Accuracy of identification of the state of the internal combustion engine with the customized model using the measuring expert system

Рассмотрены вопросы уменьшения погрешности идентификации технического состояния двигателя внутреннего сгорания и его составных частей как объекта экспертизы путем настраивания параметров применяемой в измерительной экспертной системе виртуальной модели ДВС. Для настройки модели предложено применение градиентного метода, обеспечивающего наиболее быструю минимизацию погрешности идентификации Purpose and methods. Improving the accuracy of identification for the technical condition of the internal combustion engine (ICE) in operational conditions using the engine measurement expert system (EMSE) is addressed by adjusting the computer dynamic model of the internal combustion engine. Results. Algorithmic schemes of computer models for the state of the ICE are obtained using the equations of its dynamics, which takes into account the factors such as the movement of the fuel supply body, the force on the hook - the load. The structural schemes of modeling at the input of a step-by-step action are presented. A promising method of tuning the model in the EMSE is proposed, which consists of measuring its working processes, in particular the angular acceleration of the crankshaft, for a specific brand of ICE. Then the corresponding set of models of its technical condition is obtained: normal, permissible, limit, pre-accident and emergency. By adjusting the values of the coefficients of these models in the EMSE, they achieve their coincidence with the actual state of the ICE. The identification error is minimized using the gradient method of steepest descent. The presence of several computer models is a practical advantage in the examination of the technical condition of the tested engines allowing its effective implementation in operational conditions. In this case, based on the experience of operation, the computer model closest to the actual state of the ICE is adjusted. At the same time, the efficiency of localization of ICE malfunctions increases, since the coefficients reflecting the state of the engine components and systems are consistently adjusted. Conclusions. The application of the proposed methodology using the criterion of minimizing the identification error by the gradient method allows implementation of this effective method for identifying the state of the ICE. It increases the reliability of determining the technical state of the ICE and its components by adjusting the computer model

Modelling of energy consumption in sociotechnical systems with intelligent equipment

Современные социотехнические системы в различных областях характеризуются наличием в их составе большого количества интеллектуального оборудования, которое может самостоятельно регулировать собственное потребление энергии, а также взаимодействовать с другими потребителями в процессах принятия решений и управления. Одна из таких отраслей - энергетика, где самоорганизация и системы коллективного потребления являются наиболее перспективными с точки зрения обеспечения эффективности использования энергоресурсов. Рассмотрены подходы к установлению статических и динамических тарифов на электроэнергию. Проведено сравнение двух моделей энергопотребления - статического двухтарифного и динамического, учитывающих рациональное поведение умных устройств, способных выбирать лучшие режимы для потребления электроэнергии. Показано влияние количества таких устройств на возможность достижения равномерного потребления при использовании второй модели. Modern socio-technical systems in various fields include a large number of smart equipment that can independently regulate its own energy consumption, as well as interact with other consumers in decision-making and management processes. Energy is one of these areas. Self-organization and collective self-consumption are the most promising in terms of ensuring the efficiency of energy use. Existing and prospective approaches to using static and dynamic time-based tariffs are under consideration. The paper presents a mathematical description of two models of energy consumption: a static model based on the allocation of two zones with a fixed duration and tariffs for each one and a dynamic model of two-tariff accounting with feedback, which assumes tariffs changing based on the results of the analysis of current electricity consumption. A pilot study of both models was conducted by using energy consumption data and taking into account the rational behavior of smart devices as consumers who can choose the best periods for electricity consumption. During the experiments it was investigated how an increase in the share of smart devices in the composition of electricity consumers as well as options for establishing zones and tariffs, affect the possibility of achieving uniform consumption during the day. Experiments have shown that with a small proportion of smart devices, acceptable results that reduce the variation in the consumption function can favor usage of the model without feedback. An increase in the number of actors in the system inevitably requires including a feedback mechanism into the system that allows the resource supplier to prevent excessive concentration of smart devices during the period of the cheaper tariff. However, when the share of smart devices exceeds a certain critical value, a pronounced inversion of the times of cheap and expensive tariffs occurs in two successive iterations. In this case, in order to ensure a quite even distribution of electricity consumption, it is advisable for the supplier to return to the single tariff rate. Thus, an excessive increase in the number of actors in the system can neutralize the effect of their use

Mathematical modelling for the functioning of the p53 signaling pathway following DNA damage. I. The model of activation of the p53-Mdm2-Wip1 system

Работа посвящена численному исследованию известной математической модели динамики системы p53-Mdm2-Wip1 при различных воздействиях, приводящих к повреждениям ДНК. Главное внимание уделено ранее не рассматривавшимся методическим аспектам - оценке чувствительности модели, качественному анализу свойств решения в биологически адекватном диапазоне значений параметров, анализу применимости модели к описанию критических состояний системы, связанных с известными дегенеративными заболеваниями. Показано, что простейшая модификация исходной модели делает ее существенно более эффективным инструментом для численного анализа широкого диапазона состояний системы p53-Mdm2-Wip1 In the context of the survival and death of cells with DNA damage, a special role is assigned to the p53 protein. The management of p53 and its inhibitors can provide a protective effect in a wide range of degenerative diseases, such as cancer, infarctions, and dementia. Therefore, there are increased requirements for mathematical models designed to study the mechanism of functioning of the p53 signaling pathway. Our work is devoted to the study of the properties of the well-known mathematical model of the dynamics of the p53-Mdm2-Wip1 system under various influences leading to DNA damage. A simple modification of the model is proposed. The main attention is paid to the analysis of the sensitivity and qualitative properties of solutions, as well as the validation of the model before and after its modification. In numerical experiments, it was found that within the framework of the accepted models, the stationary state of the p53-Mdm2-Wip1 system can be unstable to negligible changes in the initial conditions, so that the system can function under the same parameter values according to the bifurcation scenario with a doubling of the period. The mathematical conditions under which the multiplicity of solutions and complex dynamic modes were detected allow for a biological interpretation as a reflection of the variability in the response of the p53 protein pathway to the damage signal. The range of applicability of the models was compared using the example of a wellknown laboratory experiment, in which the most complete set of observed in vitro and in vivo states of the p53-Wip1 system was demonstrated when irradiating cancer cells with wild-type p53. It is shown that the simplest modification of the original model significantly expands the scope of its applicability, allows describing the transition from normal to critical states of the system associated with known degenerative diseases. Thus, the modified model is a more effective tool for numerical analysis of a wide range of states of the p53-Mdm2-Wip1 system

On the efficiency of high-order difference schemes for the Schro¨dinger equation

Исследуется ряд двух- и трехслойных разностных схем, построенных на расширенных шаблонах, до восьмого порядка точности для уравнения Шрёдингера. Наряду с многоточечными схемами рассматривается метод коррекции Ричардсона в приложении к схеме четвертого порядка аппроксимации, повышающий порядок точности путем построения линейных комбинаций приближенных решений, полученных на различных вложенных сетках. Проведено сравнение методов по устойчивости, сложности реализации алгоритмов и объему вычислений, необходимых для достижения заданной точности. На основе теоретического анализа и численных экспериментов выявлены методы, наиболее эффективные для практического применения The efficiency of difference methods for solving problems of nonlinear wave optics is largely determined by the order of accuracy. Schemes up to the fourth order of accuracy have the traditional architecture of three-point stencils and standard conditions for the application of algorithms. However, a further increase in the order in the general case is associated with the need to expand the stencils using multipoint difference approximations of the derivatives. The use of such schemes forces formulating additional boundary conditions, which are not present in the differential problem, and leads to the need to invert the matrices of the strip structure, which are different from the traditional tridiagonal ones. An exception is the Richardson correction method, which is aimed at increasing the order of accuracy by constructing special linear combinations of approximate solutions obtained on various nested grids according to traditional structure schemes. This method does not require the formulation of additional boundary conditions and inversion of strip matrices. In this paper, we consider several explicit and implicit multipoint difference schemes up to the eighth order of accuracy for the Schr¨odinger equation. In addition, a simple and double Richardson correction method is also investigated in relation to the classical fourth-order scheme. A simple correction raises the order to sixth and a double correction to eighth. This large collection of schemes is theoretically compared in terms of their properties such as the order of approximation, stability, the complexity of the implementation of a numerical algorithm, and the amount of arithmetic operations required to achieve a given accuracy. The theoretical analysis is supplemented by numerical experiments on the selected test problem. The main conclusion drawn from the research results is that of all the considered schemes, the Richardson-corrected scheme is the most preferable in terms of the investigated properties

Approaches to discrete optimization problems with interval objective function

В работе дается обзор подходов к решению задач дискретной оптимизации с интервальной целевой функцией. Эти подходы рассматриваются в общем контексте исследований оптимизационных задач с неопределенностями в постановках. Приводятся варианты концепций оптимальности решений для задач дискретной оптимизации с интервальной целевой функцией - робастные решения, множества решений, оптимальных по Парето, слабые и сильные оптимальные решения, объединенные множества решений и др. Оценивается предпочтительность выбора той или иной концепции оптимальности при решении задач и отмечаются ограничения для применения использующих их подходов Optimization problems with uncertainties in their input data have been investigated by many researchers in different directions. There are a lot of sources of the uncertainties in the input data for applied problems. Inaccurate measurements and variability of the parameters with time are some of such sources. The interval of possible values of uncertain parameter is the natural and the only possible way to represent the uncertainty for a wide share of applied problems. We consider discrete optimization problems with interval uncertainties in their objective functions. The purpose of the paper is to provide an overview of the investigations in this field. The overview is given in the overall context of the researches of optimization problems with uncertainties. We review the interval approaches for the discrete optimization problem with interval objective function. The approaches we consider operate with the interval values and are focused on obtaining possible solutions or certain sets of the solutions that are optimal according to some concepts of optimality that are used by the approaches. We consider the different concepts of optimality: robust solutions, the Pareto sets, weak and strong solutions, the united solution sets, the sets of possible approximate solutions that correspond to possible values of uncertain parameters. All the approaches we consider allow absence of information on probabilistic distribution on intervals of possible values of parameters, though some of them may use the information to evaluate the probabilities of possible solutions, the distribution on the interval of possible objective function values for the solutions, etc. We assess the possibilities and limitations of the considered approaches

Numerical solution of the gas compression problem at a specified law of action

Выполнено численное моделирование одномерных течений политропного газа, описывающее сжатие покоящегося газа с плотностью 1 в покоящийся газ, сжатый до значения 10. Описываемое сжатие происходит без ударных волн эффективным с точки зрения энерговложения способом, так как энергия тратится только на сжатие газа, но не на его разгон Controlled thermonuclear fusion (CTF) is an almost unlimited source of energy and scientists have been studying it for several decades. This requires an efficient and stable compression of diyterium-tritium fuel to a very high density. This work addresses shockless one-dimensional (plane, cylindrical and spherical symmetry cases) “compression from rest to rest”, when gas from the initial resting state under the influence of an impenetrable piston is shocklessly transferred to a resting homogeneous state, but compressed by 10000 times. This compression is energetically most advantageous, because work is spent only on the compression, but not on the gas acceleration. Earlier [10] this problem was solved in the opposite direction of time change. In this case, a density jump occurs on the piston which was taken into account in calculations [3] at the final moment of compression. The numerical solution of this problem in the opposite direction of time variation allows calculating the trajectory of the compressing piston in the form of a set of points ( t,r ) at which the gas velocity and density are determined. In this paper, the problem of shockless “compression from rest to rest” is numerically solved in the forward direction of time change if the compressing piston trajectory is known. The compression piston moves along a monotonous trajectory away from the axis or center of symmetry. It is important, when calculating in forward direction of time change, no internal characteristics are initially entered. They, like all gas flow in the calculation area, are determined in the process of direct calculation. This indicates that the trajectory of compressing piston is the recommendation for appropriate physical experiments

Digital pattern of safety of a territory

Современные технологии получения и обработки данных приводят к формированию новых представлений и концепций управления рисками и безопасностью территориального развития промышленных регионов. В работе предложено определение цифрового паспорта безопасности территорий, сформулированы требования к его структуре. Показана актуальность интеграции данных мониторинга за состоянием окружающей среды, контроля объектов техносферы и характеристик социосферы. Концепция цифрового паспорта безопасности территории увязывает виды рисков, характеризующие их показатели, информационное обеспечение показателей рисков с параметрами управления территорией. Разработаны информационно-аналитические модели, консолидирующие данные комплексного мониторинга, средства динамического картографирования и вебвизуализации. Выполнена систематизация мероприятий снижения рисков и смягчения последствий чрезвычайных ситуаций, позволяющая определить стратегические направления управления безопасностью с учетом физико-географических и социально-экономических характеристик территорий. Показаны возможные реализации паспорта безопасности в виде цифровых двойников с учетом мультимодальности информационных потоков Modern technologies for obtaining and processing data lead to new concepts of risk management and safety for territorial development in industrial regions. This paper formulated the definition of “Digital Pattern of Territory Safety” (DPTS) and his structure requirements. The need to create a DSPT is due to the complexity of the tasks of territorial administration, the presence of a large amount of heterogeneous data, the potential of modern intellectual technologies of analysis. The issues of monitoring data integration for the environmental state, control of technosphere objects and characteristics of the social sphere are urgent. The content of a common information space of territorial administration should be determined by the structure of indicators DPTS. The concept of a digital passport of territory safety links types of risks, indicators of their characteristics, information support of indicators with parameters of territory management. The analytical models that consolidate complex monitoring data, dynamic mapping and web visualization were developed for DPTS. Determination of strategic directions for safety territories management, taking into account for their physical-geographical and socio-economic characteristics is based on the systematization of measures to reduce risks. This article provides the examples of using the indicators of Digital Patterns to assess and manage the social, natural and technogenic risks for the systems. The implementations of the safety data sheet in the form of digital twins are possible taking into account the multimodality of information flows

Automated generation of turbulence shell models by the methods of computer algebra

Описана разработанная методика генерации уравнений каскадных моделей турбулентности с помощью систем компьютерной алгебры. Методика позволяет варьировать размер масштабной нелокальности модели, вид квадратичных законов сохранения и спектральных законов, знаменатель геометрической прогрессии масштабов. Ее использование позволяет быстро и безошибочно генерировать целые классы моделей. Может использоваться для разработки каскадных моделей гидродинамических, магнитогидродинамических и конвективных турбулентных систем. There is a great variety of shell turbulence models. Such models reproduce certain characteristics of turbulence. A model that could reproduce all turbulence regimes does not exist at the moment. Information about a particular model is contained in a set of persistent quantities, which are some quadratic forms of turbulent fields. These quadratic forms should be formal analogs of the exact conserved quantities. It is important to note that the main idea of Shell models presupposes a refusal to describe the geometric structure of movements. At the same time, it is well known that turbulent processes in spaces of two and three dimensions behave differently. Therefore, the provision of certain combinations of conserved quantities allows indirect introducing into the shell model the information about the dimension of the physical space in which the turbulent process develops. Purpose. The aim of this work was to create software tools that would quickly generate classes of models that satisfy one or another set of conservation laws. The choice of a specific model within these classes can then be specified using additional physical considerations, for example, the existence of a given probability distribution for the interaction of certain shells. Methods. The developed technique for generating equations of shell turbulence models is carried out using symbolic computation systems (computer algebra systems - CAS). Note that symbolic packages are used not for studying ready-made shell models, but for the automated generation of the equations of these models themselves. The technique allows varying the value of the scale nonlocality of the model, the form of the quadratic conservation laws and spectral laws, the denominator of the geometric progression of scales. It allows quickly and accurately generating the entire set of classes of the models. It can be used to develop shell models of hydrodynamic, magnetohydrodynamic and convective turbulent systems. Findings. It seems that the proposed technique will be useful for studying the properties of turbulence in the framework of cascade models

The role of urban development in the formation of a “heat island”

Для оценки роли городской застройки в формировании “острова тепла” и исследования его влияния на распространение загрязняющих веществ разработана микромасштабная математическая модель городской среды. В качестве модельной задачи рассматривалось локальное влияние городской застройки микрорайона г. Красноярска. Установлено, что наибольший вклад в формирование “острова тепла” вносят наружные стены зданий и их верхние конструкции - крыши. При учете теплообмена наблюдаются рост средней скорости воздушного потока внутри квартала и уменьшение низкоскоростных областей более чем на 0.5 м/с. Также выявлено, что при учете теплообмена наблюдается заброс загрязняющих веществ, поступающих от дороги, на б´ольшую высоту, чем без него. Разработанная математическая модель позволяет комплексно подойти к исследованию гидродинамики и прогнозированию экологической обстановки урбанизированных территорий Introduction. The configuration of modern micro districts leads to the formation of zones with low velocity, in which the accumulation of pollutants occurs. On the other hand, during the construction of cities, the surface of the Earth is covered with materials that actively absorb solar radiation, which leads to the formation of an urban heat island. Our work is devoted to the study of the local influence of urban development on the spread of pollutants, which takes into account the above mentioned factors. Mathematical model. For solving our problems we developed the microscale mathematical model based on the Reynolds-averaged Navier-Stokes equations for incompressible flows with variable density. For the correct calculation of the temperature on the surface of buildings, we used a model of conjugate heat transfer with a one-dimensional equation of thermal conductivity. As a model problem, we considered the Krasnoyarsk area with dense development and the presence of a highrise building for two seasons: winter and summer. The source of emission of pollutants was traffic. Results. The results of the calculations show a significant decrease in velocity around buildings. On the contrary, solar radiation leads to the intensification of free convective motion, especially in the surface area. That can double the near-surface velocity compared to the solution that does not account for the heat transfer. Conclusions. The developed mathematical model allows a comprehensive approach to solving hydrodynamic problems of prediction the ecological situation of cities

Generalized staircase model of electrochemical impedance of pores in supercapacitor electrodes

Представлена новая обобщенная лестничная модель электрохимического импеданса для пористых материалов электродов в устройствах хранения энергии. Дано краткое описание существующих моделей межфазного импеданса и их ограничений. Новая модель основана на общепринятой “лестничной” модели импеданса цилиндрических пор. Однако новая модель учитывает сложную пористую структуру электродных материалов. В частности, модель описывает импеданс электродов с иерархической пористой разветвленной структурой, в которой широкие поры разветвляются в более узкие. Новая модель позволяет вычислить импеданс межфазной границы электрод/электролит в присутствии как нефарадеевских, так и фарадеевских процессов. Модель успешно опробована для пор с простой геометрией, для которых существуют точные решения. Изучено влияние структурных параметров модельных пористых электродов на их характеристики работы в суперконденсаторах. Проанализировано влияние диаметра пор, величины расширения начал пор и разветвления пор. Сформулированы критерии направленного дизайна электродных материалов для суперконденсаторов A new generalized staircase model of the electrochemical impedance is presented for porous electrode materials in energy storage devices. A brief overview on existing models of interfacial impedance and their limitations is given. The new model is based on the conventional staircase model of the impedance in cylindrical pores. However, the new model takes into account the complex porous structure of electrode materials. In particular, the impedance of hierarchical branching porous electrodes is described, i.e. the wide pores branching into the narrower pores. The new model allows to evaluate the impedance of the electrode/electrolyte interface in the presence of both non-faradaic and faradaic processes. The model is validated using the available exact solutions and experimental data for simple pore geometries. The influence of the parameters of structure of model porous electrodes on their performance in supercapacitors is studied. In particular, the influence of the diameter of the pores, width of pore openings, branching of pores is analyzed. The guideline for focused design of electrode materials of supercapacitors is outlined