Evolutionary Algorithm for Minimizing the Characteristic Velocity for the Reorientation of the Spacecraft Orbit

The paper is dedicated to the problem of finding optimal spacecraft trajectories. The equations of spacecraft motion are written in quaternion form. The spacecraft moves on its orbit under acceleration from the limited in magnitude jet thrust. It is necessary to minimize the energy costs for the process of reorientation of the spacecraft orbital plane. The equations of spacecraft motion are written in orbital coordinate system. It is assumed that spacecraft orbit is circular and control has constant value on each part of active spacecraft motion. In this case the lengths of the sections of the spacecraft motion are unknown. We need to find the length of each section, their quantity and value of control on each section. The equations of the problem were written in dimensionless form. It simplifies the numerical investigation of the obtained problem. There is a characteristic dimensionless parameter in the phase equations of the problem. This parameter is a combination of dimension variables describing the spacecraft and its orbit. Usually the problems of spaceflight mechanic are solved with the maximum principle. And we have to solve boundary value problems with some kind of shooting method (Newton’s method, gradient descent method etc.) Each shooting method requires initial values of conjugate variables, but we have no analytical formulas to find them. In this paper spacecraft flight trajectories were found with new genetic algorithm. Each gene contains additional parameter which equals to " True" , if the gene forms the control and equals to "False" otherwise. It helps us determine the quantity of spacecraft active motion parts. The input of proposed algorithm does not contain information about conjugate variables. It is well-known that the differential equations of the problem have a partial solution when the spacecraft orbit is circular and control is constant. The genetic algorithm involves this partial solution and its speed is increased. Numerical examples were constructed for two cases: when the difference between angular variables for start and final orientations of the spacecraft orbital plane equals to a few (or tens of) degrees. Final orientation of the spacecraft plane of orbit coincides with GLONASS orbital plane. The graphs of components of the quaternion of orientation of the orbital coordinate system, the longitude of the ascending node, the orbit inclination and optimal control are drawn. Tables were constructed showing the dependence of the value of the quality functional and the time spent on the reorientation of the orbital plane on the maximum length of the active section of motion.

Attitude stability analysis of a dual-spin spacecraft in halo orbits

X-ray pulsar navigation is a complete autonomous navigation system, which has broad application prospects. Because of the huge cost of the navigation system, the implementation of ground simulation system is essential to the application of X-ray pulsar navigation. At present, most of researches on the semi physical experiment system are static. The aim of this article is to develop the dynamic simulation experiment system as well as its performance test. Specifically, this system consists of the dynamic signal database, X-ray simulation source, vacuum system and detection system designed for different science purposes. The core component of the X-ray source is the gate controlled X-ray tube, which can simulate the pulse profile of arbitrary waveform. The detecting system is based on the silicon drift detector with high time response capability. It uses trapezoidal shape for signal processing, and the timing resolution of the detection system is better than 2 s. In addition, the dynamic signal generation method is given by analyzing the time transformation model while the SINC interpolation method is provided to generate the dynamic pulse profile. Finally, the spacecraft revolving around the earth for a circle and receiving a pulse signal of Crab is simulated. In the simulation, the orbital radius of satellite is 6578 km and the orbital period is 5400 s. The Crab pulsar is selected, and the pulse period is 33.4 ms, the number of photons received by the detector is 200 per second. As a contrast, a set of static experiments is also performed. The correlation coefficient between the cumulative pulse profile and the standard pulse profile is 0.9953. However, the correlation coefficient decreases gradually, from 0.9094 at 300 s to 0.4080 at 5400 s, in the dynamic experiment. Then, the pulse period is searched from the arrival time of photons. The periodicity of the pulse signal is sinusoidal when the search period is 60 s. The change rate of photon flux is less than 2\%, and the influence on the period search is negligible. The variation of pulse period is consistent with the motion law of spacecraft, which indicates that spacecraft motion is the dominant factor in time conversion. Finally, the arrival time of photons is transformed into the time at the solar system barycenter, indicating that the correlation coefficient between cumulative pulse profile and standard pulse profile is 0.9882. The result shows that the simulation system can simulate the X-ray pulse signal received by the spacecraft in orbit, which can provide the experimental basis for verifying the navigation algorithm and calibrating the detector performance.

This paper deals with the effects of electromagnetic forces on the orbital motion of a spacecraft. The electrostatic charge which a spacecraft generates on its surface in the Earth's magnetic field will be subject to a perturbative Lorentz force. A model incorporating all Lorentz forces as a function of orbital elements has been developed on the basis of magnetic and electric fields. This Lorentz force can be used to modify or perturb the spacecraft's orbits. Lagrange's planetary equations in the Gauss variational form are derived using the Lorentz force as a perturbation to a Keplerian orbit. Our approach incorporates orbital inclination and the true anomaly. The numerical results of Lagrange's planetary equations for some operational satellites show that the perturbation in the orbital elements of the spacecraft is a second order perturbation for a certain value of charge. The effect of the Lorentz force due to its magnetic component is three times that of the Lorentz force due to its electric component. In addition, the numerical results confirm that the strong effects are due to the Lorentz force in a polar orbit, which is consistent with realistic physical phenomena that occur in polar orbits. The results confirm that the magnitude of the Lorentz force depends on the amount of charge. This means that we can use artificial charging to create a force to control the attitude and orbital motion of a spacecraft.

PurposeThe purpose of this paper is to propose an adaptive robust controller for coupled attitude and orbit control of rigid spacecraft based on dual quaternion in the presence of external disturbances and model uncertainties.Design/methodology/approachFirst, based on dual quaternion, a theoretical model of the relative motion for rigid spacecraft is introduced. Then, an adaptive robust controller which can realize coordinated control of attitude and orbit is designed in the existence of external disturbances and model uncertainties.FindingsThis paper takes advantage of the Lyapunov function which can guarantee the asymptotic stabilization of the whole system in the existence of parameters uncertainties. Simulation results show that the proposed controller is feasible and effective.Originality/valueThis paper proposes a coupled attitude and orbit adaptive robust controller based on dual quaternion. Simulation results demonstrate that the proposed controller can achieve higher control performance in the presence of parameters uncertainties.

A mathematical model was designed and developed of the Or bital Maneuvering Vehicle (OMV), a critical part of the OMV man-in-the-loop simulation at Marshall Space Flight Center, Huntsville, Alabama. The OMV evaluator is a full-scale, six- degree-of-freedom simulator that can replicate the motion of the actual OMV spacecraft in orbit. Translational and rotational equa tions of motion that model the OMV are presented. Simulation results that verify the correctness of the model are also given. This high-fidelity simulator is valuable for crew training, develop ing and testing new teleoperated equipment, and verification of the OMV final design. The evaluator also serves as an impor tant test ground for determining the capabilities of the OMV in performing orbital operations.

The equations of motion of a momentum biased spacecraft are derived in a general form. The spacecraft is assumed to be orbiting in a near-elliptical orbit. An aerodynamic torque model which accounts for the atmospheric superrotation is assumed. The equilibrium attitude angles are obtained in terms of modified Bessel functions. Analytic expressions for the long-term motion of the momentum biased axis are derived for special cases. The analysis is applicable to the Magsat mission.

CHAPTER V - SOLUTION OF EQUATIONS OF LOW ORDERS AND EXTRACTION OF ROOTS

Recently, evolutionary algorithms that can efficiently solve decomposable binary optimization problems have been developed. They are so-called model-based evolutionary algorithms, which build a model for generating solution candidates by applying a machine learning technique to a population. Their central procedure is linkage detection that reveals a problem structure, that is, how the entire problem consists of sub-problems. However, the model-based evolutionary algorithms have been shown to be ineffective for problems that do not have relevant structures or those whose structures are hard to identify. Therefore, evolutionary algorithms that can solve both types of problems quickly, reliably, and accurately are required. The objective of the paper is to investigate whether the evolutionary algorithm evolving developmental timings (EDT) that we previously proposed can be the desired one. The EDT makes some variables values more quickly converge than the remains for any problems, and then, decides values of the remains to obtain a higher fitness value under the fixation of the variables values. In addition, factors to decide which variable values converge more quickly, that is, developmental timings are evolution targets. Simulation results reveal that the EDT has worse performance than the linkage tree genetic algorithm (LTGA), which is one of the state-of-the-art model-based evolutionary algorithms, for decomposable problems and also that the difference in the performance between them becomes smaller for problems with overlaps among linkages and also that the EDT has better performance than the LTGA for problems whose structures are hard to identify. Those results suggest that an appropriate search strategy is different between decomposable problems and those hard to decompose.

Conservative tightly-coupled simulations of stochastic multiscale systems

An equation-by-equation (EBE) method is proposed to solve a system of nonlinear equations arising from the moment constrained maximum entropy problem of multidimensional variables. The design of the EBE method combines ideas from homotopy continuation and Newton's iterative methods. Theoretically, we establish the local convergence under appropriate conditions and show that the proposed method, geometrically, finds the solution by searching along the surface corresponding to one component of the nonlinear problem. We will demonstrate the robustness of the method on various numerical examples, including: (1) A six-moment one-dimensional entropy problem with an explicit solution that contains components of order $10^0-10^3$ in magnitude; (2) Four-moment multidimensional entropy problems with explicit solutions where the resulting systems to be solved ranging from $70-310$ equations; (3) Four- to eight-moment of a two-dimensional entropy problem, which solutions correspond to the densities of the two leading EOFs of the wind stress-driven large-scale oceanic model. In this case, we find that the EBE method is more accurate compared to the classical Newton's method, the MATLAB generic solver, and the previously developed BFGS-based method, which was also tested on this problem. (4) Four-moment constrained of up to five-dimensional entropy problems which solutions correspond to multidimensional densities of the components of the solutions of the Kuramoto-Sivashinsky equation. For the higher dimensional cases of this example, the EBE method is superior because it automatically selects a subset of the prescribed moment constraints from which the maximum entropy solution can be estimated within the desired tolerance. This selection feature is particularly important since the moment constrained maximum entropy problems do not necessarily have solutions in general.

Many evolutionary algorithms are designed to solve black-box multi-objective optimization problems MOPs using stochastic operators, where neither the form nor the gradient information of the problem is accessible. In some real-world applications, e.g. surrogate-based global optimization, the gradient of the objective function is accessible. In this case, it is straightforward to use a gradient-based multi-objective optimization algorithm to achieve fast convergence speed and the stability of the solution. In a relatively recent approach, the hypervolume indicator gradient in the decision space is derived, which paves the way for the method for maximizing the hypervolume indicator of a fixed size population. In this paper, several mechanisms which originated in the field of evolutionary computation are proposed to make this gradient ascent method applicable. Specifically, the well-known non-dominated sorting is used to help steering the dominated points. The principle of the so-called cumulative step-size control that is originally proposed for evolution strategies is adapted to control the step-size dynamically. The resulting algorithm is called Hypervolume Indicator Gradient Ascent Multi-objective Optimization HIGA-MO. The proposed algorithm is tested on ZDT problems and its performance is compared to other methods of moving the dominated points as well as to some evolutionary multi-objective optimization algorithms that are commonly used.

The paper considers a hemispherical resonator gyroscope. It describes the structure of a hemispherical resonator gyroscope as a measuring and computing system, as well as the problems and main factors involved in increasing its accuracy. We studied a measuring component utilising alternating voltage, its circuit layout and mathematical model. We stated the problem of synthesising a computational component taking into account possible computational resource limitations in the device in the form of a system of nonlinear algebraic equations. We considered the specifics and implementation requirements concerning the computational algorithm, as well as the specifics of utilising redundant information about the wave pattern state in the gyroscope. The equation system proposed is overdetermined. We analysed the issues peculiar to the iterative method of solving this nonlinear system, which we propose to use as the basis for the mathematical model of the computational component. The method described may be generalised as the Gauss --- Newton method. The paper provides alternative iterative methods for designing the computational component. We investigated convergence issues for the computational component model obtained via the Gauss --- Newton method. The paper presents computational component simulation results and concludes that using the computational component model obtained is possible and feasible

Purpose – The linear regression technique is widely used to determine empirical parameters of fatigue life profile while the results may not continuously depend on experimental data. Thus Tikhonov-Morozov method is utilized here to regularize the linear regression results and consequently reduces the influence of measurement noise without notably distorting the fatigue life distribution. The paper aims to discuss these issues. Design/methodology/approach – Tikhonov-Morozov regularization method would be shown to effectively reduce the influences of measurement noise without distorting the fatigue life distribution. Moreover since iterative regularization methods are known to be an attractive alternative to Tikhonov regularization, four gradient iterative methods called as simple iteration, minimum error, steepest descent and conjugate gradient methods are examined with an appropriate initial guess of regularized coefficients. Findings – It has been shown that in case of sparse fatigue life measurements, linear regression results may not have continuous dependence on experimental data and measurement error could lead to misinterpretations of the solution. Therefore from engineering safety point of view, utilizing regularization method could successfully reduce the influence of measurement noise without significantly distorting the fatigue life distribution. Originality/value – An excellent initial guess for mixed iterative-direct algorithm is introduced and it has been shown that the combination of Newton iterative approach and Morozov discrepancy principle is one of the interesting strategies for determination of regularization parameter having an excellent rate of convergence. Moreover since iterative methods are known to be an attractive alternative to Tikhonov regularization, four gradient descend methods are examined here for regularization of the linear regression problem. It has been found that all of gradient decent methods with an appropriate initial guess of regularized coefficients have an excellent convergence to Tikhonov-Morozov regularization results.

In this paper, the projected-gradient-descent (PGD) -based detector for massive MIMO system, which consists of two basic operations — projection and gradient descent (GD), is studied to achieve the performance improvement. Since the projection and GD step have different loss functions, necessary compromise has to be made to balance them during iterations. For this reason, the generalized PGD (GPGD) method is proposed with flexible choices of projection and GD. Different from performing projection and GD alternatively, we show that implementing projection after every multiple GD steps is a better solution. Meanwhile, the step-size of GD is also investigated for convergence efficiency. After that, by unfolding this proposed GPGD method with deep neural networks (DNN), the self-corrected auto-detector (SAD) is established to achieve better decoding performance, where enhancement by attention mechanism and extension by another iterative method are also given for performance improvement and efficiency.