A complete solution of an improved universal 3D coordinate similarity transformation model

When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3 D coordinate similarity transformation model in this paper.We deduced a complete solution for the 3 D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the condition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.

Controlling flexural waves in thin plates by using transformation acoustic metamaterials

In this study, we design periodic grille structures on a single homogenous thin plate to achieve anisotropic acoustic metamaterials that can control flexural waves. The metamaterials can achieve the bending control of flexural waves in a thin plate at will by designing only one dimension in the thickness direction, which makes it easier to use this metamaterial to design transformation acoustic devices. The numerical simulation results show that the metamaterials can accurately control the bending waves over a wide frequency range. The experimental results verify the validity of the theoretical analysis. This research provides a more practical theoretical method of controlling flexural waves in thin-plate structures.

Hawking effect and quantum nonthermal radiation of an arbitrarily accelerating charged black hole using a new tortoise coordinate transformation

Using a new tortoise coordinate transformation, this paper investigates the Hawking effect from an arbitrarily accelerating charged black hole by the improved Damour-Ruffini method. After the tortoise coordinate transformation, the Klein-Gordon equation can be written as the standard form at the event horizon. Then extending the outgoing wave from outside to inside of the horizon analytically, the surface gravity and Hawking temperature can be obtained automatically. It is found that the Hawking temperatures of different points on the surface are different. The quantum nonthermal radiation characteristics of a black hole near the event horizon is also discussed by studying the Hamilton-Jacobi equation in curved spacetime and the maximum overlap of the positive and negative energy levels near the event horizon is given. There is a dimensional problem in the standard tortoise coordinate and the present results may be more reasonable.

Correlation of coordinate transformation parameters

Coordinate transformation parameters between two spatial Cartesian coordinate systems can be solved from the positions of non-colinear corresponding points. Based on the characteristics of translation, rotation and zoom components of the transformation, the complete solution is divided into three steps. Firstly, positional vectors are regulated with respect to the centroid of sets of points in order to separate the translation compo- nents. Secondly, the scale coefficient and rotation matrix are derived from the regulated positions independent- ly and correlations among transformation model parameters are analyzed. It is indicated that this method is applicable to other sets of non-position data to separate the respective attributions for transformation parameters.

Uzbekistan's coordinate system transformation from CS42 to WGS84 using distortion grid model

Currently,a non-geocentric geodetic coordinate system introduced in 1942(CS42),based on the Krasovsky ellipsoid and the Baltic system of normal heights introduced in 1977,is used for geodetic works in the Republic of Uzbekistan.The development of the GNSS network proposes a task of transition to a new geocentric system based on the World Geodetic System 1984(WGS84)ellipsoid.Many software products adopt 3-or 7-parameter conversions,which can cause errors up to several meters and are not suitable for many applications.In this case,local transformations using a grid of differences between observation points with known coordinates in both datums would give the best accuracy.In this paper,we discuss various interpolation methods(Kriging,Minimum Curvature,Inverse Distance to a Power and Radial Basis Function)to solve the distortion modeling between CS42 and WGS84 systems for national datum improvement.The results show that the distortion models share a common tendency for all interpolation methods:the maximum horizontal displacements are concentrated along the West Tien Shan lineament,which is the boundary of the relief lowering.The discrepancies between the grid-based(calculated)and GPS-measured coordinates are evaluated.Statistical and spatial analysis has confirmed that for the co-ordinate transformation from CS42 to WGS84 and vice versa,grid-based transformation with Radial Basis Function interpolation has a high accuracy transformation.Analysis of the available data across the eastern part of the country shows that some positional distortions existed between the CS42 and WGS84 datums.For the best RBF method,the magnitude of these distortions is about 0.019-0.755 m with a standard deviation of 0.015 m.

Evaluation of the Direct UTM Coordinates Transformation Method Based on the Standard 7-Parameters Transformation

GNSS(global navigation satellite system)observations produce the geodetic position including latitude,longitude,and altitude(or ellipsoidal height)concerning the global reference datum WGS84(Word Geodetic System 1984),which usually should be converted to another local datum to get the desired position meaning in a physical sense,coordinates of points in the local datum are usually calculated by the seven-parameter transformation method.This paper aims to validate the methods of position transformation between WGS84 and the Iraqi local datum Karbala 1979 using the UTM(universal transverse Mercator)projected coordinates directly.The proposed algorithm was tested for 10 ground control points in Erbil city and many selected points in other different cities over all Iraqi territory.The control points are measured by the CHCNAV i73 GNSS receiver.For the evaluation procedure,the RMSE(root mean square error)of the transformed coordinates is calculated with an average value of±10.715 m as an estimated uncertainty of the direct UTM coordinates transformation method over Erbil city territory,and more than±12 m over different places over Iraqi territory.

Stability analysis of the projectile based on random center manifold reduction

The center manifold method has been widely used in the field of stochastic dynamics as a dimensionality reduction method.This paper studied the angular motion stability of a projectile system under random disturbances.The random bifurcation of the projectile is studied using the idea of the Routh-Hurwitz stability criterion,the center manifold reduction,and the polar coordinates transformation.Then,an approximate analytical presentation for the stationary probability density function is found from the related Fokker–Planck equation.From the results,the random dynamical system of projectile generates three different dynamical behaviors with the changes of the bifurcation parameter and the noise strength,which can be a reference for projectile design.

Quantum radiation of non-stationary Kerr-Newman-de Sitter black hole

By introducing a new tortoise coordinate transformation, we investigate the quantum thermal and non-thermal radiations of a non-stationary Kerr-Newman-de Sitter black hole. The accurate location and radiate temperature of the event horizon as well as the maximum energy of the non-thermal radiation are derived. It is shown that the radiate temperature and the maximum energy are related to not only the evaporation rate, but also the shape of the event horizon, moreover the maximum energy depends on the electromagnetic potential. Finally, we use the results to reduce the non-stationary Kerr-Newman black hole, the non-stationary Kerr black hole, the stationary Kerr-Newman-de Sitter black hole, and the static Schwarzshild black hole.

Forward Modeling of Gravity,Gravity Gradients,and Magnetic Anomalies due to Complex Bodies

On the basis of the results of improved analytical expression of computation of gravity anomalies due to a homogeneous polyhedral body composed of polygonal facets, and applying the forward theory with the coordinate transformation of vectors and tensors, we deduced both the analytical expressions for gravity gradient tensors and for magnetic anomalies of a polygon, and obtained new analytical expressions for computing vertical gradients of gravity anomalies and vertical component of magnetic anomalies caused by a polyhedral body. And also we developed explicitly the complete unified expressions for the calculation of gravity anomalies, gravity gradient, and magnetic anomalies due to the homogeneous polyhedron. Furthermore, we deduced new analytical expressions for computing vertical gradients of gravity anomalies due to a finite rectangular prism by applying the newly obtained expressions for gravity gradient tensors due to a polyhedral target body. Comparison with forward calculation of models shows the correctness of these new expressions. It will reduce forward calculation time of gravity-magnetic anomalies and improve computational efficiency by applying our unified expressions for joint forward modeling of gravity-magnetic anomalies due to homogeneous polyhedral bodies.

A new interpolation method based on satellite physical character in using IGS precise ephemeris

Due to the deficiency of sliding Lagrange polynomial interpolation, the author proposes a new interpolation method, which considers the physical character of satellite movement in coordinate transformation and reasonable selection of interpolation function. Precision of the two methods is compared by a numerical example. The result shows that the new method is superior to the sliding Lagrange polynomial interpolation in interpolation and extrapolation, especially in extrapolation that is over short time spans.

DISTANCE MEASURING MODELING AND ERROR ANALYSIS OF DUALCCD VISION SYSTEM SIMULATING HUMAN EYES AND NECK

A dual-CCD simulating human eyes and neck (DSHEN) vision system is putforward. Its structure and principle are introduced. The DSREN vision system can perform somemovements simulating human eyes and neck by means of four rotating joints, and realize preciseobject recognizing and distance measuring in all orientations. The mathematic model of the DSHENvision system is built, and its movement equation is solved. The coordinate error and measureprecision affected by the movement parameters are analyzed by means of intersection measuringmethod. So a theoretic foundation for further research on automatic object recognizing and precisetarget tracking is provided.

Three-dimensional tidal current numerical model of the Oujiang Estuary

The characteristics of three-dimensional （3-D） tidal current in the Oujiang Estuary are investigated according to in situ observations. The Oujiang Estuary has features of irregular coastline, complex topography, many islands, moveable boundary, and submerged dyke, therefore, σ 3-D numerical model oil an unstructured triangular grid has been degeloped. The σ coordinate transforination, the moveable boundary and submerged dyke treatment techniques were employed in the model so it is suitable for the tidal simulations in the Oujing Estuary with submerged dyke and moveable boundary problems. The model is evaluated with the in situ data, and the results show that the calculated water elevations at 19 stations and currents at 19 profiler stations are in good agreement with measured data both in magnitude and phase. This numerical model is applied to the 3-D tidal circulation simulations of experiments in stopping flow transport through the South Branch of the Oujiang Estuary, and the feasibility to cutoff the flow in the South Branch of the Oujiang Estuary is demonstrated by numerical simulation experiments. The developed numerical model simulated the 3-D tidal current circulations in complicated coastal and estuarine waters very well.

Deep Learning Predicts Stress–Strain Relations of Granular Materials Based on Triaxial Testing Data

This study presents an AI-based constitutive modelling framework wherein the prediction model directly learns from triaxial testing data by combining discrete element modelling(DEM)and deep learning.A constitutive learning strategy is proposed based on the generally accepted frame-indifference assumption in constructing material constitutive models.The low-dimensional principal stress-strain sequence pairs,measured from discrete element modelling of triaxial testing,are used to train recurrent neural networks,and then the predicted principal stress sequence is augmented to other high-dimensional or general stress tensor via coordinate transformation.Through detailed hyperparameter investigations,it is found that long short-term memory(LSTM)and gated recurrent unit(GRU)networks have similar prediction performance in constitutive modelling problems,and both satisfactorily predict the stress responses of granular materials subjected to a given unseen strain path.Furthermore,the unique merits and ongoing challenges of data-driven constitutive models for granular materials are discussed.

Automatic Method for Synchronizing Workpiece Frames in Twin-robot Nondestructive Testing System

The workpiece frames relative to each robot base frame should be known in advance for the proper operation of twin-robot nondestructive testing system. However, when two robots are separated from the workpieces, the twin robots cannot reach the same point to complete the process of workpiece frame positioning. Thus, a new method is proposed to solve the problem of coincidence between workpiece frames. Transformation between two robot base frames is initiated by measuring the coordinate values of three non-collinear calibration points. The relationship between the workpiece frame and that of the slave robot base frame is then determined according to the known transformation of two robot base frames, as well as the relationship between the workpiece frame and that of the master robot base frame. Only one robot is required to actually measure the coordinate values of the calibration points on the workpiece. This requirement is beneficial when one of the robots cannot reach and measure the calibration points. The coordinate values of the calibration points are derived by driving the robot hand to the points and recording the values of top center point（TCP） coordinates. The translation and rotation matrices relate either the two robot base frames or the workpiece and master robot. The coordinated are solved using the measured values of the calibration points according to the Cartesian transformation principle. An optimal method is developed based on exponential mapping of Lie algebra to ensure that the rotation matrix is orthogonal. Experimental results show that this method involves fewer steps, offers significant advantages in terms of operation and time-saving. A method used to synchronize workpiece frames in twin-robot system automatically is presented.

Research on Open-circuit Fault Tolerant Control of Six-phase Permanent Magnet Synchronous Machine Based on Fifth Harmonic Current Injection

This paper proposes a novel control approach for fault-tolerant control of dual three-phase permanent magnet synchronous motor(PMSM) under one-phase open-circuit fault.A modified six-phase static coordinate transformation matrix and an extended rotating coordinate transformation matrix are investigated considering the influence of the fifth harmonic space on fault-tolerant control. These mathematical models are further analyzed in the fundamental space and the fifth harmonic space after the fault and to eliminate the coupling between the d-q axis voltage equation in the fundamental wave space and the d-q axis voltage equation in the fifth harmonic space, a secondary rotation coordinate transformation matrix is proposed. To achieve the purpose of reducing torque ripple, the fault-tolerant control method proposed in this paper not only takes the minimum copper loss as the constraint condition, but also injects the fifth harmonic current. The experimental result of current and torque is used to verify the accuracy of fault-tolerant control.

Study on the effect of ground motion direction on the response of engineering structure

Due to the randomness of earthquake wave magnitude and direction, and the uncertain direction of strong axis and weak axis in the construction of engineering structures, the effect of the direction of ground motion on a structure are studied herein. Ground motion records usually contain three vertical ground motion data, which are obtained by sensors arranged in accordance with the EW （East -West） direction, NS （South- North） direction and perpendicular to the surface （z） direction, referring to the construction standard of seismic stations. The seismic records in the EW and NS directions are converted to Cartesian coordinates in accordance with the rotation of θ = 0°-180°, and consequently, a countless group of new ground motion time histories are obtained. Then, the characteristics of the ground motion time history and response spectrum of each group were studied, resulting in the following observations： （1） the peak and phase of ground motion are changed with the rotation of direction θ, so that the direction θ of the maximum peak ground motion can be determined; （2） response spectrum values of each group of ground motions change along with the direction θ, and their peak, predominant period and declining curve are also different as the changes occur; then, the angle θ in the direction of the maximum peak value or the widest predominant period can be determined; and （3） the seismic response of structures with different directions of ground motion inputs has been analyzed under the same earthquake record, and the results show the difference. For some ground motion records, such as the Taft seismic wave, these differences are significant. Next, the Lushan middle school gymnasium structure was analyzed and the calculation was checked using the proposed method, where the internal force of the upper space truss varied from 25% to 28%. The research results presented herein can be used for reference in choosing the ground motion when checking the actual damage to structures following earthquakes and explaining the seismic damage. Meanwhile, it also provides a reference value for research into the most severe ground motion.

Pattern Synthesis and Polarization Optimization of a Conical Array

A feasible method for synthesizing millimeter-wave conical array and optimizing low cross-polarization is proposed.Starting from the far-field superposition principle,an efficient approach including element mutual coupling and mounted platform effects is used to calculate the far-field patterns.A coordinate transform is applied to create polarization quantities,and a general process for the element polarized pattern transformation is performed.Corresponding numerical example is given and the desired sidelobe level and low cross-polarization are optimized.The numerical results indicate the proposed method is valid.

Generalized Birkhofflan representation of nonholonomic systems and its discrete variational algorithm

By using the discrete variational method,we study the numerical method of the general nonholonomic system in the generalized Birkhoffian framework,and construct a numerical method of generalized Birkhoffian equations called a self-adjoint-preserving algorithm.Numerical results show that it is reasonable to study the nonholonomic system by the structure-preserving algorithm in the generalized Birkhoffian framework.

Warp Drive with Positive Energy

Space and time traveling is one of the humanity’s most fascinating and challenging topics. The speed limitation makes space traveling highly difficult. Therefore, discovering the warp drive mechanism intrigued humanity to travel in space and time. Miguel Alcubierre proposed a model for warp drive. However, the energy density driven from the Alcubierre warp drive model turns to be negative everywhere. Erik Lentz proposed a shifting vector field in which we shall show that shifting vector field with appropriate spaceship geometry may provide positive energy density for warp drive. Further, we suggest looking at the spaceship geometry as a mother wavelet function with shifting, scaling, and rotation operations that may provide additional positive energy density. This sort of design requires a flexible fuselage that can be stretched and rotated.

Jump Drive, Replicators, Transporters, and Time Travel

Jumping from place to place, replicating food, biological or mechanical parts or beaming up somebody, may not be fiction, rather an issue of practical implementation as shall be observed in this paper. Devices like transporter, food replicators or warp drive intrigue our imagination. This paper is intended to show that Jump drive is an issue of coordinate transformation. Changing location from planet X to planet Y does not necessarily require travelling a distance D connecting between the two planets. The theoretical knowledge of changing the location from coordinate X to coordinate Y exists;we do that in signal processing, but, we have not yet developed such a machine. The present paper shows the feasibility of jump drive;however, much work needs to be done on the implementation.