Journal archive

The results of the development of a software microservice embedded in atmospheric air quality monitoring systems to support the identification of industrial pollution sources are presented. The emission and subsequent spread of harmful substances in the lower layers of the atmosphere is dynamic and characterized by high uncertainty due to the specific features of technological installations, their operating modes, the influence of terrain relief, buildings and meteorological factors. The relationship between the location of the emission source and the information from sensors installed in central areas of the city or on the boundaries of sanitary protection zones of large industrial facilities cannot be described analytically, Therefore, formalizing the knowledge of environmentalists and subsequently automating the detection of objects responsible for the formation of hazardous concentration levels at control points is a pressing task. The aim of the study is to develop an algorithm for the continuous optimization of search strategies using Approximate Dynamic Programming technology. This article proposes implementing the ADP mechanism based on Q-Learning, which in turn is performed in simulation mode through interaction with the Lagrange model describing the physical processes of pollution dispersion. The developed model learns to select the best search steps (actions) on a marked map of the terrain, considering the cost function approximated by a neural network, meteorological factors and terrain relief, which is a new technological solution. The design of basic information processes was carried out, including the consideration of processes for collecting and pre-processing data on the measurement of harmful substance concentrations and meteorological data at control points, the preparation of a table for Q-Learning and its use for training a neural network model, and the application of the model to solve the problem of determining the source of an emergency release. The results of experimental testing showed that the microservice developed and integrated into the digital ecomonitoring platform accurately captures the characteristics of industrial pollution dispersion processes in the atmosphere and can be used for automated identification of emission sources in dynamics. The average values of the contribution of the emergency release source to the formation of pollution in a given territory differ from the values calculated using the UPRZA example by no more than 15%, which allows us to conclude that the results are highly reliable and can be compared with GOST methods that operate in static conditions.

The research is devoted to the development of an algorithm for applying the quaternion formalism to the modeling of the dynamics of exoskeletons and similar anthropomorphic mechanisms, such as robots, space suits, simulators, and related systems. The fundamental problem of developing exoskeletons, anthropomorphic mechanisms, and robotic systems is being investigated, which requires accelerating the process of analytical construction of mathematical models described by differential equations. To tackle this problem, the authors propose the use of hypercomplex number algebra, specifically quaternions. The application of quaternion algebra to the study of locomotion in anthropoid robotic devices such as exoskeletons with active propulsion systems that control the relative positions of the joints during movement should improve the construction of the mathematical model. These arguments determine the relevance of the research topic and the scientific novelty of the study. The development of high-speed methods for writing differential equations of motion based on quaternion algebra to describe the locomotion of spatial mechanical anthropoid systems determines the practical significance of the research results. The work presents a method for constructing an algorithm to model the dynamics of the shank of an exoskeleton, represented as a link connected by a spherical joint allowing rotation with respect to a fixed reference frame. The proposed mechanical model has been implemented as a program within the universal computer algebra system Wolfram Mathematica. The program is designed for simulating the dynamics of the exoskeleton link. Since the system does not provide built-in functions for working with analytically defined quaternions, the authors developed the required routines themselves. The program consists of several modules: a module for quaternion operations; a module for transformation matrices (used for validation and debugging of the quaternion module); a module for the automated formulation of the Lagrange equations of the second kind; a module for specifying the programmed motion of the model and computing the control torques in the joints; a module for numerically solving the Cauchy problem; and a module for animation and visualization of the model’s motion as well as for exporting the graphical results of the numerical simulations. The program’s results allow for the analysis of the dynamics of a mathematical model of a system based on the solution of the direct and inverse dynamics problem, and can be recommended for the design of exoskeletons, anthropomorphic robots, and manipulators with a programmable operating mode.

Предложена многофакторная вероятностная модель продажи товара на электронной торговой площадке (маркетплейсе), позволяющая рассчитать зависимость таких ключевых показателей эффективности продаж, как объем продаж и выручка продавцов, от временных характеристик надежности товара: фактического срока службы, гарантированного (установленного производителем) срока службы и ожидаемого (желаемого потребителем) срока службы товара. Предполагалось, что товара на маркетплейсе неограниченно много и, кроме того, каждый потребитель приобретает только одну его единицу, выбирая продавца в пределах окна покупательских возможностей по минимальной цене. Показано, что объем продаж и выручка от продажи товара являются случайными величинами, математические ожидания которых, а также их законы распределения можно представить в виде функционалов от распределений вероятностей вышеперечисленных характеристик надежности товара. В рамках предложенной вероятностной модели продажи товара выведены формулы для этих функционалов. В частном случае, когда сроки службы товара не зависят от цены, а сама цена описывается одно- или двухпараметрическим показательным законом распределения, получены математические выражения для законов распределения и начальных моментов количества проданного товара и выручки продавцов. Проведен анализ зависимости математических ожиданий объема продаж и выручки от среднего фактического, среднего гарантированного и среднего ожидаемого сроков службы товара. В качестве примера, учитывающего влияние ценозависимости сроков службы товара на объем продаж, выручку и прибыль, рассмотрена продажа смартфонов на маркетплейсе «Яндекс. Маркет». На основе эмпирических данных установлена зависимость от цены отношения гарантированного срока службы к фактическому, и с ее помощью проведено численное моделирование, раскрывающее влияние параметров, входящих в законы распределения сроков службы, на средний объем продаж смартфонов и среднюю прибыль от их продажи.

A promising way to ensure the competitiveness of industrial products is to improve the energy efficiency of technological processes by reducing fuel and energy consumption. For energy-intensive production such as a chemical-engineering system for processing ore beneficiation waste, this task boils down to optimizing the operating modes of conveyor roasting machines that thermally prepare the raw material for remelting. The high computational complexity of the problem, caused by the extensive set of controlled process line parameters and the polyfractional nature of the ore raw material, limits the applicability of analytical methods. It is proposed to use a nature-inspired method based on the principles of social behavior in cockroach colonies. Its specific has led to the following modifications to the basic Cockroach Swarm Optimization. Firstly, a multicolony approach, which involves considering a multi-layered arrangement of dispersed ore components of different sizes within a single colony, is used to narrow the search space. Secondly, to improve the algorithm’s convergence rate, it is proposed to introduce elements of fuzzy set theory into it to determine the “free” parameters (the “perception” distance, which defines the maximum distance from the best solutions; the step size of agent movement within the search space toward the best solutions). The developed fuzzy multicolony method was implemented as a computer program using Python. The results of computational experiments demonstrated the convergence of the proposed method for optimizing the operating modes of a conveyor roaster, and a comparison with its standard operating mode demonstrated its potential for use in controlling the chemical-engineering process of thermally preparing polyfractional ore raw materials for remelting.

The article examines a game-theoretic model describing the interaction between two firms selling identical products, a classic duopoly model. The model expresses competition between the firms, as the players’ objective functions express their utility (profit) and are mutually inconsistent, i. e., a noncooperative, zero-sum game is considered. The players’ objective functions are formed based on the linear inverse demand function for the product and the linear cost functions of the participating firms. The solution to the game is a Nash equilibrium, determined using a system of first-order necessary optimality conditions. Unlike the classical approach, the model incorporates two new aspects. First, players are considered reflexive, meaning each player hypothesizes the counterparty’s likely response, which is formally expressed as a conjectural variation – the expected change in one player’s output in response to a single increase in the output of the other. Second, an aggregative game in a duopoly model, in which the players’ objective functions are interdependent, is analyzed from the perspective of controlling the behavior of one player by manipulating their mental representations of the other player’s intentions. The analysis of the game is based on a reflexive model of player behavior, in which players sequentially predict each other’s representations, resulting in the identification of a mental model of one player that is optimal from the perspective of the other player. An iterative procedure is proposed for inducing this mental model in the controlled player by creating phantom instances of the controlling player. Numerical experiments illustrate various aspects of the mental control process, whereby the technical characteristics of the player firms, such as their production volumes, interact with the mental behavioral parameters of decision makers, forming a cyber-physical system.

An effective way to ensure the required level of structural secrecy of code sequences used in wireless data transmission systems with multiple access and code division multiplexing is to employ a representative set of code sequence structures that can be changed according to a specific rule. A variant of increasing the structural secrecy of code sequences used in the telecommunication systems under consideration is to employ the necessary arsenal of non-repeating ensembles of multiphase orthogonal code sequences modeled by the eigenvectors of a Hermitian matrix. In known works, the functional relationship between the diagonal coefficients of a tridiagonal Hermitian matrix and the systems of its eigenvectors modeling ensembles of multiphase orthogonal code sequences has not previously been established. This precluded the demonstration of a strict deterministic relationship between the pseudo-random assignment of the phases of the diagonal coefficients of a Hermitian matrix and the properties of its eigenvectors, which determines the relevance of this study. This article proves the existence of a functional relationship between the coefficients of a Hermitian matrix and the system of its eigenvectors. It is shown that the pseudorandom uniform distribution law of the phase values of the coefficients of the second diagonal of Hermitian matrices, with constant values of their moduli, is preserved for the arguments (phases) of the coordinates of the eigenvector systems of the matrices under consideration, based on estimates by the Wald – Wolfowitz criteria, chi-square, and Welch t-criterion. Based on the analysis of the conducted experiment, it was established that the spectrum of the Hermitian matrix does not change with a pseudorandom change in the phases of its diagonal coefficients using the Mersenne Twister pseudorandom number generator with fixed values of the moduli of its diagonal coefficients. Analytical and experimental proof of the relationship between the arguments of the diagonal coefficients of a tridiagonal Hermitian matrix and the arguments of the coordinates of its eigenvector systems, considered as models of ensembles of multiphase orthogonal code sequences, shows that the statistical properties of the latter are determined by the statistical properties of the pseudorandom number generator that specifies the initial data for the stochastic transformation. A conclusion is made about the independence of the spectrum of the Hermitian matrix from the pseudo-random assignment of phase values to its diagonal coefficients with constant values of their moduli.