### INFORMATION TECHNOLOGIES AND SYSTEMS COMPUTER TECHNIQUE

METHOD OF DIAGNOSTIC SYSTEM SYNTHESIS BASED ON BOOLEAN COMPLEMENT
WITH REDUCED NUMBER OF CORRECTION ELEMENTS
Sapozhnikov Valery V., Sapozhnikov Vladimir V., Ephanov Dmitry V., Dmitry V. Pivovarov

1039

Application of Boolean complement in self-checking combinational devices synthesis is consid-ered. A method is proposed for reducing the number of correction elements in the basic block diagram of the initial combinational device diagnosis system using a 1-out-of-3 constant-weight code. The method is based on conversion of only one working function and the addition of three-digit code word in the check circuit to four-digit code word for 2-out-of-4 constant-weight code. Such an approach to the construction of diagnostic system simplifies the self-checking procedure of the structure and reduces the complexity of the final device implementation. The decrease is due to the variability of the check logic structure block and relative simplicity of codes checkers for 2-out-of-4 constant-weight codes as compared to 1-out-of-3 constant-weighted codes checkers. Examples of using the described method for synthesis of self-checking combinational devices with three or more outputs are presented.

EXPERIMENTAL VERIFICATION OF A MATHEMATICAL MODEL FOR EFFUSION ANALYZER
OF GAS VISCOSITY WITH DECREASING OUTCOMING PRESSURE
Stanislav Yu. Zhigulin, Leonid V. Ilyasov

1053

Results of experimental checking a mathematical model of developed gas viscosity analyzer are presented. A generalized scheme and operation of the considered analyzer are described. The analyzer operation is based on measuring the time required for a fixed volume of the analyzed gas to expire through a capillary. Initial equations and theoretical assumptions used to develop the mathematical model of the effusion analyzer are discussed. An experimental setup for testing the developed mathe-matical model and its operation is created. Data obtained with the mathematical model are compared to results of experimental studies. The errors of the mathematical model are determined, conclusions are made about its adequacy and the possibility of further use for the design and calculation of effusion an-alyzers of gas viscosity with decreasing outcoming pressure.

VECTOR REPRESENTATION OF WORDS USING THE APPARATUS
OF QUANTUM PROBABILITY THEORY
Alexey V. Platonov, Bessmertny Igor Alexandrovich, Koroleva Julia A.

1060

The problem of modeling the semantics of text documents based on vector representation of words in a Hilbert space is considered. The vector representation of a word reflects the words surround-ing the given word (the context of the word). If a word is found in a document more than once, the set of contexts of a word forms its generalized context, i.e. meaning of the word. Different contexts of a word may be considered as different projections, and the generalized context — as a reconstructed multidi-mensional object. The purpose of the presented study is to improve the quality of the restoration of a word the context by considering additional factors, in particular, the possible non-orthogonality of con-texts. To achieve the goal, quantum probability theory is used here, and the context recovery procedure corresponds to the problem of quantum tomography in quantum physics. The task of restoring a word context or, in terms of quantum mathematics, the probability density matrix, is solved by the method of gradient descent using machine learning. Restrictions on the learning process are implemented by a set of regularizers that ensure the convergence of the process according to the Kullback—Leibler diver-gence criterion.

### INSTRUMENTS AND SYSTEMS OF AUTOMATIC CONTROL

SYNTHESIS OF A SUBORDINATE CONTROL SYSTEM WITH PREDETERMINED OVERSHOOT
OF SERVO AXLE ELECTRIC DRIVE OF QUANTUM-OPTICAL COMPLEX
Ilya V. Shustov, Tolmachov Valeriy, Sergey Yu. Lovlin

1066

With the development of technology, the requirements for the accuracy of reproduction by ma-chines and mechanisms of the given laws of motion are constantly increasing. This trend is particularly evident in the case of electric drives of servo axis of quantum-optical systems. In the conditions of infra-low speeds of movement, non-rigidity of mechanisms and influence of variable disturbing moments on their masses, the task of ensuring high accuracy of servo axes positioning is assigned to control systems. A new analytical method of control system configuration is presented: its output, graphical interpretation and conditions of correct operation are considered. The technique allows to increase simultaneously ac-curacy of positioning of the servo axes and to keep such advantages of the subordinate structure of con-trol system as convenience of restriction of internal coordinates of system and possibility of compensa-tion of imperfections of the electric motor and the power converter. Improving the positioning accuracy of the servo axes is achieved by increasing the bandwidth of the internal speed control circuit. The maxi-mum bandwidth of the latter is limited at a level at which the value of the overshoot of its transient char-acteristics does not exceed a certain predetermined value. Another advantage of the proposed method is a more complete account of the properties of the control object, including the internal viscous friction of servo axes mechanisms. The results of simulation of the control system of the tracking electric drive of the angular axis of the quantum optical complex Stager-2 OPU LIK confirm the correctness and effec-tiveness of the developed technique.

DIGITAL TRACKING SYSTEM WITH FINITE DECAY TIME OF FREE PROCESS
Anatoly I. Korshunov

1078

The possibility to obtain a finite decay time of free process in a linearized model of a digital track-ing system using a linear discrete correction device is demonstrated. The decay time does not exceed the integer number of sampling periods equal to the order of the system continuous part, and therefore the maximum possible speed of the system is achieved. The conditions of free process damping for fi-nite time are derived: controllability and observability of the discrete model of the continuous part of the system. To comply with the conditions, the absence of common multipliers of the numerator and denom-inator of the transfer function of the continuous part is necessary. The method of choice of the simplest transfer function of the discrete correcting device considering requirements of system roughness is pro-posed. An example of a digital tracking system with a continuous part of the 3rd order is analyzed.

SPECIFIC OF USING MICROELECTRONIC COMPASSES IN COMPLEX NAVIGATION SYSTEMS
Dmitry A. Antonenkov

1087

Features of a device designed to determine the position of environmental parameters measuring module are considered. An example of adapting the standard microelectronic compasses operation to specific conditions is demonstrated. Principle of the device operation is described, the device functional diagram and software operation algorithm are presented. The device calculates the sine and cosine of the angle between the conditional axis of the compass and the magnetic meridian, generates output sig-nals in the form of DC voltage equivalent to these values, and thus makes it possible to derive the azi-muthal angle values.

### SCIENTIFIC AND PRACTICAL DEVELOPMENTS

DETERMINATION OF ACCURACY PARAMETERS OF MULTI-STAGED GEAR MECHANISMS
Timofeev Boris P., Abramchuk Mikhail V., Islam A. Bzhikhatlov

1092

Methods of calculating the kinematic accuracy parameters, or the tangential composite deviation of multi-staged gear mechanisms are considered. This error is considered as a function containing a set of components of certain frequencies and amplitudes. The installation error, which usually is not taken into account in the calculation of the tangential composite deviation, is also considered. Final calcula-tions are reduced to the output gear wheel of the studied multi-staged mechanism. To calculate the kin-ematic error, the maximum-minimum method is used, as well as the Monte Carlo probabilistic calcula-tion method. A method of calculating the kinematic error, which accounts for features of the gear mech-anisms production, is proposed. In the conditions of a specified production, if the spread of the values of the error components is known, the probabilistic calculation of the kinematic error is stated to give more accurate results as compared with the maximum-minimum method.

METHODS OF THE HAND ELECTROMYOGRAM ANALYSIS
Raisa Yu. Budko, Nikolay N. Chernov, Natalya A. Budko

1098

Comparison of the effectiveness of the convolutional neural network (CNN) and radial basis func-tions (RBFs) algorithms in the processing of forearm electromyograms (EMG) obtained over several days is performed. Pre-processed signal is used as the input data, the CNN algorithm is applied as the input feature vector for the raw data. The both methods are shown to have several perspectives for the use in device control tasks. The CNN is able to recognize the characteristic signs of EMG without prelimi-nary signal processing, despite their stochastic nature. This allows to provide feature selection or trans-formation of the signal before classification. The method of data classification with pre-processing demonstrates greater recognition accuracy for RBF. A pronounced dependence of the recognition accu-racy on the subject and on the time between obtaining samples was obtained. Thus, although the SNA algorithm showed good results for the raw EMG signal, the training sample with multi-day data allowed to achieve stable performance, which imposes limitations on its use in clinical systems.

METHOD OF MULTI-CRITERIA ANALYSIS OF WAREHOUSE PREMISES RENTING COST
Prokopenko Victor T., Majorov Evgeniy E., Ekaterina A. Yakovleva, Dagaev Alexander V., Alexey A. Sorokin, Ramiz B. Guliyev, Roman A. Kovalenko, Irina S. Tayurskaya

1105

A multi-step method of analysis and formation of the cost of rent of premises is described. A ma-trix approach to modeling the territory and infrastructure objects is proposed. The methodology allows to analyze statistical data for forecasting the cost of renting warehouse premises, choosing the optimal zone of placement of warehouse facilities. The study is aimed at development of approaches applicable for interpolation of values missing in the statistical sample, smoothing of statistical aggregate with data interpolation, and visualization of results of analysis for further expert evaluation. To solve this problem, interpolation of statistical data is performed. A Tukey boundary-based method is used to eliminate outli-ers (anomalous values); in combination with graphical modeling, the procedure is able to smooth the outliers. Cost-effective locations of storage facilities are determined by the method of multi-criteria eval-uation. As a result of the development of methods and their simulation, calculations with abstract initial data are performed. The methodology is tested on real estate objects and a set of data applicable for de-cision-making is obtained. The use of the methodology allows to obtain maps of the distribution of the rent cost, the area of influence of criteria for further expert assessment of the sector in terms of organiza-tion, placement and lease of warehouses. The technique is also proposed as a support of decision-making in the field of definition and justification of the rent price for both the tenant and the lessor.