of the registration procedure, speed of receipt, qualification of specialists and the total volume of support and benefit have been identified. The specifics of the implementation of support measures at the local, regional and federal levels have been established. The most developed and effective are the regional measures. Among the key problems at the municipal and regional levels, the procedure for registration of documents stands out, at the federal level - the volume of support. A rating of the effectiveness of the most used incentive measures has been compiled. Possible reasons for differences in the territorial features of their effectiveness have been identified, and corresponding recommendations for their improvement have been given.
- Komanich N., Chernov I. Scenario technologies in group regional management
This work is devoted to the application of scenario analysis technologies to study the problems of improving the management efficiency of ensuring stable and balanced development of regions in conditions of uncertainty and risks associated with the destructive impact of various threats. The novelty of the study lies in the use of a scenario approach to developing a regional management strategy, which is based on group management technologies that combine the principles of centralization and decentralization, public-private partnership and coordination. The proposed approach allows us to analyze the situation developing in regional systems and justify the need to transfer the decision-making center, as well as the redistribution of functions and powers between administrative and economic management entities of different levels of hierarchy, each of which has its own unique capabilities and vulnerabilities. Strategic management in such a model is carried out using a scenario-forecasting approach, which allows us to identify negative trends in regional development, including those arising as a result of external influences. A simulation model of group regional management has been developed based on the mathematical apparatus of signed oriented graphs. The study resulted in the developed scenarios of regional development, the analysis of which showed that in the conditions of increasing threats the most effective strategy is to transfer the control center to a state entity based on scenario-forecast monitoring. At the same time, it is necessary to use the principles of coordinating management and stimulation, as well as the principle of partnership to prevent contradictions in socio-economic processes within the regional system. In safe and favorable conditions, support for economic entities, as well as management of stability and balance of regional development and ensuring its security should be carried out mainly in a decentralized manner, under the control of regional management entities, the entrepreneurial sector and private business.
- Patlasov D. Forecasting the realized volatility based on information extracted from the ross recovery theorem
This article discusses an approach to predicting the realized volatility of the S&P 500 index using data extracted from options due to the Ross recovery theorem. The purpose of this study is to investigate the possibility of using the indicators obtained after applying the Ross recovery theorem as exogenous factors in the forecasting model of realized volatility of financial instruments. The methodology used to achieve the research objective eliminates the need to use historical quotations of financial assets, focusing solely on options. The paper compares the accuracy of forecasting realized volatility between the proposed models and the basic HAR-RV approach. Empirical results have shown that the proposed approach provides a higher accuracy of predictions. The approach used in the Ross recovery theorem based on the approximation of the distribution density function of the underlying option asset allows for more accurate consideration of market participants' expectations and their risk preferences, which can become statistically significant factors in forecasting models of various financial indicators. The results of the study can be used to assess systematic risk, predict the likelihood of corrections and crises in financial markets.
- Shcherbak A., Ovchinnikov P., Pogorelova L., Savelchev P. Maximizing savings in financial resources as a result of balancing the assembly line at discrete engineering enterprises
The article discusses the issues of calculating the amount of financial resources released, as well as achieving maximum economic effect by setting a mathematical optimization problem with a rational combination of parameters regulating the flow of production processes in the assembly plant. The methodological basis of the research consists of theoretical and practical data on the organization of assembly production, the economics of the enterprise, and mathematical methods for solving optimization problems. Within the framework of the study, tasks were implemented to analyze the functioning of the assembly production line; the directions that determine the release of financial resources as a result of measures to optimize the production process were identified, and recommendations were developed for the formation of a universal methodology for calculating the total economic effect when balancing the assembly production line, the optimization task was formulated, aimed at maximizing the economic effect when rational selection of controlled parameters of the assembly line operation. The general management approach to balancing the assembly line is given. As a result of balancing the assembly line, the production cycle is leveled, which, in turn, ensures: firstly, a reduction in the level of interoperable gaps as a result of interfacing technological operations for production capacity, and secondly, it helps to shorten the production cycle of manufacturing products.
- Poleshchenko D., Korenev A. Development and efficiency analysis of slag criteria during steel casting
Currently, one of the key tasks in industry is to ensure high production efficiency, also in the steel industry. One of the unsolved problems in this area in the process of continuous casting of steel is the determination of the moment when slag begins to enter the intermediate ladle when pouring metal from the ladle. A comparative analysis of methods of early slag detection shows that currently there is no highly effective slag cut-off system. In this paper, in order to solve the problem of early slag detection, the vibration method was used due to the high informativeness of the vibration acceleration signal. Two methods of analyzing the vibration acceleration signal of the protective tube manipulator were tested for timely slag cutoff and preventing its entering into the intermediate ladle. Analysis of the results of testing showed that the best efficiency, equal to one hundred percent, was provided by the approach based on the analysis of the power spectrum of the vibration acceleration signal together with the data on the weight of the melting. Slag cutoff criteria based on discrete wavelet analysis worked in 67 percent of cases, which demonstrates their performance and gives grounds for more thorough research of this method in order to increase its efficiency.
- Makarov M., Morozov Y. Features of constructing a smoothed trajectory in the presence of a large number of trajectory points
The article presents a method for smoothing the trajectory obtained using high-frequency data on the movement of motor vehicles over rough terrain in order to improve the accuracy and smoothness of trajectories in the presence of noise. The main attention is paid to the features of the application of quintic B-splines, which provide a high degree of smoothness in describing the trajectory and preliminary data filtering. The article consistently describes the technical and mathematical difficulties that arise when implementing the algorithm on real data, and suggests methods for overcoming them. One of such methods is filtering outliers to eliminate sharp deviations from the original trajectory using a digital Butterworth filter. Various approaches for working with a large number of trajectory points are considered and tested, including splitting the data into separate overlapping windows with their sequential stitching, which significantly improves the performance of the algorithm. To optimize the calculations, it is also proposed to use sparse matrices that effectively work with large amounts of data and occupy significantly less computer memory compared to traditional ones. The effectiveness of the proposed approach is confirmed by examples where smoothed trajectories obtained from noisy data are visualized.
- Moscowsky A. Scene recognition for the mobile robot global localization problem based on image vectorization and graphs approaches
The paper is devoted to the problem of localization of mobile robots based on visual semantic data. The central element of such a problem is scene recognition task, i.e. searching for a correspondence between observed objects and objects on a semantic map. Paper proposes two methods based on definition of geometric features in the observed scene and searching for them on the map using various graph approaches. The proposed method for determining the relationships between objects, used in both methods, allows taking into account the errors in estimating distances by onboard sensors. In addition to using geometric features, the paper also considers the use of neural network models forming a feature vector based on an image, determining their visual similarity. Visual similarity is used to evaluate and sort the results obtained by the proposed methods based on graph approaches. In addition, the open KITTI-360 dataset was modified to evaluate the accuracy of solving scene recognition problems. Experiments on the resulting dataset demonstrated that the proposed approach, which combines geometric features and visual similarity, significantly increases the accuracy of the considered scene recognition methods. Based on the results of the experiments, some recommendations were formulated for the use of these approaches in practice.
- Tretiakova E. Experience of applying relative positioning algorithms in the electromagnetic field of two dipoles
The solution of the problem of relative positioning of the alternating magnetic field transmitter and the receiver is to determine the radius vector between the objects under consideration and their mutual orientation. In this paper, determining the mutual spatial location and orientation of two objects in an electromagnetic field problem is set. The relevance is due to the need to improve the accuracy and reliability of the airborne electrical exploration results, especially in the presence of induced interference. The method of electromagnetic field source and receiver relative positioning in the field of two dipoles in a three-dimensional formulation is considered. Two stages are implemented: determining the source-receiver radius vector and their mutual orientation. A technique for calibrating the field source magnetic moments, which is necessary for applying the algorithms, is given. Experimental data of a new airborne electrical exploration system were processed. The results obtained for different positioning algorithms are compared: GNSS solution, two-dimensional electromagnetic positioning in the field of two dipoles, three-dimensional electromagnetic positioning in the field of two dipoles. The possibility of using the obtained solution to improve the quality of the obtained data is analyzed, namely, to control the uncertain nature residual induced interference after the standard compensation method. The study results show that the use of three-dimensional electromagnetic positioning in the two dipoles field allows determining the objects relative position with an accuracy not inferior to the standard GNSS solution, and in the future to deal with the issue of interference, which leads to an improvement in the quality of airborne electrical exploration data.
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