Horizontal Coordinates Research Articles

Estimating Locations and Moments of Multiple Dipole-Like Magnetic Sources From Magnetic Gradient Tensor Data Using Differential Evolution

In this article, we present a new method for the detection and localization of multiple dipole-like magnetic sources using magnetic gradient tensor data. We use the tilt angle that is the ratio of the vertical magnetic component to the horizontal field to determine the number of the magnetic sources and use the rotational-invariant normalized source strength (NSS) to estimate approximate horizontal coordinates of the magnetic sources. The differential evolution (DE) algorithm is used to estimate the locations and moments of the magnetic sources. Three synthetic examples, with and without random noise, are designed to validate the proposed method. The locations and magnetic moments of the magnetic sources can be well determined. The proposed method has also been applied to a field test with multiple magnetic sources and the result shows that the location of the magnetic source can be estimated well.

Finite deformation of a blunt crack represented by a parabolic cavity in a harmonic solid

We study the finite plane deformation of a blunt crack represented by a parabolic cavity in a particular class of compressible hyperelastic materials of harmonic type. A complete solution to the blunt crack problem is derived using complex variable techniques. Elementary expressions of the stresses along the real axis ahead of the vertex of the parabola and the finite deformation of the parabola are obtained. When the nominal stress intensity factors approach zero, the stress distributions along the real axis are identical to those in linear elasticity. When the nominal stress intensity factors approach infinity, the tractions along the real axis are inversely proportional to the square root of the horizontal coordinate. A finite and non-zero mode II nominal stress intensity factor will induce both shear and normal stresses along the real axis, a phenomenon quite different from that for linear elasticity.

Estimates for Operators Related to the Sub-Laplacian with Drift in Heisenberg Groups

In the Heisenberg group of dimension 2n+1, we consider the sub-Laplacian with a drift in the horizontal coordinates. There is a related measure for which this operator is symmetric. The corresponding Riesz transforms are known to be L^p bounded with respect to this measure. We prove that the Riesz transforms of order 1 are also of weak type (1, 1), and that this is false for order 3 and above. Further, we consider the related maximal Littlewood–Paley–Stein operators and prove the weak type (1, 1) for those of order 1 and disprove it for higher orders.

THREE-DIMENSIONAL PROBLEM OF FLOW OF VISCOUS LIQUID THROUGH AN OPEN CHANNEL IN THE FORMULATION OF A NUMERICAL SOLUTION

The article considers the statistically stationary incompressible flow of a viscous liquid in an open inclined channel of rectangular cross-section with large Reynolds numbers. A threedimensional numerical model with a periodic boundary condition along the axis of the main flow is proposed. Three-layer boundary conditions are placed on the wall and near the channel wall, and on the free surface - conditions of non-zero or zero tangential voltage. To solve the problem, the predictor-corrector schemes of the method of fractional steps by horizontal coordinates with a cosine-oidal spectral function by vertical coordinate are used. A general algorithm for solving the problem with an isoperimetrically optimized cross-section parameter is compiled.

THREE-DIMENSIONAL MODEL FOR NUMERICAL STUDY OF THE MOVEMENT OF A VISCOUS LIQUID ON THE ROUNDING OF AN OPEN CHANNEL

The article considers the statistically stationary flow of a viscous incompressible liquid at the turn of an open inclined channel of a rectangular cross-section with large Reynolds numbers. A three-dimensional numerical model with a periodic boundary condition along the curvilinear axis of the main flow is proposed. Three-layer boundary conditions are placed on the wall and near the channel wall, and zero tangential voltage conditions are placed on the free surface. To solve the problem, the predictor-corrector scheme of the method of fractional steps by horizontal coordinates and with a cosine-oidal spectral function by vertical coordinate are used. A general algorithm for solving the problem with an isoperimetrically optimized cross-section parameter is compiled.

AdaHC: Adaptive hedge horizontal cross-section center detection algorithm

Finding the center point of the hedge is the key to automated pruning. In a complex outdoor environment, since the horizontal cross-section of the hedge is not a regular circle, and has many approximate circular contours, the performance of mainstream circle detection algorithms is not ideal. To this end, we propose an adaptive hedge horizontal cross-section center detection algorithm, named AdaHC, which can obtain the horizontal cross-section center coordinates of the hedge in real time by inputting the top view image of the hedge. The experimental results show that our proposed algorithm is significantly better than other circle detection algorithms. Its recognition accuracy can reach 100%, the average accuracy is over 80% (corresponding to an accuracy of 1 cm), and the average time consumption is 11.6 ms, be robust to the variations in light, hedge color, and background, fully meets the industrial requirements, and lays a good foundation for automatic hedge trimming.

Hysteretic Energy Demand under Superposition of Bidirectional Ground Motions

To address the irrationality of making a structure subjected to bidirectional ground motions equivalent to an SDOF system, a new approach method is presented in this paper. The ratio between modal participation factors of the two components of the structure is expressed as γ, and the superposition of bidirectional ground motions is regarded as one-directional earthquake excitation for the equivalent SDOF system. Based on this, an energy balance equation is established, and a method used to estimate normalized hysteretic energy (NHE) is proposed. Analysis of the ratio between NHE (γ ≠ 0) and NHE (γ = 0) is suggested in order to analyze the influence of bidirectional ground motions on hysteretic energy demand, and then, “α1 = NHE (γ ≠ 0)/NHE (γ = 0)” is defined, and bidirectional ground motion records for different soil sites are selected for establishing superimposed excitations. In addition, the period range of 0–5 s for the energy spectrum is divided into 6 ranges. In each period range, the means of α1 are defined as α. The curves of α of constant ductility factors for different soil sites are established, in which α is the vertical coordinate and γ is the horizontal coordinate. Through nonlinear response history analysis, the influence of soil types at different sites, the ductility factor, the ratio of modal participation factors, and the period on the values of α are analyzed. According to the analytical results, correction coefficient αs (the simplified value of α) is obtained so that the hysteretic energy demand under bidirectional ground motions can be determined.

On the Brachistochrone problem with state constraints on the slope angle

The problem of maximizing the horizontal coordinate of a point moving in a vertical plane under the action of gravity forces, viscous friction, and the interrelated Brachistochrone problem are investigated. It is assumed that inequality-type constraints are imposed on the trajectory inclination angle. The optimal control problem with state constraints is reduced to the problem with control constraints. As a result, the sequence and the number of the reaching the phase constraints for the original problem are determined and the synthesis of the optimal control is designed.

Mathematical Model of the Deaeration of Finely Dispersed Solid Media in a Spherical Matrix of a Roller-Type Apparatus

The additional operation of deaeration (compaction) of powders affects the quality of many products of chemical industries, the conditions for their delivery. Otherwise, energy consumption increases significantly. The aim of this work is the modeling of the deaeration of solid finely dispersed media in a gap with perforated hemispherical shapes on the surfaces of the shaft and conveyor belt within the framework of the mechanics of heterogeneous systems. A plane-deformation model is described, neglecting the forces of interphase interaction and taking into account the compressibility of a solid-particle-gas mixture without elastoplastic deformations. The model assumes consideration of the movement of (1) the components of the solid skeleton together with the carrying phase as a whole; (2) gas in an isothermal state through the pores of a finely dispersed material. This work is devoted to the study of part (a), i.e., behavior of the solid particle-gas system as a whole. The efficiency of the seal-deaerator is estimated using the obtained analytical dependencies for the main strength and speed indicators. The change in the degree of compaction of a spherical granule made of kaolin with given strength characteristics is investigated. It is shown that for the initial time interval up to 3.7⨯10−2 s, the growth of the porosity value relative to the horizontal coordinate along the conveyor belt is exponential and increases by a factor of 1.1. After eight such time intervals, the porosity values stabilize along the indicated coordinate with an increase of more than 1.4 times from the initial value.

A new human-like walking for the humanoid robot Romeo

This paper seeks to define the anthropomorphic walking motion for the humanoid robot Romeo. The main characteristics of the lower and upper limb motions of the human being during walking are adapted to Romeo taking into account its kinematics and its motor power. The proposed walking includes starting, periodic and stopping motions. A boundary value problem is stated and solved to define each of these three movements, which are composed of single and double support phases. The trajectory of the zero moment point (ZMP) is explicitly defined as a function of time. Thanks to the Essential model, the two horizontal coordinates of the center of mass (CoM) are adapted to the desired ZMP trajectory and joint movements of Romeo. Numerical results show the efficiency of our strategy to design human-like walking for Romeo.

One-dimensional thermal equation modeled on a two-dimensional heat exchanger with variable solid-fluid interface

In this study, we are to present that a one-dimensional equation for vertically averaged temperature, modeled on a vertically thin, two-dimensional heat exchanger with variable top solid-fluid interface, recovers the two-dimensional thermal information, i.e. steady temperature and flux distribution on the top and temperature-fixed bottom faces. The relative error of these quantities is less than 5% with the maximum gradient of the height kept approximately below 0.5, while the computational time is reduced to 0.1–5%, when compared with direct two-dimensional computations, depending on the shape of the top face. The model equation, derived by the vertical averaging of the two-dimensional thermal conduction equation, is closed by an approximation that the heat exchanger is sufficiently thin in the sense that the second derivative of temperature with respect to the horizontal coordinate depends only on the coordinate. In this model equation, the fluid equation above the exchanger is decoupled by a conventional equation for the normal heat flux on the top surface. In principle, however, the coupling of the model and the fluid equation is possible through the temperature and heat flux on the top interface, recovered by the model equation. The type of mathematical modeling can be applicable to a wide variety of bodies with extremely small dimensions in some (coordinate-transformed) directions.

Joint 3D-Location Planning and Resource Allocation for XAPS-Enabled C-NOMA in 6G Heterogeneous Internet of Things

The sixth generation (6G) communication creates a fully connected world of terrestrial wireless and satellite communications, which achieves global seamless coverage. To obtain the tripartite balance of spectrum efficiency, system throughput and complexity at the receiving end, clustered-NOMA (C-NOMA) is recommended. With Low Altitude Platform Station (LAPS) like UAV for strengthening communication in certain areas, and High Altitude Platform Station (HAPS) for ensuring wide coverage, we put forward the XAPS-enabled (including one HAPS and multiple UAVs) C-NOMA system in 6G heterogeneous Internet of things and investigate the joint 3D-location planning and resource allocation problem by optimizing four factors systematically, which are the spectrum allocation, power control, horizontal coordinate and hovering altitude optimization of UAVs to maximize the overall system uplink achievable sum rate. Due to the strong coupling among these factors, it is a mixed integer nonlinear programming (MINLP) problem, which is extremely difficult to solve. Therefore, we decompose it and propose a two-stage solution. Specifically, in the first stage we transfer resource allocation problem into a many-to-one spectrum matching game coupled with power control, where UAVs and subchannels are two groups of participants. Then we complete the second stage by optimizing UAVs’ 3D-locations, including horizontal coordinates and hovering altitudes. Finally, we repeat these two stages iteratively until the near-optimal result is obtained. Both theoretical analysis and simulations show that our proposed approach outperforms previous solutions in terms of system uplink sum rate with relatively low complexity.

Performance evaluation of GNSS receiver clock modelling in urban navigation using geodetic and high-sensitivity receivers

AbstractIn urban areas, the Global Navigation Satellite System (GNSS) can lead to position errors of tens of meters due to signal obstruction and severe multipath effects. In cases of 3D-positioning, the vertical coordinate is estimated less accurately than are the horizontal coordinates. Multisensor systems can enhance navigation performance in terms of accuracy, availability, continuity and integrity. However, the addition of multiple sensors increases the system cost, and thereby the applicability to low-cost applications is limited. By using the concept of receiver clock modelling (RCM), the position estimation can be made more robust; the use of high-sensitivity (HS) GNSS receivers can improve the system availability and continuity. This paper investigates the integration of a low-cost HS GNSS receiver with an external clock in urban conditions; subsequently, the gain in the navigation performance is evaluated. GNSS kinematic data is recorded in an urban environment with multiple geodetic-grade and HS receivers. The external clock stability information is incorporated through the process noise matrix in a Kalman filter when estimating the position, velocity and time states. Results shows that the improvement in the precision of the height component and vertical velocity with both receivers is about 70% with RCM compared with the estimates obtained without applying RCM. Pertaining accuracy, the improvement in height with RCM is found to be about 70% and 50% with geodetic and HS receivers, respectively. In terms of availability, the HS receiver delivers an 100% output compared with a geodetic receiver, which provides an output 99⋅4% of the total experiment duration.

Cost- and Energy-Efficient Aerial Communication Networks With Interleaved Hovering and Flying

This work proposes a methodology for the energy-and cost-efficient 3-D deployment of an unmanned aerial vehicle (UAV)-based aerial access point (AAP), that exchanges a given amount of independent data with a set of ground user equipment (UE). Considering a fly-hover-communicate transmission scheme, the most energy-efficient 3-D hovering points (HPs) of the AAP are determined by decoupling the problem in the horizontal and vertical dimensions. First, we derive analytically the optimal hovering altitude that jointly maximizes the downlink and uplink global energy efficiency (GEE) of the system. Next, we propose the multilevel circle packing (MCP) algorithm to determine the minimal number of HPs and their associated horizontal coordinates, such that the AAP covers all the UEs in the given geographical area. A cost analysis is carried out to observe the variation of both fixed and variable costs; these are then minimized by suitably selecting the AAP's battery parameters, like the depth of discharge (DOD), defined as the portion of battery capacity that is consumed during a discharge cycle, and the velocity of the UAV. Simulation results show that: the UAV energy consumption has a significant impact on the 3-D HPs of the AAP; the time spent during the substitution swap of an out of power AAP has a major influence on the operational cost; the cost of the system can be optimized by suitably selecting the onboard battery and the UAV flight parameters.

RESEARCH ON THE IMPROVED IMAGE TRACKING ALGORITHM OF ATHLETES’ CERVICAL HEALTH

ABSTRACT Objective: With the increasing number and youth of patients with cervical spondylosis, people pay more and more attention to the cervical spine. Early diagnosis, intervention and treatment play an important role in the recovery of cervical spondylosis. With the continuous development of computer technology, the improvement of various modeling theories, and the application of image processing methods in orthopedics, new ideas are opened to observe cervical vertebra motion health. Methods: In this paper, the measurement of cervical motion is achieved by machine vision. A method of parameter measurement based on the constraint relationship of lower cervical motion is proposed. Based on image preprocessing, the left edge of the cervical vertebra was extracted and analyzed. Results: With the horizontal coordinate of registration point as the reference line, the changing trend of the angle between the left edge curve and the reference line of C4 and C5 vertebrae in the process of spontaneous flexion and extension of the cervical vertebrae was observed, and the movement rate of the cervical vertebrae was analyzed. Conclusions: It was found that the speed of the cervical vertebrae in the process of movement of the patients with cervical spondylosis showed jumping changes. Level of evidence II; Therapeutic studies - investigation of treatment results.

Improving the Performance of Mode-Based Sound Propagation Models by Using Perturbation Formulae for Eigenvalues and Eigenfunctions

Numerous sound propagation models in underwater acoustics are based on the representation of a sound field in the form of a decomposition over normal modes. In the framework of such models, the calculation of the field in a range-dependent waveguide (as well as in the case of 3D problems) requires the computation of normal modes for every point within the area of interest (that is, for each pair of horizontal coordinates x,y). This procedure is often responsible for the lion’s share of total computational cost of the field simulation. In this study, we present formulae for perturbation of eigenvalues and eigenfunctions of normal modes under the water depth variations in a shallow-water waveguide. These formulae can reduce the total number of mode computation instances required for a field calculation by a factor of 5–10. We also discuss how these formulae can be used in a combination with a wide-angle mode parabolic equation. The accuracy of such combined model is validated in a series of numerical examples.

Five-dimensional interpolation in the OVT domain for wide-azimuth seismic data

Abstract To improve the imaging quality of wide-azimuth seismic data and enhance the uniformity of the attributes between adjacent bins, we developed a novel interpolation method in the offset-vector tiles (OVT) domain for wide-azimuth data. The orthogonal matching pursuit (OMP) interpolation method based on the Fourier transform is a frequency-domain processing technique based on discrete Fourier interpolation that achieves the goal of anti-aliasing by extracting the weight factor in the effective band from low-frequency data without aliasing. For data reconstruction, the OMP-based data interpolation technique in the OVT domain comprehensively uses the seismic data in five dimensions: the vertical and horizontal coordinates, time, offset and azimuth. Compared with conventional three-dimensional data interpolation, five-dimensional interpolation in the OVT domain is more accurate and achieves better results in practical applications.

Design of autonomous navigation system for electric patrol Unmanned Aerial Vehicle Based on Beidou Positioning and satellite based enhancement

In order to reduce the deviation of automatic inspection of transmission tower UAV and improve the efficiency of inspection work, the design of autonomous navigation system of electric power inspection UAV Based on Beidou Positioning and satellite based enhancement is proposed. On the basis of Beidou Positioning and satellite based enhancement, the automatic inspection projector and automatic inspection navigator of transmission tower UAV are designed, and the hardware design of the system is completed. This paper analyzes the endurance of UAV, calculates the coordinates of the best shooting point of UAV, and completes the planning of automatic inspection path of transmission tower UAV according to the horizontal offset coordinates of UAV in the process of transmission tower inspection. Combined with the automatic inspection algorithm of transmission tower UAV, the system software design is completed to realize the automatic inspection of transmission tower UAV. The simulation results show that compared with the traditional inspection system, the deviation of the designed UAV automatic inspection system for transmission tower is significantly reduced.

EVALUATING THE ACCURACY OF POST-PROCESSED KINEMATIC (PPK) POSITIONING TECHNIQUE

Post-processing kinematics (PPK) is positioning process in which signals received from a mobile receiving device store location data can be adjusted using corrections from a reference station after data has been collected. The processed kinematic screening method provides the surveyor with a technique for high production survey measurements and can be used in areas with minimal satellite barriers. PPK uses significantly reduced observation times compared to static or fast static observations. This method requires least squares adjustment or another multiple basic statistical analysis that can produce a weighted average of observations. The results obtained using PPK are between 1 cm and 3 cm for horizontal coordinates and from 1 cm to 10 cm for vertical coordinates.

A test method for analyzing the deformation of landslide model

In order to study the overall deformation of geotechnical model conveniently, the worksite of landslide bridge foundation reinforced by the front and rear row anti-slide piles in Chenglan railway was taken as an example. On the basis of shaking tabe test of a 1/40 reduced scale model, the landslide deformation caused by vibration waves was monitored through burying self-made phosphor bronze strips in soil. Combined with the horizontal and vertical coordinates of the bending strain points on the phosphor bronze strips, the digital matrix was converted by applying Renka Cline random matrix generation method, and the two-dimensional contour plots were drawn based on it. The results showed that the two-dimensional contour plots reflected the basic law of landslide deformation reasonably, and it revealed the evolution process of landslide deformation and failure. The research conclusions were consistent with the test phenomenon, which met the basic requirements of overall deformation analysis of landslide model. This proposed method can monitor multiple cross sections and was practical for model test.