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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

Selection of parameters of optoelectronic systems for monitoring the wear for steam turbine rotor blading based on the value of the total error

Rodikova Liliana S. , Korotaev Valery Viktorovich, Alexander N. Timofeev, Victoria A. Ryzhova, Anton Maraev, Mikheev Sergei V. 171

Optoelectronic wear monitoring system of rotor blades of steam turbine low-pressure cylinders provide an assessment of the chord value of the working blade in static conditions on a closed cylinder. However, these systems do not allow the operator to assess the wear with the necessary error during shaft rotation. The control process is complicated by the fact that the output edge of the blade is overlapped by the input edge of the next blade; therefore it is necessary to set a scanning direction for each section that will ensure the formation of blade video frames, including both the input and output edges. The shaft rotation mode requires the use of pulsed illumination of the edges of the working blades to reduce the amount of image smudge; therefore it is necessary to select the focal length of the camera lens, the diameter of the entrance pupil of the lens and the power of pulsed radiation sources. The development of a methodology for selecting system parameters will help to reduce the complexity of designing systems for various turbine models and application technologies. Therefore, this is an important task. A methodology has been developed for selecting the parameters of the wear control systems of the working blades, which is based on the criterion of equality of the main components of the total error of the chord value. The analytical studies used the relationship of the parameters of the matrix receiver of optical radiation, illumination sources and the optical circuit with the required characteristics of the system. Computer modeling of the information conversion process in the system under study took into account the relationship between the parameters of the moving blades and the parameters of the optical circuit. The experimental estimation of the system error in statics and dynamics is based on multiple measurements after calibration of the system according to known parameters of the blades. When using the developed methodology, it is possible to achieve the required field of view and a given error in controlling the chord value, due to the choice of: matrix optical radiation receiver, focal length of the camera lens, diameter of the lens entrance pupil, and power of radiation sources. Using the example of the fifth stage of the vane device of the K-1200 high unit power turbine, which is most susceptible to wear, it is shown that for maximum values of the rotation angles of the video probe is 19° and the delay time of frame synchronization is up to 0.18 s, the focal length of the camera lens should be less than 2.4 mm with a pulse illumination time of 0.05 s. Computer modeling has shown that the marginal error of the system can reach 0.011 mm, which illustrates the possibility of reducing the total error. Using the developed methodology, the main elements were selected and a layout of the system was created. The requirements for exposure time and delay time of frame synchronization are formulated. The effectiveness of the parameter selection methodology was confirmed by experimental studies of the system layout, which showed that the estimate of the standard deviation of the random component of the chord control error in dynamics was 0.26 mm, which is three times less than that of the previously developed system and meets the requirements for evaluating the operability of the rotor blades of steam turbines during operation and repair. The proposed technique can be used by developers of other optoelectronic means of contactless control of linear dimensions of parts oriented non-perpendicular to the line of sight.

Modeling and analysis of fractal transformation of distorted images of the Earth’s surface obtained by optoelectronic surveillance systems

Andrusenko Artyom S. , Grigor’ev Andrey N., Korshunov Denis S. 182

The results of a study of methods for processing optoelectronic images of the Earth’s surface are presented. The application of fractal transformations to solve the problems of automated and automatic analysis of terrain images, ensuring the separation of natural and anthropogenic objects without the use of machine learning, is shown. The analysis of existing works has shown the absence of studies linking the result of fractal transformation with the image quality recorded in real conditions of optoelectronic photography. There is no justification for choosing a specific fractal transformation for the applied processing of images with certain typical distortions. The purpose of this work was to identify the dependence of the signal-to-noise ratio of fractal dimension on the quality of the source images, to determine the type of fractal transformation that is most resistant to the effects of the considered negative factors. Methods of fractal transformations for thematic image processing are defined, which include the prism method and the differential cube counting method, and their description is presented. To study the selected methods, real images of the Earth’s surface were used, simulating distorted images of the terrain. Image distortions determined by the instability of shooting conditions and the properties of the optoelectronic complex are considered: defocusing, smudging and noise. The mathematical models used to describe them are summarized. A technique for analyzing the signal-to-noise ratio of fractal transformation is described, involving the processing of reference and distorted images of the terrain. The aspects of distortion modeling and indicators characterizing the level of image distortion are indicated. To implement the experiment, images of the area were selected characterized by various plots. For each plot, the dependences of the signal-to-noise ratio on the indicators characterizing the studied distortions are obtained. By estimating the signal-to- noise ratio, the analysis of the influence of distorting factors on the fractal dimension field being formed was performed. The results of the experiment confirmed the possibility of using fractal transformations for thematic processing of distorted optoelectronic images. It is shown that the dependence of the signal-to-noise ratio on the distortion index has a pronounced nonlinear character. It is established that for distortions of the defocusing and smearing type, the prism method is more stable, and in the presence of noise, the differential cube method is more stable. For processing images of an area represented mainly by images of forest vegetation, the best result is shown by using the differential cube counting method.

Fast labeling pipeline approach for a huge aerial sensed dataset

Fedulin Andrei M., Natalia V. Voloshina 190

Modern neural network technologies are actively used for Unmanned Aerial Vehicles (UAVs). Convolutional Neural Networks (CNN), are mostly used for object detection, classification, and tracking tasks, for example, for such objects as fires, deforestations, buildings, cars, or people. However, to improve effectiveness of CNNs it is necessary to perform their fine-tuning on new flight data periodically. Such training data should be labeled, which increases total CNN fine- tuning time. Nowadays, the common approach to decrease labeling time is to apply auto-labeling and labeled objects tracking. These approaches are not effective enough for labeling of 8 hours’ huge aerial sensed datasets that are common for long-endurance USVs. Thus, reducing data labeling time is an actual task nowadays. In this research, we propose a fast aerial data labeling pipeline especially for videos gathered by long-endurance UAVs cameras. The standard labeling pipeline was supplemented with several steps such as overlapped frames pruning, final labeling spreading over video frames. The other additional step is to calculate a Potential Information Value (PIV) for each frame as a cumulative estimation of frame anomality, frame quality, and auto-detected objects. Calculated PIVs are used than to sort out frames. As a result, an operator who labels video gets informative frames at the very beginning of the labeling process. The effectiveness of proposed approach was estimated on collected datasets of aerial sensed videos obtained by long-endurance UAVs. It was shown that it is possible to decrease labeling time by 50 % in average in comparison with other modern labeling tools. The percentage of average number of labeled objects was 80 %, with them being labeled for 40 % of total pre-ranged frames. Proposed approach allows us to decrease labeling time for a new long-endurance flight video data significantly. This makes it possible to speed up neural network fine-tuning process. As a result, it became possible to label new data during the inter-flight time that usually takes about two or three hours and is too short for other labeling instruments. Proposed approach is recommended to decrease UAVs operators working time and labeled dataset creating time that could positively influence on the time necessary for the fine-tuning a new effective CNN models.

### AUTOMATIC CONTROL AND ROBOTICS

Adaptive suboptimal control problem and its variational solution

Blazhenov Alexey V. , Vedyakov Alexei A., Ekaterina V. Milovanovich, Slita Olga V., Tertychny-Dauri Vladimir Yu. 198

A suboptimal cross-border problem is considered about nonlinear dynamic controlled systems under deterministic, uniformly bounded external unknown disturbances. The problem is solved by applying the methods of classical variations calculus for the case when the time interval of adaptation and optimization is not set in advance. The necessary conditions for the choice of extreme motion are determined due to the proper formation of a closed suboptimal adaptive control system. The theoretical analysis is supplemented with computer calculations using a specific model example, which showed effectiveness of the considered approach. The proposed scheme of suboptimal adaptive synthesis can be used in the calculations and design of nonlinear controlled dynamic systems.

Output control for a class of nonlinear systems based on dynamic linearization

Pyrkin Anton Alexandrovich, Minh Son Ta, Nguyen Quang Cuong, Golubev Anton K. 208

A dynamic system is considered where the regulating impact is the product of the control signal on the output variable of a linear dynamic system driven by the same applied control. The essence of the proposed method consists in the dynamic linearization of a nonlinear control operator, which makes it possible to guarantee a desired regulating impact. In a particular case, this approach corresponds to vector (field-oriented) control. It is shown that dynamic linearization based on the internal model method makes it possible to decompose a nonlinear system into a cascade of two subsystems. The proposed regulator consists of two blocks connected in series where the first block solves the problem of regulation with the Luenberger observer, and the second block compensates for a nonlinear dynamic operator. To demonstrate the effectiveness of the proposed approach, an example of numerical modeling of a neutrally stable plant with an output adaptive control is given. In practice, this method may be in demand in the tasks of controlling induction and synchronous motors and multi-link robotic manipulators.

### COMPUTER SCIENCE

RuPersonaChat: a dialog corpus for personalizing conversational agents

Apanasovich Kirill S., Makhnytkina Olesia V. , Vladimir I. Kabarov, Dalevskaya Olga P. 214

Personalization is one of the keyways to improve the performance of conversational agents. It improves the quality of user interaction with a conversational agent and increases user satisfaction by increasing the consistency and specificity of responses. The dialogue with the agent becomes more consistent, the inconsistency of responses is reduced, and the responses become more specific and interesting. Training and testing personalized conversational agents requires specific datasets containing facts about a persona and texts of persona’s dialogues where replicas use those facts. There are several datasets in English and Chinese containing an average of five facts about a persona where the dialogues are composed by crowdsourcing users who repeatedly imitate different personas. This paper proposes a methodology for collecting an original dataset containing an extended set of facts about a persona and natural dialogues between personas. The new RuPersonaChat dataset is based on three different recording scenarios: an interview, a short conversation, and a long conversation. This is the first dataset for dialogue agent personalization collected which includes both natural dialogues and extended persona’s descriptions. Additionally, in the dataset, the persona’s replicas are annotated with the facts about the persona from which they are generated. The methodology for collecting an original corpus of test data proposed in this paper allows for testing language models for various tasks within the framework of personalized dialogue agent development. The collected dataset includes 139 dialogues and 2608 replicas. This dataset was used to test answer and question generation models and the best results were obtained using the Gpt3-large model (perplexity is equal to 15.7). The dataset can be used to test the personalized dialogue agents’ ability to talk about themselves to the interlocutor, to communicate with the interlocutor utilizing phatic speech and taking into account the extended context when communicating with the user.

An optimized deep learning method for software defect prediction using Whale Optimization Algorithm

Aliyu Aihong Anes, Imam Ya’u Badamasi, Ali Usman, Ahmad Abuzairu, Abdulrahman Lawal Mustapha 222

The goal of this study is to predict a software error using Long Short-Term Memory (LSTM). The suggested system is an LSTM taught using the Whale Optimization Algorithm to save training time while improving deep learning model efficacy and detection rate. MATLAB 2022a was used to develop the enhanced LSTM model. The study relied on 19 open-source software defect databases. These faulty datasets were obtained from the tera-PROMISE data collection. However, in order to evaluate the model performance to other traditional approaches, the scope of this study is limited to five (5) of the most highly ranked benchmark datasets (DO1, DO2, DO3, DO4, and DO5). The experimental results reveal that the quality of the training and testing data has a significant impact on fault prediction accuracy. As a result, when we look at the DO1 to DO5 datasets, we can see that prediction accuracy is significantly dependent on training and testing data. Furthermore, for DO2 datasets, the three deep learning algorithms tested in this study had the highest accuracy. The proposed method, however, outperformed Li’s and Nevendra’s two classical Convolutional Neural Network algorithms which attained accuracy of 0.922 and 0.942 on the DO2 software defect data, respectively.

Guarantee structural anomaly detection in streaming data using the RRCF model: selection of detector parameters and its stabilization under additive noise conditions

Timofeev Andrey V. 230

A method for stabilizing structural anomaly detection under additive noise conditions as well as an algorithm for formal selection of the parameters of the solver rule in the structural anomaly detector based on the Robust Random Cut Forest (RRCF) method are proposed. In the framework of the developed approach, in order to stabilize the process of structural anomaly detection under the influence of additive noise, it is proposed to feed to the input of the RRCF-detector a data stream which is pre-processed by one of the digital filtering methods. In this case, the decision rule for anomaly detection is strictly formalized and transparently interpreted. The selection of parameters of the RRCF-based anomaly detector stabilized by pre-filtering methods of the input data stream is formalized. The RRCF-detector parameters choice within the proposed scheme guarantees a predetermined upper bound for the false alarm probability when deciding to detect a structural anomaly. This property is rigorously proved and formalized as a theorem. The performance of the stabilized RRCF-detector is investigated numerically. The achieved results confirm the performance of the proposed approach provided that the detection threshold is selected in the way proposed in this paper. An example of practical application of the proposed method is presented. The developed approach is promising for the detection of structural anomalies in conditions of observation additive noise, in a situation where it is important to guarantee an upper bound for the probability of false alarm. In particular, the approach can find application in monitoring technological regimes of liquid pumping in pipeline systems or in systems for detecting pre-failure states of technological equipment.

ViSL One-shot: generating Vietnamese sign language data set

Dang Khanh, Bessmertny Igor Alexandrovich 241

The development of methods for automatic recognition of objects in a video stream, in particular, recognition of sign language, requires large amounts of video data for training. An established method of data enrichment for machine learning is distortion and noise. The difference between linguistic gestures and other gestures is that small changes in posture can radically change the meaning of a gesture. This imposes specific requirements for data variability. The novelty of the method lies in the fact that instead of distorting frames using affine image transformations, vectorization of the sign language speaker’s pose is used, followed by noise in the form of random deviations of skeletal elements. To implement controlled gesture variability using the MediaPipe library, we convert to a vector format where each vector corresponds to a skeletal element. After this, the image of the figure is restored from the vector representation. The advantage of this method is the possibility of controlled distortion of gestures, corresponding to real deviations in the postures of the sign language speaker. The developed method for enriching video data was tested on a set of 60 words of Indian Sign Language (common to all languages and dialects common in India), represented by 782 video fragments. For each word, the most representative gesture was selected and 100 variations were generated. The remaining, less representative gestures were used as test data. The resulting word-level classification and recognition model using the GRU-LSTM neural network has an accuracy above 95 %. The method tested in this way was transferred to a corpus of 4364 videos in Vietnamese Sign Language for all three regions of Northern, Central and Southern Vietnam. Generated 436,400 data samples, of which 100 data samples represent the meaning of words that can be used to develop and improve Vietnamese sign language recognition methods by generating many variations of gestures with varying degrees of deviation from the standards. The disadvantage of the proposed method is that the accuracy depends on the error of the MediaPipe library. The created video dataset can also be used for automatic sign language translation.

Evaluation of probabilistic-temporal characteristics of a computer system with container virtualization

Phung Van Quy , Bogatyrev Vladimir A, Karmanovskiy Nikolay S., Le Van Hieu 249

The dependence of request servicing delay on the number of deployed containers is investigated for computer systems with container virtualization. The sought-after dependency is due to the allocation of limited computational resources of the computer system between active and inactive containers loaded in the system. The conducted research proposes a comprehensive combination of analytical queuing model, simulation modeling, and natural experiments. The studied computer system is interpreted as a multi-channel queuing system with an unlimited queue. The peculiarity of the proposed approach is the study of the influence of the number of containers formed in the system on queue delays and request servicing rate. Each container is associated with a service channel, and for the operation of a container in active and inactive states, the use of part of the common resources of the computing system is required. When constructing the model, it is assumed that the input flow is simple, and the service is exponential. The service rate depends on the number of deployed containers and the number of requests in the system. The experimental dependence of service rate on the number of active containers has been established. The experimental study was carried out on a platform based on Proxmox virtualization technology with fixed resources. To study the influence of the number of active containers on service rate within the experiment, a single-threaded web server was deployed in the form of several containers managed using the portable extensible Kubernetes k3s platform. The results of calculations using the analytical model are confirmed by the results of simulation modeling implemented using the SimPy modeling library in the Python programming language. Based on the conducted research, the need to solve the optimization problem of the number of deployable containers in a computer system regarding the influence of this number on request servicing delays is shown. The conducted research can find application in the design of real-time cluster systems critical to acceptable wait service delays, ensuring the continuity of the computational process, and preserving unique data accumulated during the system operation. The proposed approaches can be applied in the creation of fault-tolerant distributed computer systems, including those operating with failure accumulation and system reconfiguration with load (request) redistribution during dynamic container migration and replication.

### ARTIFICIAL INTELLIGENCE AND COGNITIVE INFORMATION TECHNOLOGIES

A new method for countering evasion adversarial attacks on information systems based on artificial intelligence

Vorobeva Alisa A. , Matuzko Maxim A., Sivkov Dmitry I. , Safiullin Roman I., Menshchikov Alexander A. 256

Modern artificial intelligence (AI) technologies are being used in a variety of fields, from science to everyday life. However, the widespread use of AI-based systems has highlighted a problem with their vulnerability to adversarial attacks. These attacks include methods of fooling or misleading an artificial neural network, disrupting its operations, and causing it to make incorrect predictions. This study focuses on protecting image recognition models against adversarial evasion attacks which have been recognized as the most challenging and dangerous. In these attacks, adversaries create adversarial data that contains minor perturbations compared to the original image, and then send it to a trained model in an attempt to change its response to the desired outcome. These distortions can involve adding noise or even changing a few pixels. In this paper, we consider the most relevant methods for generating adversarial data: the Fast Gradient Sign Method (FGSM), the Square Method (SQ), the predicted gradient descent method (PGD), the Basic Iterative Method (BIM), the Carlini-Wagner method (CW) and Jacobian Saliency Map Attack (JSMA). We also study modern techniques for defending against evasion attacks through model modification, such as adversarial training and pre-processing of incoming data, including spatial smoothing, feature squeezing, jpeg compression, minimizing total variance, and defensive distillation. While these methods are effective against certain types of attacks, to date, there is no single method that can be used as a universal defense. Instead, we propose a new method that combines adversarial learning with image pre-processing. We suggest that adversarial training should be performed on adversarial samples generated from common attack methods which can then be effectively defended against. The image preprocessing aims to counter attacks that were not considered during adversarial training. This allows to protect the system from new types of attacks. It is proposed to use jpeg compression and feature squeezing on the pre-processing stage. This reduces the impact of adversarial perturbations and effectively counteracts all types of considered attacks. The evaluation of image recognition model (based on convolutional neural network) performance metrics based was conducted. The experimental data included original images and adversarial images created using attack FGSM, PGD, BIM, SQ, CW, and JSMA methods. At the same time, adversarial training of the model was performed in experiments on data containing only adversarial examples for the FGSM, PGD, and BIM attack methods. Dataset used in experiments was balanced. The average accuracy of image recognition was estimated with crafted adversarial imaged datasets. It was concluded that adversarial training is effective only in countering attacks that were used during model training, while methods of pre-processing incoming data are effective only against more simple attacks. The average recognition accuracy using the developed method was 0.94, significantly higher than those considered methods for countering attacks. It has been shown that the accuracy without using any counteraction methods is approximately 0.19, while with adversarial learning it is 0.79. Spatial smoothing provides an accuracy of 0.58, and feature squeezing results in an accuracy of 0.88. Jpeg compression provides an accuracy of 0.37, total variance minimization — 0.58 and defensive distillation — 0.44. At the same time, image recognition accuracy provided by developed method for FGSM, PGD, BIM, SQ, CW, and JSMA attacks is 0.99, 0.99, 0.98, 0.98, 0.99 and 0.73, respectively. The developed method is a more universal solution for countering all types of attacks and works quite effectively against complex adversarial attacks such as CW and JSMA. The developed method makes it possible to increase accuracy of image recognition model for adversarial images. Unlike adversarial learning, it also increases recognition accuracy on adversarial data generated using attacks not used on training stage. The results are useful for researchers and practitioners in the field of machine learning.

### MODELING AND SIMULATION

On the properties of

Lisitsin Daniil V. , Gavrilov Konstantin V. *M*-estimators optimizing weighted L_{2}-norm of the influence function267

The work develops the theory of stable M-estimators belonging to the class of redescending estimators, having the property of resistance to asymmetric contamination. Many well-known redescending estimators can be obtained within the framework of the locally stable approach of A.M. Shurygin, based on the analysis of the estimator instability functional (L2-norm of the influence function), or his approach based on the model of a series of samples with random point contamination (point Bayesian contamination model). These approaches are convenient for constructing various stable M-estimators and, in comparison with classical robust procedures, provide wider opportunities. The family of conditionally optimal estimators proposed by A.M. Shurygin within the framework of the first of the listed approaches can be defined as optimizing the asymptotic dispersion under a constraint on the value of instability. The corresponding problem can be represented in the form of optimization of the weighted L2-norm of the influence function. The second approach considers a specially formed nonparametric neighborhood of the model distribution, and it can also be reduced to the analysis of the weighted L2-norm of the influence function. Thus, this estimation quality criterion is quite general and useful for constructing robust estimators. The theory of estimators that are optimal in terms of weighted L2-norm of the influence function is currently underdeveloped. Specifically, for the corresponding families of estimators, the question of the uniqueness of family members remains unresolved. The question comes down to studying the convexity (concavity) of the optimized functional depending on the parameter defining the family. In the presented work, an expression is obtained in general form for the derivative with respect to the parameter of the quality functional of the optimal estimator. Inequalities are obtained for the second derivative necessary to establish its convexity (concavity) with respect to the parameter. Corollaries from these results are applied to describe the properties of a conditionally optimal family. The influence functions of a number of conditionally optimal estimators for the shift and scale parameters of the normal model are constructed. The characteristics of these estimators are studied. The stability of most of the considered estimators is shown, which is important for their practical application. The theoretical results obtained can be useful in studying the properties of compromise estimators based on two criteria as well as in studying minimax contamination levels within the framework of A.M. Shurygin’s point Bayesian contamination model. The results of the work can be used in situations of purposed data corruption by an adversary including the problems related to adversarial machine learning.

Stability of a highly elastic rectangular plate with clamped-free edges under uniaxial compression

Mikhail V. Sukhoterin, Sosnovskaya Anna A. 276

The symmetrical buckling modes of a rectangular Kirchhoff plate with two clamped and two free parallel faces (CFCF-plate) under the action of a distributed compressive load applied to the clamped faces have been studied. The function of plate deflections due to loss of stability is represented by two hyperbolic-trigonometric series with indefinite coefficients which are found when all conditions of the boundary value problem are exactly satisfied. The problem is reduced to solving a homogeneous infinite system of linear algebraic equations with respect to one sequence of uncertain coefficients which contain the desired critical load as a parameter. To obtain nontrivial solutions, the determinant of the system must be equal to zero. This eigenvalue problem has countless solutions. It is proposed to find non-trivial solutions of the system using the method of successive approximations with enumeration of the load parameter. Using computer calculations, the first four critical loads (including the Euler load) were found applied to the clamped parallel faces of a square plate and giving symmetrical forms of buckling. The influence on the accuracy of calculations of the number of terms retained in the series and the number of iterations is studied. 3D images of the found buckling modes are presented. A comparison with known solutions is provided. The results obtained can be used in the design of various flat rectangular elements in microelectronics and nanotechnology.

Models and a deformations simulation approach using ANSYS CAD for railway wagons weighing system

Denisenko Mark A. , Isaeva Alina S. , Sinyukin Alexander S., Kovalev Andrey V. 284

Possibility of fast, convenient and precise definition of wagons load mass allows enhancing transport safety and ensures assets accounting in railroad infrastructure. There are known three-dimensional solid models of railway track sector and approaches of simulation the deformation which emerge in rails by mechanical load effect transmitted through wagon wheels. In accordance with these approaches, emerging deformations are recomputed into wagons weight. The rail temperature influences on its mechanical properties and, consequently, on the deformation value. In this work, for the first time, a technique has been proposed that allows one to consider the deformation of the rail under the load influence, taking into account its temperature variance at different boundary conditions. According to the proposed approach, the wagon weight is defined by deformation values which are measured by strain gauges located on the rail web. The developed models include a rail wheel, ties and a rail fragment. The rail fragment corresponding to the railway track sector on which sensors are mounted geometrically replicates an existent rail type R50 and is situated on the ties fixed from bottom side. The wheel model complies with an existent solid-rolled wagon wheel type with tread diameter 920 mm, thereby correct contact patch retains in the model. According to the approach, finite-element mesh is generated on the developed solid models, connections between model fragments are established, and boundary and temperature conditions as well as acting forces are applied. Sequentially finite-element analysis is performed for all possible combination of wheel coordinate, load mass and temperature. For every case, deformation values are registered in four rail nodes corresponding to strain gauges placements. Comparison of finite-element analysis results for two developed solid models is carried out. The models differ by the way of the rail on the ties mounting and boundary condition setting on the end faces of the rail fragment, allowing to consider possibility of temperature stresses relaxation. In the model 1 the rail is connected with ties rigidly, in the model 2 the rail and the ties are connected by a contact allowing the rail motion along the tie with given friction coefficient. Besides that clamp bolts impact is imitated in the model 2. The approach is implemented within multiphysical simulation environment ANSYS for coupled three-dimensional problem using Static Structural and Steady-State Thermal modules. Simulation results showed that the deformation values determined by the temperature influence differ for the proposed models. Vertical deformations range of the rail fragment on which the strain gauges are fastened, at the mass 12,500 kg loaded on the wheel, is from –245 μm (bend down) to 15 μm (bend up) for the model 1 depending on the rail temperature (in the range from –20 °C to +50 °C) and from –225 μm to –100 μm for the model 2. This allows concluding that the model 2 reflects deformation process more correctly, and the temperature influence on the deformation is less relevant compared to mechanical load value. The proposed model in contrast to the known ones implies static weighing characterized by more accuracy, reliability and simplicity of use. In the future it is planned the executing of the more detail research of a model with two wheels and an axle for determining optimal simulation time and obtained results accuracy.

Application of lattice Boltzmann method to solution of viscous incompressible fluid dynamics problems

Nikita A. Brykov, Konstantin N. Volkov, Vladislav N. Emelyanov, Tolstoguzov Semen S. 293

The possibilities of simulation of viscous incompressible fluid flows with lattice Boltzmann method are considered. Unlike the traditional discretization approach based on the use of Navier–Stokes equations, the lattice Boltzmann method uses a mesoscopic model to simulate incompressible fluid flows. Macroscopic parameters of a fluid, such as density and velocity, are expressed through the moments of the discrete probability distribution function. Discretization of the lattice Boltzmann equation is carried out using schemes D2Q9 (two-dimensional case) and D3Q19 (three-dimensional case). To simulate collisions between pseudo-particles, the Bhatnagar–Gross–Crooke approximation with one relaxation time is used. The specification of initial and boundary conditions (no penetration and no-slip conditions, outflow conditions, periodic conditions) is discussed. The patterns of formation and development of vortical flows in a square cavity and cubic cavities are computed. The results of calculations of flow characteristics in a square and cubic cavity at various Reynolds numbers are compared with data available in the literature and obtained based on the finite difference method and the finite volume method. The dependence of the numerical solution and location of critical points on faces of cubic cavity on the lattice size is studied. Computational time is compared with performance of fine difference and finite volume methods. The developed implementation of the lattice Boltzmann method is of interest for the transition to further modeling non-isothermal and high-speed compressible flows.

From the construction of wavelets based on derivatives of the Gaussian function to the synthesis of filters with a finite impulse response

Semenov Vladimir I., Chumarov Sergey G. 306

For continuous wavelet transformation, wavelets based on derivatives of the Gauss function are used, and for multiscale analysis, Daubechies wavelets are used. The development of algorithms for forward and inverse continuous wavelet transform in the frequency domain made it possible in this work to synthesize digital filters with a finite impulse response (FIR) different from existing methods. The quality of the synthesized filters was checked by decomposition and subsequent reconstruction of the signals. To do this, several filters were synthesized that completely cover the frequency range of the signal. Since wavelets are bandpass filters, the authors called the filters wavelets. The more precisely the reconstructed signal repeats the shape of the original signal, the better the wavelet constructed by one method or another. A comparison of the accuracy of signal reconstruction shows that the best conversion result is obtained by using synthesized wavelets. The impulse responses of the FIR filters are synthesized so that their frequency response are similar to the frequency responses of wavelets based on derivatives of the Gaussian function of a large order. The greater the filter order, the closer the frequency response is to a square-wave shape. Algorithms for forward and inverse wavelet transformation of a signal in the frequency domain using wavelets based on derivatives of the Gauss function are proposed. Profiling of the program shows that the time of the wavelet transforms using the fast Fourier transform is 15,000 times less than with the direct numerical integration for sampling the signal of 32,768 samples. These algorithms can be used for wavelets with a square-wave frequency response. At the same time, the numerical calculation time is halved. The accuracy of the reconstruction was compared for wavelets based on second-order derivatives, Daubechies wavelets, and wavelets with a square-wave frequency response. The reconstruction accuracy is highest for the latest wavelets. The use of the wavelet construction method is preferable since this method is relatively simple and it is easy to synthesize multiband filters with any form of frequency response. If, when synthesizing using existing methods, a short transition band can be obtained only for long impulse responses, while the transition band using the method of constructing wavelets is absent even for filters of very small orders. The paper presents the impulse responses of two- band, three-band digital filters and their frequency response. FIR digital filters with a square-wave frequency response have a higher delay-band attenuation coefficient compared to existing filters, do not have transition band, and can be used to process one-dimensional and two-dimensional signals.

Partition of unity method and smooth approximation

Tolstykh Victor N. 314

This work presents a new piecewise polynomial method of smooth analytic approximation for any dimension and variability of experimental data. Alternatives to this method are cubic and bicubic splines which have their advantages and disadvantages. There are many researches in the field of big data flexible approximation; however nothing similar was found to what is presented in the work, especially concerning multivariate dependencies. Experimental data frequently depend on many variables which for the purposes of compression, prediction, and transmission locally expressed by relatively simple analytic functions. It can be local polynomials, either on some intervals in one- dimensional case or polygons — in two-dimensional cases. Presented in the work method of local functions smooth matching extends from the one-dimension piecewise polynomial approximation method to higher dimensions that has a variety of scientific and practical applications. Under this condition, it makes sense to store and transmit coefficients of local polynomials or other local functions rather than use raw data for those purposes, which frequently requires an unacceptably large amount of resources. In the method described, we use cellular subdivision of the area of interest, and define low-degree polynomials or other parametric functions on the cells. At the junctions between cells, there are overlapping transition zones where local functions match to each other. Their amount is defined by the index of the topological compact covering. As a result, the matching obtains a single double-differentiable analytic function on the entire compact. Defined in the work basic functions are second- and third-degree especial polynomials. The values of these functions smoothly transit from one to zero within a closed unit interval. Derivatives on the interval edges both are equal to zero. The matching is performed by the homotopy which maps a unit interval to the space of functions. Efficiency of the method is demonstrated for one-dimensional case by matching a set of approximating parabolas. We extend this method to the two-dimensional case by applying the known unit partitioning technique with topological maps coverage. The computational experiment demonstrates that even in this case local functions smoothly match making a double-differentiable function on the entire compact. First result is a development of a smooth matching method for experimental data approximation by local parametric functions on a large interval. Second result is development of a new method, based on a unit partitioning, for matching two-dimensional local functions making an approximation on the two-dimensional compact. Third result is a theoretical proof of the method extension from dimension of one and two to any dimension. Task of this study consisted in the development of a useful tool for efficient storage and transmission of experimental data.

Censoring training samples using regularization of connectivity relations of class objects

Nikolay A. Ignatev, Tursunmurotov Davrbek X. 322

The censoring of training datasets is considered taking into account the specific implementation of the nearest neighbor method algorithms. The censoring process is associated with the use of a set of boundary objects of classes according to a given metric for the purpose of: searching and removing noise objects and analyzing the cluster structure of the training sample in relation to connectivity. Special conditions for removing noise objects and forming a precedent base for training algorithms are explored. Recognition of objects using such a database should provide higher accuracy with minimal computational resources relative to the original dataset. Necessary and sufficient conditions for selecting noise objects from a set of boundary ones have been developed. The necessary condition for a boundary object to belong to the noise set is specified in the form of a restriction (threshold) on the ratio of the distances to the nearest object from its class and its complement. The search for the minimum coverage of the training dataset with standards is carried out based on the analysis of the cluster structure. The standards are represented by sample objects. The structure of the connectivity relations of objects according to the hypersphere system is used to group them. The composition of the groups is formed from centers (dataset objects) for hyperspheres the intersection of which contains boundary objects. The value of the compactness measure is calculated as the average number of objects in the training dataset, excluding noise, pulled in by one standard of minimum coverage. An analysis is carried out of the connection between the generalizing ability of algorithms in machine learning and the value of the compactness measure. The presence of a connection is justified by a criterion (regularizer) for selecting the number and composition of a set of noise objects. Optimal regularization coefficients are defined as threshold values for removing noise objects. The relationship between the value of the training dataset compactness measure and the generalizing ability of recognition algorithms is shown. The connection was identified using the standards of minimum sample coverage from which the precedent base was formed. It was found that the recognition accuracy using the precedent base is higher than that using the original dataset. The minimum composition of the precedent base includes descriptions of standards and parameters of local metrics. When using data normalization procedures, additional parameters are required. Analysis of the values of the compactness measure is in demand to detect overfitting of algorithms associated with the dimension of the feature space. Recognition based on precedents minimizes the cost of computing resources using nearest neighbor algorithms. Recommendations are given for the development of models in the field of information security for processing and interpreting sociological research data. For use in information security, a precedent base is being formed to identify DDOS attacks. It is proposed to obtain new knowledge from the field of sociology through the analysis of the values of indicators of noise objects and the interpretation of the results of dividing respondents into non-overlapping groups in relation to the connectedness of objects. The configurations of groups in relation to connectivity are not initially known. There is no point in calculating their centers which can be located outside the configurations. To explain the contents of groups, it is proposed to use standards of minimum coverage.

### BRIEF PAPERS

Approach to software products development in a startup

Lonkina Nataliia V. , Liubov S. Lysitsina 330

The problem of missed release deadlines under conditions of systematic changes in market requirements for a software product has been studied. The analysis of the causes of disruptions at all stages of software product development is carried out and an approach is proposed aimed at finding a compromise between the quality and the implementation period of the product being developed in order to reduce the release time. The results of the presented method are analyzed using the example of development in a startup at the early stages of development and confirmed the possibility of reducing the time for updating software products by at least 15 %.

Modeling perceiving of recommendations provided by clinical decision support system based on predictive modeling within dental preventive screening

Soldatov Alexander N. , Ivan K. Soldatov, Kovalchuk Sergey V. 335

The results of a current study of the perception of clinical decision support systems (CDSS) in the framework of preventive screening by dentists in schools of the Russian Ministry of Defense (cadet corps) are presented. Using the example of the scenario under consideration, a prototype of the CDSS based on machine learning was evaluated. To assess perception, a survey was conducted demonstrating the results of the prototype and assessing the perceived characteristics of the provided predictive modeling results. A model was built based on a Bayesian network to evaluate the considered indicators, which demonstrated an increase in the quality of prediction of perceived indicators, taking into account the influence of latent states of the operator’s subjective perception. The proposed approach is planned to be used in the future to increase the efficiency of doctor-CDSS interaction.