MODELING OF THE ULTRAFILTRATION PROCESS ON ROLL MEMBRANES IN A CENTRIFUGAL FIELD
A.B. Golovanchikov, M.C. Doan , N.A. Merentsov
The process of ultrafiltration on roll-type membranes installed in the rotor of a filter centrifuge of a special design that provides atmospheric pressure in the zone of filtrate formation behind the membrane and centrifugal pressure in the zone of retant filtration to the membrane is considered. Equations are obtained for calculating the performance of filtrate and permeate and the concentration of solute molecules in them. An example of calculation is given in comparison with the installation of a single layer of sheet membrane on the side wall of a perforated rotor. The results of numerical calculations of the main parameters of the process of ultrafiltration of an aqueous acylase solution using the developed algorithm at the rotor rotation speed ω = 100 rad/s, the rotor radius Rn = 0,25 m and the membrane width b = 0,5 m show that the area of the roll membrane increases 12 times, and the degree of concentration of the solution almost 6 times, while the permeate consumption increases almost 10 times compared to the sheet membrane laid in a single layer on the wall of the perforated rotor. However, the cleaning of permeate in a rotor with a roll membrane is reduced by almost 12.5 times, since the average concentration in permeate increases from 1·10-5 % to 2,6·10-5 %.
Keywords: ultrafiltration, roll-type membrane, centrifugal field, performance, retant, permeate, concentration.
ESTIMATION OF PAIR LINEAR REGRESSION MODELS WITH PARAMETERS IN THE FORM OF LINEAR OPERATOR MATRICES OF TWO-DIMENSIONAL VECTOR SPACE
M.P. Bazilevskiy, L.N. Vlasenko
The key problem in constructing a regression model is the choice of its structural specification, i.e. the composition of the variables and the mathematical form of the relationship between them. All currently known regression specifications are based on the fact that their unknown parameters are matrices of linear operators of a one-dimensional vector space. In this paper, for the first time, linear regression models with parameters in the form of matrices of linear operators of a two-dimensional vector space are considered. It is shown that such models can be used to predict the values of the explained variable, and for this, the researcher does not need to set the predicted values of the explanatory variable, since they are sequentially determined by the model. To estimate the proposed models, an optimization problem is formulated based on the least-squares method with restrictions. Using the method of Lagrange multipliers, it is proved that solving the formulated problem reduces to solving linear algebraic equations system. An example of estimating the proposed models for specific data is considered. As a result, the error sum of squares by the developed model turned out to be five times less than the error sum of squares by the classical pair linear regression model.
Keywords: regression model, linear operator, vector space, forecasting, ordinary least squares, method of Lagrange multipliers.
ANALYSIS OF MATHEMATICAL MODEL OF RELIABILITY OF THE RESPONSIBLE NODE OF THE RADIO ENGINEERING DEVICE IN THE PRESENCE OF RESERVE BLOCKS IN CASE OF DANGER OF SHORT CIRCUIT
J.V. Korypaeva, N.A. Aleynikova, N.E. Krasova
The problem of duplicating the responsible node of a radio engineering device with several backup units in the event of a short circuit or other potential danger of sudden disconnection of the device is considered. To study such situations, when modeling a possible sudden failure of the unit, a small positive parameter is introduced in the denominators of the failure rates of the main device and backup units. In this regard, the system of Kolmogorov equations for the considered case will be singularly perturbed. For the received model key features device reliability: the probability of loss of function of the expected time of failure of the last overlapping block variance and the risk of failure of the unit. Similar characteristics are found for the corresponding problem without reservation. On the basis of a comparative analysis of the results obtained for the reliability characteristics of the main task and their comparison with the results for the system without redundancy, a number of features are identified and conclusions are made about the feasibility of redundancy in this case. For specific values of the number of duplicate blocks, failure rates and small parameter, a table of results for the mathematical expectation of the time of failure of the last device is given and conclusions are made.
Keywords: reliability prediction, redundancy, Markov chains with a finite number of States, singular perturbations.
DISCRETE APPROXIMATION OF MODELS WITH DISTRIBUTED PARAMETERS
L.B. Afanasievsky, A.N.Gorin, M.A.Chursin, O.Y. Lavlinskaya
The relevance of the study is due to the need to develop a mathematical apparatus of approximate mathematical description in the form of discrete transfer functions for solving problems of control of continuous systems with distributed parameters. Therefore, this article discusses the model of approximation of dynamic properties of systems. Approximation is performed in the static mode area by replacing derivatives with their differential analogues applicable to the difference model of the Carson discrete transformation, sequentially differentiating the transformation results over the complex variable and moving to the limit at the zero value of this variable. The leading approach to the study of the problem of management of continuous systems with distributed parameters is the method of analytical modeling, which allows to obtain a difference model with a high degree of approximation. In the article, the results of the transformation of the model in the form of a sequence of equations providing a recursive calculation of the moments of discrete weight functions, starting from the moment of zero order. The coefficients of approximate discrete transfer functions are determined by solving systems of linear algebraic equations, the coefficients of which depend on the moments of discrete weight functions. This is an example of a calculation for a system described by two differential equations with partial derivatives. Materials of the study are of practical value for specialists of chemical industry, non-ferrous metallurgy and a number of other industries, where methods of analytical modeling of objects are widely used.
Keywords: distributed parameter systems, Carson transform, moments of discrete weight functions, discrete transfer function.
EVOLUTION OF THE OBSERVER STATE FROM PULSE TO PULSE
IN AN ELECTRIC DRIVE WITH A CONTACTLESS DC MOTOR
S.A. Vinokurov, O.A. Kiseleva, N.I. Rubtsov
The paper analyzes the current state in an electric drive with a contactless DC motor, considering that the control system in it is built as a hybrid, which is inherent in both discrete and continuous dynamics. The ideal vector control of a contactless DC motor can be described theoretically and used as a template for determining deviations in various control methods and evaluating their effectiveness. The paper compares the ideal control with discrete control, shows the possibility of implementing continuous control laws due to the displacement of control pulses in space and time. With pulse control, which is used in the electric drive at the present time, not only the pulse durations are calculated, but also the distances between them, that is, the beginning of the next pulse, and most importantly, the leading base vector is selected. The state observer in such a system performs a complex role, since there are delays in the system links, that must be considered, since they can disrupt the stability of the synchronous mode of the engine with the state observer. The paper presents a block diagram of a mathematical model of a state observer with a full-revolution detector.
Keywords: contactless DC motor, state observer, hybrid control, leading base vector.
FEATURES OF THE APPLICATION OF THE OBSERVER STATES
IN A CONTACTLESS DC MOTOR
O.A. Kiseleva, T.V. Popova, A.Y. Timoshkin
The paper deals with the analysis of the formation of discrete vector an equivalent tape to control brushless DC motor. The issues of using state observers instead of electromechanical rotor position sensors are considered. Shows the feature of constructing an observer status, for localdate that information on its input comes from continuous work-th current field, and the output it generates discrete torque control field switching of the windings of the synchronous motor power voltage inverter based on the motor parameters and actuators. To ensure synchronization, it is necessary to decide on the frequency of sensor polling and the possibility of processing this information, which leads to signal delays. It is necessary to take into account not only the time dependence associated with the beginning and end of the pulses, but also the spatial dependence associated with the alternation of the basic leading vectors. The estimation of control efficiency in electric drives with contactless DC motors and sensors of supervision is carried out. In some cases, the use of speed observers in the electric drive leads to a decrease in the speed control range. Graphs of transient processes in the electric drive at different values of the speed controller parameters are constructed.
Keywords: contactless DC motor, state observer, transient characteristics, discrete control field.
STRUCTURIZATION OF ENVIRONMENTAL INFORMATION WITH APPLICATION OF GEOINFORMATION TECHNOLOGIES
The article discusses the development of managerial decisions to improve the environment through the introduction of geographic information technologies, including methods for assessing and predicting the environmental situation based on monitoring approaches. The development of big data processing technologies has identified trends in the widespread implementation of real-time monitoring systems. In this regard, the task of monitoring natural objects is proposed to be solved as the task of determining and controlling the properties and states of a complex object in real time and actively interacting with the environment, as well as developing managerial decisions and recommendations. It is proposed to use the Fuzzy ART neural network as a mathematical apparatus for structuring environmental information, which has proven itself in real-time data processing. To visualize the received information and integrate the results of the network operation of the Fuzzy ART network into a geographic information system, it is proposed to use the Folium Python library, which is intended for graphical display of geographic data and contains all the necessary cartographic information. Using Folium, the results of the structuring of environmental data can be displayed directly on Google maps, which makes it possible to visually determine the boundaries of clusters and possible buffer zones when the map is scaled up.
Keywords: neural network, clustering, machine learning, adaptive resonance theory, Fuzzy ART network, GIS system.
EFFECTIVE METHOD OF DESIGNING CAD MODELS WITH LATTICE STRUCTURE
N.V. Tsipina, O.N. Chirkov, S.A. Slinchuk, I.V. Cheprasov, V.A. Madesov
This article shows how important it is to develop a convenient and simple method for designing lattice parts in production. The purpose of the entire experiment is to observe, analyze and solve problems in the design of lattice structures. The performance of modern tools of computer-aided design (CAD) systems was also evaluated. All the disadvantages and positive aspects of the developed method are indicated. The considered design method allows designers to choose the right lattice structure and its density. An essential part of this proposal is the use of equivalent lattice materials. This approach eliminates the need to design lattice-based CAD models and shortens the simulation time for FEMs. This methodology may be applicable in determining equivalent materials for other lattice structures. Equivalent materials also reduce FEM simulation time. The performance of modern tools of computer-aided design systems was evaluated to determine whether they adequately meet the requirements of additive manufacturing. The results show that modern CAD systems do not allow you to easily and quickly design lattice structures for additive manufacturing. It is necessary to develop modern CAE software to conduct finite element method analysis on a 3D lattice model.
Keywords: lattice structure, CAD software, finite element method (FEM).
ESTIMATION OF CAD CHARACTERISTICS IN THE CONTEXT OF DESIGNING MODELS WITH LATTICE STRUCTURE
N.V. Tsipina, O.N. Chirkov, S.A. Slinchuk, I.S. Bobylkin, E.I. Vorobiev
This article assesses the current characteristics of computer-aided design (CAD) systems in the context of the design of models with a lattice structure. During the design of the experiment, three variables were selected, two lattice structure templates, rods of lattice structures with two different sections and four sizes of parts were designed. The purpose of the whole experiment is to observe the problems that the user encounters when designing lattice structures in CAD software, as well as to determine the effect of the type and size of lattice structures on file sizes and whether modern file formats are suitable for the requirements of additive manufacturing. The obtained experimental results show that it is difficult to design CAD models with a lattice structure, since this process takes a lot of time and creates large files. In some cases, the program could not perform the desired operation. New requirements for the design of parts for additive manufacturing lead to new needs in computer-aided design. New research is needed to determine the most reliable and efficient methods for designing lattice structures in CAD software.
Keywords: CAD features, additive manufacturing, octet farm, cubic lattice structure.
MODIFICATION OF NEURAL NETWORK MODEL RKELM
WITH ADDITIONAL TRAINING
Y.A. Asanov, S.Y. Beletckaya
The aim of this work is developing of an artificial neural network model (ANN) capable of working in dynamically changing conditions. Despite a large number of research and development in this sphere, there are still no models that satisfy the limited resources of mobile systems (primarily – performance). This article proposes a developed modification of the Huang Extreme Learning Model, which differs from the original approach in the training process – training on common conditions, without increasing the weight matrix and the training sample, followed by further training for specific conditions. As a test sample of data, a dataset from the open source machine-learning repository UCI was used. Vast experiments were performed, the purpose of which was to identify the most suitable model, the choice was made from RKELM, SVM and ELM. The selection criteria for the model were performance and classification accuracy. The model with extreme training of Huang turned out to be the most suitable, it was used as the basis of the developed modification. The results of comparing the original and modified models are presented. The proposed approach surpassed the competition in speed and performance, while only slightly inferior in accuracy of data classification in the initial conditions, but turned out to be much more accurate in the new conditions in which the model was not trained.
Keywords: artificial neural network, RKELM modification, model with an additional training.