Verification of the Mathematical Model of a Multidimensional Dynamic System for Adequacy Based on the Spectral Norm of a Residual Matrix

2005 ◽  
Vol 66 (9) ◽  
pp. 1409-1422
Author(s):  
Ch. M. Hajiyev
Keyword(s):  
Mathematical Model ◽  
Dynamic System ◽  
Spectral Norm ◽  
Residual Matrix ◽  
The Mathematical Model

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 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.

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.

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

Simulation of the Dynamic Behaviors of the C Axis Drive by the Turning Center

2009 ◽  
Vol 147-149 ◽  
pp. 356-361
Author(s):  
J. Křepela ◽  
Vladislav Singule
Keyword(s):  
Mathematical Model ◽  
Dynamic System ◽  
3D Model ◽  
Worm Gear ◽  
Turning Center ◽  
The Difference ◽  
Axis Drive ◽  
Torsion Stiffness ◽  
Multi Body ◽  
The Mathematical Model

The paper describes the mathematical model for C axis of the multifunction turning center with worm gear. Talks about the mathematical model with multi-body mass dynamic system. The drive works in the positional feedback and his mathematical model is specified for detection of the dynamical behaviors of the C axis. The turning center is designed for a heavy roughing forged piece from high carbon steels by the power of main motor 71kW. The C axis must be designed as accurate angle position axis and with big dynamic stability of regulation by step or pulse loading. The C axis drive is constructed with help of a hydraulic connected up the worm gearing on a spindle. The driven side of the worm gear is created two dual worms with own servomotors. Worm wheel is solved as one part with two gears. Servomotors are controlled with the mode speed/torque coupling (MASTER-SLAVE), which guarantees the constant torque prestressing between the servomotors. The difference of a torques guarantees leaning of both worm teeth on opposite tooth faces of both gears of the worm wheel. In the dynamic model are involved the friction on the worm gears, torsion stiffness located with help of the FEM and moment of inertia for all parts. 3D models of the C axis is designed in the program ProEngineer. From complete 3D model of the C axis are transfered individual parts to the FEM in surroundings Ansys as volume parts. In this paper is main output influence of the diference between the 3D and 2D for calculation of the stiffness in the contact of the worm gear on the whole dynamic system of the C axis. The value of the torsion stiffness by more situation of the load on the worm gear is used subsequently to the multi-body mass system of the C axis drive and to the eigen frequencies analyses. Results of this paper will be sensitivity check of the changing torsion stiffness on the worm gear by the loading changing on the resulted position accuracy on the C axis. Next review is, if the control modul MASTER-SLAVE is partially this problem of the difference between values of stiffness from 2D or 3D model or also stiffness non-linearity eliminated.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

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