Trajectory Graph Research Articles

Analysis and simulation on dynamics of a partial differential system with nonlinear functional responses

We introduce a reaction–diffusion system with modified nonlinear functional responses. We first discuss the large-time behavior of positive solutions for the system. And then, for the corresponding steady-state system, we are concerned with the priori estimate, the existence of the nonconstant positive solutions as well as the bifurcations emitting from the positive constant equilibrium solution. Finally, we present some numerical examples to test the theoretical and computational analysis results. Meanwhile, we depict the trajectory graphs and spatiotemporal patterns to simulate the dynamics for the system. The numerical computations and simulated graphs imply that the available food resource for consumer is very likely not single.

Design of a novel grinding end-effector for spiral welded pipe

In the spiral welded pipe manufacturing process, grinding is one of the production processes, this process proceeds by hand grinding and fixed machine grinding. Usually, those methods have impacts larboard intensive, long production cycle and unstable product qualification rate for the final product. To prevent those factors from this paper, present a newly-designed grinding machine for a spiral welded pipe manufacturing industry, the machine has equipped with a special grinding machine with the ability to grind the spiral welded pipe the inner and outer surface simultaneously of the pipe and equipped with 6DOF grinding robot. The kinematics model of grinding robot is derived and the robot joint trajectory is calculated. The simulation result shows that the grinding mechanism can perform the job without failures under the external torque, and also trajectory graph of the robot kinematics shows there is no vibration on the robot movement to perform the job.

Gráficas de trayectorias escolares de estudiantes de bachillerato

Para las autoridades escolares es importante conocer cómo los alumnos de su institución avanzan en sus estudios, porque de esta forma pueden detectar cualquier tipo de dificultades que se presenten; sin embargo, esa información no siempre se la conoce a tiempo. El objetivo de esta investigación es proponer una metodología que permita visualizar las trayectorias escolares de los estudiantes y de esta forma se identifiquen las dificultades que tienen en la asignatura de matemáticas. Para mostrar el potencial de la metodología, se investigó a los alumnos de bachillerato de una institución educativa ecuatoriana entre 2015 y 2019, se procesaron sus calificaciones y se generaron gráficas de trayectorias escolares que presentan la evolución de sus calificaciones durante el período escolar. Mediante esta metodología se facilita la identificación de trayectorias individuales de bajo rendimiento, además, se encontró que las actividades colaborativas tienen calificaciones más altas que las individuales, también se evidenciaron las diferencias de rendimiento entre cursos. La presentación de las calificaciones mediante gráficas es una herramienta poderosa para la gestión académica, ya que facilita la detección de dificultades y la toma de decisiones oportunas.

Travel Trajectory Frequent Pattern Mining Based on Differential Privacy Protection

Now, many application services based on location data have brought a lot of convenience to people’s daily life. However, publishing location data may divulge individual sensitive information. Because the location records about location data may be discrete in the database, some existing privacy protection schemes are difficult to protect location data in data mining. In this paper, we propose a travel trajectory data record privacy protection scheme (TMDP) based on differential privacy mechanism, which employs the structure of a trajectory graph model on location database and frequent subgraph mining based on weighted graph. Time series is introduced into the location data; the weighted trajectory model is designed to obtain the travel trajectory graph database. We upgrade the mining of location data to the mining of frequent trajectory graphs, which can discover the relationship of location data from the database and protect location data mined. In particular, to improve the identification efficiency of frequent trajectory graphs, we design a weighted trajectory graph support calculation algorithm based on canonical code and subgraph structure. Moreover, to improve the data utility under the premise of protecting user privacy, we propose double processes of adding noises to the subgraph mining process by the Laplace mechanism and selecting final data by the exponential mechanism. Through formal privacy analysis, we prove that our TMDP framework satisfies ε‐differential privacy. Compared with the other schemes, the experiments show that the data availability of the proposed scheme is higher and the privacy protection of the scheme is effective.

An Approach to Spatiotemporal Trajectory Clustering Based on Community Detection

Nowadays, large volumes of multimodal data have been collected for analysis. An important type of data is trajectory data, which contains both time and space information. Trajectory analysis and clustering are essential to learn the pattern of moving objects. Computing trajectory similarity is a key aspect of trajectory analysis, but it is very time consuming. To address this issue, this paper presents an improved branch and bound strategy based on time slice segmentation, which reduces the time to obtain the similarity matrix by decreasing the number of distance calculations required to compute similarity. Then, the similarity matrix is transformed into a trajectory graph and a community detection algorithm is applied on it for clustering. Extensive experiments were done to compare the proposed algorithms with existing similarity measures and clustering algorithms. Results show that the proposed method can effectively mine the trajectory cluster information from the spatiotemporal trajectories.

IFTS: A Location Privacy Protection Method Based on Initial and Final Trajectory Segments

Privacy protection problem is one of the most concerning issues related to Location-Based Services (LBS) in our daily life. Privacy protection of LBS often requires anonymizing customer's trajectory data. Currently available methods for trajectory anonymity often assume an entire trajectory as one anonymous unit, which may lead to low anonymity efficiency due to the massive amount of trajectory data, especially for customers travel through a long road. Considering people's routine activities, the starting and ending locations of a trip often uncover the user's request intent, which may lead to exposure of user privacy. In order to address the problem of inefficient trajectory anonymity, we propose a location privacy protection method that is based on the initial and final trajectory segmentation (IFTS) in this paper. In the IFTS method, the road network structure is first transformed into an edge cluster model based on its location type. Then, the user trajectory is divided to segments according to the temporal sequence of the ingress and egress nodes. The initial and final trajectory segments are identified and divided into equivalence classes, which then are used for constructing a trajectory graph and the corresponding k-anonymous set. Our experimental results show that the proposed method can reduce the anonymous area, improve anonymity efficiency, and enhance trajectory data utilization compared to the existing methods for trajectory anonymity.

Further Understanding for Lissajous Figures

At the undergraduate level, the composite motion of simple harmonic vibrations has always been the main content of physics as well as several other scientific disciplines. Many textbooks tell us clearly that when the frequency ratio ω1/ω2 of two perpendicular vibrations is simple integer ratio n1/n2 (n1 and n2 are integers), their combined motion has stable and closed trajectories. This trajectory graph is the famous Lissajous figure. The Lissajous figure has been widely studied since it was discovered more than 100 years ago. Especially in the last 30 years, the shape, evolution trend, periodicity, and symmetry of the Lissajous figure have been studied and a series of meaningful characteristics and laws have been summarized. However there has been no analysis of the Lissajous figure from the perspective of three-dimensional space curve so far.

SIMULATION OF THE ROTATIVE-TRANSLATIVE MOTION OF THE DUMBBELL, WHEN THE CENTER OF ITS MASS MOVES IN A CIRCLE

A geometric model of the rotational-translational motion of a dumbbell in a central force field is proposed, provided that its center of mass moves in a circle of a given radius. The term dumbbell denotes a geometric object with two masses spaced apart at a certain distance, connected by a weightless rod (like a sports dumbbell). The idea of modeling is based on the compilation and solution of a system of Lagrange differential equations of the second kind. To compose the equations, the Lagrangian was used to describe the rotational-translational motion of a dumbbell in a central force field. The system of equations is formed with respect to five functions denoting five generalized coordinates. These coordinates connect the fixed and mobile coordinate systems that provide the rotational-translational movement of the dumbbell. The system of Lagrange differential equations of the second kind was solved numerically in the environment of the maple mathematical processor. The results obtained correspond to each of five different coordinate functions that can be plotted graphically. Also obtained are approximate descriptions of the derivatives of these functions depending on the parameters of the dumbbell and the initial conditions of its motion. These results made it possible to construct graphs of phase trajectories of functions of five coordinate coordinates, with the help of which it is possible to determine the nature of the dumbbell movement. The obtained time dependences for the functions of generalized coordinates make it possible to compose an algorithm for computer animation of the rotational-translational motion of the dumbbell. In this case, the parameters of the dumbbell and the initial conditions of its movement will be taken into account. Examples of modeling the trajectories of the centers of mass of the dumbbell weights are given. It is advisable to use the results obtained to illustrate the position of the dumbbell in space when studying its orbital dynamics. Computer animations of a dumbbell movement in zero gravity will make it possible to analyze the influence of the angular velocities of rotation on its movement. At this stage of research, it is advisable to use the results obtained as the basis for laboratory or coursework of the departments of geometric modeling and computer graphics.

Observability of switched Boolean control networks using algebraic forms

<p style='text-indent:20px;'>This paper addresses the observability of a switched Boolean control network (SBCN) using semi-tensor product (STP) of matrices. First, the observability of the SBCN is determined under desirable switching signals and arbitrary switching signals by encoding the switching signal as a boolean input. Then an algorithm is designed for determining the observability. Furthermore, feedback control laws are obtained to guarantee the observability of SBCNs. Examples and corresponding state trajectory graphs are given to illustrate the effectiveness of the given results.

An intelligent recognition model for dynamic air traffic decision-making

Air traffic flow management system (ATFMS) is becoming increasingly important due to the rapid growth of air traffic and serious flight delay nowadays. To aware the air traffic flow density and identify the heat airspace in terminal areas of large hub airports is essential for an ATFMS. Due to numerous parameters in air traffic flow, traditional methods based on one single parameter fail to reflect the true complexity relationship between these parameters. This study aims to develop an intelligent air traffic flow heat airspace recognition model using advanced data science technique for establishing a real-time cloud map in the terminal airspace of airports, which attempts to use machine learning models to represent the complex relationship among these parameters. In the proposed intelligent recognition model, high dimensions of parameters (basic parameters, additional parameters and time parameters) are processed to achieve a comprehensive and accurate situation awareness for support dynamic air traffic decision-making. An aircraft trajectories points clustering method is developed to generate a 4D heat airspace map. The basic parameters and time parameters are used to identify the heat airspaces; the changes of additional parameters which influence the heat airspaces are identified and analyzed by use of grid graphs of flight trajectories; probability fitting graphs are used to verify accuracy of 4D results in order to support air traffic decision-making. A case study on Beijing International Airport (PEK) is conducted to test our model and has obtained two main research findings: there are two areas of PEK that have the high density and there are hot peaks at two different heights; flight trajectories and speed of trajectories also effect on the heat airspace. The study realizes that the proposed 4D heat airspace model is better for detailed and accurate information construction, expression of spatial changes, and visualization of multiple parameters of temporal and spatial density and range. It can assist the decisions on airspace allocation, and also have a definite reference meaning on alleviating the contradiction between the current air traffic demand and airspace resource constraints.

Моделирование движения молекул H-=SUB=-2-=/SUB=- и D-=SUB=-2-=/SUB=- в секступольных магнитах

The simulation of the movement of hydrogen and deuterium molecules in the magnetic system of the installation designed to obtain nuclear spin-polarized molecules is produced. For the spatial separation of molecules with different projections of the magnetic moments of spin filtering method in a nonuniform magnetic field, superconducting sextupole magnets are used. The calculation was performed when the induction of the magnetic field near the poles of 3.7 T and the nozzle temperature of the 7K. The simulation showed that the ratio of the polarized flux of hydrogen molecules into the detector to the total flux from the source nozzle is 2.3 × 10-6, and the nuclear polarization is about 100%. For deuterium, the calculations showed that this ratio is 7 times less because of the smallness of the magnetic moment with respect to hydrogen molecules. The graphs of molecular trajectories in the magnetic system and their spatial distribution are presented. The mathematical aspects of the developed computer program algorithm are considered.

ФОРМИРОВАНИЕ БАНКА ПОХОДОК ПОЛЗАЮЩЕГО ПОИСКОВОГО РОБОТА С УПРАВЛЯЕМЫМ ТРЕНИЕМ В ОПОРАХ

The paper considers a three-link crawling snake-like robot, the links of which are connected by two-axis hinges. The robot is equipped with four bearing supports with the controlled coefficient of friction between them and the surface. The device is designed to move inside buildings after the emergencies to search for people under the debris and to transport the essentials to them. The robot is controlled by the operator in two modes: the sequential execution of commands (forward, backward, turn, etc.) and moving from the starting point to the final one. Working in each of the control modes requires the use of the gaits bank. The authors developed the classification of gaits for a crawling robot based on several criteria: the admissible periodic separation of links from a surface, the ability to control by friction in the supports, the combinations of controllable bearing supports, and the implemented type of motion. The authors studied in detail the controllable planar gaits of a robot when moving it forward and distinguished four types of gaits: longitudinal, transverse, transverse s-shaped, and longitudinal-transverse. For each gait the sequence of stages is developed, the conditions of their beginning and end imposed on the movements of the links are formulated and the vector of generalized coordinates is defined. As a result of numerical simulation, the authors built the graphs of trajectories of the centers of mass of links and the center of mass of the entire device for each gait, as well as the graphs of time dependences of the angles of rotation of links. The study identified the influence of angles of links relative positions on the distance traveled by the robot. It is revealed that for the same time of movement, the robot will pass the greatest distance with a longitudinal gait irrespective of angles of links relative position. The device will be able to march the same distance at two types of transverse gaits at the maximum possible angle of the links relative position.

Formation of Landslide Bodies at Numerical Calculations of Making Soil Constructions (Cut and Embankment)

The paper considers the problems in forming the landslide bodies taking into considerations the features of forming Stress Strain State (SSS) and stability of soil structures (cut and embankment). The investigation was carried out on the basis of calculation with the certified finite element method (FEM) GenIDE32. The analysis of phenomena of curls of the displacement vector has been done for the excavation from the uniform soil. It is shown how they influence the places of vertical cracks formation and their size and the stability of the top. Curls are not observed in the uniform embankment with the same geometrical (hu=du=const, 1:m=1:1) and other parameters as cut has. The calculation results make it possible to see the appearance and evolution of “plasticity” zones or the limiting state as “compression” and “expansion” zones. Consistent modeling of cut or embankment allows one to see how the landslide body forms including body with vertical cracks. The analysis uses graphs of trajectories of SSS variation in the space of invariants of stress tensor σij and relative deformations εij in important nods and finite elements located at the foots of constructions, where the sliding lines with kst min. appear. These make it possible to see, on graphs of form and volume deformations, where the system is located with the condition, for example, kstmin=1,33> [kst]=1,30 from the condition at which the landslide body formed: kstmin=1,00±0,02≈[kst]=1,00.

Description of the front automobile collision in a model of the system of nonlinear oscillators

The article reviewed the automobile collision process on the basis of a mathematical model of nonlinear interacting oscillators. A mathematical model for research of the front collision automobile extends to the limit of aggregates is detailed. The system was used (four masses are connected by three "springs") for mathematical modeling, where mass 1 corresponds to bumper, mass 2 corresponds to the frame with engine, mass 3, 4 to the steering mechanism with a column. Mass values were taken for the Iveco Evrocargo 75E18 car. Two types of numerical experiments were performed: at a fixed collision speed parameters changed model dependence of force on displacement; for fixed parameters of the model dependence of force on displacement changed the collision velocity. Qualitative analysis of the dynamic properties of the system is presented in the graphs of phase trajectories. It was found that the general form of the phase trajectories depends on the initial conditions, the most non-linear effects will manifest for the oscillator 1, which is shock excited. On account of nonlinearity of the return force passes "dropping" of energy, which is wasted on the deformation or destruction of the material.

ParkLoc

Locating a vehicle indoors (e.g., underground parking garages) has been a difficult problem to tackle, due to the unavailability of GPS and/or Wi-Fi signals. Current GPS-free indoor localization efforts often rely on infrastructure supports such as Wi-Fi or BLE beacons, whereas the smartphone-only proposals mostly require significant data collection and training efforts per garage. In this context, we propose ParkLoc, a novel lightweight smartphone-only solution for vehicular localization in GPS/Wi-Fi-deprived environments such as indoor parking garages. ParkLoc exploits the inherent planar graph structure of the navigable paths in parking facilities, in order to match a vehicle trajectory onto a sub-section of the map, by modeling these as sparse directed graphs. Exploiting an approximate graph matching method, ParkLoc is able to track a vehicle in real-time with a median error of 4.8m and localize a parked vehicle with a median error of 2m from the nearest parking space. Furthermore, ParkLoc adopts the popular GraphSLAM algorithm from robotics research; it learns the map graph from the observed trajectory graphs and a given set of bootstrap (seed) landmark nodes, in a semi-supervised manner. A key benefit of our approach is that ParkLoc works off-the-shelf without any expensive on-site training or sensor data collection per garage. A comprehensive evaluation of ParkLoc through extensive experiments performed in 4 different parking facilities reveals the promising performance of our graph-based approach for both localization and mapping.

Automated Coordinate Measuring Machine Inspection Planning Knowledge Capture and Formalization

Capturing the strategy followed during a coordinate measuring machine (CMM) inspection planning session has been an extremely challenging issue due to the time-consuming nature of traditional methods, such as interviewing experts and technical documents data mining. This paper presents a methodology demonstrating how a motion capture-based system can facilitate direct and nonintrusive CMM operator logging for capturing planning strategies and representing in knowledge formats. With the use of recorded motion data, embedded knowledge and expertise can be captured automatically and formalized in various formats such as motion trajectory graphs, inspection plans, integrated definition (IDEF) model diagrams, and other representations. Additionally, a part program can be generated for driving a CMM to execute component measurement. The system's outputs can be used to help understand how a CMM inspection strategy is planned, as well as training aids for inexperienced operators and the rapid generation of part programs.

Trajectory privacy protection method based on the time interval divided

Trajectory data often provides information that is well applicable to real-world scenarios such as traffic planning and location-based advertising. Individual trajectory information may disclose sensitive personal data, thus necessitating privacy protection methods. Current methods assume and utilize the same privacy requirements for all trajectories, which can impact their protection and data utilization efficiency. This paper proposes a privacy protection method based on divided time intervals which satisfy different privacy requirements. The method works by constructing a privacy requirement matrix and running trajectory pre-processing based on the different privacy requirements for trajectories in different time points and locations. It uses trajectories that satisfy the (l, δ) -constraint to construct an undirected trajectory graph. By finding the trajectory corresponding to the edge and vertex with the minimum weight, ki-anonymous sets are then constructed with trajectories which share the same or similar privacy requirements. The Manhattan distance can then be applied to calculate the space between trajectories distance, which narrows the gap between the theoretical privacy protection and the actual protective effects. Comparative experiments demonstrate that the proposed method outperforms other similar methods in regards to both privacy protection and data utilization.

Trajectory anonymisation based on graph split using EMD

Analysing and mining trajectories pose new challenges for trajectory privacy. We are addressing privacy issue for offline (historical) trajectories which are generally published for research. A fundamental research question in trajectory privacy domain is of trajectory anonymisation. k-anonymity is used as a standard for privacy which ensures that every entity in the dataset is indistinguishable from (k &minus; 1) other entities. The proposed work aims at anonymising trajectories based on graph split method. We have used technique of constructing trajectory graph to simulate spatial and temporal relations of trajectories, based on which trajectory k-anonymity sets are found through graph split. For the purpose, we have proposed a novel method that uses earth mover's distance as a metric to find trajectory k-anonymity sets in contrast to Euclidean distance. It is discovered through a series of experiments that the proposed method is outperforming in terms of low information loss and computation time.

Trajectory anonymisation based on graph split using EMD

Analysing and mining trajectories pose new challenges for trajectory privacy. We are addressing privacy issue for offline (historical) trajectories which are generally published for research. A fundamental research question in trajectory privacy domain is of trajectory anonymisation. k-anonymity is used as a standard for privacy which ensures that every entity in the dataset is indistinguishable from (k − 1) other entities. The proposed work aims at anonymising trajectories based on graph split method. We have used technique of constructing trajectory graph to simulate spatial and temporal relations of trajectories, based on which trajectory k-anonymity sets are found through graph split. For the purpose, we have proposed a novel method that uses earth mover's distance as a metric to find trajectory k-anonymity sets in contrast to Euclidean distance. It is discovered through a series of experiments that the proposed method is outperforming in terms of low information loss and computation time.

Exploiting Integrity Constraints for Cleaning Trajectories of RFID-Monitored Objects

A probabilistic framework for cleaning the data collected by Radio-Frequency IDentification (RFID) tracking systems is introduced. What has to be cleaned is the set of trajectories that are the possible interpretations of the readings: a trajectory in this set is a sequence whose generic element is a location covered by the reader(s) that made the detection at the corresponding time point. The cleaning is guided by integrity constraints and consists of discarding the inconsistent trajectories and assigning to the others a suitable probability of being the actual one. The probabilities are evaluated by adopting probabilistic conditioning that logically consists of the following steps. First, the trajectories are assigned a priori probabilities that rely on the independence assumption between the time points. Then, these probabilities are revised according to the spatio-temporal correlations encoded by the constraints. This is done by conditioning the a priori probability of each trajectory to the event that the constraints are satisfied: this means taking the ratio of this a priori probability to the sum of the a priori probabilities of all the consistent trajectories. Instead of performing these steps by materializing all the trajectories and their a priori probabilities (which is infeasible, owing to the typically huge number of trajectories), our approach exploits a data structure called conditioned trajectory graph (ct-graph) that compactly represents the trajectories and their conditioned probabilities, and an algorithm for efficiently constructing the ct-graph, which progressively builds it while avoiding the construction of components encoding inconsistent trajectories.