Origin Of Coordinate System Research Articles

Nonlinear vibration analysis and stability analysis of rotor systems with multiple localized nonlinearities

This study proposes a methodology to analyze the nonlinear vibration characteristics of rotor systems with multiple localized nonlinearities adopting the Finite Element Method (FEM), free interface Component Mode Synthesis (CMS) method, and modified Incremental Harmonic Balance (IHB) method. The rotor system is supported by squeeze film dampers (SFDs) on both sides, and at the nodes of the SFD arrangement, strong local nonlinearities will appear due to fluid-film forces. The methodology to analyze the nonlinear vibration characteristics of the system by reducing the degree of freedom of the rotating system with multiple local nonlinear factors and combining with the IHB method is proposed for the first time in this paper. The FEM is used to write motion equations in components, and the CMS method is applied to reduce the degrees of freedom of linear components. The IHB method is used to solve the motion equations of the nonlinear system. The system has one linear component and two nonlinear components. For linear components, modal coordinates are used, and for nonlinear components, the original physical coordinate system is used. By synthesizing these three components, the motion equation of the whole system is created. In order to validate the effectiveness of the method, the results obtained by the proposed method are compared with the data in the published literature, and the system responses are considered when specific parameters are changed. The stability analysis of the calculated solutions is carried out using the Floquet theory.

A Fast Conversion Method of Tube Coordinates

Inspired by the idea of the coordinate transformation of the robot arm, the tube structure is analogized to the robot arm structure, and the conversion method of the tube bend processing parameters LRA to the three-dimensional coordinate points is obtained. The method first regards the tube as a “mechanical arm”; then, using the similarity of the LRA processing parameters and D-H parameters, all the LRA parameters are converted into D-H parameters; finally, the D-H parameter method is applied to calculate the distance between each axis of the " mechanical arm ". If the first space coordinate point is defined as the origin of the base coordinate system , then the position of the origin of other coordinate systems in the base coordinate system can be obtained; It has been proved by experiments that this method fast and feasible.

An adaptive framework to select the coordinate systems for evolutionary algorithms

Many evolutionary algorithms usually utilize the fixed original coordinate system to search and cannot effectively match different function landscapes. To solve this issue, this paper proposes an adaptive framework, named STCS, to select the coordinate systems for evolutionary algorithms. In STCS, the eigen coordinate system is constructed by an archive-based covariance matrix, which can capture the feature of the function landscape. What is more, the selection process of the original coordinate system and the eigen coordinate system is defined as a Markov decision process and is controlled by reinforcement learning algorithm. STCS is applied to three popular evolutionary algorithms, i.e., differential evolution, particle swarm optimization, and teaching–learning-based optimization. The experimental results on IEEE CEC2013, IEEE CEC2014, and IEEE CEC2017 test suites demonstrate that STCS is efficient and competitive.

Force inference in granular materials: Uncertainty analysis and application to three-dimensional experiment design.

Interparticle forces are known to influence mechanical and physical properties of granular materials. A method for inferring forces in two-dimensional and three-dimensional experiments has recently been developed and applied to the problem of examining force statistics, energy dissipation, fracture mechanics, and force-property relations. However, a systematic analysis of uncertainties in the forces inferred through this method has not been undertaken. In this paper, our goal is therefore to perform such a systematic analysis. We first review and modify the force inference technique to eliminate its sensitivity to the choice of units and coordinate system origin. We then use discrete-element method simulations to perform a systematic study of how experimental uncertainties and data-processing errors lead to errors in inferred forces. For the considered experiments and simulations, we find that (1) errors in inferred force magnitudes and orientations increase as the ratio between particle stress uncertainties and a measure of stress imposed on the system increases, but remain small in the largest forces in a material; (2) the absence of a moderate number of particle stress tensors in the force inference procedure leads to negligible errors in inferred force magnitudes and orientations; and (3) particle stress tensors that cannot be directly measured during experiments can be "recovered" through the force inference procedure. Based on our results, we make recommendations for future experiment design to reduce uncertainties in inferred forces.

Shape adjustment of "FAST" active reflector

Abstract. In this paper, the relevant working principle of "FAST" Chinese Eye is studied, and a mathematical model is established to solve the equation of the ideal paraboloid. The ideal paraboloid model is obtained by rotating the paraboloid around the axis in the two-dimensional plane. On this basis, the specific solutions of each question are discussed, and the parabolic equation, the receiving ratio of the feed cabin to the reflected signal, the numbering information and coordinates of the main cable node and other parameters are obtained. This paper for solving directly above the benchmark of spherical observation of celestial bodies when ideal parabolic equation, according to the geometrical optics to knowledge should be clear all the signals of the incoming signal after the ideal parabolic will converge to the focal point of basic rules, then through converting ideal parabolic model of ideal parabolic equation in a two-dimensional plane, An optimization model was established to minimize the absolute value of the difference between the arc length and the arc length of the parabola in the diameter of 300 meters. The known conditions were substituted into Matlab to solve the equation of the ideal parabola by rotating the parabola around the axis: . In order to determine the ideal paraboloid of the celestial body, a new spatial cartesian coordinate system is first established with the line direction between the celestial body and the spherical center as the axis, so that the observed object is located directly above the new coordinate system. The same model in question 1 is established to obtain the vertex coordinates of the ideal paraboloid at this time. Then the vertex coordinates are converted to the coordinates in the original space cartesian coordinate system by rotation transformation between space cartesian coordinate systems. The solution of its vertex coordinates (-49.5287, -37.0203, -294.1763).

Analytical solutions for the mean-square displacement derived from transport theory

In this paper, exact analytical solutions are derived for the second-order moment and the mean-square displacement based on the transport theory fluence that is caused by an arbitrary anisotropic point source, which is located at the origin of a three-dimensional coordinate system. In particular, the derivations are carried out as a function of the number of scattering events. The resulting formulas in the steady-state and time domain depend, apart from the scattering coefficient and partly the absorption coefficient, only on the anisotropy factor of the considered rotationally invariant scattering phase function. We additionally present the second-order moment and the mean-square displacement for the fluence of fluorescence light in the steady-state domain.

Artificial bee colony algorithm with bi‐coordinate systems for global numerical optimization

As an effective global optimization technique, artificial bee colony (ABC) algorithm has become one of the hottest research topics in the fields of evolutionary algorithms. However, the solution search equation is not rotationally invariant, which causes the problem that the performance of ABC is sensitive to the coordinate system. Although many improved ABC variants have been developed, they rarely considered the problem. Hence, to solve the problem, we propose a new ABC variant with bi-coordinate systems (BSABC), including the original coordinate system and the eigen coordinate system. The two coordinate systems own different characteristics: (1) the former one aims to maintain the population diversity, and (2) the latter one is to adapt the search to the fitness landscape of the problems. Based on the characteristics, in the BSABC, the two coordinate systems are used in the employed bee phase and onlooker bee phase, respectively. Meanwhile, two new solution search equations are designed by utilizing the elite information, and they are respectively performed in the two coordinate systems to further improve the algorithm performance. As another contribution of this study, in the scout bee phase, the multivariate Gaussian distribution is constructed to replace the original method to generate offspring, which is helpful to save the search experience. The performance of the BSABC is verified by extensive experiments on the CEC2013 test suite and one real-world optimization problem, and four well-established ABC variants and three other evolutionary algorithms are included in the performance comparison. The comparison results confirm that the BSABC shows competitive performance by achieving better results on the majority of test functions.

Dynamic formulation of a two link flexible manipulator and its comparison analysis with a knuckle joint cantilever

In the present study a dynamic modelling technique for a two-link flexible planar manipulator is presented. The developed manipulator model can include an arbitrary number of flexible links. The gross equation of motion of each flexible link has been obtained by composing the rigid body motion and a small elastic deformation of each link. In order to bring the simplicity the modelling technique has been applied to model a two link flexible manipulator. The analytical derivation and final expression for the equation of motion has been shown for a two link flexible manipulator using the proposed modelling method. Later on, a comparison analysis has been studied between the proposed manipulator model and a simple cantilever with a knuckle joint. Finite element analysis of the beam has been done in ANSYS 17.1 considering different types of elements under different loading conditions. The various numerical results have been generated at different nodal points by taking the origin of the Cartesian coordinate system at the fixed end of the beam. Finally, a comparison analysis has been made to find a way to validate the proposed mathematical modelling.

Characterization of Rectifying Curves by Their Involutes and Evolutes

A rectifying curve is a twisted curve with the property that all of its rectifying planes pass through a fixed point. If this point is the origin of the Cartesian coordinate system, then the position vector of the rectifying curve always lies in the rectifying plane. A remarkable property of these curves is that the ratio between torsion and curvature is a nonconstant linear function of the arc-length parameter. In this paper, we give a new characterization of rectifying curves, namely, we prove that a curve is a rectifying curve if and only if it has a spherical involute. Consequently, rectifying curves can be constructed as evolutes of spherical twisted curves; we present an illustrative example of a rectifying curve obtained as the evolute of a spherical helix. We also express the curvature and the torsion of a rectifying spherical curve and give necessary and sufficient conditions for a curve and its involute to be both rectifying curves.

A new seasonal frozen soil water-thermal coupled migration model and its numerical simulation.

In this paper, a mathematical model based on spherical differential unit cell is proposed as a model for studying seasonal freeze-thaw soil space infinitesimal differential unit cell. From this model, the basic equations of permafrost moisture and heat flow motion are directly derived, then the linked equations form the permafrost water-heat coupled transport model. On this basis, the one-dimensional seasonal permafrost water-heat transport equation is derived. The model reduces the original spatial three-variable coordinate system (parallel hexahedron) into a coupled equation with a single spherical radius (R) as the independent variable, so the iterations of the numerical simulation algorithm is greatly reduced and the complexity is decreased. Finally, the model is used to simulate the seasonal freeze-thaw soil in the ShiHeZi region of Xinjiang, China. The principle of the simulation is to collect the soil temperature and humidity values of the region in layers and fixed-points using a homemade freeze-thaw soil sensor, after that we solve it by numerical calculation using MATLAB. The analysis results show that the maximum relative error of the model we proposed is 4.36, the minimum error is 0.98, and the average error is 2.515. The numerical simulation results are basically consistent with the measured data, then the proposed model is consistent with the matching states of permafrost moisture content and soil temperature in the region at different times. In addition, the experiments also demonstrate the reliability and accuracy of the model.

Path Planning Algorithm for Mobile Robot Based on Improved Ant Colony Algorithm

Due to the influence of full traversal environment, the path length obtained by existing methods is too long. In order to improve the performance of path planning and obtain the optimal path, a full traversal path planning method for omnidirectional mobile robots based on ant colony algorithm is proposed. On the basis of the topology modeling schematic diagram, according to the position information of the mobile robot in the original coordinate system, a new environment model is established by using the Angle transformation. Considering the existing problems of ant colony algorithm, the decline coefficient is introduced into the heuristic function to update the local pheromone, and the volatility coefficient of the pheromone is adjusted by setting the iteration threshold. Finally, through the design of path planning process, the planning of omnidirectional mobile robot’s full traversal path is realized. Experimental results show that the proposed method can not only shorten the full traversal path length, but also shorten the time of path planning to obtain the optimal path, thus improving the performance of full traversal path planning of omnidirectional mobile robot.

Nondestructive testing algorithm of building concrete material defects based on machine learning

In order to pay more attention to the quality of construction concrete and accurately judge whether concrete material meets the standard, a nondestructive testing algorithm of building concrete material defects based on machine learning is proposed. Through the ray tracing algorithm of Snell’s theorem, the shortest path between two random punctuation marks of building concrete is calculated. The original coordinate system and grid size were set, the trend and length of the line in the grid were calculated, and the coordinates between the grid corner points and the transmitting probe were calculated so as to obtain the position of the intermediate refractive points of the two probes. Finally, the vector dot product of the local defects is obtained by the optimal hyperplane calculation of the binary classification in the support vector machine. Experimental results show that the proposed method has the advantages of high precision.

Detection and fast motion parameter estimation for target with range walk effect based on new axis rotation moving target detection

In order to address the range walk (RW) effect in the field of radar high speed target detection, the axis rotation MTD (AR-MTD) class algorithms based on long-time coherent integration, i.e., AR-MTD, improved axis rotation MTD (IAR-MTD), and modified location rotation transform (MLRT) have been proposed in recent works. However, they are faced with detection performance loss and large computational complexity. In this paper, a new axis rotation MTD (NAR-MTD) algorithm is proposed. Different from the previous AR-MTD class algorithms, NAR-MTD first selects the image center of 2-D compressed signal as the coordinate system origin, and then simplifies the axis rotation relationship to reduce the rotation error caused by the coordinate transformation and correct the RW to the initial range location. Furthermore, by exploiting the geometrical information of mismatched NAR-MTD, the adaptive AR-MTD (AAR-MTD) is proposed to realize efficient motion parameter estimation of the moving target in different SNR environments. Numerical simulations and real data process indicate that NAR-MTD has a better detection ability than that of AR-MTD class algorithms. Meanwhile, the computational efficiency of AAR-MTD is about two orders of magnitude higher than that of direct 2-D search of NAR-MTD.

Flat lens design to rotate a cylindrical beam of a line source to an arbitrary angle.

The theory of transformation optics is used to adjust the direction of emitted beams from a flat lens. In this paper, a planar lens is presented based on the transformation optics approach, which converts cylindrical beams emitted from a line source into a planar beam at the desired angle. The index profile of a planar inhomogeneous lens is considered as the refractive index of the original coordinate system. So, this yields a lens that produces a flat wave at an arbitrary angle. The performance of the structure is confirmed by COMSOL software.

On the Sensitivity of the Gamma of the Quantum Cryptographic System AKM2017 to Changes in the Session Key

The quantum cryptographic system AKM2017 is considered. The results of the analysis of the dependence of the degree of difference between the encryption and decryption gamut on the degree of difference between the corresponding session keys are presented. The equality of these degrees of distinction is revealed and substantiated. For an arbitrarily fixed encryption session key, the distribution of session decryption keys by classes is revealed and described, depending on the value of the degree of difference between the encryption and decryption gamuts. One class is made up of all session decryption keys, leading to the same value of the degree of difference between the encryption and decryption gamuts. A geometric interpretation of the specified distribution by classes is given in the form of placement along circles (class is a circle) on the surface of a sphere of unit radius centered at the origin of the Euclidean rectangular coordinate system in a three-dimensional linear space over the field of real numbers. The stated results can be used to solve the problems of optimizing the values of the parameters of accuracy and reliability of the functioning of variants of practical implementations of the quantum cryptographic system AKM2017, for example, when setting up a session decryption key, which makes it possible to guarantee a predetermined small value of the mathematical expectation of the number of incorrectly decrypted binary plain text.

New fluid kinematics

Fluid kinematics describes the fluid motion without consideration of any force. Classical fluid kinematics adopts Helmholtz velocity decomposition, which is equivalent to Cauchy-Stokes (CS) velocity gradient tensor decomposition. CS decomposes the velocity gradient tensor into a strain-rate (symmetric) tensor and a vorticity (anti-symmetric) tensor. However, several questions arise: (1) since vorticity cannot represent fluid rotation, the vorticity tensor is a mixture of vorticity shear and rigid rotation, (2) since the strain-rate tensor cannot represent fluid shear, the strain-rate tensor is a mixture of stretching and shear, (3) the stretching and shear in the CS decomposition are dependent on the selection of coordinate system and are therefore not Galilean invariant. On the other hand, Liutex is a new physical quantity to represent the rigid fluid rotation and a principal coordinate system can be set up based on Liutex. A principal decomposition of the velocity gradient tensor, or the rotation-stretching-shear decomposition, can be easily carried out in the principal coordinate system with a clear physical meaning, which represents the rigid rotation, stretching (compression) and shear (symmetric and anti-symmetric shear). In the principal decomposition, all elements in three sub-tensors are Galilean invariant and, therefore, the principal decomposition is unique, Galilean invariant and independent of coordinate system. The principal decomposition is then transformed back to the original xyz coordinate system. The Liutex-based principal decomposition creates the new fluid kinematics which is ready for building up new fluid dynamics. Since fluid kinematics is the foundation of the fluid dynamics, the new fluid kinematics could replace the classical fluid kinematics, Helmholtz or CS decomposition, and open a new gate to develop new fluid dynamics especially for vortex science and turbulence research.

EPR Paradox, Einstein-Rosen bridges and teleportation

In this review, we go over the bases of quantum teleportation, ER bridges in General relativity, and the foundational work on the hypothesis ER=EPR and summarize the resulting wormhole teleportation protocol. We then discuss that − resulting from ER=EPR − certain wormholes have to be either traversable or at the very least let information permeate, resulting in the exploration of the possibility that incoming matter might change the metric outside of wormhole throats. In this study, made in the Schwarzschild metric with the original coordinate system, we managed to find a non-zero energy-momentum tensor produced by a particular solution of the electromagnetic wave equation in curved spacetime, implying a change in the overall metric by Einstein’s Equation.

Processing Framework for Landslide Detection Based on Synthetic Aperture Radar (SAR) Intensity-Image Analysis

We present an object-based image analysis (OBIA) approach to identify temporal changes in radar-intensity images and to locate land-cover changes caused by mass-wasting processes at small to large scales, such as landslides. Our approach is based upon change detection in SAR intensity images that remain in their original imaging coordinate system rather than being georeferenced and map-projected, in order to reduce accumulation of filtering artifacts and other unwanted effects that would deteriorate the detection efficiency. Intensity images in their native slant-range coordinate frame allow for a consistent level of detection of land-cover changes. By analyzing intensity images, a much faster response can be achieved and images can be processed as soon as they are made publicly available. In this study, OBIA was introduced to systematically and semiautomatically detect landslides in image pairs with an overall accuracy of at least 60% when compared to in-situ landslide inventory data. In this process, the OBIA feature extraction component was supported by derived data from a polarimetric decomposition as well as by texture indices derived from the original image data. The results shown here indicate that most of the landslide events could be detected when compared to a closer visual inspection and to established inventories, and that the method could therefore be considered as a robust detection tool. Significant deviations are caused by the limited geometric resolution when compared to field data and by an additional detection of stream-related sediment redeposition in our approach. This overdetection, however, turns out to be potentially beneficial for assessing the risk situation after landslide events.

Approximate filtered back-projection algorithm for plane curves in tomography problems

In previous works by the author and colleagues, it was proposed in some tomography problems to convert the fan-shaped projection measurement scheme into a system of parallel rays by deforming reconstructed image. The deformation of the tomogram for each direction of observation will be different, but the one-to-one nature of these deformations allows one to return back to the original coordinate system. Further, this method is generalized to a family of plane curvilinear trajectories that allow one-to-one transitions to parallel rays. For each back projection, the image is modulated by a known function following from the path differential of a given trajectory. Illustrations of the operation of this algorithm are given on examples of parabolic, sinusoidal and fan-beam paths of rays. The applicability of the algorithm in problems of visualization of discontinuities, in problems of ROI-tomography (local tomography) is shown.References

RESTRICTIONS OF THE TYPE OF POLYHEDRAL DISPLACED CONE IN LINEAR PROGRAMMING PROBLEMS

The paper considers the linear programming problem. A method is proposed to simplify its solution by identifying a class of constraints of a special type, due to which the desired plan will belong to a polyhedral convex cone located in a non-negative orthant. In this case, you must perform the following algorithm of actions. First, the original coordinate system is parallel transferred to the top of the selected cone. Then a transition to another space is made, which will lead to significant changes: a decrease in the number of restrictions. Next is the solution to the problem in any convenient way, for example, by the simplex-method – the most frequently used algorithm for finding solutions to linear extremal problems. One of its features is that with a large number of restrictions, its effectiveness decreases. This is a significant drawback in solving a number of problems, in particular, those of an economic nature, which, as a rule, striving to most accurately reflect the real state of affairs, impose a large number of restrictions on the desired plan. Therefore, if possible, it is better to reduce their number, even by increasing the variables, as this can happen in the proposed method for solving the selected class of problems. After finding the optimal plan, you need to return to the original space, and then to the old coordinate system. An important condition of this algorithm is the non-negativity of the cone elements. Thanks to this assumption, when a task is modified, new constraints are excluded. To track the implementation of this requirement, a condition is given in the work that guarantees its fulfillment. At the end of the work, the technique of searching for the operator (transition matrix) is described, with the help of which the task is transferred to another space. It is based on the search for vectors aligned with the generators of the cone.