Design method of worn rail grinding profile based on Frechet distance method

Due to the large volume and high running density of railway freight lines, rail deterioration occur frequently. Thus, it is necessary to grind the rail in time to improve the wheel-rail relationship. The profile data of the worn rail were measured at different measuring points in a section, and the Frechet distance method was adopted to analyze the data. The representative profile reflecting the overall condition of rail wear in this section is obtained. Combined with NURBS curve theory, a fitting algorithm in which the rail profile with certain discrete points was established. Taking the reduction of the amount of grinding material removed as the objective function, setting wheel-rail matching characteristics, and the reduction of rail wear as the constraint conditions, a calculation model for rail grinding profile was established. The dynamic characteristics of standard profile CN75 and g grinding profile OP75 were analyzed by the vehicle track dynamics model. The results showed that compared with the standard profile CN75, the amount of grinding material removed of the grinding profile OP75 is reduced by 44.7%, and the height reduction of the rail top is reduced by 0.39 mm. After [Formula: see text] km of running, the wear amounts of grinding profile OP75 is about 36.1%–36.5% less than that of standard profile CN75.In the small curve section, the derailment coefficient of grinding profile OP75 is reduced by 11.7% compared with that of standard profile CN75. The dynamic performance is improved. The grinding target profile has better dynamic characteristics and is beneficial to reduce wheel-rail wear.

Composite Line Designs and Accuracy Measurements for Tactile Line Tracing on Touch Surfaces

Eyes-free operation of mobile devices is critical in situations where the visual channel is either unavailable or attention is needed elsewhere. In such situations, vibrotactile tracing along paths or lines can help users to navigate and identify symbols and shapes without visual information. In this paper, we investigated the applicability of different metrics that can measure the effectiveness of vibrotactile line tracing methods on touch screens. In two user studies, we compare trace Length Error, Area Error, and Fréchet Distance as alternatives to commonly used trace Time. Our results show that a lower Fréchet distance is correlated better with the comprehension of a line trace. Furthermore, we show that distinct feedback methods perform differently with varying geometric features in lines and propose a segmented line design for tactile line tracing studies. We believe the results will inform future designs of eyes-free operation techniques and studies.

The Topological Correctness of PL Approximations of Isomanifolds

Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate multivalued smooth function $$f: {\mathbb {R}}^d\rightarrow {\mathbb {R}}^{d-n}$$ f : R d → R d - n . A natural (and efficient) way to approximate an isomanifold is to consider its piecewise-linear (PL) approximation based on a triangulation $$\mathcal {T}$$ T of the ambient space $${\mathbb {R}}^d$$ R d . In this paper, we give conditions under which the PL approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently fine and thick triangulation $$\mathcal {T}$$ T . This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL approximation. Finally, we show analogous results for the PL approximation of an isomanifold with boundary.

A Modification of the Frechet Distance for Nonisomorphic Trees

The paper presents a modification of the Frechet distance for nonisomorphic trees. While the classical Frechet distance between nonisomorphic trees is undefined, a new measure called similarity of a tree to a reference tree is given that is defined for a wider class of trees. A polynomial-time algorithm is given to determine whether one tree’s similarity to another is less than a given number.