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

scholarly journals Set-membership identifiability of nonlinear models and related parameter estimation properties

2016 ◽  
Vol 26 (4) ◽  
pp. 803-813 ◽  
Author(s):  
Carine Jauberthie ◽  
Louise Travé-MassuyèEs ◽  
Nathalie Verdière
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Dynamic System ◽  
Nonlinear Models ◽  
Differential Algebra ◽  
Related Parameter ◽  
Set Membership ◽  
Estimation Problems ◽  
The Mathematical Model

Abstract Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.

scholarly journals Modeling of Management Processes of Construction Company Business for Increase in its Competitive Stability

2019 ◽  
Vol 5 (1) ◽  
pp. 246
Author(s):  
Vladimir Evgenievich Bazanov
Keyword(s):  
Mathematical Model ◽  
System Analysis ◽  
A Priori ◽  
Identification Algorithm ◽  
Construction Company ◽  
Construction Companies ◽  
Construction Organizations ◽  
Stability Rating ◽  
Construction Organization ◽  
Smart Technologies

The construction organizations lack adaptive infrastructure. It is required to use more intensively SMART-technologies of design and construction. Purposes of this article: a) the system analysis of categories "competitiveness", "stability", "rating of the company" for the construction organizations; b) to construct and investigate economic and mathematical model of competitiveness of the construction organization; c) to determine parameters of self-organization of construction company; d) to construct an identification algorithm for model. These new tasks also answer the purposes of modern construction business, problems of forecasting of its development. Using methods of the system analysis and modeling, in work three levels of the analysis of construction business are considered: macrolevel (level of the state), mesolevel (level of the region) and microlevel (level of the company). For example, 10 various classes of competitiveness of construction companies are offered. It improves the classification used traditionally. The new economic and mathematical model on the basis of production functions of type of Cobb-Douglas is constructed. The algorithm of its identification on the basis of situational scenarios is also developed. The algorithm finds parameters which will allow to define competitiveness of construction company a priori. The offered research has a development, for example, is possible to use for the forecast of adaptation of the enterprise.

scholarly journals Determining the width of the ship’s course using a mathematical model to ensure the safety of the ship’s navigation

2021 ◽  
Vol 2131 (3) ◽  
pp. 032034
Author(s):  
O Lebedev ◽  
I Lipatov
Keyword(s):  
Mathematical Model ◽  
Time Interval ◽  
Safe Operation ◽  
Drift Angle ◽  
Model Experiments ◽  
Urgent Task ◽  
The Mathematical Model ◽  
Over Time ◽  
Shift Angle

Abstract Determination of the ship’s course width necessary for the ships safe operation is an urgent task due to the increase in the modern ships’ dimensions. The existing methods for assessing the fairway are calculated with a full re-positioning of the propulsion-rudder complex, according to the maximum drift angle. The vessel movement is considered to be steady, that is, the speed, the drift angles do not depend on time. The relevance of this study is associated with the assessment of determining the width of the fairway at any time interval. This is due to the fact that when passing the river sections, the vessels perform maneuvering with the rudder gear shifted for short periods of time and not at the maximum shift angle. Determination of the parameters of the ship’s movement over time when the navigator manipulates the ship’s controls (control of the rudder device, changing the parameters of the main engines) can be determined by the mathematical model of the ship’s movement. This article discusses the issues of creating a model that adequately describe the processes of vessel movement, including in the conditions of vessel movement along a limited ship’s course. The adequacy of the model was verified using the data of field and model experiments. According to the compiled mathematical model, the calculations were made for various projects of dry cargo ships.

Design Tension Controller of Unwinding System Based on LMI-Based H∞ Robust Control

2012 ◽  
Author(s):  
Shanhui Liu ◽  
Xuesong Mei ◽  
Fanfeng Kong ◽  
Jian Li ◽  
Zhihui Liu
Keyword(s):  
Mathematical Model ◽  
Tension Control ◽  
Linear Matrix ◽  
Robust Controller ◽  
Printing Quality ◽  
Time Varying Parameters ◽  
Working Principle ◽  
The Stability ◽  
The Mathematical Model ◽  
Printing Machine

The unwinding system is the most important section for tension generating of the gravure printing machine, and how to maintain the stability of the tension in unwinding system is a key problem to ensure the printing quality. In this paper, an H∞ controller based on Linear Matrix Inequality (LMI) method is presented to strengthen the stability of the tension in unwinding section, and the controller is analyzed and verified by the simulation. Firstly, a nonlinear mathematical model is established according to unwinding system’s working principle, and a linear mathematical model is constructed by analyzing the uncertain and time-varying parameters. Secondly, based on the mathematical model and LMI framework, a H∞ robust controller is designed. Finally, the performance of the H∞ controller is verified by the simulation, and the results show that the proposed tension controller has better robustness and disturbance rejection than traditional PID controller in tension control of the unwinding system.

scholarly journals Mathematical model of the road vibrating roller

2020 ◽  
Vol 1 (1) ◽  
pp. 133-139
Author(s):  
Pavel Aleksandrovich KORCHAGIN ◽  
Keyword(s):  
Mathematical Model ◽  
Dynamic System ◽  
Road Construction ◽  
Well Being ◽  
Point Of View ◽  
Engineering Industry ◽  
Supporting Surface ◽  
The Road ◽  
Vibration Protection ◽  
The Mathematical Model

Introduction. The process of compaction of the soil foundation by a road vibrating roller is considered as the object of the study. The main purpose of vibrating rollers used in road construction is to reduce the energy consumption of the compaction process and increase the productivity of the operations performed Since the 80s of the last century, the engineering industry has noted a tendency to abstention the production of static rollers. By reducing the amplitude of oscillations or completely disconnecting the vibrator, you can get the same static modes, and accordingly the results of rolling. In addition, the reduction of dynamic impacts positively affects the physical condition of an operator of the road-building machine, stabilizes the well-being and increases productivity. Materials and methods. The mathematical model of the dynamic system “Supporting surface–roller–operator” is presented. The main components of the dynamic system are described in the form of ordered and interacting subsystems. The forces acting on the dynamic system are determined; they are sources of dynamic effects. The calculation schemes of the subsystems “Operator” and “Roller”, which are of the greatest interest from the point of view of vibration protection, are reflected. Results. The result of the work can be considered the compilation of generalized scheme of the dynamic system; calculation scheme of the dynamic system; mathematical model “Supporting surface–operator–roller”; implementation of the mathematical model in MathLab, its additional Simulink extension package. Discussion and conclusion. The presented mathematical model allows carrying out research of the processes occurring in the dynamic system “Supporting surface–roller–operator”. The most rational mathematical model can be used in the development of methods and tools aimed at improving the vibration protection system for operators of road rollers. The mathematical model of a road roller is planned to be used as a basis for creating a robotic complex with an automated control system designed to perform operations to compact coatings and foundations in road construction.

Experimental and Numerical Analysis Applied on Steel Bars Cooling

2014 ◽  
Vol 1016 ◽  
pp. 342-346 ◽  
Author(s):  
Paul Campos Santana Silva ◽  
Paulo Henrique Terenzi Seixas ◽  
Caroline Rodrigues ◽  
Leonardo Fonseca ◽  
Rudolf Huebner
Keyword(s):  
Experimental Data ◽  
Heat Treatment ◽  
Mathematical Model ◽  
Numerical Analysis ◽  
Cooling Rate ◽  
Initial Temperature ◽  
Maximum Deviation ◽  
Time Interval ◽  
Steel Bars ◽  
The Mathematical Model

AISI 1020 steel bars cooling have been investigated aiming to obtain their cooling rate during heat treatment. Hot steel bars just taken out of the furnace are piled over other ones that were taken out of the furnace earlier. A mathematical model has been created and implemented using the software EES, Engineering Equation Solver. An experiment was conducted to validate the mathematical model. The experiment consists in three loads of three bars each with a time interval of 5 minutes between them. The initial temperature of each bar was 150oC. The mathematical model can obtain the thermal profile of each bar and the average and maximum deviation when confronted with experimental data were about 8% and 20% respectively.

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 Selection of rational parameters of the cone roller for deep compaction of road bases

2021 ◽  
Vol 7 (1) ◽  
pp. 82-89
Author(s):  
K.Z. Tilloev ◽  
◽  
E.I. Kromsky ◽  
S.V. Kondakov ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Axial Force ◽  
Cone Angle ◽  
Original Method ◽  
Frozen Soil ◽  
Design Parameters ◽  
Total Force ◽  
Cost Criterion ◽  
Optimal Value ◽  
The Mathematical Model

The article is devoted to the method of designing a cone roller for deep compaction of soil used as the working body of a crawler excavator. One of the most important design parameters of a cone roll is the angle of the cone. Known methods allow determining the cone angle for other technological tasks, for example, for loosening frozen soil, and cannot be directly applied to solve the problem. The authors propose an original method for selecting rational parameters of a cone roller head, including the angle of the cone. The method uses a mathematical model of the interaction of a cone roller with compacted soil. In the process of solving the mathematical model are the following parameters: the dependence of the area of the lateral surface of a cone, the dependence of the volume of displaced soil on the contact surface of the cone from the contact patch, the total force, cone force acting on the ground torsional, and axial force in the implementation of the cone, applied by the excavator boom. To identify the optimal value of the cone angle, the function of the volume of displaced soil from the cone angle and the axial force during penetration from the cone angle was studied. As a result, it is determined that the optimal angle of the cone is 240, which will provide the greatest efficiency according to the performance / cost criterion.

Theoretical and Experimental Researches Regarding the Influence of the Suspension Car Stiffness on the Dynamic Behavior of Vehicles

2016 ◽  
Vol 822 ◽  
pp. 36-43
Author(s):  
Dumitru Neagoe ◽  
Dumitru Bolcu ◽  
Loreta Simniceanu ◽  
Mario Trotea
Keyword(s):  
Mathematical Model ◽  
Dynamic System ◽  
Dynamic Behavior ◽  
Experimental Research ◽  
Experimental Results ◽  
Negative Effects ◽  
Experimental Researches ◽  
The Mathematical Model ◽  
Theoretical Results

In this paper the authors present the results of theoretical and experimental research in order to optimize suspension rigidity in case of Daewoo Nubira vehicle. The paper presents the mathematical model obtained by assimilating car with a dynamic system with 5 rigid solids with elastic and viscous linking between them. Theoretical results obtained based on this model and the experimental results are presented, and it is presented a solution to optimize suspension in order to remove the negative effects observed driving on gravel runways or damaged runaways. Theoretical results, compared with the experimental ones, allow us to say that it is possible to optimize suspension by analyzing specific parameters equivalent mathematical model.

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