Method of Identification of the Mathematical Model of a Single Class of Linear Dynamic Systems with Variable Parameters

Мокін, Б. І.; Мокін, О. Б.; Kryvonis, Oleksandr

doi:10.31649/1997-9266-2018-141-6-62-76

Cited by 3 publications

(8 citation statements)

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“…If the graphs of the processes in the electric drive system of the crane, which are shown in Fig. 6-8, and obtained by simulation using the mathematical models synthesized in [8][9][10], taking into account time and space variables, to compare with the graphs of processes in the electric drive system of the crane with approximately the same characteristics, obtained experimentally by the authors of the work [7], then it is possible to see that they are the same character and only slightly differ in scale, which indicates the adequacy of our mathematical models to real processes that take place in this class of dynamical systems. And at the same time, if there are graphs of processes, obtained by the authors of [7] using mathematical models with stable parameters both in time and space for the two-mass structure of the object, then it is easily possible to make sure that they have a different nature.…”

Section: Discussion Of Research Resultsmentioning

confidence: 99%

“…To simulate a full cycle of lifting a load by a crane, it was taken into account that the equation of dynamics (2) for the period of motion of an electric drive with a steady angular velocity, as shown in our works [9,10], takes the form:…”

Section: Methodsmentioning

confidence: 99%

“…where t 1 , t 2 , t 3 -in accordance with the moment when the angular velocity of the electric motor reaches a constant value after starting, the moment of completion of motion with a constant angular velocity and the moment of stopping the motion. And in order to be able to assess the longitudinal vibrations arising in the cables, in our works [9,10], it is proposed to integrate the models…”

Section: Problem Descriptionmentioning

confidence: 99%

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Adequacy Evaluation of the Synthesis of Mathematical Models for One Class of Linear Dynamic Systems With Parameters, Variable in Time and in Space

Мокін¹,

Мокін²,

Kryvonis³

2020

ScienceRise

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The object of research: the authors of this work have synthesized in previous publications a mathematical model of one class of linear dynamic systems with variable parameters in time and space, which includes the system for lifting and lowering a load with a crane in the case of taking into account the influence of longitudinal vibrations that arise in the cable of the lifting mechanism, and shift in time of the moment of inertia of the rotating masses reduced to the motor shaft. Investigated problem: simulation models are synthesized in the Simulink graphical software environment of the MATLAB application package to assess the adequacy of the specified mathematical model. A calculation was carried out using the passport data and characteristics of all components of the crane structure to find the numerical values of the parameters of simulation models, including the electric motor, cable and gearbox. The main scientific results: the results of modeling the dynamics of the electric drive system during acceleration, deceleration, the prevailing velocity are given. By comparing the results obtained on the simulation model with the results of experimental studies of the same class of dynamical systems carried out by other authors, the adequacy of the mathematical models synthesized by the authors of this work is proved. It is proved that the use of the classical equation of the dynamics of the electric drive system, which contains a constant moment of inertia and a constant moment of load, leads to errors in the estimates of the processes accompanying the lifting and lowering of loads by cranes. And this, in turn, does not allow predicting the behavior of the system in various operating modes with sufficient accuracy. The area of practical use of the research results: enterprises of the machine-building industry, specializing in the production, modernization of lifting equipment. Innovative technological product: a simulation model of a crane mechanism, which makes it possible to take into account the influence of longitudinal vibrations that arise in the cable of the hoisting mechanism, and the shift in time of the moment of inertia of the rotating masses reduced to the motor shaft. Scope of application of the innovative technological product: design and development of control systems for electric drives of lifting equipment.

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Section: Discussion Of Research Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Problem Descriptionmentioning

confidence: 99%

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Adequacy Evaluation of the Synthesis of Mathematical Models for One Class of Linear Dynamic Systems With Parameters, Variable in Time and in Space

Мокін¹,

Мокін²,

Kryvonis³

2020

ScienceRise

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“…The withdrawal of the design ratio for method of synthesis of mathematical models of nonlinear dynamic systems as the initial conditions of the method, as well as in [8,9,11], there had been taken first the condition set in the [18], stating that the nonlinear dynamic system under consideration may be presented as a serial connection of the two structural units, as shown in Fig. 1, where one of the links characterizes the inertial properties and is described by impulse response g(t), and the second, the inertia-free one characterizes the nonlinear properties, connecting its input with the output Z of an ordered polynomial: This precondition, as shown even in the same work [18], allow to bind an input signal x(t) of the system with the output z(t)…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…One of the authors started to research the possibilities for practical application of the ideas suggested in [18] at the beginning of the 80-th of the last century, suggesting in the work [9] a recovery method for the input signals of the measuring systems with non-linear polynomial function of conversion with the presentation of these systems by frequency characteristics of inertial part as well as using the integral Volterra equation for their binding into one mathematical structure. The modified algorithm of this method was suggested in [8] for the simultaneous solution of the problem of input signals recovery in nonlinear dynamical systems, as well as the problem of synthesis of mathematical models of these systems.…”

Section: Introductionmentioning

confidence: 99%

The Synthesis of Mathematical Models of Nonlinear Dynamic Systems Using Volterra Integral Equation

Мокін

Mokin

Мокін

et al. 2022

IAPGOS

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The problem of creating mathematical models of nonlinear dynamical systems does not have an unambiguous solution and requires the creation of a separate synthesis method for each such object. To develop a method for synthesizing mathematical models of an extensive class of nonlinear dynamical systems with polynomial nonlinearities. The work uses a method based on the solution of the Volterra integral equation in the ideology set forth in Van Trees H.L., according to which the structure of a nonlinear dynamical object present47s a series connection of the linear part, characterizing the inertial properties of the system, and the nonlinear element, given by static characteristic. The difference of the suggested version of the method from the classical one, proposed in the works of Van Trees H.L., is an expansion of their input and output signals into Fourier series and a representation of the inertial part of these systems by their Bode plots, connected into one structure with input and output signals and non-linearity by Volterra integral equation. The algorithm of the proposed method is disclosed by the example of solving the problem of identifying a nonlinear dynamical system which impulse response of the inertial part satisfies the separability requirement, the order of the polynomial nonlinearity is three, and the model of the input signal has the form of a sinusoid "raised" over the time axis on a priori given constant level. A computational experiment was carried out on the example of nonlinear dynamical systems with the third order of the nonlinear characteristic and the first and second orders of the model of the inertial part of these systems with the specified algorithms of their parametric identification. The suggested method allows to synthesis the mathematical model of a nonlinear dynamical system with the polynomial static characteristic to the case when the input signal has an arbitrary number of harmonics, and the model of the inertial part and the nonlinear polynomial function have an arbitrary order.

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INTELLIGENT METHOD WITH THE REINFORCEMENT OF THE SYNTHESIS OF OPTIMAL PIPELINE OF THE DATA PRE-PROCESSING OPERATIONS IN THE MACHINE LEARNING PROBLEMS (Eng)

Dratovanyi

Mokin

2022

SWVNTU

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The paper is devoted to the synthesis and optimization of the pipelines of the data pre-processing operations in the problems of the machine learning models construction. It is noted that it is important to optimize the triad of these pipelines -select optimal sequence of the optimal operations with the optimal parameters. In this case, the change of even one element immediately influences the choice of all other elements and their parameters. In general case, there exists a great number of the admissible variants of such pipelines for each model of machine learning and input data (random values or time series) and, as a rule, there is no marked datasets of model training for the synthesis of such pipelines. The survey of the known approaches to the solution of such problems has been carried out, the conclusion that the best way is to formalize them as the problems of reinforcement machine learning has been substantiated t. Typical approaches to the formalization and intellectual methods of similar problems solution have been presented.It is noted that the solution of the problems with reinforcement, as a rule, is complicated due to large dimensionality of the possible sets of the types and subtypes of the operations with different parameters and has problems with the coincidence to really optimal value during limited time. That is why, several improvements, enabling to solve this problem at certain conditions, are suggested. First, it is suggested to allocate variable and constant sections of the pipeline of the data pre-processing operations. It is also suggested for different types of the machine learning models what operations should be referred to the first and last unchangeable links and what operationsto variable link and only to this link it is suggested to apply reinforcement learning. Secondly, the algorithm of the initial setting of RL-policy parameters depending on certain statistical and other characteristics of the input data is suggested. The proposed improvement of the method with the reinforcement of the synthesis of the optimal pipeline of the operations can be applied not only for pre-processing operations but for other problems with the similar data formalization and problem set up.

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Method of Identification of the Mathematical Model of a Single Class of Linear Dynamic Systems with Variable Parameters

Cited by 3 publications

References 1 publication

Adequacy Evaluation of the Synthesis of Mathematical Models for One Class of Linear Dynamic Systems With Parameters, Variable in Time and in Space

Adequacy Evaluation of the Synthesis of Mathematical Models for One Class of Linear Dynamic Systems With Parameters, Variable in Time and in Space

The Synthesis of Mathematical Models of Nonlinear Dynamic Systems Using Volterra Integral Equation

INTELLIGENT METHOD WITH THE REINFORCEMENT OF THE SYNTHESIS OF OPTIMAL PIPELINE OF THE DATA PRE-PROCESSING OPERATIONS IN THE MACHINE LEARNING PROBLEMS (Eng)

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