Innovations in
aviation and cosmonautics-2011 Scientific
practical Conference of young scientists and students of the Moscow Aviation Institute ( Stream
"Mathematical problems in the aerospace industry" A.A.Puntus Moscow
Aviation Institute ( Moscow, Russia In order to promote
the research work of students and young scientists of MAI, a scientific
practical conference of young scientists and students of Moscow Aviation
Institute "Innovations in aviation and cosmonautics-2011" was hold on April
26-30 of 2011. This conference is the third annual conference of the Moscow Aviation
Institute, which is conducted to develop research work of students and young
scientists, and its main focus is modernization of The holding of this conference
is certainly one of the most important events this year, which is the year of Russian
space exploration as announced by the order of the President of Russia, and is
one of the commemorative activities to maximize the reach of the youth
audience, increase its knowledge about our country's role in space exploration
and about modern and future Russian space exploration, and increase interest in
careers that provide a progress in cosmonautics. The goal of this conference is
to attract students and young scientists in At this
conference, participants had a popular the direction of "Mathematical problems
in the aerospace industry", which has been implemented in the sections
"Application of mathematical methods to engineering and economic problems" and
"Mathematical and software systems for information processing and management".
In these sections, which were chaired by professors of the department "Applied
Mathematics and Physics" of MAI A.A.Puntus and A.V.Panteleyev, respectively,
informative reports were presented by undergraduate and graduate students of
the institute. Main advantage of these reports was the objective and
interesting information presented in a modern way, which showed an increase in
scientific interest of young people to
applied research, technology, innovation and scientific creativity. Abstracts
of these reports are presented in this publication. On November 26 of 2009, the
Moscow Aviation Institute is promoted to the category of the "national research
university in the field of training in all aspects of designing and testing aircrafts,
aerospace and rocketry" by order of the Ministry of Education and Science of
the According to the results of
the conference, which was held on April 26-30, the authors of the best reports
were given the opportunity to publish articles in the leading journals, as well
as were given the recommendation to participate in the conference, XI
all-Russian exhibition of scientific and technical creativity of youth "STCY- Member of the
Conference Organizing Committee, the Chair of
the Section "Application of mathematical methods to solve engineering and
economic problems", Stream "Mathematical problems in the aerospace industry" Professor
A.A.Puntus. А.А.Ermakov, P.A.Fomkin, S.N.Padalko. (Moscow Aviation Institute, Mathematical
methods in the field of microbiological safety: detection and localization of
microorganisms in the image. The task of pattern
recognition of microorganisms is just "first step", or so called preprocessing
in resolving task to "the higher level" (for example the recognition of
microorganisms). The task of detecting the microorganisms
on the image appears more than simple for the human sight; however, with an
attempt at the construction of the automatic acquisition system of
microorganisms it is necessary to contend for the sake of the following
complexities: -
Strongly being varied exterior view in different
microorganisms; -
The possible presence of specific features
substantially complicates automatic recognition; -
The conditions for survey (illumination, the color
balance of camera, the distortions of image, by system's optics, image quality)
to a considerable degree influence the obtained image of microorganisms; The existing algorithms of the
detection of microorganisms can be broken beside two wide categories. In the
first category the methods, which are repelled from the experience of man
before the recognition of microorganisms and which make the attempt to
formalize and to algorithmize this experience, are placed, after constructing
beyond its basis mathematical [mozhel] of recognition. The second category
rests beyond the set of instruments of pattern recognition, examining the task
of detecting the microorganisms as a special case of the task of recognition. A.V.Teryohin,
A.A.Puntus. (Moscow Aviation Institute, Strap down inertial system as
a basis of system of orientation
in space. In the given research work a strap
down inertial system based on three axial gyroscopes and accelerometers, edited satellite navigational
system, for system engineering of orientation of a motorcycle research and the
analysis of a possibility of use is conducted in space and by that a
possibility of installation of the fact of its falling at movement. Besides,
the analysis of the various integrated means of safety, search of various
necessary devices and solutions for prevention and the prevention of accidents,
and also recommendations about their improving and introduction is carried out.
Mathematical security is considered with reference to a subsystem of security
of the fact of detection of a vehicle in special situations. In work the
methods described for creation of onboard intelligence systems of pilot less
flying machines and various vehicles are used, functional algorithms, models of
errors are considered. Also motorcycle movement at turn is modeled, on purpose
to learn a maximum possible angle of a deviation from a vertical. Besides,
during the given work economic validity of development of the given device with
a view of operative reaction to incidents is affected. Thus, the purpose of the
given work is the analysis of use of onboard intelligence systems in various
cases. Within last decade,
development of onboard intelligence systems is one of the basic directions of
research of motor industry, with a view of a raise of safety and comfort of four-wheel
vehicles. These new process engineering's
are already presented in the automobile market and their development,
certainly, is fast and effective. However, such process engineering's in
motorcycles, with a view of a raise of safety and comfort of drivers, have not
received now so a wide circulation and undoubtedly should be are worked in more
details. We will reduce the detailed review of some onboard intelligence
systems, making the greatest impact on safety and
awareness of the motorcyclist. It is the notification about movement
velocities, that is informing of the driver in
those situations when the motorcycle velocity exceeds admissible, on the given
site of road. The information on an admissible velocity undertakes from maps
and co-operates with the data received from a motorcycle. The prevention
of turn radius is intended to notify the driver about a high risk not entrances
in turn. The information that the velocity is excessively high, arrives by сравнивания
the planned profile of a velocity, acceleration and jerk, and also the
information received of a road map. Recommendations about a velocity, at
entrance in turn, represent values of a velocity which the motorcycle should
have in the following some seconds for a successful input in turn. The
prevention of face-to-face collision works when there is a risk of origin of
collision with an obstacle, discovered in the field of motorcycle
determination. It is reached by installation in a forward part of a motorcycle
of laser reading out installation which not only discovers an obstacle, but
also estimates weight of collision. This function consists of two minorants:
One is a safe distance, namely, notifies, if the distance is too close in
comparison with time of a response of the driver and the second is a safe ratio
a velocity-way, that is the prevention if ahead the car intersects a trajectory
or slowly goes, and the driver does not react, probably that he has turned
away. As a result of scientific work
the object in view has been reached, namely: the possibility of use of onboard
intelligence systems as a basis for creation of system of safety of the various
vehicles realizing the information to the driver about a velocity and a
position of the nearest vehicles, the prevention of the driver in case of
potentially dangerous evolution, from the point of view of possible collision
is shown. Models of possible errors, algorithms of orientation, and also use of
onboard intelligence systems for correction of output data's with a view of a
safety and comfort raise are taken apart at movement of vehicles. A.I.Yemel 'kin, A.A.Puntus, V.I.Polezhaev. (Moscow Aviation Institute, Parametric study of heat
transfer and flow structures in an inclined layer in the heated end face. Convection and heat
transfer in an inclined layer in the presence of a longitudinal temperature
gradient (the case of heating the layer from the end) have been studied much
less than in the case of an inclined layer in the transverse heat input. However,
this case is also interesting for the theory of heat convection and has a
practical value (convection during crystal growth in a horizontal
"boat", fueled by lower layers in the vertical shafts, cooling down
wells, advective flow in the atmosphere, ocean, asthenosphere) and others. In
this paper we continue the parametric study of convection and heat transfer in
inclined layer without the assumption of a periodic structure along the fiber
is treated with a heated face of the horizontal and vertical layers heated from
below, as well as the intermediate position, achieved by turning the layer.
Calculations were performed for different Calculations are based on a networked computer laboratory IA Mech RAS. A.I.Safonov, O.V.Kholostova. (Moscow Aviation Institute, Construction of a non-resonant
periodical solution in Hamiltonian systems in the neighborhood of a stationary
rotation. In many devices of
the aerospace engineering one of the operating modes is the mode of a
stationary rotation. It is of interest to study the influence on such motions
small periodical in time and angular coordinate perturbations. The first step
in this research is to examine a general non-resonant case, when there're no
special form constraints. The motion of the The
goal of this work is to determine conditions of existence and to construct a
non-resonant periodical solution of the total system in the neighborhood of the
stationary rotation of the unperturbed system. Using the
Deprit-Hori's method and the Poincaré's
method of a small parameter an algorithm of constructing a non-resonant
periodical solution of the system in the neighborhood of the stationary
rotation of the unperturbed system is made. For this solution the positional
coordinate and the conjugated momentum are
periodical with the period equal to the period of perturbations, as well as
momentum conjugated with "almost cyclic" coordinate. Explicitly written out the
solution to the first approximation of the small parameter. Following
conditions, when this solution exists, are found: 1) fluctuating
frequency of a cyclic coordinate is integer; 2) small
oscillations frequency of the unperturbed reduced system in the neighborhood of
the equilibrium is not integer; 3) there are some
special restrictions at the harmonics of the perturbed part of the Hamiltonian,
that only depend on the "almost cyclic" coordinate and time. As an application
it is considered a model problem of the spherical pendulum with the point of
suspension that performs horizontal oscillations at an arbitrary frequency and small
amplitude. A periodic solution in the neighborhood of it's conic motion in the
case of vibrating point of suspension is constructed. This work is supported by
"State support of leading scientific schools" (SS-3797.2010.1) A.M.Bulatova,
A.A.Puntus, E.B.Kuznetsov. (Moscow Aviation Institute, Problem
about dynamics of nonlinear viscously plastic rod. The
purpose of the given scientific work is the numerical solution of a problem
about longitudinal blow on a viscously plastic rod by means of chosen for this
numerical method. The physical model of a considered problem is investigated by
means of its information to corresponding mathematical model of viscously
plastic blow. The given mathematical model represents a boundary value problem
which in turn for the purpose of its approached numerical solution is reduced
to a Cauchy problem. Thus, a main objective of the given work is research of
longitudinal blow on nonlinear viscously plastic rod. For a solution of the given
considered physical problem, and, hence, its mathematical model, one of
numerical methods is applied. Subject domain analysis is spent, the
representation is formulated and the choice of a method for a problem solution
is carried out. The following chosen numerical methods will be applied to this
purpose - a method of shooting and a Runge-Kutt method of the fourth order of
accuracy. So, in the given work one of
approaches to a problem solution about longitudinal blow on one of end faces
originally the motionless semi limited rod within the limits of its viscously
plastic model is considered. Problem statement is reduced to the following. The
origin of co-ordinates is located in the rod beginning, and the rod axis
coincides with an abscissa axis so that its points belong to a semi-infinite
interval of the given axis. In an initial considered instant on a rod end face
blow therefore the rod material starts moving is made. At a solution of the
given problem we consider a rod thin and it is neglected by a side swelling and
influence of cross-section strains. We suppose also that contracting voltages
are positive and displacement of all points of any cross-section are equal and
parallel to a rod axis. Further the equation of movement worked out thus and
special attention is considered thus converted on - a velocity of transition of
points of a rod. Besides, the indicial equation describing mechanical
properties of a viscously plastic material and establishing connection between
a velocity of a strain and voltage of the considered rod is introduced. The
equation of this kind describes a plastic strain at high-speed blow. In the
equation received thus the magnitudes defining a material of a rod are
considered as constants: a static yield point, and also the data of a viscously
plastic material, characterizing influence of velocities of a strain. In case
of small strains at equation construction connection of a velocity of a strain
with displacement is considered. For a solution of the boundary
value problem put thus, namely for the approached determination of a solution
of a boundary value problem, the method of an information of the given solution
to a multiple solution of a Cauchy problem by means of a known method of the
shooting which essence consists in a multiple solution of a Cauchy problem for
the purpose of deriving of the approached numerical solution of the given
boundary value problem is carried out. Values of the outcomes received by means
of the developed program in which the used numerical method has been realized,
are shown in the corresponding table and their comparison with the exact values
received analytically is spent. Outcome of the given work is
the made and realized program of calculation. In the basic final outputs the
received numerical values of magnitudes of a velocity of a strain have special
value. The discovered values allow to estimate rod acceleration that as a
result allows to draw conclusions on a strain of a viscously plastic rod. The
given values can be used at practical calculations of the corresponding applied
problems connected with performance of many technological operations in
mechanical engineering, aircraft, building and other numerous branches at shock
handling and destruction of various materials. The problem about transition
of points of a rod at blow on one of its end faces has independent value in the
mechanic and represents, for example, interest for the theory and practice of
deriving of multilayered materials by explosive process engineering. A.O.Simonenko, A.V.Panteleyev. (Moscow Aviation Institute, Estimation of economic
efficiency of investment projects in conditions of uncertainty. The interval analysis, as an
effective method of work with uncertainties is considered. At use of the
interval analysis the data which is not giving in to the exact description, is
represented as the interval numbers set by an interval of values, instead of
the fixed quantity. The interval and interval uncertainty are initial concepts
of the interval analysis. Interval uncertainty is a condition of incomplete
knowledge of quantity for which is known only the belonging to some interval,
which is the closed numerical interval. The mathematical discipline, studying
problems with interval uncertainties and methods of their decision, is called
as the interval analysis. However
the classical version of a method has a number of essential restrictions: as an
initial interval it is possible to set only an interval which is not containing
neither zero, nor infinity, as well as the given method does not allow finding
all roots of the equation on the specified initial interval, but only one root. In the given work the
algorithm of the modified As a basis of the modified
interval method of By means of the developed
modification of a method applied problems of an estimation of efficiency of
investment projects which generally can't be solved by means of a classical
variant of the given method are solved. The detailed algorithm of
application and the software of methods of an estimation of economic efficiency
of the investment project of modernization of manufacture without the
inflationary factor and taking into account the inflationary factor are
created. Also the problem of calculation of the basic cost indexes of activity
of the enterprise is considered, and is created algorithmic and the software of
application of methods of the interval analysis for its decision. Efficiency of
the software is shown on modeling examples. V.N.Panovskiy, A.V.Panteleyev. (Moscow Aviation Institute, Implementation of contractors
in the form of a program in C#. The purpose of this work was to create a program in C#, which solves
problem of execution of restrictions with
contraction operators of Gauss, Kravchik and Gauss-Zeidel. Problem of execution of restrictions imply a set
of relations (or constraints), relating the variables belonging to some areas,
which are assumed for simplicity as intervals. The solution to this problem will allow finding
the solutions of systems of both linear and nonlinear equations or
inequalities. When compressing the problem of execution of
restrictions source parallel tope, or an interval vector (Cartesian product of
intervals) is replaced with a smaller area. The set of solutions in this case remains
unchanged, thus effectively applying contraction operators, the initial region
will converge to the solution set. Classic Gauss elimination algorithm (solves the problem of execution of
restrictions of a linear system with a square matrix) has been modified in
accordance with the properties of interval matrices and vectors. Contraction
operators of Kravchik (problem of execution of differentiable restrictions,
where the number of restrictions equals the number of variables) and Gauss-Zeidel
(solves a problem similar to the method of Gaussian elimination) can be
obtained by using interval arithmetic to a method, based on the notion of a
fixed point. The result of this work is the creation of a library on the algorithmic
language C#, which implements the previously mentioned contraction operators. It is planned to
supply the created library with contraction operators based on a parallel
linearization, forward and backward method and others. The importance of
the contractors comes from the fact that they are a fundamental component of
the solution operators: methods for solving square systems of nonlinear
equations, global optimization (algorithms of Moore-Skelbo, Hansen), the
minimax optimization. Solution operators do not directly use the inclusion functions and
interval calculations, they only create the strategy of contraction operators
and ensure a way out of impasses (e.g., by bisection of the original area and
applying the algorithm to the resulting sub-areas). D.V.Metlitskaya,
A.V.Panteleyev. (Moscow Aviation Institute, Application of genetic algorithms with binary and real
coding to an optimal control problem of the aircraft. In the given work
genetic algorithms of conditional optimization with binary and rуal coding are considered. Genetic algorithms
concern met heuristic methods of search of a conditional global extreme of
functions of many variables. At the heart of their work the modeling of some
natural ways of optimization (evolution) lies: genetic inheritance and natural
selection. Essence of the mechanism of natural selection: in the course of
evolution the most adapted individuals survive and breed. Thanks to the
mechanism of genetic inheritance their descendants keep the basic qualities of
parents, and being exposed to casual mutations, get also a number of new
properties. If new properties are useful, they also remain and inherited.
Average fitness of the individual with each generation thus grows. Genetic algorithms
with binary and real coding find the decision which can differ a little from
optimum, but thus is comprehensible from the practical point of view. Genetic
algorithms find a global extreme of functions with difficult structure of level
lines, and also find the decision when almost completely there is no
information on properties of investigated function. Working out of
algorithmic maintenance of genetic algorithms is necessary for the decision of
various applied problems. In work application of genetic
algorithms of conditional optimization with binary and real coding to a problem
of search of optimum control of continuous dynamic systems is considered. The
technique of application of genetic algorithms to the considered problem is
developed. On its basis the applied optimal control problem of the aircraft - a
control problem of the missile "air-to air" average range has been
solved. It is required to translate
the missile from the set initial position with the set initial speed and a
trajectory angle of slope in a point with the set height and the maximum range
at fixed time of flight of the missile. For this purpose it is necessary to
generate the control providing flight of the missile on energetically favorable
trajectory. Control of the missile is made by means of control of a
cross-section overload. Control process of the missile is considered in the
determined statement. On all trajectory of operated flight process of
realization of the set overloads is considered without inertia - at each
present situation of time conformity between an overload and a balancing angle
of attack is established. It is considered that the missile is counterbalanced
concerning the center of weights, i.e. is in a balancing mode. Influence of all
set of random factors and simplifications is considered by introduction of an
additional making cross-section overload (equivalent loading). Acceptance of
such assumptions has allowed not describing rotation of the missile round the
center of weights that has essentially simplified system of the equations of
movement of the missile. Rocket movement is considered only in a vertical
plane, in one channel of prompting. By means of the offered
algorithms optimal control of the missile, and an optimum trajectory of flight
of the missile have been found. Comparison of the received results with results
of other methods which has shown efficiency of genetic algorithms has been
made. D.G.Filimonov, A.A.Puntus,
E.B.Kuznetsov. (Moscow Aviation Institute, Definition of limiting
conditions of elastoplastic bodies. The given scientific work is
devoted the analysis of the intense-deformed condition of a rod in the field of
fluidity of the diagram of a stretching-compression. The considered area
superimposes essential restrictions on use of mathematical methods owing to
that the exposition of the intense deformed condition leads to singular
differential equations because of rushing in zero of a tangential stiffness
factor. Deriving of algorithm of a regularization of the problem was a primal
problem, allowing to avoid singularities and to use traditional numerical
methods for a task in view solution. At a solution of problems about
deformation of bodies from an ideal elastoplastic material at some values of
exterior forces limiting conditions - equilibrium configurations in which
strains are converted in infinity are reached. Corresponding loading is called
as limiting. Universal method of solution of problems on elastoplastic
deformation of bodies with arbitrary geometry is the finite element method.
After digitization of an initial differential equation by a finite element
method procedure of definition of equilibrium configurations of a body is
reduced to step by step integration of nonlinear system of ordinary
differential equations. In a limiting condition of a body the matrix of this
system is degenerated. In standard procedures of step by step integration of
system of ordinary differential equations as deformation parameter exterior
force is used. In neighborhoods of maximum loads it is necessary to use small
pitches on loading for definition of equilibrium configurations. Thus
repetitive processes of an improvement of a solution converge slowly or
disperse. In the present work the finite element
method is supplemented with a method of prolongation of a solution on the best parameter
which reduces procedure of definition of equilibrium configurations of a body
to step by step integration of system of ordinary differential equations. The
algorithm of regularization in which basis the method of prolongation of a
solution on the best parameter lies is with that end in view offered, allowing
to avoid the singularity in the field of fluidity of the diagram of a
stretching-compression. This algorithm consists of following basic stages. At
first to an initial differential equation the finite element method is applied.
Practically it is realized as follows. The considered rod from an elastoplastic
material is divided into some number of finite elements. In each finite element
the system of indexed knots in which values of required function are unknown
quantities gets out. To each indexed knot basis function such is assigned that
in this knot it is equal to unit, and in remaining indexed knots of rated area
- to zero. The number of basis functions is equal in rated area to number of
indexed knots, and for various knots they possess property of linear
independence on all rated area. The problem solution approximately is under
construction in the form of a linear combination of basis functions on all
indexed knots of rated area. This solution is substituted in a differential
problem, and as the solution approached, outcome of substitution will be not
identical zero, and some functional discrepancy. The received system of the
linear algebraic equations is differentiated on the best parameter and dares
concerning the received derivatives. Then the system of differential equations
is integrated by means of one of methods of numerical integration. The finite element method applied in
work is almost added by a method of prolongation of a solution on the best parameter
which has allowed to reduce considered procedure of definition of equilibrium
configurations of a body to step by step integration of system of ordinary
differential equations. Efficiency of algorithm is shown at a solution of a
test problem about a stretching of a rod from an ideal elastoplastic material. E.A.Alyoshina,
A.V.Panteleyev. (Moscow Aviation Institute, PSO
Application to the optimal control of discrete deterministic system. Particle Swarm Optimization
(PSO) is met heuristic and Swarm Intelligence method for searching the global extreme.
The idea of PSO is to simulate the behavior of flocks of animals in search of
food. When implementing the PSO the following basic principles are used: -
the extreme is searched by set of individuals
(particles); -
each particle receives information on the movements of
its neighbors; -
each particle moves towards the target by imitating
the neighbor's actions; -
the information about the purpose, i.e. the value of
the objective function is also used; -
each particle uses its own past experience. In solving the problem of
synthesizing an optimal control of discrete systems by the PSO the control
vector is optimized, so that the value of criterion has been extreme. During
calculations the state vector of the system is determined by state equations
using the initial state and the control vector. We created a program able to
solve the problem for the case of linear system and quadratic or
linear-quadratic criterion using different parameter values of the method. The software is formed on the
C# language in the Microsoft Visual Studio 2005. The user interface allows
setting the parameters of the problem and of the algorithm, using the
modification of the algorithm and analyzing the results in a convenient graphic
form. At the end of computational process the result is displayed in tabular
form, as well as graphs of the optimal control and state vectors. The result
can be placed in a file for later use. Due to the random nature of the PSO
there is an opportunity to produce a series of solutions of the problem with
logging results in the program. With this program, test
problems whose solution can be compared with the solution obtained analytically
have been solved. In solving the example we chose modification of the PSO with
a local search, because it is the most effective. Testing of the developed
software shows that the PSO succeeded solving this class of problems. With
increasing lifetime of the system solution accuracy becomes worse; however,
when using the algorithm with local search, it is acceptable in comparison with
traditional techniques of optimization. In future research we should
expand the range of the problems to be solved by PSO. We must also focus on the
optimal control of continuous deterministic systems in order to have the
possibility of solving more complex problems. 1.
Kennedy, J. and Eberhart, R. Particle
Swarm Optimization. http://
www.engr.iupui.edu/~shi/Coference/ psopap4.html 2.
Panteleev A.V., Bortakovsky A.S. Control theory in examples and
problems. - М:
High school, 2003. 3.
Alyoshina E.A., Panteleyev A.V.
Algorithmic and program support elaboration of PSO method//Scientific bulletin
MSTUCA, © 145, 2009. P. 32-39. E.A.Vishenkova,
O.V.Holostova. (Moscow Aviation Institute, Studying
an effect of high-frequency horizontal vibrations on the mechanic system such
as a double pendulum. Studying an effect of
high-frequency horizontal vibrations on the running devices and machinery in
the aerospace sector is an actual area of the scientific researches. Any kind
of such researches begins with an examination of
model problems, among which the interest is a pendulum-type model. In this work the motion of a
double pendulum - a system consisting of two hinged thin uniform rods revolving
around horizontal axes is investigated. It is assumed that the point of
suspension, which coincides with the end of one of the rods, performs
horizontal high-frequency harmonic oscillations of small
amplitude. This work's goal is
to study the stability of four different positions of relative equilibrium of
the double pendulum on the vertical as well as the question of the existence,
bifurcations and stability of the lateral high-frequency periodical motions of
the pendulum. It is shown, that among the
four different positions of relative equilibrium on the vertical only the lower
("hanging") position may be stable in case when the oscillation frequency of
the point of suspension doesn't exceed a certain limit. It is established, that
this equilibrium is stable for the majority of (in the
terms of Lebegue's measure) initial conditions and formally stable. It is shown that in case of
pendulum with two uniform rods the lateral periodical motions exist only when a
lower position of relative equilibrium is unstable. The number of lateral motions
may be from one to six, and each one has a symmetric pair. One or two pairs of
motions are stable for the majority of initial conditions and formally stable,
others are unstable. In the plain of angular quantities geometrical locus is
built, where these quantities may (for different frequencies) receive "average"
values of angles of derivation of the pendulum rods from vertical positions,
for the periodical motions has been built. This research is examined
using the method of Deprit-Hory, method of normal modes, KAM-theory and
Computer Algebra Methods. This work is supported by
"State support of leading scientific schools" (SS-3797.2010.1). I.V.Gucaev, A.G.Golovachev. (Moscow Aviation Institute, Abstract deduction in
decision-making systems. This paper observes the problem of solutions search with the use of
knowledge base, based on the abstract associative deduction. Besides it
investigates the effectiveness of an abstract approach to the problems of providing
comprehensive knowledge and recognition of the situation by the mobile robot
(UAV). For efficient logic deduction in application task an intelligent system
should possess imaginative situational thinking, based on similarity-difference
(reducibility) operation. There exist a number of techniques that allow
reducibility: neural networks, soft computing, fuzzy logic, abstraction, etc.
The abstraction approach has a significant advantage over other models. Fuzzy
logic, neural networks and other generalizations of the classical logic act in
the same base space. Abstraction works in two spaces - the original and the
abstract. Abstraction - is a logical process that maps the representation, the
original description of the problem to abstract representation, much more
compact and easy to handle. Abstraction allows the decision-making agent to
allocate a substantial connections between the objects. Mapping objects to
abstract space establish links between objects of different classes more
flexibly. Comparison operation between members from different classes are
produced in an abstract space, which it introduced a partial order. From a
computational point of view an abstraction - technology for practical learning
and planning algorithms in large-scale applications (partial implementation of
an abstraction is made in the language Prolog through the inheritance tree). The act of abstraction is executed in three
steps. The first makes the display of objects from different basic spaces into
a single abstract space. Objects are transformed into abstract states. Second
step produced comparison of this abstract states (by unification). The third
does the reverse mapping from the abstract space into the original, in which
the agent returns to the set of possible solutions. The number of solutions
depends on the level of abstraction. Selecting the most appropriate solution
also can be provided by the unification operation, which involves the potential
solutions and the knowledge base of decision-making agent. However, it is
impossible to describe all the environment situations, events and their links.
Abstraction is looking the most likely solution based on accumulated
experience. Unification in logical deduction - is process of casting different
states of the objects to the same value. In this case, unrelated values from
one state to be filled with values from another state. Thus, if the unification
operation involves two objects and each associated with own values through the
properties and components, and then performing a comparison. If an object is
not linked, then performed equating values. And if the object is involved in
the unification with the presence of unrelated parts, these parts take their
values from the same parts of another state. Unification can be used as a
comparison and as a reduction to the same values. Unification-comparison
establishes the possibility of potential equivalence of two objects of
different classes. In the process of solving an application task, such as automatic flight
control, there is an acute problem of the knowledge base for decision-making.
Achieving completeness can be arrived through the reducing to known situations
with use of abstract associative technique. Quality of produced solutions
depends on the quality and quantity of the knowledge base of decision-making. I.F.Dmitrakov,
A.V.Panteleyev. (Moscow Aviation Institute, The optimal control synthesis
of the deterministic systems by means of simulated annealing and differential
evolution methods. Problems of search of unconditional and conditional global extreme of
functions of many variables and search of optimal control for the discrete and
continuous deterministic systems are considered. For their decision it is
offered to use met heuristic optimization methods, namely the simulated
annealing method, the differential evolution method and their modifications.
Detailed algorithms of application of the methods set forth above are
generated. The differential evolution method is based on the analysis of
evolutionary processes. Feature of algorithms of differential evolution is use
of distinctions between individuals (values of argument of criterion function),
realized by the linear operator, and named "differentiation". The simulated annealing method is based on the analysis of process of
freezing of liquids or recrystallization of metals in the course of annealing.
Algorithms of simulated annealing with some probability suppose transition in a
condition with higher value of criterion function in the course of decision
search that the point could leave a vicinity of a local minimum. The software environment of visualization of process of work of
optimizing algorithms in which the set forth above methods are added is
developed. The given software allows to: -
work easily with parameters of the checked up method; -
analyze efficiency of its work on test functions; -
analyze a method convergence; -
"visualize" the process of its work; -
set parameters of problem statement conveniently and to receive the decision: in
case of search of optimal control by the
deterministic systems - the control, a
corresponding trajectory and value of quality functional, in case of search of
a global unconditional or conditional extremum of function - its value and
corresponding argument; -
effectively to form a policy of method's parameters
choice that has crucial importance at use of met heuristic methods of
optimization; -
see intermediate results of the account; -
spend convenient comparison of the chosen method with
other methods of global optimization for the subsequent analysis of results and
delivery of recommendations. Efficiency of the developed software is shown on model examples. Applied
problems of optimum control by two
chemical processes are solved. At a correct choice of parameters of methods,
results practically coincided with the exact values received analytically. M.A.Lebedev, A.A.Puntus, V.I.Polezhaev. (Moscow Aviation Institute, Modelling of the current, heat
exchange and the hysteresis phenomena in inclined layers. The problem about a convection
and heat exchange in inclined layers is considered at heat stream directed
across a layer. Depending on an angle of slope here operates two mechanisms of
a thermal gravitational convection corresponding to two limiting cases: balance
is possible, but can be steady or unstable (having warmed up from below), and
balance is impossible (having warmed up sideways). Thus a lot of cells the
structure of a current typical for reley-benar convection mechanism, is
replaced global lifting to lower by structure. This change of structures is a
consequence of convective interaction and has hysteresis character: the current
and heat exchange in one of directions doesn't coincide with heat exchange in
the opposite direction. Despite a considerable quantity of works on inclined
layers, data on a hysteresis at various relations of a layer aren't numerous. In the given work parametrical
researches of a convection and heat exchange in an inclined layer without the
assumption of periodic structure along a layer that allows investigating
influence of the relation of the parties of a layer proceed. The basic
attention is given to definition of influence of the relation of the parties of
a layer, including construction of diagrams of characteristic modes number of Grasgof
- the relation of the parties at different angles of slope. Dependence of an angle of
slope at which there is a current reorganization, from number of Prandtl (the
corner changed from 0 degrees to 180, then upside-down from 180 to 0 degrees
with step 15) is considered. Are received local and averages of Nusselt for
various numbers of Prandtl (0,71; 1,74; 7; 13,5; 43,9). The received dependence
of number of Nusselt on an angle of slope has appeared is ambiguous. During
work two modes were observed: cellular and vortical and as it was observed
unstable (saddles) a condition. It is shown that both modes lead to increase
thermal stream in comparison with molecular, corresponding to a plane-parallel
current. The cellular mode provides much more intensive thermal carrying over,
than vortical. As a result transitive character of this phenomenon of
hysteresis type which leads close in relation to initial, to structure of a
convection and the number of Nusselt different at opposite rotation from the
initial is accurately observed. Calculations received by means of computer laboratory COMGA. O.V.Ryazantseva,
A.V.Panteleyev. (Moscow Aviation Institute, Global
optimization by directed tabu search method. Currently, widely used met heuristics global optimization methods in
solving design problems of space-rocket complexes and the search for optimal
control. These methods allow to get close enough to the true result without
significant simplifications of mathematical statements of problems and a
reasonable time. An example of this method is a Directed Tabu Search method for
the global optimization. The problem
is: search of a global extreme of functions of many variables on set of
admissible decisions where admissible values of corresponding variables are
segments. In the
Directed Tabu Search method involves three phases: Exploration, Diversification
and Intensification. On the Exploration phase is the generation of new points
near the current solution. Novel concepts of Tabu Search memory elements are
introduced to provide anti-cycling rules and applied to escape from local
minima. One of the elements of memory - Visited Regions List - is an element of
Diversification phase, which is used to organize the search in unvisited areas
of study space. It is assumed that one of the best points found in the
Exploration and Diversification phase, close to the global minimum. Therefore,
the Intensification phase found "good" points are improved in order
to produce a result with desired accuracy. The concept of
memory plays a major role in Tabu Search. It is represented by several
elements: Tabu List, Tabu Regions, Semi-Tabu Regions and Visited Region List.
When implementing the method uses four types of search: -
exploration neighborhood search; -
local search; -
diversification search; -
intensification search. In the search strategy is a
well-known Nelder-Mead method and Adaptive Pattern Search. To implement the method formed
the software in C++. The functions of the program include: -
select the function, -
input parameters for the method, -
solve the problem and conclusion of
the detailed information, including step-by-step, -
display information about the solution
in the text, -
construction graph, -
viewing of a detailed protocol of the
decision, -
granting of the help information. The program
interface is represented by a set of tabs, each of which is responsible for the
respective functions. Comparing the results obtained using the developed
program, the exact solutions proves the effectiveness of Directed Tabu Search
for this class of problems. The program realization of method can be useful in
the course of training as demonstration of work of global extreme search
algorithm. P.A.Panteleev, A.G.Badalova. (Moscow Aviation Institute, Methods for determining the type of crisis in the
adaptive system of strategic risk management for enterprises of
aviation-industrial complex. Need for a transition to an innovative type of economy in the We propose a functional diagram of a system of risk management of
aviation-industrial complex (AIC), which specializes in the development of new
types of aircraft, which is a system with four feedbacks corresponding to the
four horizons of management. In the proposed scheme, developed in accordance
with the basic management principles: continuity, focus, system, integration,
structured targets for risk management on the horizon control, in accordance
with the value management approach. In each of the control loops to develop an
appropriate strategy and risk management techniques necessary to determine the
risk level by analyzing the financial performance of the company. If in the
process of risk management system there is a situation in which, despite the
use of different methods of blocking the risks of possible risks, and realized
a number of business units the company reached the crisis, the system of
strategic risk management needs to be supplemented by new feedbacks reflecting
the effect of adaptation to emerging new situations. In this current problem is
to find the type of crisis (local, comprehensive, global) and the development
of appropriate management decisions. A local crisis usually covers one
functional business unit, a comprehensive crisis - more than one. Global Crisis
covers the whole enterprise as a whole. The reasons for escalation of realized
risks in crises are: a sharp increase in the level of risk, and increase the
number of realized risks the emergence of new external factors. To solve the problem of determining the level of risk and the type of
crisis, the apparatus used fuzzy systems. An algorithm for forming fuzzy system,
which is used to find the type of crisis on the scale on the basis of
linguistic values of the percent crisis-ridden business units and the total
number of realized risks. Operation algorithm of fuzzy system contains:
fuzzification (input crisp variables are converted into fuzzy), the application
of fuzzy inference mechanism (from the base of fuzzy inference rules linking
the input fuzzy variables (background) with the output of fuzzy variables
(conclusions) are selected so-called active rules applicable to this situation.
The result of fuzzy inference mechanism is not clear conclusion);
defuzzification (fuzzy conclusion is converted into clear. In this case, the
goal is to find the type of crisis with respect to a given scale). Setting the
fuzzy expert system holds that changes: the number of linguistic values of
input and output variables, the task of universal sets; form of membership
functions and their parameters, linguistic inference rules, the method of
processing information about the input variables, the method of defuzzification. In the operation of the proposed fuzzy system it is performed: fuzzification
(it is determined the values of all membership functions for each input
variable), establishing correspondences (the definition of rules that apply in
the current situation) to find output fuzzy set; aggregation; defuzzification.
The obtained results allow us to create an effective mathematical tool for the
implementation of the methodological foundations of realized risk management,
which could escalate into crises. P.A.Fomkin, А.А.Ermakov, L.B.Stroganova. (Moscow Aviation Institute, Technical
aspects of the study of microbiological samples in a hermetically closed
volume. One of the most important operating
conditions for the manned spacecraft is their ecological safety, which includes
the guarantee of reliable control besides the physical, chemical and biological
parameters of living environment, including above the microbiological factor. With the realization of the
manned interplanetary expeditions, including the autonomous vital activity of
crew in flight down Mars, in connection with the absence of the possibility of
the sending taken samples to the earth for the analysis, the system of measures
and methods of guaranteeing of monitoring and control besides the state of
microbiological situation on board the spacecraft must ensure possibility of
conducting the necessary studies and processing the obtained results directly
as far as crew members on board the automatic spacecraft. First priority task on the
method of solution of this problem - these are selection and the study of the
microbiological tests, undertaken based on the elements of interior and
equipment of spacecraft. For these purposes in 2007-2008 the Research Institute
of space instrument manufacture together with SRF of RF - IMBP RAN [ Besides the selection of
microbiological tests it was necessary to create the modified mathematical
model of pattern recognition of microorganisms, called with the aid of the
computational means to conduct the identification of bacteria discovered in the
course of flight and fungi. The principle of pattern recognition was for this
purpose investigated and the logic circuit of the construction of the
mathematical model interesting us was comprised. Still much work is in
prospect, but solution of the problems before the complex mentioned above will
compulsorily bring us down the stated goal, but the proposed approaches can
find wide application not only before the space branch, but also before
clinical medicine. P.V.Shevchenko,
A.A.Puntus. (Moscow Aviation Institute, Mathematical
model of movement of the space vehicle of distant sounding of the Earth
concerning its centre of masses. The purpose of the given
research work is working out of incorporated mathematical model of movement of
the space vehicle intended for security of engineering processes of planning of
distant sounding of the Earth, considering as movement of the centre of masses
of the space vehicle on an orbit, and movement of the space vehicle concerning
the centre of masses taking into account the set technical requirements on its
attitudes. The given incorporated model is developed on the basis of
mathematical model of movement of the centre of masses of the space vehicle
existing at present, described system of differential equations in a
rectangular Greenwich frame and considering influence on orbital flight of the
space vehicle of such revolting forces, as a field of forces of an attraction
of the Earth together with their anomalies and forces of resistance to movement
of the space vehicle by atmosphere of the Earth. Originally the mathematical
model of movement of the space vehicle concerning its centre of the masses,
considering the restrictions superimposed on an absolute angular velocity,
absolute angular acceleration and boundary conditions of position of the space
vehicle from an instant of a start of motion by final time is developed. This
model is described by system of differential equations of movement by the
rectangular frame connected with the space vehicle. Research of mathematical
model of movement concerning the centre of masses is based on use of the
theorem of Euler about final turn of a rigid body. Space vehicle movement is
considered as rotation in one plane concerning some axis with the subsequent
passage to three-dimensional movement. Thus function of an angle of rotation is
approximated by a spline of the seventh order. Further, sufficient the
algorithm of definition of the minimum interval of time of a route of distant
sounding is developed for preparation for entrance in connection between the
space vehicle and the companion-repeater. Time interval will be considered
sufficient if values of parameters of an attitude on this interval satisfy to
the set boundary conditions and the restrictions superimposed on an absolute
angular velocity and absolute angular acceleration. Then the special software
which on the basis of the developed mathematical model and a gang of the
initial data allows defining the minimum interval of time, sufficient for
preparation for entrance in connection with the companion-repeater is
developed. Following magnitudes are defined also: co-ordinates of position of
the centre of masses of the space vehicle and a component of its vector of a
velocity in the Outcome of work is working out
of the special software which, on the basis of the developed mathematical model
and a gang of the initial data, ensures calculation of the prognosis of parameters
orbital and a space vehicle attitude. As a result the prognosis of position of
the centre of masses of the space vehicle and components of a vector of a
velocity in the Outcomes of the given research
work are offered to be used by working out of the special software of complexes
of program means of the automated planning of distant sounding of the Earth.
Given results can be used in onboard complexes of control by engineering
processes of planning of distant sounding of the Earth, and also in onboard
complexes and time schedule controls an attitude of the space vehicle
concerning its centre of masses. S.V. Ivanov, A.V. Naumov. (Moscow Aviation Institute, An
algorithm for solving a linear discrete stochastic programming problem with the
quantile criteria. We consider a linear
stochastic programming problem with the quantile criteria in the case when
random parameters vector has a discrete distribution with a finite number of
realizations. Sufficient conditions for the existence of a solution are considered. To solve the problem we use
the confidence method [1]. The idea of this method is to approximate the
original quantile optimization problem by a deterministic minimax one. In the
equivalent problem the inner problem is to maximize objective function on the
selected confidence set of the random parameters realizations, and the external
minimum - on optimization strategies. Selection of the optimal confidence set
is a challenge problem. In the case of a discrete distribution with a finite
number of realizations we can propose an algorithm for solving the problem
based on exhaustive search of confidence sets. But in the case of a large
number of random parameters vector realizations, the algorithm resulted in significant
computational difficulties. We propose a method for reducing the original
problem to a mixed linear programming problem of large dimension. The variables
of this problem are divided into two types: the variables of the original
problem, which correspond to the appropriate optimization strategy, and the
variables of binary type, corresponding to the vertices confidence set. To
solve this problem we apply Benders decomposition method [2]. Using this method
the resulting problem of large dimension is reduced into multiple subproblems
with smaller dimensions. To find an optimal solution we add some new
constraints to subproblems at each
iteration of the algorithm. The structure of new constraints allow
significantly reduce the dimension of subproblems. Furthermore, we give a way
to determine the optimal values of the binary variables before applying the
decomposition method. This way is based on the well known theorem [1] about the
form of the optimal confidence set. We estimate the complexity of the algorithm. Proposed algorithm has
exponential complexity as the algorithm based on on exhaustive search of
confidence sets, but the results of numerical experiments show that in practice the number
of iterations is much smaller than their estimate, so using the proposed
algorithm we can find the optimal solution significantly faster than using exhaustive search of confidence sets. 1.
I.F.Kibzun, Yu.S.Kan. Stochastic
Programming Problems whith the Probobilty Criterias. 2.
Alexander Schrijver. Theory of Linear and Integer Programming.
John Wiley & Sons, 1998. S.D.Makhijanova,
A.A.Puntus. (Moscow Aviation Institute, About
limit cycles in the double oscillator, raised by a nonlinear friction. In the presented research work
mathematical modelling of a two-mass oscillator with a piecewise-nonlinear dry
friction is spent and research of corresponding model is conducted, and also
problems of modelling of phase portraits of a two-mass oscillator on the
personal computer are considered. The method of research of considered
mathematical model consists in an analytical solution of the autonomous system
of differential equations received as a result of modelling, modelling of the
given system on the computer further is spent, the choice of a corresponding
numerical method is spent, the program of calculation with use of computer
facilities is made and then program calculation on the computer is realized. As
a result corresponding phase portraits are modelled on the computer. The autonomous system of differential
equations - a special case of system of differential equations when
to explanatory variables of such system time is systems, however in this case
the given explanatory variable is not included evidently into the functions
setting system. We will notice that self-oscillatory
systems are named autonomous systems in
which periodic oscillations can
be realized, and energy losses continuously replenish with inflow of energy
from a radiant which is not possessing characteristic oscillating properties.
Auto-oscillations thus are such
undamped oscillations, an aspect and which properties do not depend on entry
conditions and are defined only by properties of system, and energy losses
replenish with inflow of energy from a radiant which is not possessing
characteristic oscillating properties. The phase portrait of auto-oscillations is a
graphic representation of system on a phase plane (or in many-dimensional
space) on which co-ordinate axes values of magnitudes of variables of system
are put aside. Each point of a phase plane reflects one condition of system and
is called as phase, representing or a representative point. The
modification of a condition of system is mapped on a phase plane by movement of
this point. The track from movement of a representing point is called as a phase trajectory. As a limit
cycle is called the isolated closed phase trajectory. The term
"isolated" means that in enough small ring-shaped neighborhood of
this trajectory there are no other closed phase trajectories. It distinguishes
limit cycles from the closed phase trajectories corresponding, for example, to
periodic oscillations round a singular point of type the centre. In the course of performance
of the given scientific work the mathematical model of a two-mass oscillator
with a piecewise-nonlinear dry friction has been constructed, the analytical
solution of the equations in two areas is reduced. Analytical and numerical
modelling of the given system on the computer is considered, corresponding
phase portraits are received as a result of the given research. Limit cycles we
will receive by the following technique. On pressing of button
"Start" of the program the algorithm of a solution on the introduced
temporary gap is fulfilled. After its end final values of variables are noted
in fields of entry conditions, and at following start of algorithm are used as
entry conditions. So that to receive a limit cycle, it is necessary to fulfill
algorithm while the picture on phase planes will not cease to vary. So, in
the given research work the analytical solution received as a result of
mathematical modelling of a two-mass oscillator of autonomous system of
differential equations is passed. Besides, in the given research work the
method of research of considered mathematical model of a double oscillator and
as a result applications of this method construction of limit cycles in such
double oscillator raised by a nonlinear friction is fulfilled is presented. For
task in view realization, construction and research of considered limit cycles
is fulfilled, modelling of the given system on the personal computer is spent,
the choice of a corresponding numerical method is realized, the necessary
program of calculation is made, calculation on the computer is realized and
phase portraits of a two-mass oscillator corresponding to various entry
conditions and in various considered areas of a phase plane are received. Y.O.Khan,
A.A.Puntus, A.I.Fedyushkin. (Moscow Aviation Institute, Mathematical
modeling of natural convection in normal and reduced gravity. Distinguish
convection of two types: gravity and non-gravitational type. Consider the
natural convection. This work is devoted to solving the test problem of natural
convection in a square cavity, heated from the side. The aim is to construct a
mathematical model to calculate the thermal, concentration and termo-concentration
convection in dimensionless variables at different We
consider the problem of thermal and concentration convection of a viscous
incompressible fluid in a square closed area with a thermally insulated
horizontal walls and a set temperature at the boundary of vertical walls. A
mathematical model of this problem is a two-dimensional Navier-Stokes equations
in dimensionless variables in the Boussinesq approximation. To speed on all the
boundaries we impose the condition of attachment, but to put such conditions of
temperature: the lower and upper horizontal boundaries - insulated (adiabatic)
and the left and right vertical boundaries - isothermal. As the initial
conditions given by the stationary liquid with a linear heat-conduction
temperature distribution. This problem of natural
convection in a square domain was solved in dimensional primitive variables
velocity-pressure-temperature. To simulate the considered convection problem,
we used the dimensionless equations, data recording, which includes the
dimensionless parameters - the Prandtl number (characterizes the ratio of kinematical
viscosity and thermal), as well as the The calculation results were
compared with the "reference" solution, obtained by extrapolation of
the numerical solutions on different grids on the grid with zero pitch. The
calculation results also showed that under given boundary and initial conditions
with increasing Concentration determined by
the thermal convection model The result is that the
concentration heterogeneity under normal conditions is less than in conditions
of reduced gravity. Under the joint action of
thermal and concentration convection first suppresses the action of the second
at high As a result of this work, the
dependence of thermal and concentration convection, the effect of Raleigh
number and the influence of changes in Prandtl number and Schmidt on the motion
of fluid in a closed volume. Artur Agafonovich Puntus, Professor
of department of differential equations of the Moscow Aviation Institute (State
Technical University). An area of scientific researches is the qualitative
theory and applied problems of the differential equations, problems of teaching
of courses of higher mathematics, problems of preparation of qualified
professionals. |
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