Analysis of Asymmetrical Deformation of Surface and Oblique Pipeline Caused by Shield Tunneling along Curved Section

The deformation of existing pipelines caused by the tunneling of a shield machine along curved sections has not been sufficiently researched, and a corresponding theoretical prediction formula is lacking. This paper derives a prediction formula for the deformation of an existing pipeline caused by shield machine tunneling along a curved section. Further, a finite difference model (FDM) corresponding to an actual project is built. Finally, the deformation of the surface and existing pipelines caused by shield machine tunneling along the curved section is analyzed. The research results show that the results of theoretical prediction, FDM calculation, and field monitoring data are consistent. In addition, the deformation of the surface and the existing pipeline are asymmetrically distributed when the shield machine tunnels along the curve section instead of symmetrically distributed (for straight line segment). When the pipeline is perpendicular to the tunnel axis, the maximum deformation position of the existing pipeline deviates from the tunnel axis by about 0.5 times the tunnel radius. In addition, as the angle β between the pipeline axis and the tunnel axis increases, the maximum deformation position of the pipeline gradually approaches the tunnel axis.

An Approach to Growth Delimitation of Straight Line Segment Classifiers Based on a Minimum Bounding Box

Several supervised machine learning algorithms focused on binary classification for solving daily problems can be found in the literature. The straight-line segment classifier stands out for its low complexity and competitiveness, compared to well-knownconventional classifiers. This binary classifier is based on distances between points and two labeled sets of straight-line segments. Its training phase consists of finding the placement of labeled straight-line segment extremities (and consequently, their lengths) which gives the minimum mean square error. However, during the training phase, the straight-line segment lengths can grow significantly, giving a negative impact on the classification rate. Therefore, this paper proposes an approach for adjusting the placements of labeled straight-line segment extremities to build reliable classifiers in a constrained search space (tuned by a scale factor parameter) in order to restrict their lengths. Ten artificial and eight datasets from the UCI Machine Learning Repository were used to prove that our approach shows promising results, compared to other classifiers. We conclude that this classifier can be used in industry for decision-making problems, due to the straightforward interpretation and classification rates.

RADISHCHEV PLOT IN MULTIVARIATE ANALYSIS OF THE PROBLEM OF MULTIPLE TARGETS GROUP PURSUIT

This article discusses a kinematic model of the problem of group pursuit of a set of goals. The article discusses a variant of the model when all goals are achieved simultaneously. And also the possibility is considered when the achievement of goals occurs at the appointed time. In this model, the direction of the speeds by the pursuer can be arbitrary, in contrast to the method of parallel approach. In the method of parallel approach, the velocity vectors of the pursuer and the target are directed to a point on the Apollonius circle. The proposed pursuit model is based on the fact that the pursuer tries to follow the predicted trajectory of movement. The predicted trajectory of movement is built at each moment of time. This path is a compound curve that respects curvature constraints. A compound curve consists of a circular arc and a straight line segment. The pursuer's velocity vector applied to the point where the pursuer is located touches the given circle. The straight line segment passes through the target point and touches the specified circle. The radius of the circle in the model is taken equal to the minimum radius of curvature of the trajectory. The resulting compound line serves as an analogue of the line of sight in the parallel approach method. The iterative process of calculating the points of the pursuer’s trajectory is that the next point of position is the point of intersection of the circle centered at the current point of the pursuer’s position, with the line of sight corresponding to the point of the next position of the target. The radius of such a circle is equal to the product of the speed of the pursuer and the time interval corresponding to the time step of the iterative process. The time to reach the goal of each pursuer is a dependence on the speed of movement and the minimum radius of curvature of the trajectory. Multivariate analysis of the moduli of velocities and minimum radii of curvature of the trajectories of each of the pursuers for the simultaneous achievement of their goals i based on the methods of multidimensional descriptive geometry. To do this, the projection planes are entered on the Radishchev diagram: the radius of curvature of the trajectory and speed, the radius of curvature of the trajectory and the time to reach the goal. On the first plane, the projection builds a one-parameter set of level lines corresponding to the range of velocities. In the second graph, corresponding to a given range of speeds, functions of the dependence of the time to reach the target on the radius of curvature. The preset time for reaching the target and the preset value of the speed of the pursuer are the optimizing factors. This method of constructing the trajectories of pursuers to achieve a variety of goals at given time values may be in demand by the developers of autonomous unmanned aerial vehicles.

Analysis of the Mechanical Properties and Parameter Sensitivity of a U-Shaped Steel Damper

To clarify the mechanical properties of the U-shaped steel damper under tension and compression along the opening direction and the energy dissipation mechanism in the energy dissipation system, a mechanical model was established to describe the plastic failure response of the damper, and the formula for theoretical calculation of its mechanical properties was derived. Using the straight line segment length, radius of circular arc, and opening direction as parameters for testing four specimens, through the design of reasonable pulling and pressing fixture, four specimens were tested for tension and compression. The initial stiffness and yield load test results and theoretical analysis were good and verified that the opening direction of the U-shaped steel damper affected its mechanical performance. Further analysis of the U-shaped steel damper’s mechanical properties using numerical finite element analysis of the arc radius and the straight line segment length, width and thickness in relation to the initial stiffness shows that increasing the straight section length and end arc radius can reduce initial stiffness, and increase the thickness and width can increase initial stiffness.

Build 3D Abstractions with Wireframes

This chapter serves as an introduction to 3D representations of scenes or Structure From Motion (SfM) from straight line segments. Lines are frequently found in captures of man-made environments, and in nature are mixed with more organic shapes. The inclusion of straight lines in 3D representations provide structural information about the captured shapes and their limits, such as the intersection of planar structures. Line based SfM methods are not frequent in the literature due to the difficulty of detecting them reliably, their morphological changes under changes of perspective and the challenges inherent to finding correspondences of segments in images between the different views. Additionally, compared to points, lines add the dimensionalities carried by the line directions and lengths, which prevents the epipolar constraint to be valid along a straight line segment between two different views. This chapter introduces the geometrical relations which have to be exploited for SfM sketch or abstraction based on line segments, the optimization methods for its optimization, and how to compare the experimental results with Ground-Truth measurements.

Use of Mechanisms Marking Centers of Simplexes in Their 2-Dimensional Projections as Axonographs of Multidimensional Spaces

A brief historical excursion into the graphics of geometry of multidimensional spaces at the paper beginning clarifies the problem – the necessary to reduce the number of geometric actions performed when depicting multidimensional objects. The problem solution is based on the properties of geometric figures called N- simplexes, whose number of vertices is equal to N + 1, where N expresses their dimensionality. The barycenter (centroid) of the N-simplex is located at the point that divides the straight-line segment connecting the centroid of the (N–1)-simplex contained in it with the opposite vertex by 1: N. This property is preserved in the parallel projection (axonometry) of the simplex on the drawing plane, that allows the solution of the problem of determining the centroid of the simplex in its axonometry to be assigned to a mechanism which is a special Assembly of pantographs (the author's invention) with similarity coefficients 1:1, 1:2, 1:3, 1:4,...1:N. Next, it is established, that the spatial location of a point in N-dimensional space coincides with the centroid of the simplex, whose vertices are located on the point’s N-fold (barycentric) coordinates. In axonometry, the ends of both first pantograph’s links and the ends of only long links of the remaining ones are inserted into points indicating the projections of its barycentric coordinates and the mechanism node, which serves as a determinator, graphically marks the axonometric location of the point defined by its coordinates along the axes х1, х2, х3 … хN.. The translational movement of the support rods independently of each other can approximate or remote the barycentric coordinates of a point relative to the origin of coordinates, thereby assigning the corresponding axonometric places to the simplex barycenter, which changes its shape in accordance with its points’ occupied places in the coordinate axes. This is an axonograph of N-dimensional space, controlled by a numerical program. The last position indicates the possibility for using the equations of multidimensional spaces’ geometric objects given in the corresponding literature for automatic drawing when compiling such programs.

Constant-Time Complete Visibility for Robots with Lights: The Asynchronous Case

We consider the distributed setting of N autonomous mobile robots that operate in Look-Compute-Move (LCM) cycles and use colored lights (the robots with lights model). We assume obstructed visibility where a robot cannot see another robot if a third robot is positioned between them on the straight line segment connecting them. In this paper, we consider the problem of positioning N autonomous robots on a plane so that every robot is visible to all others (this is called the Complete Visibility problem). This problem is fundamental, as it provides a basis to solve many other problems under obstructed visibility. In this paper, we provide the first, asymptotically optimal, O(1) time, O(1) color algorithm for Complete Visibility in the asynchronous setting. This significantly improves on an O(N)-time translation of the existing O(1) time, O(1) color semi-synchronous algorithm to the asynchronous setting. The proposed algorithm is collision-free, i.e., robots do not share positions, and their paths do not cross. We also introduce a new technique for moving robots in an asynchronous setting that may be of independent interest, called Beacon-Directed Curve Positioning.

A geometric study of different curves for the rotor profiles of a twin-screw compressor

This paper presents the results of comparisons among some patented solutions for profiling the contours of the rotors in twin-screw compressors. Referring to a base case where all the generating curves are circumferences, patents suggesting to replace arcs of circumference with arcs of conic sections, i.e. parabola, ellipse and hyperbola, but even a straight line segment, are presented and guidelines for rotor profile construction are reported. After setting the size of the compressor, attention is paid to the inter-lobe area, as the sum of the area between two consecutive lobes in the male rotor and of the area of the groove in the female rotor. Actually, this area is strictly related to the volume displacement. Limited to the current case study, the profile including an elliptic segment seems to be the preferable solution for higher inter-lobe area, then for higher displacement, though a number of considerations should be necessary for a broader context.

A MATHEMATICAL MODEL FOR SUMMING ROTARY MOTIONS

In this work, using the means of applied mathematics, problems are solved related to the field of automation and control of technological processes, namely, the analytical description of superpositions of rotations that occur during the operation of numerous mechanisms. The practical aspect of the topic is determined by the fact that in mechanisms such as planetary gears, cutter drives in machines for cleaning pipes of large diameters, etc. summation of rotational motions is realized, and the shape of the hodograph is useful information in the design of such devices. The prerequisite for consideration is the principle of summation of rectilinear uniform movements. The aim of the work is to determine how things are in a similar situation when adding rotational synchronous movements. It was found that just as the result of the addition of two uniform rectilinear mechanical movements is also a uniform rectilinear movement, the result of the addition of two uniform unidirectional circular movements is also a uniform circular movement. The hodograph when two uniform oppositely directed circular motions are added is an ellipse. In a particular case, the ellipse can degenerate into a straight line segment. When two asynchronous rotations are added, hodographs in the form of a cochlea are possible, which is similar to Pascal's cochlea.

Bidirectional Sliding Window for Boundary Recognition of Pavement Construction Area Using GPS-RTK

Unmanned pavement construction is of great significance in China, and the primary issue to be solved is how to identify the boundaries of the Pavement Construction Area (PCA). In this paper, we present a simple yet effective method, named the Bidirectional Sliding Window (BSW) method, for PCA boundary recognition. We first collected the latitude and longitude coordinates of the four vertices of straight quadrilaterals using the Global Positioning System—Real Time Kinematic (GPS-RTK) measurement principle for precise single-point positioning, analyzed single-point positioning accuracy, and determined the measurement error distribution models. Next, we took points at equal intervals along one straight line segment and two curved line segments with curvature radii of 70 m to 300 m, for simulation experiments. BSW was adopted to recognize the Possible Irrelevant Points (PIP) and Relevant Points (RP), which were used to identify PCA boundaries. Experiments show that when the proposed BSW algorithm is used and the single-point positioning accuracy is at the centimeter level, PCA boundary recognition for straight polygons reaches single-point positioning accuracy, and that for curved polygons reaches decimeter-level accuracy.