Geometric Point Research Articles

Fatigue strength characterization of high and ultra-high-strength steel cut edges

This paper investigates the fatigue strength characteristics of CO2 laser, fiber laser and plasma cut edges of S690 and S1100 steel grades. The effect on fatigue performance of surface quality, which was examined by contact measurements and 3D scanning, residual stresses and microhardness profile, is studied and edge surface characteristics are compared for different cutting methods and 8 mm and 12 mm plate thicknesses. Four main experimental fatigue test series were performed and analyzed to estimate fatigue performance (defined as FAT classes) of the cut surface. Additional tests were conducted to study critical defects and residual stresses influence on fatigue properties. Scanning electron microscopy (SEM) revealed multiple critical locations in the specimens. Fatigue properties were characterized based on critical defects and crack initiation and propagation origins. Geometrical discontinuity points in the cut edges were found to have a significant influence on fatigue performance. It is concluded that classification of thermally cut edges by cut edge characteristics could be used in fatigue strength assessment as an alternative to standard FAT classes.

Derivation of the Generalized Phase-Shifted Angles by Using Phasor Diagrams for the CHB Converter With Unbalanced DC Voltage Sources

The cascaded H-bridge (CHB) converter is widely used in a lot of applications. When the dc port voltages of the inverter cells are the same, the conventional modulation strategy can ensure that there is no double switching frequency harmonic component. However, when the dc voltages are unbalanced, which is very common in practical applications, voltage distortion occurs. Focused on the harmonic reduction at twice switching frequency, this article proposes an insightful calculation method from the geometrical point of view. The proposed method uses the phasor diagrams to obtain the phase-shifted angles for the CHB converter with any number of inverter cells. The calculation process is very clear and no complex mathematical optimization algorithm is required. Finally, the effectiveness of the proposed method is verified by the experimental CHB platform with five inverter cells.

A study of non-positive operators between real normed linear spaces

We introduce the concept of non-positive operators with respect to a fixed operator defined between two real normed linear spaces. Significantly, we observe that, in certain cases, it is possible to study such type of operators from a geometric point of view. As an immediate application of our study, we explicitly characterize certain classes of non-positive operators between particular pairs of real normed linear spaces. Furthermore, we present a complete characterization of smooth and strictly convex Radon planes in connection with non-positive operators.

Accuracy evaluation of geometric error calibration using a laser tracer via a formulaic approach

In this work, we examine the accuracy of the geometric error calibration of machine tools using a laser tracer, via the multilateration or sequential multilateration principle. An uncertainty analysis of geometric errors or target point coordinates, based on the Monte-Carlo method, is often adopted to assess the accuracy of measurement results. However, this approach is not comprehensive, and can be time-consuming. This paper adopts the average volumetric localization accuracy to assess the quality of geometric error calibration, where the accuracy is evaluated approximately by means of a formulaic method, based on the multivariate law of propagation of uncertainty. Using this method, the accuracy of measurement results can be denoted quantitatively with a single indicator, and the influence of measurement strategy on measurement accuracy can be analyzed more intuitively. To further improve the average volumetric localization accuracy, we employ an optimization method for the measurement path, based on the greedy algorithm. Simulations and experiment are then conducted to verify the proposed method; the results show that both the laser tracer setup and measurement path have a great deal of influence on the measurement accuracy of geometric errors.

Facial image recognition for biometric authentication systems using a combination of geometrical feature points and low-level visual features

This paper proposes a method for biometric-driven facial image recognition, based on multivariate correlation analysis, which extracts geometrical feature points and low-level visual features. The low-level visual features, such as colour and texture, are extracted at local from the selected prominent regions of the facial image. The geometrical features are captured using the Active Shape Model (ASM). The colour features are extracted from the YCbCr colour model, and the autocorrelation method is deployed to extract the texture features. The extracted features are formed as a feature tensor matrix. The feature matrix of the key face image is compared to the feature matrices of the target face image that are stored in the feature vector database using the Canonical Correlation method. The correlation between the key and target feature matrices is tested, whether it is highly significant or not. If it is significantly correlated, then it is inferred that the key and target face images are the same; otherwise, it is concluded that they are different. The benchmark facial image datasets, GT, LFW, and Pointing ’04 datasets, considered for the experiments; in addition to the datasets, a facial image database has been constructed with celebrities on our interest which has also been subjected to experiments. The proposed method resulted in a mean precision score (mP@α) of 95.27%, 94.20%, 96.19%, and 96.05 forGT, LFW, Pointing ‘04, and our datasets, respectively. Also, the F-score was calculated that are, 96.78%, 95.15%, 97.08%, and 96.96%forGT, LFW, Pointing ‘04, and our datasets, respectively. The results obtained by the proposed method are comparable to the existing methods.

3D stem model construction with geometry consistency using terrestrial laser scanning data

ABSTRACT The traditional stem model is inconsistent with the real geometry of the stem. Terrestrial laser scanning (TLS) provides a possibility of constructing a realistic stem model. In this study, we present a 3D stem model, which includes the stem axis curve and stem cross-sectional profile curve, with geometrical consistency and stem parameter retrieval methods using TLS data. The 3D stem axis curve is interpolated based on the geometric central points, which are calculated from stem slices formed by stem cross-sections. From the 3D stem axis curve, the stem shape characteristic is clearly depicted in 3D space. Stem parameters, such as the location of a stem cross-section, stem diameter, height, length, curvature and torsion at any position along the stem, are calculated. The stem cross-sectional profile curve is interpolated based on the stem cross-sectional profile points, which are calculated from stem cross-sectional points by angle simplification. Then, the convex-concave characteristic of the stem cross-section is represented by the stem cross-sectional profile curve, and from this, the integral method for basal area calculation is presented. The presented methods were tested on stem points from different tree species with different shape properties. The feasibility and validity of the 3D stem model was demonstrated by 3D stem model visualization. The root mean square error (RMSE) of the presented stem diameter method was 0.129 cm. Compared with the basal area calculated from the cross-sectional profile curve, the mean absolute percentage error (MAPE) and RMSE values of the traditional method were 8.921% and 49.926 cm2, respectively. The stem parameter retrieval experiment demonstrated the accuracy and practicability of the 3D stem model. Compared with the traditional stem model, the 3D stem model can accurately represent the geometric structure of the stem and provide accurate calculations of stem parameters. It will help improve the applications of TLS in forestry inventories.

SOME MATHEMATICAL CONCEPTS IN GEOMETRY OF MASSES

The study of the distribution of geometrical points, loaded by some scalars plays an important role in various fields of science, of theoretical and practical character. Since such study was first applied and studied when mass had the role of played a scalar, the mass loaded point was named material point, and the discipline dealing with the arrangement of material points in space is called the geometric mass. In that discipline, in the general case under mass one should imply a scalar of arbitrary nature, which can be negative as well. For example, the discipline includes the study of distribution of magnetic or electrical masses, which can be positive and negative. This paper presents some concepts from the geometry of masses that play an important role, particularly in mechanics and physics.

Descending Packing Algorithm for Irregular Graphics Based on Geometric Feature Points

The packing for two-dimensional irregular graphics is one of the NP-complete problems and widely used in industrial applications. In this paper, a descending nesting algorithm for a two-dimensional irregular graph based on geometric feature points is proposed. Before the packing, the parts to be packed are sorted, matched, and spliced, and the matching of the rectangular pieces and the rectangular-like pieces is carried out according to the plate size. On this basis, the geometric feature points of the parts are used to construct the packing baseline, and the packing is accurately carried out according to the principles of the bottom left, the principle of the lowest center of gravity, and combination with virtual moving, rotating collision calculation. The computation of the moving collision distance between the graphics is replaced by the projecting computation of the geometric feature points of the graphic parts, so the computation amount can be reduced. Also, this method is used to test a number of benchmarks examples which are provided by ESICUP (EURO Special Interest Group on Cutting and Packing), which show that the proposed algorithm not only can improve packing but also has better stability and reliability.

A Gramian approach to entanglement in bipartite finite dimensional systems: the case of pure states

It has been observed that the reduced density matrices of bipartite qudit pure states possess a Gram matrix structure. This observation has opened a possibility of analysing the entanglement in such systems from the purely geometrical point of view. In particular, a new quantitative measure of an entanglement of the geometrical nature, has been proposed. Using the invented Gram matrix approach, a version of a non-linear purification of mixed states describing the system analysed has been presented.

On the topological convergence of multi-rule sequences of sets and fractal patterns

In many cases occurring in the real world and studied in science and engineering, non-homogeneous fractal forms often emerge with striking characteristics of cyclicity or periodicity. The authors, for example, have repeatedly traced these characteristics in hydrological basins, hydraulic networks, water demand, and various datasets. But, unfortunately, today we do not yet have well-developed and at the same time simple-to-use mathematical models that allow, above all scientists and engineers, to interpret these phenomena. An interesting idea was firstly proposed by Sergeyev in 2007 under the name of “blinking fractals.” In this paper we investigate from a pure geometric point of view the fractal properties, with their computational aspects, of two main examples generated by a system of multiple rules and which are enlightening for the theme. Strengthened by them, we then propose an address for an easy formalization of the concept of blinking fractal and we discuss some possible applications and future work.

A geometric probability randomized Kaczmarz method for large scale linear systems

For solving large scale linear systems, a fast convergent randomized Kaczmarz-type method was constructed in Bai and Wu (2018) [4]. In this paper, we propose a geometric probability randomized Kaczmarz (GPRK) method by introducing a new index set Jk and three supervised probability criteria defined on Jk from a geometric point of view. Linear convergence of GPRK is proved, and the way of argument for the analysis of GPRK also leads to new sharper upper bounds for the randomized Kaczmarz (RK) method and the greedy randomized Kaczmarz (GRK) method. In practice, GPRK is implemented with a simple geometric probability criterion, i.e., the most efficient one of the aforementioned three supervised probability criteria defined on Jk. The numerical results demonstrate that GPRK is robust and efficient, and it is faster than GRK in most of the tests in the sense of computing time.

Analysis of post-processing influence on the geometrical and dimensional accuracy of selective laser melting parts

PurposeThis study aims to analyze the effect of the different common post-processes on the geometrical and dimensional accuracy of selective laser melting (SLM) parts.Design/methodology/approachAn artefact has been designed including cubic features formed by planar surfaces orientated according to the machine axes, covering all the X-Y area of the working space. The artefact has been analyzed both geometrically (flatness, parallelism) and dimensionally (sizes, distances) from coordinate measuring machine measurement results at three stages, namely, as-built, after sand-blasting and after stress-relieving heat treatment.FindingsResults from the SLM machine used in this study lead to smaller parts than the nominal ones. This effect depends on the direction of the evaluated dimension of the parts, i.e. X, Y or Z direction and is differently affected by the sandblasting post-process (average erosion ratio of 68, 54 and 9 µm, respectively), being practically unaltered by the HT applied after.Originality/valueThis paper shows the influence, from a geometric and dimensional point of view, of two of the most common post-processes used after producing SLM parts, such as sand-blasting and stress-relieving heat treatment, that have not been considered in previous research.

The Reliability of IoT Networks With Characteristics of Abnormal Induced Signals

The abnormal nodes of the Internet of Things (IoT) are closely related to the reliability of the network, but it is always a difficulty to predict the characteristics of the induced signals that threaten reliability. In this article, a feature analysis method for the abnormal signal inducing the unreliable anomaly in IoT based on chaos attractor is proposed to make phase space reconstruction of the abnormal signal that the nodes of IoT can induce unreliability. The phase space structure is constructed by the sequence of abnormal signals. The chaotic attractor is used to analyze the phase space characteristics and reflect the phase space characteristics of unreliable signals induced by the network from the geometric point of view. The mutual information method is used to solve the time delay of the unreliable abnormal signal of IoT, calculate the embedding dimension, find out the chaotic attractors under different characteristics, and judge the reliability change characteristics by analyzing the chaotic attractors. The experimental results show that the method has a better time slot consumption, throughput, and idle energy indexes. Furthermore, our experiments show that the chaos attractor method can effectively predict the reliability trend of IoT, and better predict the reliability anomalies of IoT.

Laws of the iterated logarithm on covering graphs with groups of polynomial volume growth

Abstract Moderate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any intermediate spatial scalings between those of laws of large numbers and those of central limit theorems. The corresponding rate functions are given by quadratic forms determined by the Albanese metric associated with the given random walks. We apply MDPs to establish laws of the iterated logarithm on the covering graphs by characterizing the set of all limit points of the normalized random walks.

Investigation of the influence of certain factors on the quality of processing during hard grinding

The surface roughness of wood products has a direct impact on many technological and operational properties of parts as a whole and is an important production factor, which is associated with the consumption of materials and the technical and economic efficiency of many technological operations such as gluing, grinding, varnishing, etc.We must not forget about the aesthetic properties of wood - reflective and absorbing ability, which is directly affected by surface roughness. The urgency of the problem of obtaining the required quality of the treated wood surface is now becoming increasingly important in connection with the increasing requirements for the quality of woodworking products and obtaining the greatest economic effect for the enterprise. A polished surface is formed as a result of the simultaneous action of many factors. The main ones are geometric factors, plastic and elastic deformations that accompany the grinding process.From a geometric point of view, the roughness is created due to the copying of the path of the cutting tool of a certain geometric shape on the wood surface. Plastic and elastic deformations occurring during the cutting process strongly distort the microrelief resulting from the action of geometric factors.

Improved effective notch strain approach for fatigue reliability assessment of load-carrying fillet welded cruciform joints in low and high cycle fatigue

An improved effective notch strain (ENSN) approach is developed for the fatigue reliability assessment of load-carrying fillet welded cruciform joints in low and high cycle fatigue regions. The ENSN approach is improved in the ENSN estimation using an analytical approach, and the improvement is verified using some published experiments performed in the low cycle fatigue regime. The cruciform joint is modelled as a correlated two-component series-system, and various sources of uncertainties are considered. The fillet weld geometry uncertainty is modelled by correlated position variations of geometrical control points. To avoid iterative calls of the finite element analysis in the fatigue reliability assessment, response surface models are constructed, and they are used to approximate the influence of position changes. A critical fatigue notch factor is proposed to represent the fatigue resistance for a given fatigue loading and material, which allows a direct reliability approximation. The critical fatigue notch factor for an ice-induced fatigue loading is derived. The ENSN approach is more reasonable to be used for this type of fatigue loading than the high cycle fatigue approach. A cruciform joint subjected to ice-induced fatigue loading is assessed to demonstrate the application of the fatigue reliability assessment procedures.

THE SCHOLARSHIP AWARDING DECISION SUPPORT SYSTEM USES THE TOPSIS METHOD

Education has an important role as an effort to educate the nation. Education is the right of everyone, but not everyone can continue higher education for various reasons. One of them is limited financial and financial resources. TOPSIS is a multi-criteria dynamic strategy or elective decision which is an elective that has the littlest good ways from the positive ideal arrangement and the largest distance from the negative ideal solution from a geometric point of view using the Euclidean distance. This study aims to determine the criteria for scholarship recipients that can be implemented in a campus, school, or other social institution that provides funds for scholarship assistance. The research results are expected to serve as a reference for the decision making process. The results showed a preference value of 0.66 which is based on academic achievement

Geometric multidimensional scaling: A new approach for data dimensionality reduction

Multidimensional scaling (MDS) provides a possibility to present the multidimensional data visually. It is a very popular method of this class. MDS minimizes some stress functions. In this paper, the stress function and multidimensional scaling, in general, have been considered from the geometric point of view. The so-called Geometric MDS has been developed. The new interpretation of the stress allows finding the proper step size, and the descent direction forwards the minimum of the stress function analytically if we consider and move a separate point of the projected space. The exceptional property of the new approach is that we do not need the analytical expression of the stress function. There is no need for numerical evaluation of its derivatives, too. Moreover, we do not need for the linear search that is used for local descent in optimization. Theoretical analysis disclosed that the step direction, determined by Geometric MDS, coincides with the steepest descent direction. The analytically found step size is such that it guarantees the decrease of the stress in this direction. Two realizations of Geometric MDS are proposed and examined. The comparison with SMACOF realization of MDS looks very promising.

Weak form of self-testing

The concept of self-testing (or rigidity) refers to the fact that for certain Bell inequalities the maximal violation can be achieved in an essentially unique manner. In this work we present a family of Bell inequalities which are maximally violated by multiple inequivalent quantum realisations. We completely characterise the quantum realisations achieving the maximal violation and we show that each of them requires a maximally entangled state of two qubits. This implies the existence of a new, weak form of self-testing in which the maximal violation allows us to identify the state, but does not fully determine the measurements. From the geometric point of view the set of probability points that saturate the quantum bound is a line segment. We then focus on a particular member of the family and show that the self-testing statement is robust, i.e. that observing a non-maximal violation allows us to make a quantitative statement about the unknown state. To achieve this we present a new construction of extraction channels and analyse their performance. For completeness we provide two independent approaches: analytical and numerical. The noise robustness, i.e. the amount of white noise at which the bound becomes trivial, of the analytical bound is rather small (~0.06%), but the numerical method takes us into an experimentally-relevant regime (~5%). We conclude by investigating the amount of randomness that can be certified using these Bell violations. Perhaps surprisingly, we find that the qualitative behaviour resembles the behaviour of rigid inequalities like the Clauser-Horne-Shimony-Holt inequality. This shows that at least for some device-independent applications rigidity is not a necessary ingredient.

COST-BENEFIT ANALYSIS OF RAIL TUNNEL INSPECTION FOR PHOTOGRAMMETRY AND LASER SCANNING

Abstract. The civil engineering and construction sector, including the railway industry, is seeking innovative approaches to reduce costs on repetitive and labour-intensive tasks and avoid the use of highly qualified staff for simple manual duties. Such tasks can include the visual inspection of tunnels, where the process is still dominated by manual operations. Our work compares Close Range Photogrammetry (CRP) and Terrestrial Laser Scanning (TLS), both performed with low-end sensors to reflect the industry’s tendency towards easy to use and easy to maintain hardware. It also analyses the benefits of substituting conventional visual inspections of tunnels with automated survey approaches and computer vision techniques. The project’s outcomes suggest that photogrammetry is a valid alternative to laser scanning for visual inspection of concrete segmentally lined tunnels: from the geometric point of view it provides global accuracy at comparable level to laser scanning, in addition it halves the time to generate the 3D model and provides the user with photo-realistic outputs. It is generally more versatile and it is easier to inspect, visualise and navigate the data. The authors argue that the results presented here will push tunnel inspection in the direction of automated approaches with direct benefits on surveying costs as well as Health & Safety (H&S). Utilising available technology supports risk-based asset management and thus ensures safe and operational performance of a railway for passengers to use.