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.

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.

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.

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.

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.

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.

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.

Transformation between polar and rectangular coordinates of stiffness and dampness parameters in hydrodynamic journal bearings

The stiffness and dampness parameters of journal bearings are required in rectangular coordinates for analyzing the stability boundary and threshold speed of oil film bearings.On solving the Reynolds equation,the oil film force is always obtained in polar coordinates;thus,the stiffness and dampness parameters can be easily obtained in polar coordinates.Therefore,the transformation between the polar and rectangular coordinates of journal bearing stiffness and dampness parameters is discussed in this study.

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.

Improvement of Orbit Prediction Algorithm for Spacecraft Through Simplified Precession-Nutation Model Using Cubic Spline Interpolation Method

For the on-orbit flight missions,the model of orbit prediction is critical for the tasks with high accuracy requirement and limited computing resources of spacecraft.The precession-nutation model,as the main part of extended orbit prediction,affects the efficiency and accuracy of on-board operation.In this paper,the previous research about the conversion between the Geocentric Celestial Reference System and International Terrestrial Reference System is briefly summarized,and a practical concise precession-nutation model is proposed for coordinate transformation computation based on Celestial Intermediate Pole(CIP).The idea that simplifying the CIP-based model with interpolation method is driven by characteristics of precession-nutation parameters changing with time.A cubic spline interpolation algorithm is applied to obtain the required CIP coordinates and Celestial Intermediate Origin locator.The complete precession nutation model containing more than 4000 parameters is simplified to the calculation of a cubic polynomial,which greatly reduces the computational load.In addition,for evaluating the actual performance,an orbit propagator is built with the proposed simplified precession-nutationmodel.Compared with the orbit prediction results obtained by the truncated series of IAU2000/2006 precession-nutation model,the simplified precession-nutation model with cubic spline interpolation can significantly improve the accuracy of orbit prediction,which implicates great practical application value in further on-orbit missions of spacecraft.

Modeling and Simulation of Nine-Phase Permanent Magnet Synchronous Motor

To study the operation characteristics of the nine-phase PMSM(Permanent Magnet Synchronous Motor),this paper derived the Clarke transformation matrix of the nine-phase PMSM with the winding 3Y shifted by 20°via analyzing the harmonic subspace of the multi-phase PMSM,and further obtained its mathematical model under the rotating coordinate system.Then,a nine-phase PMSM based on the proposed model was built in SIMULINK and the operation mode of starting,braking and phase missing is simulated.The simulation results show that the nine-phase PMSM has good dynamic performance and steady-state performance,which also verifies the correctness and rationality of the motor model.

Migration of the ICS Local Terrestrial Reference System to RRS04

In order to comply with the recommendations of the new mining code, as well as to facilitate data acquisition and exchange, and to guarantee the reliability of these data, the Chemical Industries of Senegal (named ICS) have decided to switch from their local terrestrial reference system to the Senegalese terrestrial reference system created in 2004 and called RRS04. This move allows ICS to take advantage of new measurement techniques such as GNSS and a more global terrestrial reference system. A combination of geodesy with the least squares method was implemented for the resolution of the problem and the optimization of the solution. For this purpose, a GNSS observation campaign was carried out on selected points. The raw data obtained were processed with the Leica Infinity 3.0 software before being used in our calculations for the estimation of the parameters of this passage which has many stakes for the ICS. The obtained results were then presented, applied before being checked and validated.

Vector Control of the Single-Phase Inverter Based on the Extended and Virtual Circuits

A vector control based on the extended equivalent circuit and virtual circuits is proposed for the single-phase inverter.By the extended circuit,the other two phase voltages can be extended by the output voltage of the single-phase inverter so as to construct the voltage vector.The voltage outer-loop is to control the voltage vector in dq coordinate system,and the output voltage can track the target value without deviation in steady state.By designing the virtual circuit,the voltage inner-loop can achieve approximate decoupling and improve the dynamic response under the changeable load.Compared with the traditional dual closed-loop control,the proposed dual closed-loop control scheme only needs to detect and control the voltage without the current.It not only can achieve good control effect,but also reduce the complexity of the hardware.Finally,the simulation and experimental results show that the single-phase inverter has good static and dynamic characteristics regardless of stable load or changeable load.

Light-Cone Coordinate System in General Relativity

If there exists a null gradient field in 3 + 1 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is helpful for simplifying and solving the Einstein’s field equation. This light-cone coordinate system has wonderful properties and has been used widely in astrophysics to calculate parameters. We discuss the structure of space-time with light-cone coordinate system in detail. We show how to construct the light-cone coordinate system and obtain the conditions of its existence, and then explain their geometrical and physical meanings.

Simulation Analysis of Transponder Power Based on Target Flight Trajectory

The directional angle of the exterior trajectory measurement equipment in the transponder antenna coordinate system is an important basis for interpreting the transponder antenna gain, analyzing the uplink and downlink power of the transponder, and evaluating the measurement and tracking ability of the equipment. The mathematical model established in this paper deduces the direction angle of the exterior trajectory measurement equipment in the transponder antenna coordinate system according to the track information of the flight target, and then obtains the transponder power received by the exterior trajectory measurement equipment combined with the installation position of the transponder, the antenna pattern and the secondary radar formula. It can effectively evaluate the tracking ability of the equipment in measuring segment and adjust the working state of the equipment according to the actual situation. At the same time, it provides a theoretical basis for the ground measurement equipment to receive the transponder power is too low, resulting in the measurement data accuracy is not up to standard, or even lost.

A multi-class time-dependent model for the analysis of waiting phenomena at a motorway tollgate

The planning, design and operational management of motorway toll booths are of great interest in traffic engineering, as these facilities directly influence the quality of the service offered to users. This paper focuses on a time-dependent queue model based on the coordinates transformation criterion for operations assessment at a motorway tollgate. This model allows to face the whole spectrum of situations that may characterize a toll booth,some of which often fall outside the boundaries of the probabilistic theory for stationary queues.The paper proposes an M=G=1 multi-class queue model for the evaluation of evolutionary profiles of waiting times and queue lengths by closed-form equations. The results obtained for three numerical test cases show a good approximation level, compared with the mean values of queue parameters obtained reiterating a discrete-state simulation model.The proposed time-dependent equations will be useful in technical cases, allowing to operate quickly and compactly even when probabilistic queue theory is not applicable or produce unrealistic results, and the burden of complexity of the simulation approach is not conveniently absorbable. The discussion highlights a significant flexibility of the model proposed in addressing situations with conventional vehicles, i.e., with total human control and proposes some considerations for application in future scenarios with the presence of connected vehicles(CVs).

Fast registration of multisource three-dimensional city models in GeoGlobe

We address the registration problem of multisource three-dimensional(3D)human-made buildings with remote sensing images and the earth’s surface in the context of virtual globes.Challenges include fast transformation of 3D coordinates with different reference systems as well as the efficient use of original model information for rigorous and accurate model registration.This paper introduces a novel fast and scalable registration approach that can establish correspondences between heterogeneous external 3D city models and images/terrain surfaces of virtual globes in an efficient and accurate manner.The approach utilizes the projected 3D feature information of 3D city models to develop robust coordinate transformation and reliable model registration methods.The proposed approach builds a solid foundation for the fusion of multisource geospatial data in a united virtual globe reference framework.We report experimental results of online registration tasks for up to over 13K buildings in an integrated 3D virtual globe platform,namely,GeoGlobe.

Influence of geometry on the thermal performance of water pit seasonal heat storages for solar district heating

The aim of the study is to investigate the influence of geometry on the thermal capacity and stratifications of a water pit heat storage for solar district heating.A TRNSYS component model for a truncated cone water pit was developed based on the coordinate transformation method and validated by experimental results from the water pit heat storage in Huangdicheng in 2018.The thermal performance of 26 water pits with different heights and side wall slopes was calculated for 10 consecutive years.It takes four to six years for the water pit to reach steady-state operation.The operation data from the tenth year was selected to evaluate the thermal performance of each configuration.The results show that because of the thermal insulation on top of the water pit,the height to diameter ratio of a water pit with minimum annual heat loss was always smaller than 1.0.The annual storage efficiency of a water pit increases with side wall slope due to the reduced side wall area.There is an almost linear increase in the thermal stratification number of a water pit with height.With an increase in the height,thermal stratification in water pits with a steeper slope increased more gradually than water pits with a lower slope.The findings in this paper are relevant for the design optimization of water pits as seasonal thermal energy storages.

State of the art and computational aspects of time-dependent waiting models for non-signalised intersections

Time-dependent models are of great importance in highway engineering as they are appropriate for evaluating waiting times and queue lengths at intersections,which are integral parts of various activities in planning,verification and decision support for infrastructure.After reviewing the literature of the main time-dependent models based on the coordinate transformation method and a discussion about some computational issues in time-evolution profiles for non-signalised intersections,the paper identifies the requirements these models have to satisfy in order to be used as"basic"cases for analysing complex evolutionary situations.Three"basic"cases are presented with their timedependent equations for vehicle waiting times and vehicle number;they have been completed and dimensionally homogenised in this paper.As they are recursive,these formulas can be applied for sequential intervals in the time domain in both vehicles and passenger car units.The closed-form expressions for state variables show to be mutually equivalent in comparison with discrete event simulation models and imbedded Markov chain results.For all the three models the paper presents a common deterministic simplification for average waiting time,with good approximation results in the tested cases.The proposed time-dependent formulas will contribute to a better adherence to the real phenomena,compared to the extremely simplified and unrealistic methods suggested by the international manuals for level of service assessment.The proposed formulas will be useful for current applications and possible future development in order to meet the emerging needs of road and transport engineering.

A Second Order Finite-Difference Ghost-Point Method for Elasticity Problems on Unbounded Domains with Applications to Volcanology

We propose a finite-difference ghost-point approach for the numerical solution of Cauchy-Navier equations in linear elasticity problems on arbitrary unbounded domains.The technique is based on a smooth coordinate transformation,which maps an unbounded domain into a unit square.Arbitrary geometries are defined by suitable level-set functions.The equations are discretized by classical nine-point stencil on interior points,while boundary conditions and high order reconstructions are used to define the field variables at ghost-points,which are grid nodes external to the domain with a neighbor inside the domain.The linear system arising from such discretization is solved by a multigrid strategy.The approach is then applied to solve elasticity problems in volcanology for computing the displacement caused by pressure sources.The method is suitable to treat problems in which the geometry of the source often changes(explore the effects of different scenarios,or solve inverse problems in which the geometry itself is part of the unknown),since it does not require complex re-meshing when the geometry is modified.Several numerical tests are successfully performed,which asses the effectiveness of the present approach.