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Editor-in-Chief

**Nikiforov**

Vladimir O.

D.Sc., Prof.

Vladimir O.

D.Sc., Prof.

Partners

**Summaries of the Issue**

### OPTICAL ENGINEERING

Designing a side-emitting lens using

the composing method

Romanova Galina Eduardovna, Xuanlin Qiao, Vladimir E. Strigalev 147

The paper considers a design method for a side-emitting lens working with a single LED source and providing a narrow light beam in the horizontal direction within 360°. The authors deal with the composing method in the design, which is usually used to synthesize the initial scheme of the imaging systems. However, in this case, a similar approach is applied to the synthesis of a system, the task of which is to provide a certain shape and characteristics of the light beam. The stage of choosing an initial principal design and synthesis for non-imaging optics is especially important since this area is characterized by the use of so-called local optimization, the result of which strongly depends on the original system. Therefore, the stage of forming an initial approximation of the system becomes crucial. In this case, the composing method can provide the most effective choice of an initial scheme of a side-emitting lens. The application of the composing method and the theory of aberrations in the field of synthesis of the initial design of a side-emitting lens is shown. The paper describes a method for selecting the key parameters of the system, and presents the relationships that allow a preliminary evaluation of the characteristics of the designed system without the use of time-consuming calculation or optimization procedures. The presented approach makes it possible to ensure the choice of the initial point of the system for further optimization, as well as to achieve high efficiency of using the light flux by the optical system of the lens (up to 90 %), only due to the optimal size of the zones into which the beam is divided and to the optimal parameters of the generating curves. In this case, the lens profile is formed by two zones in each the profile is a conic curve, hence, the curve can be described by a small number of parameters, which is very convenient at the stage of searching the initial scheme. The proposed approach can be applied in the design of such systems, as well as applied at the stage of preliminary assessment of achievable characteristics, which can significantly speed up the development process.

Laser multiparameter method for incoming inspection of the mounting elements used in the volume of sealed neodymium laser emitters

Belikov Andrei , Klochkov Ivan S. , Alekseev Ivan V. , Kapralov Sergey A. 154

The paper investigates the parameters of the deposition zones as a result of laser radiation effect on the surface of an optical element. For the research, conditions have been created to simulate the inner space of a laser emitter, which contains various mounting elements. The possibilities of using mounting elements in the volume of sealed neodymium laser emitters during their operation have been determined. The authors developed a novel installation, which includes a YAG:Nd laser with a wavelength of 1064 nm, a laser pulse energy of 100 mJ, a laser pulse duration of 10-15 ns, a laser pulse repetition rate of 10 Hz, and a sealed test-cuvette with a mounting element inside it. When laser radiation passes through the space of the test-cuvette for 10 000 s, volatile substances released from the materials of the mounting element absorb the laser radiation and form a deposition zone on the optical elements of the test-cuvette. Optical, geometric, color parameters of these deposition zones and their resistance to the action of solvents are investigated. The work explored the ten mounting elements most frequently used for the manufacture of sealed neodymium laser emitters. It was determined that wires with fluoroplastic insulation, polyolefin heat-shrinkable tubing and indium foil do not create deposition zones on the surface of the optical elements of the test-cuvette. At the same time, it was found that wires with silicone and fluoropolymer insulation, tin-lead alloys (solders) with a tin content of 61 % with and without rosin, polyolefin heat-shrink tubing with an adhesive base and ceramic-polymer heat-conducting dielectric materials do create a deposition zone on the surface of the optical elements of the test-cuvette. Hence they cannot be used in the volume of sealed neodymium laser emitters during their operation. The results can be relevant for the development and manufacture of laser devices, as well as for assessing the possibility of placing mounting elements in the volume of sealed neodymium laser emitters.

Adaptive anti-thermal imaging protection for moving objects

Mikheev Sergei V., Novikov Igor A. 163

The paper provides a classification and outlines the current state of anti-thermal imaging protection of military equipment. Currently, improving the reliability of such objects in combat conditions is one of the key tasks. The authors carried out the analysis and considered the prospects for the development of existing systems of anti-thermal imaging protection for moving objects as an important factor in increasing their reliability. It has been shown that the most promising are active-type anti-thermal imaging protection systems. The paper proposes a way to improve the reliability of armored and other vehicles in modern conditions. As an example, an anti-thermal imaging protection system consisting of active cooling modules is considered for armored vehicles. It can operate in two modes: stealth and rapid supercooling of the object’s surface (“black hole”). During the operation of the anti-thermal imaging protection, the system uses controlled cooling of active modules with liquid nitrogen. A design is proposed and a method for calculating the parameters of active cooling modules is developed. The advantages of the developed anti-thermal imaging system for protecting the object are as follows: dual-mode operation of the system and the use of a pre-stored “cold” source, which makes it possible to eliminate the need for additional energy consumption during operation. The proposed system of modular active anti-thermal imaging protection can be used for different vehicles with appropriate adaptation to the object of the general design of the system and modification of the adjustable cooling active module.

### AUTOMATIC CONTROL AND ROBOTICS

The parametric convergence performance improvement in the direct adaptive multi-sinusoidal disturbance compensation problem

Marina M. Korotina, Stanislav V. Aranovskiy, Bobtsov Alexey Alexeevich, Lyamin Andrey Vladimirovich 172

The paper presents an approach to the parametric convergence performance improvement applied to the direct adaptive multi-sinusoidal disturbance compensation problem. The proposed method improves the performance of the existing solutions and ensures the transient monotonicity. The Dynamic Regressor Extension and Mixing (DREM) procedure followed by the discrete gradient estimator is applied for disturbance parameters estimation. The paper proves the applicability of Kreisselmeier’s scheme as an extension of the algorithm in procedure dynamic regressor extension. A numerical simulation is presented to illustrate the improvement of the transient processes of estimating the parameters of an unmeasured perturbation using the DREM procedure. The work can be used in solving practical problems in the fields of processing and evaluating harmonic and multi-harmonic signals, e.g., to suppress vibrations in electromechanical systems.

179

The review focuses on the development of theories of sensitivity and modal sensitivity, robustness and roughness of dynamic systems. In modern theory of dynamic systems and automatic control systems, there is a need to study the properties of sensitivity, robustness and roughness of systems in their interconnection. An import application of sensitivity theory is associated with the design and creation of high-precision and low-sensitivity systems. The most significant results were achieved in the development of differential methods for the analysis and synthesis of low-sensitivity systems. One approach to the analysis and synthesis of linear systems of low parametric sensitivity in the space of states was developed using the functions of modal sensitivity or, in other words, the method of modal sensitivity. A review of robustness theory considers methods of studying and ensuring the robust stability of interval dynamical systems, paying attention to both algebraic and frequency directions of robust stability. The work presents the main results of the original algebraic method of robust stability of interval dynamical systems for continuous and discrete time. The section “Basic development stages of the theory of roughness of systems” describes the main principles of the theory and method of topological roughness of dynamical systems, based on the concept of roughness according to Andronov–Pontryagin. Applications of the topological roughness method to synergetic systems and chaos have been used to investigate many systems, such as the Lorenz and Rössler attractors, the Belousov–Zhabotinsky, Chua, predator-prey, Hopf bifurcation, Schumpeter and Caldor economic systems, etc. The review proposes applying the approach of analogies of theoretical-multiple topology and the abstract method for studying weakly formalized and informal systems. Further research suggests the development of theories of sensitivity, robustness, roughness and bifurcation for complex nonlinear dynamic

### MATERIAL SCIENCE AND NANOTECHNOLOGIES

Numerical simulation of functional characteristics of solar elements InGaAsN/Si

Oleg V. Devitsky, Sanakulov Sohibjon O. 191

For the ﬁrst time, numerical simulation and optimization of the current-voltage characteristics of a fundamentally new single-junction solar cell based on the InxGa1–xAs1–yNy/Si heterostructure were carried out. The integration of multicomponent layers A3B5 and dilute nitrides A3B5N with silicon substrates is currently a technologically complex process. Despite the complexity of this integration, there are certain prerequisites that may make it possible to obtain InxGa1–xAs1–yNy layers with a relatively low defect density. The InxGa1–xAs1–yNy solid solution is quite promising for use in optoelectronics, but at the same time it is poorly studied. Numerical modeling was carried out using the AFORS HET v2.5 software product. When numerically calculating the parameters of the solar cell In0.02Ga0.98As1–yNy/Si, we obtained the following data: the nitrogen concentration y varied in the range from 0 to 5 %; the thickness of the In0.02Ga0.98As1–yNy layer varied within 0,3–0,8 μm; the degree of doping of the base and the emitter of the SC varied in the range 1016–8·1019 cm–3. The dependences of the current-voltage and spectral characteristics on the thickness and composition of the emitter, as well as the degree of doping of the layers were investigated. It is shown that solar cells consisting of the In0.02Ga0.98As0.98N0.02/Si heterojunction can achieve an efﬁciency of 22.2 % under illumination AM1.5. Modeling the effect of nitrogen concentration on the efﬁciency of solar cells showed that a change in nitrogen concentration from 0 to 5 % in the In0.02Ga0.98As1–yNy layer leads to a decrease in the efﬁciency of 21.9 % to 21.82 %, respectively. This fact is primarily due to a decrease in the value of the energy gap of the emitter and, as a consequence, to a decrease in the value of the open circuit voltage of the solar cell. It was found that an increase in the impurity concentration in the In0.02Ga0.98As0.98N0.02 emitter in the range 1016–8·1019 cm–3 leads to an increase in the solar cell efﬁciency from 17.11 % to 21.89 %, respectively. With an increase in the impurity concentration in the p-Si base in the range from 1016–5·1017 cm–3, a steady increase in efﬁciency is observed up to 22.2 %, and then a monotonic decrease to 10.87 % at an impurity concentration of 5·1017 cm–3. With a decrease in the emitter thickness, the quantum efﬁciency of a solar cell increases due to a decrease in the number of photogenerated charge carriers. As a result of numerical simulation in the AFORS HET v2.5 software product, it was determined that the open-circuit voltage of solar cells based on the n-In0.02Ga0.98As0.98N0.02/p-Si heterostructure is 716.8 mV, at a short-circuit current density of 36.52 mA/cm2, ﬁll factor equal to 84.81 % and efﬁciency equal to 22.2 %.

Solgel synthesis of Gd

Moussaoui Amir , Bulyga Dmitry V. , Natalia K. Kuzmenko, Ignatiev Alexander I , Sergei K. Evstropiev, Nikonorov Nikolay V. _{2}O_{3}:Nd^{3+}nanopowders and the study of their luminescent properties198

The paper presents the results of the sol-gel synthesis of Gd2O3:Nd3+ nanopowders by the citrate method, as well as the study of their structure and luminescent properties. A technique for using two different organic stabilizers with different thermal stability in sol-gel synthesis has been proposed and tested. The luminescent properties of the obtained Gd2O3:Nd3+ powders have been studied in the ultraviolet and near infrared spectral regions. The citrate sol-gel method was used to synthesize the materials. Aqueous solutions of metal nitrates were used as the main initial components. Citric acid and polyvinylpyrrolidone were used as organic modifying components, playing a double role in the synthesis process, i.e. acting as stabilizers of forming nanoparticles in colloidal solutions and serving as a fuel additive in the process of heat treatment of materials. Infrared spectroscopy and differential thermal and thermogravimetric analyses were used to study the evolution of the structure of materials during synthesis. Crystalline Gd2O3:Nd3+ nanopowders were obtained by a low-temperature sol-gel method using citric acid and polyvinylpyrrolidone as stabilizers. The data of infrared spectroscopy and differential thermal and thermogravimetric analyses show that the formation of Gd2O3:Nd3+ nanoparticles begins at the stage of the crude gel and the evolution process develops during the drying and heat treatment of materials. It is shown that the use of two different organic stabilizers with different thermal stability provides stabilization of the forming Gd2O3:Nd3+ nanoparticles at different stages of synthesis in a wide temperature range. The luminescence spectra are observed in the UV spectral region under excitation of the synthesized nanopowders by radiation with a wavelength of 238 nm. They are determined by electronic transitions in the Gd2O3 crystalline matrix. The synthesized Gd2O3:Nd3+ nanopowders exhibit intense photoluminescence in the UV and near-IR spectral regions. The results can be used in the development of a technology for the synthesis of various composite phosphors, as well as in the creation of luminescent nanopowders for nanothermometry in medicine.

### COMPUTER SCIENCE

Detection of a small target object in blurry images affected by affine distortions

Andrey V. Timofeev 206

The paper proposes a novel and practically effective method for detecting, classifying, and estimating the coordinates of the image center of a small-size target object on a noisy scene, which is invariant to linear conformal transformations (rotation, shift, and scale). We consider a binary classifier that decides whether a particular part of the scene contains the desired image or only the background. The proposed approach implies an interactive procedure for finding an extremum of a function that approximates the likelihood function of the binary classifier. A two-step procedure based on the Nelder-Meade method is used to implement the extremum search. In order to ensure the robustness to noise and linear conformal transformations, both special training methods and the approach based on using an ensemble of classifiers, each of which corresponds to a certain scale, are applied in training the classifier. The author created a method for detecting a blurred image of a small-sized object in a scene that is distorted by correlated noise and proposes simultaneous estimation of the coordinates of the center of the target image. The method is robust to linear conformal distortions and has been successfully tested both on the artificial model and real images. The results of numerical study confirmed the robustness of the method to correlated noise of additive type and to linear conformal transformations. Within the framework of the proposed approach, the problem of constructing a confidence set for the coordinates of the target image center has been formally solved, and the efficiency of the obtained solution has been numerically investigated. The properties of the confidence set are formalized in the form of a theorem. The work also makes a comparison with the classical correlation-extreme method. If necessary, the proposed method can be easily generalized to the multiclass case. The method can be applied to machine vision systems, including online analysis of aerial survey data and to systems for video monitoring of the mechanical condition of complex technical equipment under conditions of strong meteorological disturbance.

An information system for spatial visualization of prognostic and retrospective data on the probability of observing auroras

Vorobev Andrei V. , Vorobeva Gulnara R. , Khristodulo Olga I. 225

The paper presents the results of the development of an open-access web-based system operating in predictive and retrospective modes and providing the user with an interactive tool for monitoring spatial data using the example of visualizing the probability of observing aurora borealis. The work proposes an algorithm for web rendering of spatial images, which provides an increase in the reactivity of web applications due to the formation of a rendered layer on the server side, in contrast to the known approaches solving the problem of interpolation and generation of a spatial layer at the client level. The paper describes the architecture of the information system whose distinctive feature is the combination of various patterns of web programming, i.e. from a monolithic application to a microservice one with elements of a modular architecture of the “model–view–controller” type. The experimental studies allowed establishing an increase in the rendering speed of a spatial image by an average of 8.1 times. The results of the studies have shown that the considered approach to visualization as applied to the geophysical parameters in the region of the auroral oval will provide an increase in the efficiency of studying the dynamics of the auroral oval, which will help to reveal new knowledge regarding the topology of the magnetosphere and its changes, for example, during geomagnetic storms and substorms.

Applying bagging in finding network traffic anomalies

Rzayev Babyr T. , Lebedev Ilya S 234

The authors consider approaches to solving the problem of identifying anomalous situations in information and telecommunication systems, based on artificial intelligence methods that analyze the statistical information on traffic packets in various modes and states. We propose a method for detecting an anomalous situation based on the obtained tuples of values of network traffic packets by applying bagging classifying algorithms of machine learning. The network traffic is treated as a set of tuples of packet parameters, distributed over sample time. In contrast to the existing ones, the method does not require special data preparation; the errors in the classification of tuples of package values by individual classification algorithms are averaged by “collective” voting of the classifying algorithms. The given solution to the increase of the accuracy index makes it possible to use the classifying algorithms optimized for different types of events and anomalies, trained on various training samples in the form of tuples of network packet parameters. The difference between the algorithms is achieved by introducing an imbalance to the training sets. We describe an experiment conducted by using Naïve Bayes, Hoeffding Tree, J48, Random Forest, Random Tree and REP Tree classification algorithms of machine learning. The evaluation was performed on the open NSL-KDD dataset while searching for parasitic traffic. The paper presents the results of evaluation for each classifier individually and with bagging classifying algorithms. The method can be used in information security monitoring systems to analyze network traffic. The peculiarity of the proposed solution is the possibility of scaling and combining it by adding new classifying algorithms of machine learning. In the future, in the course of operation, it is possible to make changes in the composition of the classifying algorithms, which will improve the accuracy of the identification of potential destructive impact.

An analysis of the ways to reduce the vulnerability of networks based on the sequential removal of key elements

Semenov Kirill V. , Fedor L. Shuvaev, Vitenzon Kirill I. 241

The research focuses on the metrics that allow assessing the stability of a graph and centrality measures. Their calculation underlies the percolation of the key elements of the graph. The experiment involved methods for calculating the average path length of vertex connectivity, clustering coefficient, and graph efficiency based on graph theory. To determine the optimal network stability metric, the principal component method was used, based on the theoretical provisions of mathematical statistics. In this study, the authors solved two scientific tasks: the main and auxiliary ones. The latter was to review the existing network stability metrics, which allowed them to choose the optimal one. The choice of the metrics was carried out using the principal component method. As a result, the average path length proved to be optimal. The solution of the auxiliary problem enabled the authors to analyze the ways to reduce the network stability based on the sequential removal of key elements, which is the main scientific task of the study. The analysis revealed that the nodes whose importance is expressed based on the measurement of centrality by degree are best suited for reducing the network stability. To estimate the stability of networks, an original complex two-criterion coefficient was developed. The analysis of the ways to reduce the stability was carried out by measuring this coefficient in model and real networks. Thus, testing of the proposed methods confirmed their efficiency and enabled their application in various fields of science and technology, e.g., sociology, medicine, physics and radio engineering.

The robust distributed ledger model for a multidimensional blockchain security analysis

Shilov Ilya M. , Zakoldaev Danil A. 249

The paper considers the problem of constructing a model of the robust distributed ledger for security proof of a multidimensional blockchain. Several requirements for the model are imposed, among which most important are compatibility with existing models and presence of functionalities for external transactions. The authors present an approach to extending existing models based on the analysis of these solutions, their advantages and disadvantages. The model construction is based on universal composability framework. Two models are proposed: a model of the robust distributed ledger and a model of the search and verification protocol. These are meant to be used in security proofs for scaling and registration in a multidimensional blockchain. The proposed model of the robust distributed ledger is an extension of models used in security proofs for consensus mechanisms: proof of work and proof of stake. It duplicates their functions and additionally maintains external transactions. The model of the search and verification protocol implements ideal functionality used for external transaction verification. The results prove that the proposed model does not damage essential security parameters of the robust distributed ledger in presence of external transactions. The study confirms the compatibility of the proposed models with existing analogues implementing robust distributed ledgers. This fact allows using the universal composability theorem for constructing security proofs of multidimensional blockchain and search and verification protocol. The proposed method of extending existing models for security proofs can be used to create new models with additional functions not implemented for security proof of a multidimensional blockchain.

Building knowledge graphs of regulatory documentation based on semantic modeling and automatic term extraction

Mouromtsev Dmitry I, Shilin Ivan A., Pliukhin Dmitrii A. , Baimuratov Ildar R. , Rezeda R. Khaydarova, Dementyeva Yulia Yu. , Ozhigin Denis A. , Malysheva Tatiana A. 256

The paper proposes a new complex solution for automatic analysis and terms identification in regulatory and technical documentation (RTD). The task of terms identification in the documentation is one of the key issues in the digitalization dealing with the design and construction of buildings and structures. At the moment, the search and verification of RTD requirements is performed manually, which entails a significant number of errors. Automation of such tasks will significantly improve the quality of computer-aided design. The developed algorithm is based on such methods of natural language analysis as tokenization, search for lemmas and stems, analysis of stop words and word embeddings applied to tokens and phrases, part-of-speech tagging, syntactic annotation, etc. The experiments on the automatic extraction of terms from regulatory documents have shown great prospects of the proposed algorithm and its application for building knowledge graphs in the design domain. The recognition accuracy for 202 documents selected by experts was 79 % for the coincidence of names and 37 % for the coincidence of term identifiers. This is a comparable result with the known approaches to solving this problem. The results of the work can be used in computer-aided design systems based on Building information modeling (BIM) models, as well as to automate the examination of design documentation.

### MODELING AND SIMULATION

Influence of the temperature factor on the deformation properties of polymer filaments and films

Victoria V. Golovina , Pavel P. Rymkevich , Shakhova Ekaterina A. , Olga B. Prishchepenok 267

The paper presents a study of the deformation properties of polymer materials. The authors consider the effect of the temperature factor, unaccounted for previously in modeling and forecasting, on the deformation properties of polymer filaments and the influence of changes in material temperature during deformation. The derivations of the main thermodynamic functions for polymer materials are given. The work examines the energy diagram typical for polymers that shrink. An explanation is given for the “dormancy” of the recovery process, as well as for the identical values of the highly elastic deformation when the load is removed during the recovery process in polymer threads and films. Based on the equation of condition for polymer filament and the well-known thermodynamic identities, the following basic thermodynamic functions were determined: internal energy, enthalpy and entropy depending on temperature and dimensionless stress. The cases of application of the first law of thermodynamics to deformation processes are examined. From the standpoint of thermodynamics, the main models of deformation are considered, i.e. creep, stress relaxation and active stretching of polymer filaments and films. Explanations are given for some of the phenomena observed experimentally in course of these processes. It was concluded that it is necessary to take into account the change in local temperature. Based on the model on the equation of condition for polymer filament and the analogue of the Clapeyron-Clausius equation, an expression for the temperature coefficient of material pressure is obtained. The work enabled to explain the “dormancy” of the recovery process of polymer and to determine the basic thermodynamic functions for a polymer material which take into account the material temperature change during deformation. The thermodynamic coefficient for the polytropic process is obtained. The described temperature coefficient makes it possible to analyze the tensile diagrams depending on the strain rate and the temperature change rate of the sample. The highly elastic part of deformation in thermodynamic function is expressed through the elastic deformation determined by the mechanical stress, which can be measured directly during the experiment.

A one-step optimization method for a compressor wheel of a microturbine engine

Bulat Mikhail P., Чернышов М. В., Vokin Leonid O. , Kurnukhin Anton A. 275

The work deals with the design acceleration of optimal turbomachines. For its solution, it is proposed to apply mathematical optimization methods at the initial design stage. The goal of the study was to develop a one-step algorithm for optimal compressor wheel design. The application of the algorithm has a decisive advantage in comparison to the traditional iterative method for turbomachines design. The task of designing a turbomachine is multi-parameter and interdisciplinary and involves different requirements, which often contradict each other, consequently several optimality criteria can be used simultaneously. The traditional method consists in performing one-dimensional thermal and gas-dynamic calculations with subsequent refinement using numerical study. Further fine-tuning of the wheel geometry includes variation of the blade angle at the exit from the impeller, as well as of the height of the flow path at the exit from the wheel. One-step global optimization was performed by using a particle swarm algorithm involving eleven variable parameters. The objective function is thermodynamic efficiency, calculated by stagnation parameters. The authors compare the results of calculating the geometry of the centrifugal compressor wheel by the traditional sequential method and by the newly developed global optimization method. The compressor wheel has an outer diameter of 200 mm, the diameter of the hub is 52 mm, the rotational speed is 60,000 rpm and the required compression ratio is 3.7. In the traditional optimization method, the blade angles and the profile thickness are varied in three or four blade cross sections. The novelty of the developed one-step algorithm consists in the optimization of the initially three-dimensional shape of the flow path. Testing has shown that the one-step global optimization method provides an efficiency gain of about 2 %. Compared to the traditional method, the required time decreased 6 to 18 times. The proposed method can be applied to the design of turbomachines of various dimensions. The developed algorithm can be used as a basis for external modules in various existing packages, such as Ansys, Comsol and SolidWorks.

The influence of viscosity and turbulence on the supersonic flow compression and expansion corner

Volkov Konstantin N., Ilina Ekaterina E., Volobuev Igor A. 283

Super- and hypersonic flow around aircraft elements is accompanied by the formation of a complex flow structure, which is characterized by the presence of strong shock waves, rarefaction waves, contact discontinuities, separation and reattachment of the flow. For such problems, the interaction of shock waves with viscous boundary layers is characteristic. Such interaction is quite complex and largely determines the effectiveness of aircraft. When flowing around complex structures of aircraft and their power plants in the vicinity of convex corner points of the geometry, compression and expansion flows are locally realized. The calculation of oblique shock waves, formed when flowing around the compression angle, and simple expansion waves, formed around the flowing angle of expansion, is included as an element of solving many problems of constructing streamlines and finding the pressure distribution on the streamlined surface. Based on the technology of adaptive meshes, a numerical model is proposed for studying two-dimensional effects arising from supersonic flow around the angles of compression and expansion. Numerical simulation was performed using various models such as inviscid, laminar or turbulent. In the calculations, the Mach number of the incident shock wave varies from 2 to 15, and the flow angle varies from 5 to 15 degrees. The Reynolds number, calculated from the characteristics of the unperturbed flow, is equal to 105. The working gas is air (γ = 1.4). A qualitative picture of the flow during diffraction of a shock wave on steps of different geometry is considered. When the shock wave interacts with the compression angle, flow separation and the formation of a recirculation region are observed, and when the shock wave interacts with the expansion angle, the Prandtl–Mayer wave is misaligned. The results of calculations are compared with theoretical data on the parameters of the flow behind the shock front or fan of the rarefaction wave. Studies have shown the influence of the effects of viscosity and turbulence on the flow structure and distribution of flow characteristics when flowing around the angles of compression and expansion. The simulation results can find application in solving problems related to the design of air intakes of high-speed flying aircrafts, in particular, in parametric and optimization calculations of gas-dynamic flows that arise in the elements of propulsion systems of supersonic and hypersonic aircraft.

Modeling the relationship between the hardness and wear resistance of materials during their comparative testing by the “block-on-ring” method

Leonid V. Efremov, Tikalov Andrey V. 297

The authors propose a novel model accounting for the hardness of materials in a simplified algorithm in order to evaluate their wear resistance by the “block-on-ring” method during tests on a friction machine. This work is relevant for the study of the factors influencing wear and continues to improve this method based on the Taylor series and the testing results for a number of materials in a wide range of hardness. The problem is solved by correlation analysis of the dependence of the hardness of materials on the Mohs scale on the experimental wear parameters, including the volumetric wear resistance of these materials. A complete software that has been developed implements a simplified version of the “block-on-ring” method for wear testing of materials, taking into account their hardness. The high correctness and efficiency of the proposed model is confirmed by the increasing hardness of a polytetrafluoroethylene composite filled with ultrafine diamond. Practical significance. The model of the relationship between the wear resistance and the hardness of materials proposed and justified in the paper is ready for use in their tests by the “block-on-ring” method in production conditions.

Application of a short-pulse ultra-wideband probing signal for estimating reflective characteristics

Samoilenko Marina V. 303

The paper presents a method developed for processing coherent short-pulse ultra-wideband signals reflected from a certain control zone, which makes it possible to evaluate the distribution of reflective characteristics over this zone. To implement the method, we used a plurality of integral type receiving sensors and one source of probing coherent short-pulse ultra-wideband signals that irradiates the area of responsibility. The solution to estimating the distribution of reflective characteristics over the control zone is based on the principles of multichannel tomography. This approach implies formulating the mapping equation and its further solution. An essential factor influencing the solution to this problem is the nonstationarity of the probing signal. Taking this factor into account, we developed a method derive an extended mapping equation, which allows one to estimate the distribution of reflection characteristics when using non-stationary probing signals. The work investigated three methods for estimating the distribution of reflective characteristics by the extended mapping equation, namely: Wiener estimation, pseudo-inversion method, and matrix-iterative method. The dependences of estimation errors on measurement errors were obtained in computer experiments for various degrees of filling the control zone with reflective elements. The Wiener estimation and the matrix-iterative method yielded the best results. The developed mathematical model of the propagation of the probing signal shows the effect of changing the shape of the probing pulses when they are reflected from the control zone. The obtained results make it possible to study the distribution of reflective characteristics in space using non-stationary ultra-wideband probing signals.