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Fuzzy cognitive modeling of heterogeneous electromechanical systems

The article presents a method of fuzzy cognitive modeling for heterogeneous electromechanical systems (HEMSs) in the management of innovative design solutions. During the operation of the HEMSs, as a result of their operational aging, the properties of the windings parametric matrices and the HEMSs vector space properties change. Periodic testing of the HEMSs vector space allows obtaining reliable information about the current technical condition of the HEMSs, about its changes during operation and about the risks of operating capability loss. At the same time (I) the presence of proportional changes in signals during sequential testing indicates the homogeneous operational aging of the HEMSs and its rate; (II) a disproportionate change in one of the signals indicates the damage or the development of a heterogeneous aging process; (III) a change in signals with a change in the angular position of the rotor indicates worn bearings or damage of the HEMSs rotor. The article presents the HEMSs model, describes the method for the topological research of the vector space and the method for forming the diagnostic matrices. The deviations of their elements are fuzzy due to the uncertainty of the load, influencing environmental factors and unstable supply voltages. Therefore, for predictive estimation of the HEMSs state, it is proposed to use fuzzy relational cognitive models that allow implementing a completely fuzzy approach to modeling problem situations in these systems. The presented data confirm the growth of the HEMSs heterogeneity under conditions of uncertainty of external influences. The proposed method for predictive estimation of the HEMSs state, based on fuzzy relational cognitive models, provides resistance to an increase in the uncertainty of the estimation results for various models of system dynamics due to a reasonable set of fuzzy vector-matrix operations. Read more...

A computer program for electromechanical system operational diagnostics based on the topological approach

The paper presents a method, a mathematical model, and a computer program for the operational diagnostics of an electromechanical system (EMS). During EMS operation, service aging changes the properties of the parametric matrices of the windings and, as a consequence, the characteristics of the EMS vector space. Periodic testing of the vector space offers relevant and reliable data on the current health of the EMS, its changes during operation, and the risk of loss of function. The object of the study is an asynchronous electric motor (AEM). It is urgent to automate the process of assessing the current health of an AEM and to organize the storage of information on its states at different stages of its life cycle. To solve the problem, software (SW) for accumulation of information on AEM operation and for evaluation of its basic performance metrics has been developed in the Python programming language. The SW is based on the topological approach to diagnostics, which implies the analysis of the current responses of motor rotor windings to phase voltage pulses. The SW enables one to determine the rate of the service aging of an item, the probability of its survival and residual life, to obtain access to the history of previous diagnostics, and to visualize the in-service history of the above-mentioned performance metrics. The developed SW can be used to increase the AEM operation efficiency and to plan engineering or repair work; it can also be used as an information source for re- engineering and modification of existing AEMs. The described SW can be extended to perform operational diagnostics based on the topological approach of devices of various types. Also, this SW can be considered as a separate information component of the digital twin of a complex EMS, which will allow us to study the main indicators of its reliability, fault tolerance and operational efficiency at all stages of the life cycle. Read more...

Fuzzy relational cognitive temporal models for analyzing and state prediction of complex technical systems

The effectiveness of fuzzy cognitive modeling methods for analyzing and predicting the state of complex technical systems (STS) is justified by the following reasons: significant interdependence, non-linear nature and incompleteness of information about the mutual influence of the analyzed parameters of the CTS; a variety of effects of internal and external factors on the CTS; complexity and cost of conducting experimental studies during the operation of these systems. The main limitations of fuzzy cognitive models for modeling STS dynamics are: the complexity of taking into account the mutual influence of parameters with their different time lags relative to each other; the need for their constant operational adjustment and training of component models for all parameters during the operation of the CTS. In this paper, Fuzzy Relational Cognitive Temporal Models (FRCTM) are developed. These models combine the advantages of various types of fuzzy cognitive models, and at the same time neutralize the main limitations of the analysis and prediction of the state of the CTS, which are inherent in the well- known fuzzy cognitive models. The paper also proposes models of system dynamics that take into account the specifics of the FRCTM. We have also developed an approach and implemented a method for calculating fuzzy dependencies in vector-matrix form for dynamic modeling of the CTS. The proposed method makes it possible to solve the problems of increasing the uncertainty of the results and the output of fuzzy values of the FRCTM concepts beyond the ranges of the base sets due to the execution of mass iterative computations. An example of modeling heterogeneous electromechanical systems based on FRCTM is given. The results obtained are the basis for solving a whole range of tasks of analysis, predictive evaluation, modeling of different scenarios of the functioning and development of heterogeneous electromechanical systems for various system factors, operating modes and external conditions. Read more...

Computer program for modeling of technical state indicators of electromechanical systems

The article is aimed at solving the problem of scientific justification of criteria and methods for assessing the technical state of electromechanical systems based on the topological diagnostic method. Mathematical model and computer program for simulation of technical state indices of asynchronous electric motors (AEM) are presented. Functions and Green matrices, as well as deviation matrices, are considered as such indicators. The basis of the program is the mathematical model of the AEM with a non-accelerated rotor and non-homogeneous windings. AEM is supplied from pulse voltage source. The action is carried out in different directions of the vector space of the motor in order to determine its characteristics and degree of homogeneity. Based on the reactions of the object, the program calculates and analyzes technical indicators for intact and damaged states of the AEM. A computer program for mathematical modeling of the technical state indicators of the AEM was carried out using the Maple package of symbolic and numerical calculations, which provides extensive opportunities for mathematical studies of various levels. A description of a software implementation of the proposed mathematical model is given. An example of using a program to model the performance of a serial motor with specified technical characteristics is given. The article presents the results of modeling the object indicators corresponding to the object different operational states. A reference state, a damaged state characterized by a change in the properties of the vector space during long-term operation, as well as a limit state, which corresponds to a break in one of the phases of the rotor winding, were defined as these states. Conclusions on each of the given electric motor states are given. Read more...

Computer program for modeling the technical quality indicators of inductors of linear asynchronous electric motors

The determination of indicators of the technical quality of electric motors, as well as their modeling, are in demand in the organization, final control of the technical quality of products, in the procedures for diagnosing and monitoring the technical condition of electrical equipment during operation. A large role in substantiating the criteria for the technical quality of electric motors and developing methods for their determination is given to computer modeling. Along with rotating electric motors, linear asynchronous electric motors (LAEM) are increasingly being used in technical systems. Criteria and test methods developed for rotating electrical machines are not adequate to the specifics of the LAEM. As applied to LAEM inductors, a method is proposed for assessing the technical quality indicators of three-phase inhomogeneous inductors with a non-uniform distribution of magnetic properties along the magnetic circuit. The method is based on the impulse effects of a voltage source on the LAEM inductor. A mathematical model, an algorithm and a program for modeling the technical quality indicators of LAEM inductors that implement the proposed method have been developed and presented. The program is written using its own interpreted programming language of the Maple software product and requires the user to enter the parameters of an electrical device. At the output, the user automatically receives an image of the Green’s matrix, oscillograms of phase currents based on the results of three experiments, and numerical values of quality indicators. The simulation results indicate that the proposed method can serve as a tool for the technical control of inductors, and also that the developed technical quality criteria, mathematical model, algorithm and program allow modeling and evaluating the technical qualities of LAEM inductors both during final tests and during monitoring the technical condition of the device during operation. Read more...

Mathematical model for the design of linear asynchronous electric motors and its software implementation

Mathematical models are the main tool for the layout design of linear asynchronous electric motors. Existing design models of linear asynchronous electric motors assume that the device is powered from a source of multiphase symmetrical positive sequence current, which excludes from consideration the asymmetry of the inductor phase currents and the associated reduction in traction force. This approach is not flexible enough, since the operation of linear asynchronous electric motors in a wide range of movement speeds assumes a functional relationship between the current asymmetry coefficient and the movement speed. The study developed a mathematical model for design purposes that implements the functional relationship between the current asymmetry coefficient and the speed of movement. The mathematical model represents 13 linear equations linking geometric dimensions, current loads, electromagnetic field characteristics and mechanical forces with the speed of the secondary element of the electric motor. The current load of an electric motor has a variable degree of ellipticity depending on the speed of movement. An algorithmic study of the mathematical model was carried out and corresponding software modeling tools were developed. The proposed program algorithm, containing two subroutines, is implemented using the Maple symbolic computing software package. In order to expand the range of users, the software model is additionally implemented in C++. In this case, the functional dependence of the asymmetry coefficient of the exciting current wave on the speed of movement is implemented in the form of an iterative procedure for the case of connecting the winding of the linear asynchronous electric motors inductor to a source of symmetrical three-phase voltage according to the “triangle” circuit. Using the example of a three-phase linear asynchronous electric motors, the electromagnetic and mechanical characteristics of the electric motor were simulated. It was stated that the influence of current asymmetry on the mechanical characteristics of the linear asynchronous electric motors is small and is expressed in the region of high speeds. This makes it possible, in design tasks for the layout of an electric motor, to use models that involve powering the linear asynchronous electric motors from a symmetrical current source or to introduce a fixed asymmetry coefficient into them. Read more...

Application of mathematical modeling apparatus to the problem of diagnosing the state of the mechanical circuit of an asynchronous electric motor

The research is aimed at improving the reliability of complex technical systems, including a component such as an asynchronous electric motor, by monitoring their current state. The general objective of the study is to substantiate the possibility of using such a factor as the stator current vector, the oscillations of which are taken as an observable parameter, to diagnose a fault in the mechanical circuit of an electric motor. To substantiate the legitimacy of such a decision, a mathematical modeling apparatus was used with a computational experiment. For this purpose, the purpose and conditions for its implementation were preliminarily formulated, which made it possible to obtain a sufficient evidence base. The mathematical model of an asynchronous electric motor is supplemented with pulse load functions in the form of Fourier series, represented by rectangular alternating and constant sign pulses, the repetition frequency of which is equal to the rotational speed of the electric motor shaft. To conduct a computational experiment, a problem-­oriented algorithm and a Maple program were developed. An original feature of the mathematical model, algorithm and program is the linking of the load torque with the angle of rotation of the rotor, which is typical for damaged mechanical circuits of asynchronous electric motors. Using a mathematical model, the effects on a serial asynchronous electric motor of load torque pulses from a damaged bearing are revealed, as well as the effects of torque pulses from periodic impacts occurring in a damaged mechanical circuit. In both cases, oscillations of the modulus of the stator current vector were recorded, coinciding with the rotor rotation frequency. The results of the computational experiment indicate that stator current fluctuations make it possible to reliably judge the state of the mechanical circuit of the electric motor. The research materials can be used by operating organizations to create systems for instrumental monitoring of the current technical condition of a fleet of asynchronous electric motors. Read more...

Model for quality control of magnetic cores of linear electric motors at the manufacturing stage

The article presents the results of implementing an integrated approach to quality control of linear electric motor inductors at the production stage. The approach is based on the use of mathematical modeling methods and computational experiment. To assess the quality of inductors, it is proposed to use two types of indicators: differential and integral. Differential indicators are determined by conducting a series of experiments with each tooth division of the inductor. Integral indicators allow us to assess the quality of the inductor magnetic circuit as a whole, for which criterion relationships are used. To test the effectiveness of the proposed approach and the reliability of the obtained indicators, a simulation mathematical model of an electric motor inductor with detailing down to one tooth division was developed. Based on this model, an algorithm and a computer program were created that implement the proposed method of quality control during technical testing. The program is written in the Maple software product’s own interpreted programming language and requires the user to enter the parameters of the inductor and power source. As a result of the program, the user receives a conclusion on the quality of the inductor magnetic circuit, as well as numerical values of the differential and integral quality indicators. The materials of the prototype inductor with a high-quality and low-quality magnetic core were used to test the quality criteria using mathematical modeling and computational experiment methods. The results of the experiment confirmed the feasibility of implementing the proposed approach and showed that it adequately reflects the technical quality of inductor magnetic cores. The software product created as a result of the study is intended for technical control of inductor magnetic cores during their production and information support for measures to improve their quality. Read more...