scholarly journals PARAMETRIC IDENTIFICATION OF STOCHASTIC SYSTEM BY NON-GRADIENT RANDOM SEARCHING

2017 ◽  
Vol 16 (3) ◽  
pp. 256-261 ◽  
Author(s):  
A. A. Lobaty ◽  
V. Y. Stepanov
Keyword(s):  
Mathematical Model ◽  
Mathematical Simulation ◽  
Stochastic System ◽  
Stochastic Systems ◽  
A Priori ◽  
Quality Criteria ◽  
Identification Problem ◽  
Operational Capability ◽  
Identification Method ◽  
The Mathematical Model

At this moment we know a great variety of identification objects, tasks and methods and its significance is constantly increasing in various fields of science and technology.  The identification problem is dependent on a priori information about identification object, besides that  the existing approaches and methods of identification are determined by the form of mathematical models (deterministic, stochastic, frequency, temporal, spectral etc.). The paper considers a problem for determination of system parameters  (identification object) which is assigned by the stochastic mathematical model including random functions of time. It has been shown  that while making optimization of the stochastic systems subject to random actions deterministic methods can be applied only for a limited approximate optimization of the system by taking into account average random effects and fixed structure of the system. The paper proposes an algorithm for identification of  parameters in a mathematical model of  the stochastic system by non-gradient random searching. A specific  feature  of the algorithm is its applicability  practically to mathematic models of any type because the applied algorithm does not depend on linearization and differentiability of functions included in the mathematical model of the system. The proposed algorithm  ensures searching of  an extremum for the specified quality criteria in terms of external uncertainties and limitations while using random searching of parameters for a mathematical model of the system. The paper presents results of the investigations on operational capability of the considered identification method  while using mathematical simulation of hypothetical control system with a priori unknown parameter values of the mathematical model. The presented results of the mathematical simulation obviously demonstrate the operational capability of the proposed identification method.

Evaluation of Oil Viscosity Influence on Hydraulic Shock in Long Pipe

2014 ◽  
Vol 630 ◽  
pp. 85-90 ◽  
Author(s):  
Adam Bureček ◽  
Lumír Hružík ◽  
Martin Vašina
Keyword(s):  
Mathematical Model ◽  
Mathematical Simulation ◽  
Experimental Measurement ◽  
Hydraulic System ◽  
Pipe Wall ◽  
Hydraulic Shock ◽  
Oil Viscosity ◽  
Oil Flow ◽  
End Pressures ◽  
The Mathematical Model

This article is aimed at mathematical simulation and experimental measurement of dynamics of liquid and pipe wall during hydraulic shock. Liquid compressibility and hydraulic line elasticity are taken into account in this case. The mathematical model is created using Matlab SimHydraulics software. The long pipe is simulated by means of segmented pipe. Experimental measurement is performed on a hydraulic system, which consists of flow-controlled aggregate, long pipe and seat valve. The hydraulic shock is caused by step closing of the seat valve that is located at the pipe end. Pressures at the end of the long pipe, oil flow and temperature are experimentally measured.

scholarly journals IMPLEMENTATION OF THE METHODS OF IDENTIFICATION OF STATIC CONTROL OBJECTS

2017 ◽  
pp. 72-78
Author(s):  
Sergey Pachkin ◽  
Sergey Pachkin ◽  
Roman Kotlyarov ◽  
Roman Kotlyarov
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Automatic Control ◽  
Automatic Control System ◽  
Mathematical Description ◽  
Control Object ◽  
Parametric Identification ◽  
Identification Problem ◽  
Temperature Control System ◽  
The Mathematical Model

One of the main tasks solved in the development of automatic control systems is the identification of the control object, which consists in obtaining its mathematical description. The nature and type of the mathematical model is determined by the goals and tasks for which it will be used. In the present case, the aim of obtaining the model is the synthesis of an automatic control system. Proceeding from the requirements of control problems, the identification problem consists in determining the structure and parameters of the mathematical model that ensure the best similarity of the model and object responses to the same input action. The article considers the experimental method of obtaining a mathematical description of the control object based on the results of measuring its input and output parameters and then processing the obtained results. The control object is the EP10 emulator made by the Oven Company, which is a miniature furnace. The emulator is used in experimental research in the process of commissioning using thermostat controls, and also applicable for educational purposes as part of training and research stands. As a result of structural identification with subsequent adjustment of the coefficients with the help of parametric identification, a model of the control object in the form of a second order aperiodic link is obtained. Parameters and type of the mathematical model allowed to make calculations and determine the parameters of adjustment of the TRM251 PID-controller. The software implementation of the automatic control system in the MatLAB environment made it possible to evaluate transient processes in a closed system. Thus, the calculation and analysis of the automatic control system in the first approximation were made. The final result can be obtained at the stage of commissioning the automatic temperature control system in the EP10 emulator using adaptation algorithms.

scholarly journals THE PROBLEM OF IDENTIFICATION OF THE MATHEMATICAL MODEL IN THE PRESENCE OF IMMEASURABLE EXTERNALINFLUENCES ON THE SIMULATED OBJECT

2020 ◽  
pp. 37-55
Author(s):  
Sergei Kultyshev ◽  
◽  
Liudmila Kultysheva ◽  
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Identification Problem ◽  
Identification Of Parameters ◽  
External Influences ◽  
Real Objects ◽  
The Mathematical Model ◽  
Simulated Object

A theorem and an algorithm for approximate identification of parameters and immeasurable external influences for mathematical models of real objects are obtained. This identification problem is one of key importance for design the mathematical models in real mathematics applications.

Parametric Identification Method for an Absorption Air Conditioning Parabolic Trough Collector Solar Plant

2020 ◽  
Vol 9 (4) ◽  
pp. 01
Author(s):  
Jorge Díaz - Salgado ◽  
Sandra García - López ◽  
Yuridiana R Galindo - Luna ◽  
R. J. Romero
Keyword(s):  
Mathematical Model ◽  
Air Conditioning ◽  
Least Squares Method ◽  
Flow Line ◽  
Parametric Identification ◽  
Unknown Parameters ◽  
Thermal Plant ◽  
Identification Method ◽  
Solar Plant ◽  
The Mathematical Model

In this work is established a parametric identification method for an absorption air conditioning solar plant. A scaled thermal plant, consisting of a thermal capacitor and a flow line that acts as a capacitor and thermal energy radiator is used. As the mathematical model of the scaled plant is structurally identical to that of the solar plant the first is used to determine the methodology that can be used later for the identification of the PTC solar plant. Parametric identification is a necessary step that allows to determine the unknown parameters of the mathematical model of any solar/thermal plant. This model then can be used to analyze the plant characteristics and design an appropriate control algorithm. Although the system model is nonlinear it can be expressed in the form of a linear regressor in the parameters. This permits to use the least squares method as the identification method. The method is applied to the thermal plant to identify the useful form that the covariance matrix and excitation signals should have to ensure that when applied to the solar plant its unknown parameters can be properly estimated. Once the solar plant parameters are properly estimated model can be used to analyze and simulate the operation of the absorption air conditioning system.

On the equation describing the transient flow of a compressible liquid through deformable porous media

1978 ◽  
Vol 56 (6) ◽  
pp. 691-695
Author(s):  
B. S. BačlićF ◽  
D. P. Sekulić
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Porous Media ◽  
Transient Flow ◽  
A Priori ◽  
Nonlinear Partial Differential Equation ◽  
Compressible Liquid ◽  
Deformable Porous Media ◽  
The Mathematical Model

The effect of the linearized treatment of the equation describing the transient flow of a compressible liquid through elastic porous media is studied analytically in this paper. It is shown that if there is a need for a simplified description based on the linearization of the original nonlinear partial differential equation, then it has to be done in an optimal sense. However, even then the mathematical model may degenerate for certain boundary conditions and some values of parameters defining the dependence of fluid and media properties on pressure. This fact is illustrated by the help of a simple example of transient filtration in a semi-infinite Hookeian medium. The reliability and adequateness of the a priori linearized equation is discussed.

scholarly journals Numerical Simulation of Laboratory Experiments on the Analysis of Filtration Flows in Poroelastic Media

2020 ◽  
pp. 16-31 ◽  
Author(s):  
V.E. Borisov ◽  
E.V. Zenchenko ◽  
B.V. Kritsky ◽  
E.B. Savenkov ◽  
M.A. Trimonova ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Mathematical Simulation ◽  
Laboratory Experiments ◽  
Applied Mathematics ◽  
Fluid Filtration ◽  
Fluid Displacement ◽  
Russian Academy Of Sciences ◽  
Set Up ◽  
Academy Of Sciences ◽  
The Mathematical Model

The work is devoted to mathematical simulation of laboratory experiments on the single-phase fluid displacement in synthetic porous samples. The basis of the mathematical model used is the system of poroelasticity equations in terms of the Biot's model, which implies that the processes of fluid filtration and the dynamics of changes in the stress-strain state of a continuous medium are considered together in the framework of a single coupled statement. For simulation, the software package developed at the Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, was used. The laboratory experiments considered in this work were performed at the Institute of Geosphere Dynamics, Russian Academy of Sciences. The mathematical model used is briefly presented; the main computational algorithms and the features of their software implementation are described. A detailed description of the laboratory set-up, laboratory experiments themselves and their results are given. A significant part of the work is devoted to the problem statement description in terms of mathematical simulation. The results of calculations are presented; the calculated and experimentally observed dependencies are compared. The possible causes of the observed deviations are analyzed.

Application of Multifractal Statistics Method on Time Series

2014 ◽  
Vol 556-562 ◽  
pp. 4559-4562
Author(s):  
Yun Fa Li
Keyword(s):  
Mathematical Model ◽  
Time Series ◽  
Stochastic System ◽  
Multifractal Analysis ◽  
Financial Time Series ◽  
Plasma Turbulence ◽  
Turbulent Plasma ◽  
Financial Time ◽  
The Mathematical Model

The fluctuations observed in tokamaks, stellarators and linear machines were similar with turbulent plasma in fusion devices, which were stochastic system, and the application of statistics method on them is studied in depth. First, the relating theories were summarized; Second, the mathematical model of the multifractal process is analyzed; Finally, the simulation on multifractal analysis of plasma turbulence and financial time series is carried out, results show that this method can be applied in time series effectively.

scholarly journals Optimization for Nonlinear Uncertain Switched Stochastic Systems with Initial State Difference in Batch Culture Process

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Jinlong Yuan ◽  
Jun Xie ◽  
Honglei Xu ◽  
Enmin Feng ◽  
Zhilong Xiu
Keyword(s):  
Batch Culture ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Identification Problem ◽  
Complex Nature ◽  
Initial State ◽  
Approximation Techniques ◽  
System Parameters ◽  
Continuous State ◽  
State Difference

Based on the deterministic description of batch culture expressed in form of switched ordinary differential equations, we introduce a switched stochastic counterpart system with initial state difference together with uncertain switching instants and system parameters to model the process of glycerol biodissimilation to 1,3-propanediol (1,3-PD) induced byKlebsiella pneumoniae(K. pneumoniae). Important properties of the stochastic system are discussed. Our aim is to obtain the unified switched instants and system parameters under the condition of different initial states. To do this, we will formulate a system identification problem in which these uncertain switched instants and system parameters are regarded as decision variables to be chosen such that the relative error between experimental data and computational results is minimized. Such problem governed by the stochastic system is subject to continuous state inequality constraints and box constraints. By performing a time-scaling transformation as well as introducing the constraint transcription and local smoothing approximation techniques, we convert such problem into a sequence of approximation subproblems. Considering both the difficulty of finding analytical solutions and the complex nature of these subproblems, we develop a parallelized differential evolution (DE) algorithm to solve these approximation subproblems. From an extensive simulation, we show that the obtained optimal switched instants and system parameters are satisfactory with initial state difference.

Identification of the Mathematical Model of Failure Frequency of Overhead Lines of Power System Main Grid

2020 ◽  
pp. 100-111
Author(s):  
N.E. Zubov ◽  
I.M. Galiaskarov ◽  
V.N. Ryabchenko
Keyword(s):  
Mathematical Model ◽  
Dynamic System ◽  
A Priori ◽  
Original Method ◽  
Linear Matrix ◽  
Time Interval ◽  
Identification Algorithm ◽  
Electrical Grid ◽  
Failure Frequency ◽  
The Mathematical Model

Based on the analysis of accidents of 500 kV over-head lines of the main electric electrical grid of a wide region over a long-time-interval, the failure frequency (failure flux parameter) was determined under the influence of natural and socio-economic factors. It is proposed to consider the indicated failure rate as the output signal of a discrete positive dynamic system with many difficult formalizable inputs. To identify the mathematical model of a dynamic system, it is proposed to use the original method, the identifiability criterion of which is based on the compatibility condition of the linear matrix equation, and the numerical identification algorithm is based on the solution formula using zero-divisors and generalized inverse matrices. The method does not require a priori information about the parameters of the mathematical model of the electric electrical grid, does not involve solving the forecasting problem, and does not apply statistical calculations

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