Mathematical model of the inverse problem of thermal diagnostics of engines with errors in the initial data in the problems of aerospace materials science

2021 ◽  
Author(s):  
S. M. Serebryansky ◽  
A. N. Tyrsin
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Initial Data ◽  
Materials Science ◽  
Aerospace Materials ◽  
Thermal Diagnostics

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

History of foundry production. Why does the slash bell sound

2020 ◽  
pp. 57-68
Author(s):  
V. A. Sidorov ◽  
E. V. Osowska
Keyword(s):  
Mathematical Model ◽  
Initial Data ◽  
Complementary Methods ◽  
History Of ◽  
High Level

The article is devoted to the history of foundry production-casting of bells. This art was passed down from generation to generation, there were successful variants, but there were also defective bells. The authors analyzed in detail the different production of slotted bells. Bells are unique single products. They confirm the high level of skill of the master. The loss of sound properties of slotted bells depends on the ratio of the main dimensions, the size of the slits and their locations. The use of complementary methods for measuring mechanical and visualizing sound vibrations allows us to obtain initial data for the development of a mathematical model of sound vibrations of a bell. A continuation of the material about the art of manufacturing and the secrets of production will be published in the next issue of the magazine.

Математическое описание и анализ сигнала виброиндукционного преобразователя при воздействии нормальной составляющей магнитных потоков рассеяния над дефектным участком

2021 ◽  
Vol 7 ◽  
pp. 19-27
Author(s):  
Ю.Л. Николаев ◽  
П.Н. Шкатов ◽  
Э.Ф. Ахметшина ◽  
А.А. Саморуков
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Initial Data ◽  
Vibration Frequency ◽  
Magnetic Field Intensity ◽  
Theoretical Research ◽  
Leakage Magnetic Field ◽  
Induction Transducer ◽  
Experimental Researches ◽  
Defective Area

Theoretical and experimental researches of vibration-induction transducer (VIT) outlet signal formed during exposure to normal leakage magnetic field intensity component Hn over the defective area were carried out. Theoretical research is based on an assumption that VIT signal is a trigonometric series that is limited by first five harmonics. As initial data for mathematical model creation, well-known conformities for Hn distribution over the defective area were used. Based on acquired mathematical model conformities of VIT signal harmonical composition permutation during its movement over the defective area with varying amplitudes and vibration frequency were found. Theoretical research results were proven experimentally. Moreover, additional possibilities of this way of magnetic testing are shown in comparison with conventional ones.

Mathematical model identification of gas turbine engine with account for initial data uncertainty

2021 ◽  
Vol 28 (3) ◽  
pp. 171-185
Author(s):  
Oleg Baturin ◽  
Paul Nikolalde ◽  
Grigorii Popov ◽  
Anastssia Korneeva ◽  
Ivan Kudryashov
Keyword(s):  
Mathematical Model ◽  
Initial Data ◽  
Gas Turbine ◽  
Model Identification ◽  
Gas Turbine Engine ◽  
Data Uncertainty ◽  
Turbine Engine

Coordination of Movements of Two-Handed 12-DOF Robot Manipulators at Their Joint Manipulation

2021 ◽  
pp. 11-18
Author(s):  
L.A. Karginov ◽  
E.I. Vorobyov ◽  
A.K. Kovalchuk
Keyword(s):  
Inverse Problem ◽  
Initial Data ◽  
Degrees Of Freedom ◽  
Control Flow ◽  
Flow Chart ◽  
Hierarchical Approach ◽  
Kinematic Scheme ◽  
Kinematic Constraints ◽  
Generalized Coordinates ◽  
Research Show

The study focuses on a two-handed robot with twelve degrees of freedom, six for each arm, and gives an example of calculating generalized coordinates for the two-armed robot limbs at their joint manipulation. The initial data for obtaining generalized coordinates are represented by the location of the work object, which is a cube. When solving the problem, the last arm links reach the faces of the work object with a given orientation. To obtain generalized coordinates, we used a hierarchical approach, which is based on an algorithm for solving the inverse problem of kinematics, and developed a control flow chart. The values ??of generalized robot coordinates were obtained for each location of the object of work, taking into account the kinematic constraints in the joints of the robot actuator. Findings of research show that it is possible to obtain generalized coordinates for the coordinated movement of the robot actuators with tree-like kinematic scheme.

Influence of Alteration of Variance of Normal Distribution of Microsphere Cavity Radius on the Proccess of Helium Sorption by Microspheres

2011 ◽  
Vol 6 (2) ◽  
pp. 24-27
Author(s):  
Anton S. Vereshchagin
Keyword(s):  
Mathematical Model ◽  
Initial Data ◽  
Normal Distribution ◽  
Theoretical Investigation ◽  
Solid Particles ◽  
Uneven Distribution ◽  
Cavity Radius

Theoretical investigation of the proccess of helium sorption by hollow permeable solid particles (microspheres) is done. Mathematical model of the proccess is derived under the assumption of uneven distribution of radius of microsphere cavity. It's shown that the rate of sorption changes insignificantly for investigated ranges of initial data within normal distribution of microsphere cavity radius

Preface: Advances in computational aerospace materials science and engineering

2018 ◽  
Vol 07 (01n02) ◽  
pp. 1802001
Author(s):  
Zhen Liu ◽  
Teng Yong Ng ◽  
Zishun Liu
Keyword(s):  
New Technologies ◽  
Materials Science ◽  
Rapid Development ◽  
Aerospace Engineering ◽  
Special Topic ◽  
Computational Techniques ◽  
Aerospace Materials ◽  
Science And Engineering ◽  
Aerospace Structures ◽  
Materials Science And Engineering

In the last two decades, with the rapid development of Chinese Aerospace Engineering, many emerging new technologies and methodologies have been proposed and developed in the aerospace engineering discipline. This special topic issue will offer our valued readers insights into the current development of aerospace engineering related computational aerospace materials science and engineering research now being undertaken in China. These 11 research papers include the latest research into the vibration and strength of aerospace structures, aerodynamics of aerospace shuttles and satellite structures, and aeroacoustic noise of aerospace structures. We trust this series papers will provide an overview of aerospace engineering activities in China, focussing in the most advanced computational techniques and powerful numerical methodologies being developed and employed to advance this field.

scholarly journals Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Serdal Pamuk
Keyword(s):  
Mathematical Model ◽  
Initial Data ◽  
Tumor Angiogenesis ◽  
Cell Movement ◽  
Steady State Solution ◽  
Stability Criteria ◽  
Data Perturbation ◽  
Capillary Formation ◽  
The Stability ◽  
Perturbation Approximation

We present a mathematical model for capillary formation in tumor angiogenesis and solve it by linearizing it using an initial data perturbation method. This method is highly effective to obtain solutions of nonlinear coupled differential equations. We also provide a specific example resulting, that even a few terms of the obtained series solutions are enough to have an idea for the endothelial cell movement in a capillary. MATLAB-generated figures are provided, and the stability criteria are determined for the steady-state solution of the cell equation.

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