No 2 (2022)
SEMI-EMPIRICAL MATHEMATICAL MODEL OF NITROGEN OXIDES EMISSION FROM LOW-EMISSION COMBUSTION CHAMBER AS A PART OF AUTOMATIC CONTROL SYSTEM OF AN AERO ENGINE
Abstract
The article is devoted to the problem of automatic control of nitrogen oxide emissions from a low-emission combustion chamber (LECC) of a gas turbine engines' (GTE) new generation. Since the measurement technologies have not reached the required level of availability today, and the reliability of the automatic control system (ACS) depends on the validity of input information about the engine state, it is proposed to use the built - in predictive mathematical model of the LECC. The model equations are functions of the measured parameters. The compact design requirements and significant nonlinearity of combustion determine the stochastic nature of the LECC. Taking into account the strict ICAO standards for the emission of harmful substances, all this leads to a narrow range of stable operating modes, limited, on the one hand, by the normalized level of nitrogen oxide emissions, and, on the other hand, by unacceptable modes of flame blowout or vibration combustion (thermoacoustic vibrations). It is proposed to build into the ACS a hybrid model of the processes of generating harmful emissions in the MEKS GTE, consisting two parts. The first semi-empirical submodel combines the physical equation of Zeldovich and the generalized empirical coefficient calculating as a function of several critical variables. This submodel allows generating training samples for the second submodel in case of insufficient experimental data. The second submodel is based on a neural network. The article discusses the development and testing of the first submodel, which identification algorithm is based on the accepted hypothesis of the possibility of applying the principle of superposition in describing the interaction of diffusion and homogeneous flames. The algorithm is based on the Zeldovich equation, which makes it possible to determine the dependence of the generation of nitrogen oxides on the composition of the air-fuel mixture using the distribution function of the probability density of its pulsations depending on the value of the integral equivalent ratio φ, which characterizes the concentration of fuel in the mixture. A feature of the LECC is the presence in the flame tube of longitudinal acoustic waves, excited by the release of heat during combustion, having a frequency equal to natural frequency of the gas-air column. These acoustic waves are leading to fluctuations of φ and causing the harmonic fluctuations in the mathematical expectation of the mixture composition. In this work the numerical modeling of the distribution of the inhomogeneity and pulsation of the fuel-air mixture concentration over the area of the flames in the CFX package allowed to obtain the characteristics of the mathematical expectations and dispersion, as well as the natural frequencies of the object. The distribution functions of the probability density of pulsations of the mixture concentration for diffusion and homogeneous circuits are calculated analytically, taking into account the acoustics of the combustion chamber. The analysis of the effect of dispersion of acoustic waves on the form of the resulting probability density curves in diffusion and homogeneous plumes is carried out.
Applied Mathematics and Control Sciences. 2022;(2):7-33
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CLASSIFICATION OF THE TECHNICAL CONDITION OF WATER PUMPING EQUIPMENT USING CONVOLUTIONAL NEURAL NETWORKS
Abstract
The problem of equipment repair management in water supply systems is considered. The purpose of the study is to study the issues of the possibility of classifying the technical condition of pumping equipment through the use of modern machine learning models. Classification is carried out on the data that were obtained by vibration diagnostics during the maintenance of pumping units. The initial data is converted into chalk spectrograms, the results of the conversion are presented as images. The model classifies time series according to one of three states: satisfactory, acceptable, not acceptable. Accuracy assessment is carried out by calculating indicators such as: precision, recall, F1-score. Since each class has a different number of measurements in the source data, the accuracy is determined by calculating each of the indicators for each class separately and then averaging them. Convolutional neural networks are used to classify images. To solve the problem, a network with a deep ResNet-50 architecture was chosen. The accuracy indicators that the network showed in other classification tasks and the speed of network learning determined the choice of this configuration. The average value of the precision indicator reaches 0.81, recall 0.90, and F1-score 0.85, which is a good result for the top-1 criterion. Classification of chalk spectrograms obtained from the initial data shows good results, despite the fact that the data has not been cleared of noise. The proposed methods and models have been tested on real data, which confirms the possibility of their use in the development of an intelligent information system for managing the technical condition of pumping equipment.
Applied Mathematics and Control Sciences. 2022;(2):37-53
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MINING MACHINE SIMULATION MODEL REFINEMENT ACCORDING TO THE ENGINES ENERGY CONSUMPTION DATA
Abstract
The importance of mining factories planning for ore extraction is indicated. The created simulation model with open and normative data is presented. Significant deviations of the simulation results from the real data of the mining machines monthly operating time of are shown. The goal is to refine the model with the available mining machine operation real data. As a source of data, it is proposed to use miming machines engines energy consumption. The source this information is described. Information about the mining machine engines is given. That information can be used for mining machines analyzing to determine the times of the states. There are 8 such engines in total, their sequential switching on and off allows us to understand the time of 4 technological operations that make the greatest contribution to the mining machines operating time. A fragment of the algorithm which allows to determine the operations time is given. Two combines were selected with the production differs most from the model in the direction of increase and decrease. For both combines the duration of ore breaking and ore loading from the storage hopper to the self-propelled car is determined. First, an analysis was made for the mining machine that breaks more ore than was obtained in the calculations. The analysis showed the existence of a previously undescribed state of the mining machine-simultaneous ore breaking into the storage hopper and ore loading from the storage hopper to a self-propelled car After including that state in the model, a new calculation was made. Calculation shows increasing in the model total output. In addition, analysis was made of the existing stochastic delay during ore breaking. Analysis shows that statistical distribution stochastic delay can corresponds to a negative binomial distribution. Further, the study of data for a mining machine with the producing less than the model amount was carried out. It allows to study the stochastic delay during ore loading. It is shown that such a delay can also correspond to a negative binomial distribution. The simultaneous inclusion of described delays significantly reduces the total estimated production amount. In conclusion, it is discussed that the simultaneous addition of a new state and stochastic delays with a negative binomial distribution to the model significantly reduces the modeling error.
Applied Mathematics and Control Sciences. 2022;(2):54-70
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FORMATION OF TNE METHODOLOGY OF STRATEGIC AND OPERATIONAL MANAGEMENT OF INDUSTRIAL ENTERPRISES IN THE CONDITIONS OF GLOBAL INSTABILITY
Abstract
The strong aggravation of military and political instability in the world, the introduction by the United States of America and other Western countries of a huge number of various and unjustified sanctions against Russia created very difficult conditions for doing business in our country's industrial enterprises. In this regard, the issues of forming a methodology for the strategic and operational management of industrial enterprises, which need to ensure survival and further development, despite the harmful effects of Western states and the most difficult problems with resource support for production, as well as sales of products outside the Russian Federation, are of particular importance. The article discusses the main directions of development of scientific thought in the field of strategic and operational management of industrial enterprises, including in modern conditions, characterized not only by the military-political aggravation of the situation in the world, but also in many respects related to these processes, the emergence of economic crises in the largest regions of America and Europe. The authors propose a new aggregated algorithm for managing industrial enterprises, both at the strategic and operational levels, based on mathematical models and methods, taking into account the characteristics of modern industry markets. It is also noted that the modern world economy is subject to cyclical phenomena due to the very nature of capitalist relations, and not only from the desire of the Western world to destroy Russia and its powerful industrial potential. The article also presents a number of mathematical models developed by the authors for assessing the production efficiency of industrial enterprises both for the options for the functioning of manufacturing companies in a stable environment and increased demand for enterprise products, and for their working conditions during periods of crisis. The most relevant today are the models of choosing strategic decisions in the context of the global crisis. Thus, the paper proposes a methodology for the preparation of managerial decision - making by the management of industrial enterprises, which ensures the minimization of costs for the production and sale of finished products, as well as the feasibility of technical re - equipment by enterprises in various periods of the functioning of the world economy. It is also reported how the proposed methodology for the strategic and operational management of industrial enterprises in the quite recent past allowed Russian manufacturing companies to achieve fairly high performance and competitiveness at the international level.
Applied Mathematics and Control Sciences. 2022;(2):73-94
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ASSESSMENT OF THE STATE OF SECURITY OF OBJECTS ON COMMUNICATIONS PROTECTED BY ROSGVARDIYA
Abstract
At the moment, there is an increase in the volume of tasks for the units of the Russian Guard for the protection of objects of varying degrees of importance, in particular objects on communications. Assessment of the effectiveness of the state of security of these facilities makes it possible to implement the right strategy for the distribution of forces and means, which will ensure the safety of the facility. The paper proposes a model for calculating the indicator of assessing the state of security of an object in communications based on expert survey data, which will assess the effectiveness of building a system of protection of a protected object. The developed model is supposed to be improved and based on it to create a methodology for evaluating the effectiveness of the use of units in the protection of objects in communications.
Applied Mathematics and Control Sciences. 2022;(2):95-108
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THE SYSTEM OF SUPPORT FOR THE DIDACTIC DESIGN OF ACADEMIC DISCIPLINES OF THE HUMANITIES AND SOCIO-ECONOMIC CYCLE
Abstract
The article presents a software package that allows to support the design of teaching materials by a teacher of disciplines of the humanities and socio-economic cycle. The problems of the organization of didactic design by a university teacher with the need to compile directly by an expert teacher supporting lecture notes and other methodological materials, including the need to select a number of literary sources taking into account their specifics for different educational tasks and types of educational activities, are presented. The problems of adaptation and development of methodological materials to changes in the ontology of the subject area are discussed, for example, in connection with changing trends in the scientific environment, when established positions are transformed, which creates a problem for the teacher to additionally engage in didactic design and adjust teaching materials. Thus, there is an urgency of automatic analysis of text materials, which will significantly reduce the complexity of this process when developing, making changes and adapting courses of humanitarian and socio-economic orientation. The step-by-step process of transition from the competence-oriented requirements of the subject area to the functional requirements of the information system is analyzed, on the basis of which a decision-making model was formulated that closely imitates the process of didactic design, subject to automation, and allows using software tools to control its logic. The results of the infological and physical design of the system are presented, including a database model and a deployment diagram using an object-oriented modeling language. Methods and tools of software implementation of the application are discussed with justification of the relevance of their choice for the software solution of the task. The results of the system's operation confirm its functional suitability, and the results of testing allow us to judge a significant reduction in the complexity of the didactic design process by the teacher. The developed tool can be widely used both in the development of educational and methodological materials of the main literature, and for the methodological equipment of the organization of independent work of students.
Applied Mathematics and Control Sciences. 2022;(2):109-123
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