scholarly journals Method of graphoanalytical finding borders space-time areas of reachability service spacecraft man-made space objects in geostationary orbit

2020 ◽  
Vol 4 (2) ◽  
pp. 96-106
Author(s):  
A. N. Gluzdov ◽  
P. V. Gorbulin ◽  
E. V. Kotyashov ◽  
O. L. Kuvaev
Keyword(s):  
A Priori ◽  
Initial Approximation ◽  
Control Program ◽  
Time Intervals ◽  
Graphical Comparison ◽  
Space Objects ◽  
Velocity Impulse ◽  
Time Required ◽  
Flight Scheme ◽  
Phase Angles

At the present time at various stages of creation and development there are several projects of service spacecraft. One of the tasks of which is to service orbital objects as soon as possible. During the planning maintenance is needed to perform a large amount of calculations associated with the choice of a rational flight scheme. To reduce the amount of computation, an approach is needed that provides a search for the set of realized flight paths. One of such approaches is the method for determining the boundaries of the spatiotemporal reachability regions, which allows one to evaluate the a priori capabilities of service spacecraft for servicing orbital objects located in circular orbits. To construct spatiotemporal reachable regions, the mathematical apparatus of the hodograph theory is used, which allows, sequentially, based on the analytical solution of the optimization problem of a two-pulse flight, to determine the minimum and maximum duration of the spacecraft’s movement, which is understood as the time required for the flight from the point of maneuvering to the meeting point with the serviced an orbital object under the condition of the application of one velocity impulse. A graphical comparison of the trajectories of the serviced orbital objects and spatiotemporal reachable areas of the service spacecraft makes it possible to determine the potential for service, as well as the time intervals and phase angles at which such service is possible. The proposed methodological apparatus can be used to find a solution providing an initial approximation for the subsequent accurate calculation of the trajectory of motion by numerical methods, as constructing a control program for the spacecraft.

scholarly journals Statistical Uncertainty of DNS in Geometries without Homogeneous Directions

2021 ◽  
Vol 11 (4) ◽  
pp. 1399
Author(s):  
Jure Oder ◽  
Cédric Flageul ◽  
Iztok Tiselj
Keyword(s):  
Channel Flow ◽  
A Priori ◽  
Time Integration ◽  
Navier Stokes ◽  
Statistical Uncertainty ◽  
Time Step ◽  
Order Of Magnitude ◽  
Averaging Time ◽  
The Individual ◽  
Time Required

In this paper, we present uncertainties of statistical quantities of direct numerical simulations (DNS) with small numerical errors. The uncertainties are analysed for channel flow and a flow separation case in a confined backward facing step (BFS) geometry. The infinite channel flow case has two homogeneous directions and this is usually exploited to speed-up the convergence of the results. As we show, such a procedure reduces statistical uncertainties of the results by up to an order of magnitude. This effect is strongest in the near wall regions. In the case of flow over a confined BFS, there are no such directions and thus very long integration times are required. The individual statistical quantities converge with the square root of time integration so, in order to improve the uncertainty by a factor of two, the simulation has to be prolonged by a factor of four. We provide an estimator that can be used to evaluate a priori the DNS relative statistical uncertainties from results obtained with a Reynolds Averaged Navier Stokes simulation. In the DNS, the estimator can be used to predict the averaging time and with it the simulation time required to achieve a certain relative statistical uncertainty of results. For accurate evaluation of averages and their uncertainties, it is not required to use every time step of the DNS. We observe that statistical uncertainty of the results is uninfluenced by reducing the number of samples to the point where the period between two consecutive samples measured in Courant–Friedrichss–Levy (CFL) condition units is below one. Nevertheless, crossing this limit, the estimates of uncertainties start to exhibit significant growth.

scholarly journals CRITICAL TIMESCALES AND TIME INTERVALS FOR COUPLED LINEAR PROCESSES

2013 ◽  
Vol 54 (3) ◽  
pp. 127-142 ◽  
Author(s):  
MATTHEW J. SIMPSON ◽  
ADAM J. ELLERY ◽  
SCOTT W. MCCUE ◽  
RUTH E. BAKER
Keyword(s):  
Differential Equations ◽  
Applied Mathematics ◽  
Finite Measure ◽  
Single Species ◽  
Diffusion Reaction ◽  
Morphogen Gradient ◽  
Time Intervals ◽  
Linear Processes ◽  
Gradient Formation ◽  
Time Required

AbstractIn 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and co-workers [A. M. Berezhkovskii, C. Sample and S. Y. Shvartsman, “How long does it take to establish a morphogen gradient?”Biophys. J. 99(2010) L59–L61] rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single-species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalize the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications, for example the analysis of models describing coupled chemical decay and cell differentiation processes.

Restoration of Bridge Networks after an Earthquake: Multicriteria Intervention Optimization

2012 ◽  
Vol 28 (2) ◽  
pp. 427-455 ◽  
Author(s):  
Paolo Bocchini ◽  
Dan M. Frangopol
Keyword(s):  
Unique Solution ◽  
Transportation Network ◽  
Optimization Procedure ◽  
Pareto Solutions ◽  
Santa Barbara ◽  
Time Intervals ◽  
Total Cost ◽  
Design Variables ◽  
Bridge Networks ◽  
Time Required

This paper presents an optimization procedure for the restoration activities associated with the bridges of a transportation network severely damaged by an earthquake. The design variables are (i) the time intervals between the occurrence of the distress and the start of the interventions on each bridge of the network; and (ii) the restoration pace of the interventions, which represents a measure of the funding allocated to each bridge. The objectives of the optimization are the maximization of the network resilience, the minimization of the time required to reach a target functionality level, and the minimization of the total cost of the restoration activities. Because the first two objectives clearly conflict with the last one, the optimization procedure does not provide a unique solution, but an entire set of Pareto solutions. A numerical example involving a complex, existing transportation network in Santa Barbara, California, illustrates the capabilities of the proposed methodology.

scholarly journals Classification of the state of the dynamic system, which is functioned by which is described by vector autoresis

2019 ◽  
Vol 4 (123) ◽  
pp. 131-154
Author(s):  
Oleksandr Pavlovych Sarychev
Keyword(s):  
Dynamic System ◽  
Power Plants ◽  
A Priori ◽  
Technical Condition ◽  
Regression Equations ◽  
Unknown Parameters ◽  
Term Operation ◽  
Space Objects ◽  
Input Variables

Within the framework of the article, the problem of statistical classification of states of a dynamic system is solved, which can be in two classes of states, in each of which its operation is described by its own system of autoregressive equations with a priori unknown parameters. It is assumed that the following conditions are fulfilled: a) two classes of states are described by the same sets of observed input and output variables; b) the output variables, both in the first and in the second class, are determined by different sets of regressors (input variables); c) the models of functioning in the first and second classes are different both in terms of coefficients and in the structure of autoregressive models; d) the covariance matrices of random variables in the functioning models and the observation models for the first and second classes are different. The rule of classification is constructed and its properties are investigated.The experience of successfully solving problems of detecting changes in the properties of dynamic systems based on regression equations in the work, where an approach to constructing mathematical models for monitoring the technical condition of power and power plants in long-term operation was proposed, shows the feasibility of applying this approach to solving problems of controlling the operation of rocket-space objects technology.The problem of classifying states of a dynamic system, which can be in two classes of states, is considered. The functioning of the system in classes is described by various systems of autoregressive equations. The rule of classification is constructed and its properties are investigated.

scholarly journals Evolution of surface motor activation zones in hemiplegic patients during 20 sessions of FES therapy with multi-pad electrodes

2016 ◽  
Vol 26 (2) ◽  
Author(s):  
Jovana Malešević ◽  
Matija Štrbac ◽  
Milica Isaković ◽  
Vladimir Kojić ◽  
Ljubica Konstantinović ◽  
...  
Keyword(s):  
Electrical Stimulation ◽  
Temporal Change ◽  
A Priori ◽  
A Priori Knowledge ◽  
Motor Activation ◽  
Stimulation System ◽  
Time Required ◽  
Automated Optimization ◽  
Virtual Electrodes ◽  
Therapy Sessions

The purpose of this study was to examine surface motor activation zones for wrist, fingers and thumb extension movements and their temporal change during 20 therapy sessions using advanced multi-pad functional electrical stimulation system. Results from four hemiplegic patients indicate that certain zones have higher probability of eliciting each of the target movements. However, mutual overlap and variations of the zones are present not just between the subjects, but also on the intrasubject level, reflected through these session to session transformations of the selected virtual electrodes. The obtained results could be used as a priori knowledge for semi-automated optimization algorithm and could shorten the time required for calibration of the multi-pad electrode.

ALGORITHM FOR SELECTION OF LAUNCH ELEMENTS IN THE PRESENCE OF A PRIORI INFORMATION ABOUT ITS COMPOSITION AND STRUCTURE

2018 ◽  
pp. 114-119
Author(s):  
O. I. Nemykin
Keyword(s):  
Decision Making ◽  
Loss Function ◽  
Selection Process ◽  
A Priori ◽  
Measurement Information ◽  
A Priori Information ◽  
Space Objects ◽  
Alternative Hypotheses ◽  
Priori Information ◽  
Selection Of

Traditional methods of the theory of statistical solutions are developed for cases of making single-valued two-alternative or multialternative solutions about the class of an object. Assuming the possibility of ambiguous multi-alternative (in the case of solving the problem of selection of space objects of three-alternative) decisions on the classification of of space objects at the stages of the selection process, a modification of the traditional statistical decision making algorithm is required. Such a modification of the algorithm can be carried out by appropriate selection of the loss function. In the framework of the Bayes approach, an additive loss function is proposed, the structure of which takes into account a priori information on the structure and composition of launch elements in relation to the classes «Launch vehicle» and «spacecraft». The algorithm of decision making is synthesized under the conditions of a priori certainty regarding the probabilistic description of the analyzed situation. It is shown that the problem of verifying three-alternative hypotheses can be reduced to an independent verification of three two-alternative hypotheses, which makes it possible to take particular solutions in the solution process and use a different set of the signs of selection for the formation of solutions for individual classes of space objects. The peculiarities of the implementation of the selection algorithm are discussed in the presence of a priori information and measurement information on starts of a limited volume. The synthesized Bayesian decision making algorithm has the properties necessary to solve the problem of selection of space objects at launch in real conditions in the presence of measuring information specified in the form of a training sample. Its architecture allows to form unambiguous and ambiguous decisions about each space object in the launch.

METHOD OF COMPENSATION OF IONOSPHERE ERRORS OF SPACE OBJECTS COORDINATES DEFINITION BY MEANS OF TWO POSITION RADAR OBSERVATION

2018 ◽  
pp. 45-49
Author(s):  
P. S. Galkin ◽  
V. N. Lagutkin
Keyword(s):  
Probability Density ◽  
A Priori ◽  
Position Estimation ◽  
Estimation Accuracy ◽  
Posteriori Probability ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
Space Object ◽  
A Posteriori Probability ◽  
Space Objects

The algorithm of estimation and compensation of ionosphere influence on the measurement of parameters of the motion of space objects in two-position radar system with account of radio physical effects depending on elevation angles and the operating frequency is developed. It is assumed that the observed space object is traсked object, the orbital parameters which are well known, including the dependence of the velocity of the point on the orbit, and the uncertainty of the current coordinates of the object is caused mainly by forecast error of its position of in orbit (longitudinal error). To estimate the true position of space object in the orbit and the parameter, determining the influence of the ionosphere, a joint optimal processing of measurement of ranges to the object, obtained by two separated radars, taking into account the relevant ionospheric propagation delays and available a priori data on observable object trajectory. Estimation of unknown parameters are obtained on the basis of the criterion of maximum a posteriori probability density for these parameters, taking into account the measured and a priori data. The task of searching for maximum a posteriori probability density is reduced to task of searching of minimum weighted sum of squares, for the solution of which the cascade algorithm of iteration through is implemented in the work. Estimation accuracy of the position of space objects in orbit after compensation of ionosphere influence have been studied by Monte-Carlo method. Dependencies of mean square error of the position estimation of space objects upon elevation angles, operation frequency and solar activity have been obtained. It is shown that the effectiveness of the algorithm increases with the spatial base of measurements (for a fixed orbit of the object).

Identification of the Polyharmonic Vibration From Combination With a Normal Random Noise by the Use of High-Order Moments of Instantaneous-Value Distribution

1995 ◽  
Author(s):  
Alexander Steinwolf
Keyword(s):  
Random Vibration ◽  
Random Noise ◽  
A Priori ◽  
Periodic Signal ◽  
Gaussian Form ◽  
Complete Identification ◽  
Multiple Frequencies ◽  
Time Domain Averaging ◽  
Non Gaussian ◽  
Phase Angles

Abstract Polyharmonic oscillation with multiple frequencies is inherent in many applied problems. However, it rarely exists in the pure form and is often accompanied by a random vibration. Separation of the periodic signal from the actual record measured is usually restricted to determining the harmonic amplitudes only. The paper presents a method for complete identification of polyharmonic process including the phase angles that were unattainable when its period is unknown a priori. The approach is based on the fact that the presence of a periodic component transforms the instantaneous-value probability distribution of the combined signal to the non-Gaussian form. The solution obtained is compared with the results of time domain averaging.

Nonlinear Systems for Distances and Displacements Measurement

1999 ◽  
Author(s):  
Almantas Mozuras ◽  
Asta Kontvainaite
Keyword(s):  
Physical System ◽  
Signal To Noise Ratio ◽  
A Priori ◽  
Measurement Range ◽  
Experimental Investigations ◽  
Signal To Noise ◽  
Measuring Process ◽  
Time Intervals ◽  
Nonlinear Distortions ◽  
Typical Time

Abstract In conventional methods, a physical system is considered more suitable for measurement purposes the greater its linearity is. However, purely linear converting systems are not available. The use of the linear features in the measurement process causes the drawbacks: systematic error due to nonlinear distortions, low signal-to-noise ratio, low measurement range, necessity to evaluate a great number of a priori parameters in order to obtain an absolute result, and low thermal stability because every a priori parameter itself has a temperature dependence. To exclude these drawbacks a method has been developed using nonlinearities in the base of displacements measuring process. The method is implemented using electretic, electrostatic, and photoelectric transducers. The contactless transducer is placed parallel to the surface of the object which displacements are measured. The transducer is driven to harmonic oscillations. Typical time intervals of the coded signal are measured. The object displacements are determined according to the changes of the typical time intervals. The method itself has no errors because approximations have been not made while deriving the relations. The source of errors is inaccurate registration of the start and end of the typical time intervals. The measurement is possible only if the physical system is nonlinear. The results of experimental investigations confirm the theoretical conclusions. The method allows one to increase measurement range significantly (for example, measurement range of the conventional capacitance meters is ∼10−2mm and in the proposed method measurement range using capacitance converter is about 1 mm).

On the Expansion of a Class of Open-Loop Evasion Control in the Simplest Two-Criteria Pursuit-Evasion Game of Two Purposes

2019 ◽  
Vol 20 (9) ◽  
pp. 524-531
Author(s):  
E. Ya. Rubinovich
Keyword(s):  
A Priori ◽  
Negative Answer ◽  
Open Loop ◽  
Quality Of Control ◽  
Pursuit Evasion ◽  
True Target ◽  
Evasion Game ◽  
False Target ◽  
Evasion Control ◽  
Time Required

The article is devoted to the formulation and solution of the two-criterion pursuit-evasion game on the plane of one pursuer against two targets, one of which is false. A false target is used to distract the pursuer, allowing the true target (in the process of diverting) to maximize the minimum possible distance to the pursuer. The specificity of the pursuer is that it has a circular classification zone of radius R, within which it has the ability to instantly classify the target as false or true. The game is that the pursuer minimizes the time required to approach one of the targets to a distance not exceeding R (R-encounter), and the targets, acting in concert, maximize the minimum distance between the pursuer and the remaining target. The game continues until the R-meeting of the pursuer with the first (false) target, i.e. until the classification of the false target. It is assumed that the first target is false a priori the persecutor is not known. The strategy of using a false target is precisely to release it to distract the pursuer from the true target. In reality, the false target is a mobile drone, which is controlled programmatically by the on-Board computer. In the class of open-loop controls the staging was investigated in 1984 by Ivanov M. N. and Maslov E. P. There is a natural question: what will give an extension of a class of open-loop controls of the false targets to the class of closed-loop controls, i.e. to the class of controls with a feedback? This question is quite appropriate in connection with the great progress in the development of microprocessor technology and improving the performance of on-Board computers, which makes it possible to use more complex algorithms for controlling Autonomous mobile objects. This article gives a negative answer to the above question, namely, it is shown that the extension of the class of open-loop controls by a false target does not improve the quality of control. It is proved that in this game there is a Nash equilibrium in the program strategies of the players.

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