Reactor field reconstruction from sparse and movable sensors using Voronoi tessellation-assisted convolutional neural networks

The aging of operational reactors leads to increased mechanical vibrations in the reactor interior.The vibration of the incore sensors near their nominal locations is a new problem for neutronic field reconstruction.Current field-reconstruction methods fail to handle spatially moving sensors.In this study,we propose a Voronoi tessellation technique in combination with convolutional neural networks to handle this challenge.Observations from movable in-core sensors were projected onto the same global field structure using Voronoi tessellation,holding the magnitude and location information of the sensors.General convolutional neural networks were used to learn maps from observations to the global field.The proposed method reconstructed multi-physics fields(including fast flux,thermal flux,and power rate)using observations from a single field(such as thermal flux).Numerical tests based on the IAEA benchmark demonstrated the potential of the proposed method in practical engineering applications,particularly within an amplitude of 5 cm around the nominal locations,which led to average relative errors below 5% and 10% in the L_(2) and L_(∞)norms,respectively.

A typhoon-induced storm surge numerical model with GPU acceleration based on an unstructured spherical centroidal Voronoi tessellation grid

Storm surge is often the marine disaster that poses the greatest threat to life and property in coastal areas.Accurate and timely issuance of storm surge warnings to take appropriate countermeasures is an important means to reduce storm surge-related losses.Storm surge numerical models are important for storm surge forecasting.To further improve the performance of the storm surge forecast models,we developed a numerical storm surge forecast model based on an unstructured spherical centroidal Voronoi tessellation(SCVT)grid.The model is based on shallow water equations in vector-invariant form,and is discretized by Arakawa C grid.The SCVT grid can not only better describe the coastline information but also avoid rigid transitions,and it has a better global consistency by generating high-resolution grids in the key areas through transition refinement.In addition,the simulation speed of the model is accelerated by using the openACC-based GPU acceleration technology to meet the timeliness requirements of operational ensemble forecast.It only takes 37 s to simulate a day in the coastal waters of China.The newly developed storm surge model was applied to simulate typhoon-induced storm surges in the coastal waters of China.The hindcast experiments on the selected representative typhoon-induced storm surge processes indicate that the model can reasonably simulate the distribution characteristics of storm surges.The simulated maximum storm surges and their occurrence times are consistent with the observed data at the representative tide gauge stations,and the mean absolute errors are 3.5 cm and 0.6 h respectively,showing high accuracy and application prospects.

Advances in Studies and Applications of Centroidal Voronoi Tessellations

Centroidal Voronoi tessellations(CVTs) have become a useful tool in many applications ranging from geometric modeling,image and data analysis,and numerical partial differential equations,to problems in physics,astrophysics,chemistry,and biology. In this paper,we briefly review the CVT concept and a few of its generalizations and well-known properties.We then present an overview of recent advances in both mathematical and computational studies and in practical applications of CVTs.Whenever possible,we point out some outstanding issues that still need investigating.

10-year fundus tessellation progression and retinal vein occlusion

AIM： To access the 10-year fundus tessellation progression in patients with retinal vein occlusion. METHODS： The Beijing Eye Study 2001/2011 is a populationbased longitudinal study. The study participants underwent a detailed physical and ophthalmic examination. Degree of fundus tessellation was graded by using fundus photographs of the macula and optic disc. Progression of fundus tessellation was calculated by fundus tessellation degree of 2011 minus degree of 2001. Fundus photographs were used for assessment of retinal vein occlusion. RESULTS： The Beijing Eye Study included 4403 subjects in 2001, 3468 subjects was repeated in 2011. Assessment of retinal vein obstruction and fundus tessellation progression were available for 2462 subjects（71.0%）, with 66 subjects fulfilled the diagnosis of retinal vein occlusion. Of the 66 participants, 59 participants with unilateral branch retinal vein occlusion, 5 participants with unilateral central retinal vein occlusion, 1 participant with bilateral branch retinal vein occlusion, and 1 participant with branch retinal vein occlusion in one eye and central retinal vein occlusion in the other eye. Mean degree of peripapillary fundus tessellation progression were significantly higher in the whole retinal vein occlusion group（0.33±0.39, P〈0.001）, central retinal vein occlusion group（0.71±0.8, P=0.025） and branch retinal vein occlusion group（0.29±0.34, P=0.006） than the control group（0.20±0.26）. After adjustment for age, prevalence of tilted disc, change of best corrected visual acuity, axial length, progression of peripapillary fundus tessellation was associated with the presence of retinal vein occlusion（P=0.004; regression coefficient B, 0.094; 95%CI, 0.029, 0.158; standardized coefficient B, 0.056）. As a corollary, after adjusting for smoking duration, systolic blood pressure, anterior corneal curvature, prevalence of RVO was associated with more peripapillary fundus tessellation progression（P〈0.001; regression coefficient B： 1.257; OR： 3.517; 95%CI： 1.777, 6.958）. CONCLUSION： Peripapillary fundus tessellation progresses faster in individuals with retinal vein occlusion. This may reflect the thinning and hypoperfusion of choroid in patients with retinal vein occlusion.

Edge-Weighted Centroidal Voronoi Tessellations

Most existing applications of centroidal Voronoi tessellations(CVTs) lack consideration of the length of the cluster boundaries.In this paper we propose a new model and algorithms to produce segmentations which would minimize the total energy—a sum of the classic CVT energy and the weighted length of cluster boundaries.To distinguish it with the classic CVTs,we call it an Edge-Weighted CVT(EWCVT).The concept of EWCVT is expected to build a mathematical base for all CVT related data classifications with requirement of smoothness of the cluster boundaries.The EWCVT method is easy in implementation,fast in computation,and natural for any number of clusters.

High-resolution Remote Sensing Image Segmentation Using Minimum Spanning Tree Tessellation and RHMRF-FCM Algorithm

It is proposed a high resolution remote sensing image segmentation method which combines static minimum spanning tree(MST)tessellation considering shape information and the RHMRF-FCM algorithm.It solves the problems in the traditional pixel-based HMRF-FCM algorithm in which poor noise resistance and low precision segmentation in a complex boundary exist.By using the MST model and shape information,the object boundary and geometrical noise can be expressed and reduced respectively.Firstly,the static MST tessellation is employed for dividing the image domain into some sub-regions corresponding to the components of homogeneous regions needed to be segmented.Secondly,based on the tessellation results,the RHMRF model is built,and regulation terms considering the KL information and the information entropy are introduced into the FCM objective function.Finally,the partial differential method and Lagrange function are employed to calculate the parameters of the fuzzy objective function for obtaining the global optimal segmentation results.To verify the robustness and effectiveness of the proposed algorithm,the experiments are carried out with WorldView-3(WV-3)high resolution image.The results from proposed method with different parameters and comparing methods(multi-resolution method and watershed segmentation method in eCognition software)are analyzed qualitatively and quantitatively.

Numerical Simulation of a Domain-Tessellation Pattern on a Spherical Surface Using a Phase Field Model

A numerical simulation scheme is proposed to analyze domain tessellation and pattern formation on a spherical surface using the phase-field method. A multi-phase-field model is adopted to represent domain growth, and the finite-difference method (FDM) is used for numerical integration. The lattice points for the FDM are distributed regularly on a spherical surface so that a mostly regular triangular domain division is realized. First, a conventional diffusion process is simulated using this lattice to confirm its validity. The multi-phase-field equation is then applied, and pattern formation processes under various initial conditions are simulated. Unlike pattern formation on a flat plane, where the regular hexagonal domains are always stable, certain different patterns are generated. Specifically, characteristic stable patterns are obtained when the number of domains, n, is 6, 8, or 12;for instance, a regular pentagonal domain division pattern is generated for n = 12, which corresponds to a regular dodecahedron.

The Tessellation Rule and Properties Programming of Origami Metasheets Built with a Mixture of Rigid and Non-Rigid Square-Twist Patterns

Metamaterials constructed from origami units of different types and behaviors could potentially offer a broader scope of mechanical properties than those formed from identical unit types.However,the geometric design rules and property programming methods for such metamaterials have yet to be extensively explored.In this paper,we propose a new kind of origami metasheet by incorporating a family of different square-twist units.The tessellation rule of these metasheets is established to allow compatible mountain-valley crease assignments and geometric parameters among neighboring units.We demonstrate through experiments that the energy,initial peak force,and maximum stiffness of the metasheets can be obtained by a summation of the properties of the constitutional units.Based on this,we are able to program the mechanical properties of the metasheets over a wide range by varying the types and proportions of the units,as well as their geometric and material parameters.Furthermore,for a metasheet with a fixed number of units,all the geometrically compatible tessellations can be folded out of the same pre-creased sheet material by simply changing the mountain-valley assignments,thereby allowing the properties of the metasheet to be re-programmed based on specific requirements.This work could inspire a new class of programmable origami metamaterials for current and future mechanical and other engineering applications.

2D Centroidal Voronoi Tessellations with Constraints

We tackle the problem of constructing 2D centroidal Voronoi tessellations with constraints through an efficient and robust construction of bounded Voronoi diagrams, the pseudo-dual of the constrained Delaunay triangulation.We exploit the fact that the cells of the bounded Voronoi diagram can be obtained by clipping the ordinary ones against the constrained Delaunay edges.The clipping itself is efficiently computed by identifying for each constrained edge the(connected) set of triangles whose dual Voronoi vertices are hidden by the constraint.The resulting construction is amenable to Lloyd relaxation so as to obtain a centroidal tessellation with constraints.

Cooperative Sensing and Distributed Control of a Diffusion Process Using Centroidal Voronoi Tessellations

This paper considers how to use a group of robots to sense and control a diffusion process.The diffusion process is modeled by a partial differential equation (PDE),which is a both spatially and temporally variant system.The robots can serve as mobile sensors,actuators,or both.Centroidal Voronoi Tessellations based coverage control algorithm is proposed for the cooperative sensing task.For the diffusion control problem,this paper considers spraying control via a group of networked mobile robots equipped with chemical neutralizers,known as smart mobile sprayers or actuators,in a domain of interest having static mesh sensor network for concentration sensing.This paper also introduces the information sharing and consensus strategy when using centroidal Voronoi tessellations algorithm to control a diffusion process.The information is shared not only on where to spray but also on how much to spray among the mobile actuators.Benefits from using CVT and information consensus seeking for sensing and control of a diffusion process are demonstrated in simulation results.

Noneuclidean Tessellations and Their Relation to Regge Trajectories

The coefficients in the confluent hypergeometric equation specify the Regge trajectories and the degeneracy of the angular momentum states. Bound states are associated with real angular momenta while resonances are characterized by complex angular momenta. With a centrifugal potential, the half-plane is tessellated by crescents. The addition of an electrostatic potential converts it into a hydrogen atom, and the crescents into triangles which may have complex conjugate angles;the angle through which a rotation takes place is accompanied by a stretching. Rather than studying the properties of the wave functions themselves, we study their symmetry groups. A complex angle indicates that the group contains loxodromic elements. Since the domain of such groups is not the disc, hyperbolic plane geometry cannot be used. Rather, the theory of the isometric circle is adapted since it treats all groups symmetrically. The pairing of circles and their inverses is likened to pairing particles with their antiparticles which then go on to produce nested circles, or a proliferation of particles. A corollary to Laguerre’s theorem, which states that the euclidean angle is represented by a pure imaginary projective invariant, represents the imaginary angle in the form of a real projective invariant.

Modular responsive facade proposals based on semi-regular and demi-regular tessellation:daylighting and visual comfort

Responsive facades can reduce building energy consumption and control daylight and natural ventilation to improve user comfort.This study aims to develop alternative responsive facade systems based on semi-regular and demi-regular tessellations.For this purpose,first,the tessellation method used to generate responsive facades is introduced.Then,the geometric and parametric design principles and the movement capabilities of the proposed facade systems are presented.Finally,a set of analyses are performed to test and compare the performances of the facade systems based on daylight metrics and indoor glare comfort.This study contributes to the literature with the proposed facade systems that can adapt to changing environmental conditions,provide flexibility in shape control and simplicity in mechanism design,and improve building performance.The analysis results show that all the proposed facade systems provide the desired visual comfort and daylight levels at different configurations.

GPU Tessellation全球地形可视化方法

目的目前全球大规模地形可视化问题基本都衍生于分块LOD(level of detail)方法,该方法在快速地表漫游中依然存在GPU-CPU的数据传输瓶颈,其基于裙边的缝隙修复方法既需要额外资源,还存在依然无法完全消除的痕迹。为解决这些问题,提出了一种GPU网格生成的地形可视化方法。方法结合GPU Tessellation方法、基于视点与屏幕空间误差的LOD方法、局部坐标系渲染等算法,使得全球地形可视化的生成效率有明显提高。结果实现了一个全球地形可视化系统GTVS,提供全球高精度地形数据与多分辨率高清卫星影像数据的调度与渲染等。论文对该系统进行了详实的实验和数据分析,相比传统基于GPU的分块LOD方法,FPS(frames per second)提升100%以上,很好地解决了系统瓶颈问题。结论结果表明所提方法实用、鲁棒、扩展性好,可广泛地适用于大规模的全球渲染系统中。

Investigation of stress-induced progressive failure of mine pillars using a Voronoi grain-based breakable block model

The Voronoi grain-based breakable block model(VGBBM)based on the combined finite-discrete element method(FDEM)was proposed to explicitly characterize the failure mechanism and predict the deformation behavior of hard-rock mine pillars.The influence of the microscopic parameters on the macroscopic mechanical behavior was investigated using laboratory-scale models.The field-scale pillar models(width-to-height,W/H=1,2 and 3)were calibrated based on the empirically predicted stress-strain curves of Creighton mine pillars.The results indicated that as the W/H ratios increased,the VGBBM effectively predicted the transition from strain-softening to pseudo-ductile behavior in pillars,and explicitly captured the separated rock slabs and the V-shaped damage zones on both sides of pillars and conjugate shear bands in core zones of pillars.The volumetric strain field revealed significant compressional deformation in core zones of pillars.While the peak strains of W/H=1 and 2 pillars were relatively consistent,there were significant differences in the strain energy storage and release mechanism.W/H was the primary factor influencing the deformation and strain energy in the pillar core.The friction coefficient of the structural plane was also an important factor affecting the pillar strength and the weakest discontinuity angle.The fracture surface was controlled by the discontinuity angle and the friction coefficient.This study demonstrated the capability of the VGBBM in predicting the strengths and deformation behavior of hard-rock pillars in deep mine design.

Relationship between polyhedral structures formed by tangent planes of ellipsoidal particles and system sound velocity

Internal polyhedral structures of a granular system can be investigated using the Voronoi tessellations.This technique has gained increasing recognition in research of kinetic properties of granular flows.For systems with mono-sized spherical particles,Voronoi tessellations can be utilized,while radial Voronoi tessellations are necessary for analyzing systems with multi-sized spherical particles.However,research about polyhedral structures of non-spherical particle systems is limited.We utilize the discrete element method to simulate a system of ellipsoidal particles,defined by the equation(x a)2+(y1)2+(z 1/a)2=1,where a ranges from 1.1 to 2.0.The system is then dissected by using tangent planes at the contact points,and the geometric quantities of the resulting polyhedra in different shaped systems,such as surface area,volume,number of vertices,number of edges,and number of faces,are calculated.Meanwhile,the longitudinal and transverse wave velocities within the system are calculated with the time-of-flight method.The results demonstrate a strong correlation between the sound velocity of the system and the geometry of the dissected polyhedra.The sound velocity of the system increases with the increase in a,peaking at a=1.3,and then decreases as a continues to increase.The average volume,surface area,number of vertices,number of edges,and number of faces of the polyhedra decrease with the increase in sound velocity.That is,these quantities initially decrease with the increase in a,reaching minima at a=1.3,and then increase with further increase of a.The relationship between sound velocity and the geometric quantities of the dissected polyhedra can serve as a reference for acoustic material design.

Adaptive triangular mesh coarsening with centroidal Voronoi tessellations

We present a novel algorithm for adaptive triangular mesh coarsening. The algorithm has two stages. First, the input triangular mesh is refined by iteratively applying the adaptive subdivision operator that performs a so-called red-green split. Second, the refined mesh is simplified by a clustering algorithm based on centroidal Voronoi tessellations (CVTs). The accuracy and good quality of the output triangular mesh are achieved by combining adaptive subdivision and the CVTs technique. Test results showed the mesh coarsening scheme to be robust and effective. Examples are shown that validate the method.

Convergent Adaptive Finite Element Method Based on Centroidal Voronoi Tessellations and Superconvergence

We present a novel adaptive finite element method(AFEM)for elliptic equations which is based upon the Centroidal Voronoi Tessellation(CVT)and superconvergent gradient recovery.The constructions of CVT and its dual Centroidal Voronoi Delaunay Triangulation(CVDT)are facilitated by a localized Lloyd iteration to produce almost equilateral two dimensional meshes.Working with finite element solutions on such high quality triangulations,superconvergent recovery methods become particularly effective so that asymptotically exact a posteriori error estimations can be obtained.Through a seamless integration of these techniques,a convergent adaptive procedure is developed.As demonstrated by the numerical examples,the new AFEM is capable of solving a variety of model problems and has great potential in practical applications.

一种基于GPU Tessellation的地形渲染方法

为了在大规模地形实时渲染过程中提高渲染效率和得到更平滑逼真的地形,该文提出了一种基于GPU Tessellation技术的地形可视化方法。该方法首先对地形预处理构建四叉树;使用视锥体裁剪和LOD选择降低CPU-GPU数据传输量;在三角化阶段利用GPU代替传统的CPU进行三角化方法极大地减轻CPU的负担并且提高了渲染速率;同时引入地形粗糙度计算GPU Tessellation算法内部细分因子,达到平滑而又不失细节的地形表面渲染效果;以数据细节层次动态设置GPU Tessellation算法的外部细分因子消除了T型裂缝。实验结果表明,该方法CPU利用率低,能够以较小计算代价消除T型裂缝,在地形实时交互式漫游系统中能以较高的渲染帧率输出平滑、逼真的三维虚拟数字地形。该文方法可运用到大规模地形可视化系统中。

Tessellations in GIS:Part I—putting it all together

This article attempts to describe the role of tessellated models of space within the discipline of geographic information systems(GIS)—a speciality coming largely out of geography and land surveying,where there was a strong need to represent information about the land’s surface within a computer system rather than on the original paper maps.We look at some of the basic operations in GIS,including dynamic and kinetic applications.We examine issues of topology and data structures and produce a tessellation model that may be widely applied both to traditional“object”and“field”data types.Based on this framework,it can be argued that tessellation models are fundamental to our understanding and processing of geographical space,and provide a coherent framework for understanding the“space”in which we exist.This first article examines static structures,and a subsequent article looks at“change”—what happens when things move.

An address regional tessellation method for spatial subdivision and geocoding in digital earth system

With the increased use of locational information,spatial location referencing and coding methods have become much more important to the mining of both geographical and nongeographical data in digital earth system.Unfortunately,current methods of geocoding,based on reverse lookup of coordinates for a given address,have proven too lossy with respect to administrative and socioeconomic data.This paper proposes a spatial subdivision and geocoding model based on spatial address regional tessellation(SART).Given a hierarchical address object definition,and based on the‘region of influence’characteristics of an address,SART creates multiresolution spatial subdivisions by irregular and continuous address regions.This model reflects most of the geographical features and many of the social and economic implications for a given address.It also better reflects the way people understand addresses and spatial locations.We also propose an appropriate method of geocoding for standard addresses(SART-GC).The codes generated by this method can record address footprints,hierarchical relationships,and spatial scales in a single data structure.Finally,by applying our methods to the Shibei District of Qingdao,we demonstrate the suitability of SART-GC for multi-scale spatial information representation in digital earth systems.