Geometric Datasets Research Articles

Fourier representation of geometrical imperfection for probabilistic buckling analysis

This research studies the first part of the failure of a compression member structure due to buckling. This unstable equilibrium collapse, exposes brittle failure which occurs suddenly and therefore should be avoided wherever possible. Unavoidable geometric imperfections due to structural fabrication, will weaken the structure against buckling. The behavior of bar under compression will be closely examined by taking a set of geometric imperfection data synthesized from previously available from the measurement of conical shells. Therefore, the two-dimensional surface imperfection is converted into several one-dimensional imperfection with some probability properties. In order to obtain a comparison tool for different type of imperfections, Fourier analysis is used to convert the imperfection into coefficients of trigonometric function. By examining the coefficients, geometric imperfection patterns introduced by a certain fabrication process are able to be identified. The study successfully demonstrates the applicability of Fourier analysis in representing inherent geometric imperfections as an initial step for conducting probabilistic buckling analysis. Fourier analysis has shown its capability to simultaneously characterize imperfections in two crucial parameters - the magnitude and configuration of the imperfection.

Parametric design optimization and thermodynamic analysis of plate fin heat exchanger for helium liquefaction system

The plate-fin heat exchanger is one of the most important components of helium liquefaction system as it recovers cold energy from helium gas in the cold box. Because of larger heat transfer surface area and compact geometrical configuration, plate-fin heat exchangers are widely used. The design of heat exchanger using helium as a cryogenic fluid needs high thermodynamic performance with minimum pressure drop which particularly requires the optimization of dimensional array and its geometrical configurations. In this regard, a parametric investigation was performed to compute the effective geometrical parameters and its effect on thermodynamic (effectiveness and log-mean temperature difference) performance has been discussed in detail. The present study aims to design optimization and thermodynamic performance evaluation of plate-fin type heat exchangers used in helium liquefaction systems. The developed helium liquefaction model has been simulated for the most critical liquefier with and without liquid nitrogen precooling, mixed mode, and refrigeration mode. Each component of the liquefaction model has been technically and thermodynamically analyzed and, in particular, four plate-fin heat exchangers have been considered and designed accurately using Aspen EDR®. Initially, the sensitivity analysis was carried out to characterize the most significant geometrical parameters (fin thickness, height, number and arrangement of layers, frequency, and fin type) and their effect on thermodynamic performance and pressure drop. After that, the artificial intelligence model was used to determine the optimal range of such geometrical variables in which the heat exchanger has maximum effectiveness and log mean temperature difference. Finally, the operating conditions obtained from cycle modeling and optimized geometrical datasets have been applied in commercial simulation software Aspen EDR® for plate-fin heat exchangers design. Finally, a comparative thermodynamic analysis has been carried out to determine the performance of all the designed heat exchangers operating at four different modes (boundary conditions).

Combination of geometric and gravimetric data sets for the estimation of high-resolution mass balances of the Greenland ice sheet

SUMMARY In this study, we develop a model that allows to combine gravimetric and geometric data. By the combination, we improve the spatial resolution of the resulting mass balance estimate compared to a purely gravimetric one. The equivalent ice or firn density of the changing ice volume is estimated within a mathematical inversion model, which includes geometric information about the volumetric change of the ice sheet and the resulting gravity change. This gravity change is computed from monthly GRACE gravity fields. They have a limited spatial resolution of a few 100 km, but allow direct conclusions about the true mass changes over Greenland. The ice-volume changes are described by a product by the Climate Change Initiative of European Space Agency, which is based on altimetry data. They have a very fine spatial resolution (down to a few km), but are not directly sensitive to mass changes. By combining both data sets in a common mathematical model, the advantages of both data types (direct sensitivity to mass versus high spatial resolution) are made use of. In this way, we improve the spatial resolution of mass balance estimates over Greenland. This leads to a map of mass trends, which has the same spatial resolution as the input map of geometric changes, but which is consistent with the input gravity fields. It will enable improving the localization of mass change signals of ice sheets and glaciers, which are usually rather small-scale. We compare our estimates to the results of complementary studies regarding the total mass loss of the Greenland ice sheet and its surrounding land surface. Our study leads to a value of $-213\pm 37\, \text{Gt}\,\text{a}^{-1}$ in the time span from 2011 to 2015. We also discuss the problem of separating the mass contribution of the Greenland ice sheet itself and its surrounding region.

New hybrid segmentation algorithm: UNet-GOA.

The U-Net architecture is a prominent technique for image segmentation. However, a significant challenge in utilizing this algorithm is the selection of appropriate hyperparameters. In this study, we aimed to address this issue using an evolutionary approach. We conducted experiments on four different geometric datasets (triangle, kite, parallelogram, and square), with 1,000 training samples and 200 test samples. Initially, we performed image segmentation without the evolutionary approach, manually adjusting the U-Net hyperparameters. The average accuracy rates for the geometric images were 0.94463, 0.96289, 0.96962, and 0.93971, respectively. Subsequently, we proposed a hybrid version of the U-Net architecture, incorporating the Grasshopper Optimization Algorithm (GOA) for an evolutionary approach. This method automatically discovered the optimal hyperparameters, resulting in improved image segmentation performance. The average accuracy rates achieved by the proposed method were 0.99418, 0.99673, 0.99143, and 0.99946, respectively, for the geometric images. Comparative analysis revealed that the proposed UNet-GOA approach outperformed the traditional U-Net architecture, yielding higher accuracy rates.

GEO-Nav: A geometric dataset of voltage-gated sodium channels

Voltage-gated sodium (Nav) channels constitute a prime target for drug design and discovery, given their implication in various diseases such as epilepsy, migraine and ataxia to name a few. In this regard, performing morphological analysis is a crucial step in comprehensively understanding their biological function and mechanism, as well as in uncovering subtle details of their mechanism that may be elusive to experimental observations. Despite their tremendous therapeutic potential, drug design resources are deficient, particularly in terms of accurate and comprehensive geometric information. This paper presents a geometric dataset of molecular surfaces that are representative of Nav channels in mammals. For each structure we provide three representations and a number of geometric measures, including length, volume and straightness of the recognized channels. To demonstrate the effective use of GEO-Nav, we have tested it on two methods belonging to two different categories of approaches: a sphere-based and a tessellation-based method.

Symmetric Volume Maps: Order-invariant Volumetric Mesh Correspondence with Free Boundary

Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence—a natural extension relevant to shapes extracted from simulation, medical imaging, and volume rendering—presents unique challenges that do not appear in the two-dimensional case. In this work, we propose a method for mapping between volumes represented as tetrahedral meshes. Our formulation minimizes a distortion energy designed to extract maps symmetrically, i.e., without dependence on the ordering of the source and target domains. We accompany our method with theoretical discussion describing the consequences of this symmetry assumption, leading us to select a symmetrized ARAP energy that favors isometric correspondences. Our final formulation optimizes for near-isometry while matching the boundary. We demonstrate our method on a diverse geometric dataset, producing low-distortion matchings that align closely to the boundary.

Shake-table testing of a stone masonry building aggregate: overview of blind prediction study

City centres of Europe are often composed of unreinforced masonry structural aggregates, whose seismic response is challenging to predict. To advance the state of the art on the seismic response of these aggregates, the Adjacent Interacting Masonry Structures (AIMS) subproject from Horizon 2020 project Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe (SERA) provides shake-table test data of a two-unit, double-leaf stone masonry aggregate subjected to two horizontal components of dynamic excitation. A blind prediction was organized with participants from academia and industry to test modelling approaches and assumptions and to learn about the extent of uncertainty in modelling for such masonry aggregates. The participants were provided with the full set of material and geometrical data, construction details and original seismic input and asked to predict prior to the test the expected seismic response in terms of damage mechanisms, base-shear forces, and roof displacements. The modelling approaches used differ significantly in the level of detail and the modelling assumptions. This paper provides an overview of the adopted modelling approaches and their subsequent predictions. It further discusses the range of assumptions made when modelling masonry walls, floors and connections, and aims at discovering how the common solutions regarding modelling masonry in general, and masonry aggregates in particular, affect the results. The results are evaluated both in terms of damage mechanisms, base shear forces, displacements and interface openings in both directions, and then compared with the experimental results. The modelling approaches featuring Discrete Element Method (DEM) led to the best predictions in terms of displacements, while a submission using rigid block limit analysis led to the best prediction in terms of damage mechanisms. Large coefficients of variation of predicted displacements and general underestimation of displacements in comparison with experimental results, except for DEM models, highlight the need for further consensus building on suitable modelling assumptions for such masonry aggregates.

Hubble speed from first principles

We introduce a way of measuring ${H}_{0}$ from a combination of independent geometrical data sets, without the need for calibration or the choice of a cosmological model. We build on the distance duality relation, which sets the ratio of the luminosity and angular diameter distance to a fixed scaling in redshift for any metric theory of gravity with standard photon propagation and constitutes a founding block of any theory describing our Universe. Our method allows us to determine ${H}_{0}$ from first principles, unleashing the measurement of this fundamental constant from calibration and the assumption of a cosmological model. We find ${H}_{0}=69.5\ifmmode\pm\else\textpm\fi{}1.7\text{ }\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ at 68% C.L., showing that the Hubble constant can be constrained at the percent level with minimal assumptions.

Evolutionary Patterns of Modularity in the Linkage Systems of the Skull in Wrasses and Parrotfish.

The concept of modularity is fundamental to understanding the evolvability of morphological structures and is considered a central framework for the exploration of functionally and developmentally related subsets of anatomical traits. In this study, we explored evolutionary patterns of modularity and integration in the 4-bar linkage biomechanical system of the skull in the fish family Labridae (wrasses and parrotfish). We measured evolutionary modularity and rates of shape diversification of the skull partitions of three biomechanical 4-bar linkage systems using 205 species of wrasses (family: Labridae) and a three-dimensional geometric morphometrics data set of 200 coordinates. We found support for a two-module hypothesis on the family level that identifies the bones associated with the three linkages as being a module independent from a module formed by the remainder of the skull (neurocranium, nasals, premaxilla, and pharyngeal jaws). We tested the patterns of skull modularity for four tribes in wrasses: hypsigenyines, julidines, cheilines, and scarines. The hypsigenyine and julidine groups showed the same two-module hypothesis for Labridae, whereas cheilines supported a four-module hypothesis with the three linkages as independent modules relative to the remainder of the skull. Scarines showed increased modularization of skull elements, where each bone is its own module. Diversification rates of modules show that linkage modules have evolved at a faster net rate of shape change than the remainder of the skull, with cheilines and scarines exhibiting the highest rate of evolutionary shape change. We developed a metric of linkage planarity and found the oral jaw linkage system to exhibit high planarity, while the rest position of the hyoid linkage system exhibited increased three dimensionality. This study shows a strong link between phenotypic evolution and biomechanical systems, with modularity influencing rates of shape change in the evolution of the wrasse skull.

Wood identification of Cyclobalanopsis (Endl.) Oerst based on microscopic features and CTGAN-enhanced explainable machine learning models.

Accurate and fast identification of wood at the species level is critical for protecting and conserving tree species resources. The current identification methods are inefficient, costly, and complex. A wood species identification model based on wood anatomy and using the Cyclobalanopsis genus wood cell geometric dataset was proposed. The model was enhanced by the CTGAN deep learning algorithm and used a simulated cell geometric feature dataset. The machine learning models BPNN and SVM were trained respectively for recognition of three Cyclobalanopsis species with simulated vessel cells and simulated wood fiber cells. The SVM model and BPNN model achieved recognition accuracy of 96.4% and 99.6%, respectively, on the real dataset, using the CTGAN-generated vessel dataset. The BPNN model and SVM model achieved recognition accuracy of 75.5% and 77.9% on real dataset, respectively, using the CTGAN-generated wood fiber dataset. The machine learning model trained based on the enhanced cell geometric feature data by CTGAN achieved good recognition of Cyclobalanopsis, with the SVM model having a higher prediction accuracy than BPNN. The machine learning models were interpreted based on LIME to explore how they identify tree species based on wood cell geometric features. This proposed model can be used for efficient and cost-effective identification of wood species in industrial applications.

Improved kinetics for mineral dissolution reactions in pore-scale reactive transport modeling

Recent numerical investigations revealed that the heterogeneity of the dissolution rate observed in numerous experiments cannot be explained by fluid transport effects. This heterogeneity is attributed to intrinsic surface reactivity. Therefore, reactive transport models (RTM) require parameterization of the surface reactivity for accurate predictions. For this purpose, a nanotopographic parametrization based on surface slope has been recently suggested. In this study, we utilize and improve this parametrization for RTMs of pore-scale systems, from the crystal surface to the single crystal geometry, going beyond the previous reactivity parametrization. 2D and 3D RTMs were developed using COMSOL Multiphysics for calcite systems based on experimental measurements. We compared the results between classically parameterized RTMs, RTMs with new slope parameterization, and experimental data. The effect of flow on dissolution under conditions far-from-equilibrium is found to be negligible, highlighting the importance of surface reactivity in the dissolution reaction. For the first time, the new slope factor was able to accurately reproduce the experimental results on a crystal surface with large field-of-view, large height variability of the topography, and over a long-term reaction period. The new parameterization had greatly improved sensitivity for intermediate reactivity ranges compared to the previous parameterization. A 3D model is used to present the general applicability of the parameterization for use in realistic geometric data sets. Thus, we also show that neglecting surface reactivity in an RTM leads to incorrect predictions regarding the porosity, pore geometry, and surface topography of the system. Our new slope factor can successfully serve as a first-order proxy for the distribution of surface reactivity in 3D pore-scale rock systems. The description of surface reactivity is crucial for accurate long-term modeling of natural rock systems.

Intrinsic dimension of geometric data sets

The curse of dimensionality is a phenomenon frequently observed in machine learning (ML) and knowledge discovery (KD). There is a large body of literature investigating its origin and impact, using methods from mathematics as well as from computer science. Among the mathematical insights into data dimensionality, there is an intimate link between the dimension curse and the phenomenon of measure concentration, which makes the former accessible to methods of geometric analysis. The present work provides a comprehensive study of the intrinsic geometry of a data set, based on Gromov's metric measure geometry and Pestov's axiomatic approach to intrinsic dimension. In detail, we define a concept of geometric data set and introduce a metric as well as a partial order on the set of isomorphism classes of such data sets. Based on these objects, we propose and investigate an axiomatic approach to the intrinsic dimension of geometric data sets and establish a concrete dimension function with the desired properties. Our model for data sets and their intrinsic dimension is computationally feasible and, moreover, adaptable to specific ML/KD-algorithms, as illustrated by various experiments.

조선 네스팅 문제의 부재 페어링을 위한 딥러닝 기반 부재 분류 방법

With the rapid development of artificial intelligence technology, deep learning-based classification techniques have had enough reliability to be applied to industrial sites. However, while the study of the object classification on data acquired with 3D scanners or cameras has made remarkable progress, research activity based on geometric data sets is still in its infancy. In particular, in order to improve the classification performance of ship parts based on deep learning in the nesting problem to increase productivity in shipbuilding, the study of the construction of part datasets and data pre-processing is necessary. In this paper, we introduce a method to apply the artificial neural network technology of deep learning to the nesting algorithm for shipbuilding. Labeled with histogram-based shape contexts for constructing a dataset for classifying ship parts using Convolutional Neural Networks (CNNs). In addition, we introduce the preprocessing method of the geometric information of the ship parts for learning and the no-fit polygon (NFP) method for classified parts to pair up. To train the classification model for the 23,201 ship parts, a data set of 842 classes was constructed through the shape matching algorithm. The trained CNN model was able to classify those parts with an accuracy of 85.13%.

Satellite‐Based Estimate of Intrinsic Predictability Limits at Convective Scales Over Northeast India

AbstractSpheroscale estimates are essential not only for incorporating the seemingly incompatible phenomenon of atmospheric convection within the framework of wide‐range horizontal and vertical scaling in the atmosphere, but also to make semi‐empirical estimates of the storm‐scale atmospheric predictability limits. Since spheroscales are extremely variable, this study computes yearly spheroscales during convective weather events over a selected part of northeast India for 5 different years using the ensemble‐averaged fluctuations of radar reflectivity from the CloudSat geometric profile data set. All these spheroscale estimates are consistently less than 100 m and are directly proportional to the maximum reflectivity observed during the corresponding year. This is in agreement with the fact that spheroscales for unstable atmospheric fields are larger than that of stable atmospheric fields. The semi‐empirical angle‐averaged predictability limits estimated using these spheroscale estimates illustrate that atmospheric fields with larger spheroscales are weakly stable and have smaller intrinsic predictability limits thereby making them less predictable.

Graph-Based Shape Analysis for Heterogeneous Geometric Datasets: Similarity, Retrieval and Substructure Matching

Practically all existing shape analysis and processing algorithms have been developed for specific geometric representations of 3D models. However, the product development process always involves a large number of often incompatible geometric representations tailored to specific computational tasks that take place during this process. Consequently, a substantial effort has been expended to develop robust geometric data translation and conversion algorithms, but the existing methods have well known limitations.The Maximal Disjoint Ball Decomposition (MDBD) was recently defined as a unique and stable geometric construction and used to define universal shape descriptors based on the contact graph associated with MDBD. In this paper, we demonstrate that by applying graph analysis tools to MDBD in conjunction with graph convolutional neural networks and graph kernels, one can effectively develop methods to perform similarity, retrieval and substructure matching from geometric models regardless of their native geometric representation. We show that our representation-agnostic approach achieves comparable performance with state-of-the-art geometric processing methods on standard yet heterogeneous benchmark datasets while supporting all valid geometric representations.

Identifying Geomorphological Changes of Coastal Cliffs through Point Cloud Registration from UAV Images

Cliff monitoring is essential to stakeholders for their decision-making in maintaining a healthy coastal environment. Recently, photogrammetry-based technology has shown great successes in cliff monitoring. However, many methods to date require georeferencing efforts by either measuring geographic coordinates of the ground control points (GCPs) or using global navigation satellite system (GNSS)-enabled unmanned aerial vehicles (UAVs), significantly increasing the implementation costs. In this study, we proposed an alternative cliff monitoring methodology that does not rely on any georeferencing efforts but can still yield reliable monitoring results. To this end, we treated 3D point clouds of the cliff from different periods as geometric datasets and further aligned them into the same coordinate system using a rigid registration protocol. We examined the performance of our approach through a few small-scale experiments on a rock sample as well as a full-scale field validation on a coastal cliff. The findings of this study would be particularly valuable for underserved coastal communities, where high-end GPS devices and GIS specialists may not be easily accessible resources.

GeoGraph

In many applications of graph processing, the input data is often generated from an underlying geometric point data set. However, existing high-performance graph processing frameworks assume that the input data is given as a graph. Therefore, to use these frameworks, the user must write or use external programs based on computational geometry algorithms to convert their point data set to a graph, which requires more programming effort and can also lead to performance degradation. In this paper, we present our ongoing work on the Geo- Graph framework for shared-memory multicore machines, which seamlessly supports routines for parallel geometric graph construction and parallel graph processing within the same environment. GeoGraph supports graph construction based on k-nearest neighbors, Delaunay triangulation, and b-skeleton graphs. It can then pass these generated graphs to over 25 graph algorithms. GeoGraph contains highperformance parallel primitives and algorithms implemented in C++, and includes a Python interface. We present four examples of using GeoGraph, and some experimental results showing good parallel speedups and improvements over the Higra library. We conclude with a vision of future directions for research in bridging graph and geometric data processing.

Manoeuvring speed estimation of a lane-change system using geometric hermite interpolation

Autonomous vehicles demand a continuous path to provide the passengers with physical ease and relaxation. Smooth experience in autonomous vehicles is very essential and can be accomplished by having good trajectories. The trajectory generated by the interpolation algorithm for Geometric Hermite is provided in this paper. The proposed algorithm calculates a path based on a set of geometric Hermite data that consists of predefined points including prescribed tangent angles and curvature values. The generated path has the potential to determine the maximum speed allowed for safe autonomous driving on roads by providing curvature information. It describes an alternative way to estimate design speed permitted on the road for autonomous lane change systems.

ArcStereoNet: A New ArcGIS® Toolbox for Projection and Analysis of Meso- and Micro-Structural Data

ArcStereoNet is a new ArcGIS® based toolbox for stereographic projections that we implement here using Python 2.7 programming language. The reason to develop another stereographic projection package arises from the recent use of Python as an exclusive programming language within the ArcGIS® environment. This permits a more flexible approach for the development of tools with very intuitive GUIs, and also allows the user to take full advantage of all potential GIS mapping processes. The core of this new projections toolbox is based on the capability to easily apply and compare most of the commonly used statistical methods for cluster and girdle analysis of structural data. In addition to the well-known Fisher, K-means, and Bingham data elaborations, a completely new algorithm for cluster analysis and mean vector extraction (Mean Extractor from Azimuthal Data), was developed, thereby allowing a more reliable interpretation of any possible structural data distribution. Furthermore, as in any other GIS platform, users can always precisely correlate each single projected data point with the corresponding geographical/locality position, thereby merging or subdividing groups of structural stations with a simple selection procedure. ArcStereoNet also creates rose diagrams, which may be applied not only to fault/joint planes orientation data, but also for the analysis of 2D microstructural fabric parameters. These include geometrical datasets derived from the minimum bounding approach as applied to vectorized grains in thin sections. Finally, several customization settings ensure high-quality graphic outputs of plots, that also allow easy vector graphics post-processing.

Neutral and Multicharged Ions of Small Aluminum Oxides: Structures, Spectroscopy, and Energetics.

We use accurate ab initio methodologies at the Coupled Cluster level to compute the stable forms of AlxOyq+ (x = 1, 2; y = 1, 2; q = 0-3) species for which we derive an accurate set of geometrical and vibrational spectroscopic data. We also determine their adiabatic single, double, and triple ionization energies. These spectroscopic and thermodynamical data may help for identifying these species in laboratory, in astrophysical media, and in plasma and confirm previous observations of multi-charged AlxOy clusters by Atom Probe Tomography (ATP) coupled to mass spectrometry. They should help for identifying and understanding the complex chemical processes occurring during the Al2O3 growth in laboratory and in astrophysical media and those taking place at the degradation of Al-containing materials by high temperature corrosion/oxidation.