Global Coordinate System Research Articles

Influence of Prestress on Vibration Frequency of Beam String Structures Based on Exact Matrix Stiffness Method

Beam string structures (BSS) are frequently employed in large-span spatial structures due to their high load-carrying efficiency and elegant appearance. Owing to the neglect of the influence of prestress, the natural frequency of the BSS is often overestimated which could be crucial to the dynamic behavior of BSS. This paper presents an exact matrix stiffness analysis method (MSM) for investigating the relationship between prestress and the natural frequency of the planar BSS. A novel dynamic stiffness matrix of beam–columns considering the natural frequency and axial force is used to develop the MSM. The dynamic analysis of the structural vibration stability of BSS is performed by using the global structural stiffness matrix which is assembled from the element stiffness matrices in the global coordinate system. The proposed MSM with the exact dynamic element stiffness matrix for the dynamic analysis of the BSS is verified by comparing with previous results based on the finite element method. The illustrative examples demonstrate that the prestress in the cable has a negative effect on the natural frequency of the BSS and should be considered in the dynamic analysis. As the axial force increases from zero to the buckling load [Formula: see text], the natural frequency of the BSS decreases from the maximum vibration frequency to zero. The influence of prestress on the vibration frequencies of BSS is particularly significant when the prestress to balance the loads is large, especially in the case of large dead and live loads (e.g. floor slabs).

Biomechanical effects of clear aligner with different shape design at extraction space area during anterior teeth retraction.

This study aimed to investigate the biomechanical effects of clear aligner (CA) with different shape designs at extraction space (CAES) area during space closing. A finite-element method (FEM) model of mandibular dentition, periodontal ligaments, attachments, and corresponding CA was established. The connecting rod design of CAES was modelled for the control group. Eight test groups with different heights of CAES from -4 mm to +4 mm were designed. Tooth displacement tendencies were calculated. The maximum principal stress in PDLs, teeth, and CAs was analysed. Both global coordinate system and local coordinate system were also used to evaluate individual tooth movements. Across all groups, stresses concentrated on the lingual outer surface of CAESs. For the lowered CAES groups, both the stress value and the stress distribution area at CAESs were increased. The lowered CAES groups showed reduced movement in anterior teeth and less tipping tendency of the canines. The shape of CAES has a biomechanical impact on anterior teeth movement and should be considered in aligner design. The results suggest that increasing the height of CAES can enhance anterior teeth retraction, while lowered CAES may facilitate controlled root movement. Changes in the shape of CAES represent a potential direction for biomechanical improvement of clear aligner in extraction cases and are worth exploring.

Transverse vibration of plate with multiple curved through cracks

A modeling method for transverse vibration of cracked plate containing multiple internal curved through cracks is presented and experimental studies are performed to validate its effectiveness. The cracked plate is assumed to be divided into several rectangular and curved trapezoidal domains in the global coordinates system. For each sub-domain, the transverse displacement is expanded as Chebyshev orthogonal polynomials series in local coordinates system. As for the shared edges between neighboring two sub-domains, the local collocation method is adopted and a number of Chebyshev zero points are selected to ensure the displacement continuity condition. To verify the convergence and correctness of the presented model and solutions, the natural frequencies, mode shapes and dynamic responses for several cases are compared with reference results and experimental results, with good agreement observed. In addition, the influence of several significant parameters of cracks are investigated, including the number, location and geometrical shape of the cracks. It is shown that the crack inside the plate presents less influence than that at the boundary on the mode change of the plate. The investigations in the study implies that the present model method is effective and convenient for plate with multiple curved through cracks.

Global Newlander–Nirenberg Theorem for Domains with C2 Boundary

The Newlander–Nirenberg theorem says that a formally integrable complex structure is locally equivalent to the standard complex structure in the complex Euclidean space. In this paper, we consider two natural generalizations of the Newlander–Nirenberg theorem under the presence of a C2 strictly pseudoconvex boundary. When a given formally integrable complex structure X is defined on the closure of a bounded strictly pseudoconvex domain with C2 boundary D⊂Cn, we show the existence of global holomorphic coordinate systems defined on D‾ that transform X into the standard complex structure provided that X is sufficiently close to the standard complex structure. Moreover, we show that such closeness is stable under a small C2 perturbation of ∂D. As a consequence, when a given formally integrable complex structure is defined on a one-sided neighborhood of some point in a C2 real hypersurface M⊂Cn, we prove the existence of local one-sided holomorphic coordinate systems provided that M is strictly pseudoconvex with respect to the given complex structure. We also obtain results when the structures are finite smooth.

A novel global calibration method for vision measurement system based on mirror-image stereo target

Using three-dimensional (3D) targets to solve the transformation relationship between the local and global coordinate systems is a common global calibration method. However, 3D targets have complex structures and high costs. And multiple coordinate transformations during global calibration can cause significant cumulative errors. Therefore, based on reflection imaging, this paper designs a new mirror-image stereo target (MST) and analyzes its view area and three structural parameter constraints. A new global calibration method is proposed, as well as three optimization algorithms for pose solution between MST, optical 3D sensor and global camera to improve the global calibration accuracy. The experimental results show that the registration errors of two workpieces are 0.086 mm and 0.114 mm, respectively, confirming the feasibility and precision of the proposed method. Our method is flexible, requiring only a planar target and a mirror, rather than complex 3D targets, to achieve global calibration with non-overlapping field of view.

An ordinary state-based peridynamic model for granular fracture in polycrystalline materials with arbitrary orientations in cubic crystals

Granular fracture holds significant implications in material mechanics. However, the previous studies in ordinary state-based peridynamic (OSB-PD) framework often neglect the internal crystalline structure of particles or only consider limited crystal orientation. To address this gap, a novel OSB-PD model for granular fracture within polycrystalline materials is proposed, in which the periodic functions are incorporated in the PD strain energy density, taking into account the inherent random orientation in cubic crystals. By comparing energy density from PD and the classical continuum mechanics, four PD material parameters are defined. Moreover, the corresponding surface correction method in the global coordinate system is also proposed. Several numerical examples including fracture analysis of polycrystalline materials are conducted to validate the effectiveness of the proposed method. The proposed ordinary state-based peridynamic model offers a fresh perspective for investigating granular fracture behaviors within polycrystalline materials.

Robotic compliant assembly for complex-shaped composite aircraft frame based on Gaussian process considering uncertainties

Robots are finding increasing application in aircraft composite structure assembly due to their flexibility and the growing demand of aircraft manufacturers for high production rates. The contact force of the composite frame in a robotic assembly of the aircraft composite fuselage panel can hardly be controlled due to the multi-surface variable contact stiffness caused by compliance and complex shape with multiple mating surfaces. The paper proposes a robotic assembly system for the aircraft composite fuselage frame with a compliant contact force control strategy using the Gaussian process surrogate model. First, a robotic assembly system is introduced, and the global coordinate system transformation model is built. Then, a compliant force control architecture is designed to generate the desired output force. Subsequently, a Gaussian process surrogate model with uncertainties is utilized to model the complicated relationship between the robot’s output force and the normal contact force acting on the mating surface of the composite frame. Furthermore, an optimal contact force control strategy is implemented to improve the contact quality. Finally, an experiment demonstrates that the proposed methodology can ensure that the contact force on each surface is within the limit of the engineering specification and uniformly distributed, improving the quality compared to the traditional assembly process.

Template-Guided Hierarchical Multi-View Registration Framework of Unordered Bridge Terrestrial Laser Scanning Data.

The registration of bridge point cloud data (PCD) is an important preprocessing step for tasks such as bridge modeling, deformation detection, and bridge health monitoring. However, most existing research on bridge PCD registration only focused on pairwise registration, and payed insufficient attention to multi-view registration. In addition, to recover the overlaps of unordered multiple scans and obtain the merging order, extensive pairwise matching and the creation of a fully connected graph of all scans are often required, resulting in low efficiency. To address these issues, this paper proposes a marker-free template-guided method to align multiple unordered bridge PCD to a global coordinate system. Firstly, by aligning each scan to a given registration template, the overlaps between all the scans are recovered. Secondly, a fully connected graph is created based on the overlaps and scanning locations, and then a graph-partition algorithm is utilized to construct the scan-blocks. Then, the coarse-to-fine registration is performed within each scan-block, and the transformation matrix of coarse registration is obtained using an intelligent optimization algorithm. Finally, global block-to-block registration is performed to align all scans to a unified coordinate reference system. We tested our framework on different bridge point cloud datasets, including a suspension bridge and a continuous rigid frame bridge, to evaluate its accuracy. Experimental results demonstrate that our method has high accuracy.

Waypoint Transfer Module between Autonomous Driving Maps Based on LiDAR Directional Sub-Images

Lane graphs are very important for describing road semantics and enabling safe autonomous maneuvers using the localization and path-planning modules. These graphs are considered long-life details because of the rare changes occurring in road structures. On the other hand, the global position of the corresponding topological maps might be changed due to the necessity of updating or extending the maps using different positioning systems such as GNSS/INS-RTK (GIR), Dead-Reckoning (DR), or SLAM technologies. Therefore, the lane graphs should be transferred between maps accurately to describe the same semantics of lanes and landmarks. This paper proposes a unique transfer framework in the image domain based on the LiDAR intensity road surfaces, considering the challenging requirements of its implementation in critical road structures. The road surfaces in a target map are decomposed into directional sub-images with X, Y, and Yaw IDs in the global coordinate system. The XY IDs are used to detect the common areas with a reference map, whereas the Yaw IDs are utilized to reconstruct the vehicle trajectory in the reference map and determine the associated lane graphs. The directional sub-images are then matched to the reference sub-images, and the graphs are safely transferred accordingly. The experimental results have verified the robustness and reliability of the proposed framework to transfer lane graphs safely and accurately between maps, regardless of the complexity of road structures, driving scenarios, map generation methods, and map global accuracies.

Гармонический анализ горизонтальных движений точек земной поверхности в системе ITRF

The latest implementation of the international global coordinate system ITRF2020 enables taking into account not only linear time parameters of points’ coordinates changes participating in its construction, but also periodic terms reflecting their seasonal (intra-annual) variation, as well as post-seismic effects in tectonically active areas. These shifts for control points are not only caused by the actual physical movement of the point itself relative to neighboring ones or together with them on the tectonic plate. It also includes the influence of joint processing

Robust and optimal alignment of high-dimensional data using maximum likelihood estimation through a random sample consensus framework

AbstractCorrecting spatial orientations of groups of high-dimensional data sets such that they are all in a consistent coordinate system is often a time-consuming and error-prone process. Automation of this process can be accomplished by using Generalized Procrustes Analysis to estimate the relative orientations among a population of high-dimensional data sets. A least squares Procrustes solution is applied through a maximum likelihood estimation and random sample consensus framework for robustness. The likelihood model is comprised of a mixture distribution where inliers are modeled using t-distribution and outliers from a uniform distribution. Applications will focus on a synthetic data set that emulates triaxial acceleration data and also real shock data from a population of triaxial accelerometers. Outliers represent either non-rigid body responses, environmental noise, and/or sensor and data acquisition issues. The intended application for the methodology is to robustly automate the rotation of populations of experimentally collected triaxial accelerometer data sets to a single global coordinate system.

Innovation of Physical Education and Health Curriculum Teaching Models in Colleges and Universities in the Digital Era and Its Contribution to Students’ Core Literacy

Abstract Physical education and health curricula in colleges and universities are obsolete, and there is an urgent need to innovate teaching models and methods. To achieve innovation in physical education and health teaching, this paper utilizes cutting-edge information technology like motion recognition to construct a physical education and health data monitoring model. Firstly, the positional relationship between coordinate systems is determined, and the established coordinate system is used to describe the orientation and position of human postural joints, and the rotation matrix is used to define the rotation from the global coordinate system to the current orientation of the local coordinate system of bones. A human motion joint skeletal chain model is created that has 21 bones and 21 joints. The joint pose solution method is proposed, and the human kinematic model is constructed by combining robot ortho kinematics and coordinate transformation. A position estimation algorithm combining inertial navigation and a human kinematics model has been designed. After analyzing the performance of the recognition model, analyze the effects of its application on the innovation of college physical education courses. It is found that the model in this paper monitors the heart rate data with an error of only 3 or less, and the accuracy of human movement recognition on the MHealth and PAMAP2 datasets is 97.38% and 96.63%, respectively, and the learning ability is optimal. After one semester of innovative mode teaching and the use of a physical education and health data monitoring model, the mean values of physical education and health knowledge, physical education behavior, physical fitness and health, motor skills, and physical character of the experimental class were 35.77, 25.53, 25.04, 35.73, and 31.56 points higher than those of the control class, respectively. Motivation, skill acquisition, after-school sports, and sports concern were significantly higher in the experimental class, with scores of 5.66, 6.71, 5.61, and 3.65 points higher than the control class. This paper’s innovative teaching mode and model have been effective in improving teaching quality and stimulating students’ sports and health habits.

Область правильной координации пространства нормальными коническими координатами

The field theory is widely represented in spherical and cylindrical coordinate systems, since the mathematical apparatus of these coordinate systems is well studied. Field sources with more complex structures require new approaches to their study. The purpose of this study is to determine the correct coordination of space by normal conic coordinates. This is necessary in subsequent studies, the task of which will be to simplify the expressions for the characteristics of the field by introducing a special coordination of space, which reflect the shape of the source and/or sink of the field. For example, a field with a rectilinear source is more convenient to refer to cylindrical coordinates, and a field with a point source - to spherical coordinates. Basically, the use of field theory in the study of physical processes by methods of applied geometry is limited to two classical curvilinear systems, although their presentation in arbitrary curvilinear coordinates is known. We will distinguish between global and local coordinate systems. The global system, as well as the coordinates of a point in this system, will be denoted by x, y, z. She is unchanging. The local system, as well as the coordinates of a point in this system, will be denoted by t, u, v. Local system variable. At each point in space belonging to the area of existence of the system, the local coordinate system is defined

CID-SIMS: Complex indoor dataset with semantic information and multi-sensor data from a ground wheeled robot viewpoint

Simultaneous localization and mapping (SLAM) and 3D reconstruction have numerous applications for indoor ground wheeled robots such as floor sweeping and food delivery. To advance research in leveraging semantic information and multi-sensor data to enhance the performances of SLAM and 3D reconstruction in complex indoor scenes, we propose a novel and complex indoor dataset named CID-SIMS, where semantic annotated RGBD images, inertial measurement unit (IMU) measurements, and wheel odometer data are provided from a ground wheeled robot viewpoint. The dataset consists of 22 challenging sequences captured in nine different scenes including office building and apartment environments. Notably, our dataset achieves two significant breakthroughs. Firstly, semantic information and multi-sensor data are provided meanwhile for the first time. Secondly, GeoSLAM is utilized for the first time to generate ground truth trajectories and 3D point clouds within two-centimeter accuracy. With spatial-temporal synchronous ground truth trajectories and 3D point clouds, our dataset is capable of evaluating SLAM and 3D reconstruction algorithms in a unified global coordinate system. We evaluate state-of-the-art SLAM and 3D reconstruction approaches on our dataset, demonstrating that our benchmark is applicable. The dataset is publicly available on https://cid-sims.github.io.

The Harmonic Map Compactification of Teichmüller Spaces for Punctured Riemann Surfaces

In the paper [The Teichmüller theory of harmonic maps, J. Differential Geom. 29 (1989), no. 2, 449–479], Wolf provided a global coordinate system of the Teichmüller space of a closed oriented surface S S with the vector space of holomorphic quadratic differentials on a Riemann surface X X homeomorphic to S S . This coordinate system is via harmonic maps from the Riemann surface X X to hyperbolic surfaces. Moreover, he gave a compactification of the Teichmüller space by adding a point at infinity to each endpoint of harmonic map rays starting from X X in the space. Wolf also showed this compactification coincides with the Thurston compactification. In this paper, we extend the harmonic map ray compactification to the case of punctured Riemann surfaces and show that it still coincides with the Thurston compactification.

EVALUATING NAVIGATION PERFORMANCE OF ELASTICALLY CONSTRUCTED HD MAP WITH MULTI-SENSOR FUSION ENGINE SYSTEM

Abstract. In response to the rapid development of autonomous vehicles and the increasing demand for HD maps, the conventional mapping processes following HD maps guidelines require significant manpower and time resources. Therefore, we propose flexible procedures and methods for HD maps creation, aiming to reduce cost expenditure by employing diverse source of ground control point, sensor data collection, and mapping algorithm. This approach accelerates the production speed and capability of HD maps. In this study, we select Taiwan's National Highway No. 8 as the trial field for the elastic HD map construction method, and equipped with autonomous vehicle-grade GNSS, IMU, and LiDAR systems.We align the constructed-map data to the global coordinate system, in order to realize the concept of control point cloud map. To assess the assistance and correction capabilities of HD maps in autonomous vehicle navigation systems, we conduct accuracy evaluation through both direct and indirect methods, and analyse the strengths and weaknesses of each approach. The analysis result demonstrates that the elastic method-built HD maps not only meet the mapping accuracy requirements specified in the HD maps verification and validation guidelines, but also assist autonomous vehicles in realizing positioning, navigation, and timing with “where in lane” level (0.5 meter) accuracy.

One-dimensional numerical model of landslide over high-steep slopes: Theory and verification to the analytical solution

At the steep slope areas, landslide events may suddenly occur due to prolonged heavy rain and seriously affect humans’ lives and their properties. Numerical models simulating landslides help us to predict the real landslide phenomenon effectively because they are not only time-saving compared to physical models but also acceptable accuracy. In this paper, the one-dimensional nonlinear shallow water equations using the global coordinate system are established as the proposed model governing equations. The hybrid finite difference-finite volume method, the implicit method and the automatical time step controlling technique are employed to stably simulate the landslide events over the high-steep slopes. To validate the proposed numerical model to the analytical solution, authors continuously derive the non-dimensional governing equations in one dimension as well as using the global coordinate system. The numerical results are in good agreement with the analytical solution. The proposed numerical model can be used to simulate the landslides and the landslide-induced tsunami events, especially for simulating the high-steep slope conditions.

Panoramic three-dimensional optical digitization system assisted by a bi-mirror.

The digitization of objects' full surfaces finds widespread applications in fields such as virtual reality, art and design, and medical and biological sciences. For the realization of three-dimensional full-surface digitization of objects within complex sceneries, we propose a straightforward, efficient, and robust panoramic three-dimensional optical digitization system. This system contains a laser-based optical three-dimensional measurement system and a bi-mirror. By integrating mirrors into the system, we enable the illumination of the object from all angles using the projected laser beam in a single scanning process. Moreover, the main camera employed in the system can acquire three-dimensional information of the object from several different viewpoints. The rotational scanning method enhances the efficiency and applicability of the three-dimensional scanning process, enabling the acquisition of surface information of large-scale objects. After obtaining the three-dimensional data of the sample from different viewpoints using laser triangulation, mirror reflection transformation was employed to obtain the full-surface three-dimensional data of the object in the global coordinate system. The proposed method has been subjected to precision and validity experiments using samples with different surface characteristics and sizes, resulting in the demonstration of its capability for achieving correct three-dimensional digitization of the entire surface in diverse complex sceneries.

Coupled drillstring dynamics modeling using 3D field-consistent corotational beam elements

Drilling is essential to extract subsurface hydrocarbons and geothermal energy, or store waste fluids/gases underground. Drilling efficiency directly affects the economics of well construction, and is to a large extent determined by the non-productive time (NPT) associated with downhole tool failure, bit wear/damage, unexpected drillstring vibrations, and insufficient surface-to-bottom energy transfer. Various models have been developed since the 1960s to understand and mitigate undesired drilling system oscillations to ensure efficient drilling operations and help optimize the well design. Significant recent advancements in drilling engineering technology, sensor development, and data science make it possible to develop and apply a faster and more comprehensive drilling system dynamic model that can be used for real-time drilling optimization and automation.In this study, a novel control-oriented physic-based drillstring dynamic modeling framework is developed using 3D field-consistent corotational beam elements with an updated Lagrangian formulation. The structure and element kinematics are firstly derived in global and local coordinate systems respectively, based on which the system dynamics are formulated by integrating the element stiffness, damping, and mass matrices. Different drilling boundary conditions and forms of external loads, including bit-rock interaction, wellbore-drillstring contact, stabilizers, bottom hole assembly (BHA) eccentricities, and gravity/buoyancy are defined within the modeling framework. The numerical accuracy of the model with linear/quintic beam elements is discussed and verified in four different static/dynamic loading cases, which are typically used for beam analysis. Simulations of different drilling scenarios, including dynamics during the pipe connection process, bit on/off bottom process, and pipe rocking during slide drilling, are conducted for an actual L-shape well configuration with comparison to field data. The simulated drillstring tri-axial vibrations exhibit diverse characteristics and patterns in terms of oscillation amplitudes, frequencies, and modes at varying depths, generating valuable understanding of potential drilling dysfunctions and insights for real-time drilling optimization and automation.

Definition of a Global Coordinate System in the Foot for the Surgical Planning of Forefoot Corrections

Forefoot osteotomies to improve the alignment are difficult procedures and can lead to a variety of complications. Preoperative planning in three dimensions might assist in the successful management of forefoot deformities. The purpose of this study was to develop a global coordinate system in the foot for the planning of forefoot corrections. Two strategies (CS1 and CS2) were developed for defining a global coordinate system that meets the criteria of being well-defined, robust, highly repeatable, clinically relevant, compatible with foot CT scans, independent of the ankle joint angle, and does not include bones in the forefoot. The absolute angle of rotation was used to quantify repeatability. The anatomical planes of the coordinate systems were visually inspected by an orthopedic surgeon to evaluate the clinical relevancy. The repeatability of CS1 ranged from 0.48° to 5.86°. The definition of CS2 was fully automated and, therefore, had a perfect repeatability (0°). Clinically relevant anatomical planes were observed with CS2. In conclusion, this study presents an automated method for defining a global coordinate system in the foot according to predefined requirements for the planning of forefoot corrections.