Grid Vertices Research Articles

Optimizing radiation exposure in dynamic radioactive environments: Dynamic ACO-RRT* path planning algorithm

Abstract Radioactive environments are often dynamic for various reasons, such as the dismantling of nuclear facilities, leakage of radiation sources, and nuclear accidents. Path planning in a dynamic radioactive environment is one of the important issues in radiation protection for nuclear facility workers. In traditional dynamic optimal path planning, there are phenomena, in which the optimal path is not found within the allowable time or the quality of the path searched within the allowable time is low. To solve this problem, we propose a hybrid algorithm that combines meta-heuristic and sample-based algorithms, called dynamic ant colony optimization-rapidly exploring random tree star (ACO-RRT*). A low-level grid optimal path consisting of grid vertices is obtained by the ACO algorithm, and then it is further refined by the RRT* algorithm. At every instant of environmental change, the vertices of the grid optimal path are divided into vertices with and without samples, and new samples are generated only around vertices without samples. Sampling optimization is performed only around the grid optimal path using new samples and already existing samples. Simulations in a virtual radioactive environment showed that the proposed algorithm reduces computational costs and improves the quality of the optimal path compared to traditional algorithms.

Inverse distance weighting to rapidly generate large simulation datasets

Obtaining large biomechanical datasets for machine learning is an ongoing challenge. Physics-based simulations offer one approach for generating large datasets, but many simulation methods, such as computed muscle control (CMC), are computationally costly. In contrast, interpolation methods, such as inverse distance weighting (IDW), are computationally fast. We examined whether IDW is a low-cost and accurate approach for interpolating muscle activations from CMC.IDW was evaluated using lateral pinch simulations in OpenSim. Simulated pinch data were organized into grids of varying sparsity (high, medium, and low density), where each grid point represented the muscle activations associated with a unique combination of mass and height of a young adult. For each grid, muscle activations were calculated via CMC and IDW for 108 random mass-height pairs that were not coincident with simulation grid vertices. We evaluated the interpolation errors from IDW for each grid, as well as the sensitivity of lateral pinch force to these errors. The root mean square error (RMSE) associated with interpolated muscle activations decreased with increasing grid density and never exceeded 4%. While CMC received a target thumb-tip force of 40 N, errors from the interpolated muscle activations never impacted the simulated force magnitude by more than 0.1 N. Furthermore, the computation time for CMC simulations averaged 4.22 core-minutes, while IDW averaged 0.95 core-seconds per mass-height pair.These results indicate IDW is a practical approach for rapidly estimating muscle activations from sparse CMC datasets. Future works could adapt our IDW approach to evaluate other tasks, biomechanical features, and/or populations.

Thalweg and Ridge Network Extraction From Unaltered Topographic Data as a Basis for Terrain Partitioning

AbstractHigh‐resolution grid digital elevation models (DEMs) are increasingly used by scientists and engineers to describe the current state and evolution of Earth and planetary topography. These data, however, are commonly altered by depression filling and grid coarsening procedures. Alteration of observed topographic data may cause significant information loss and limit the capabilities of models. This study shows that physically meaningful thalweg and ridge networks can be extracted automatically from any unaltered high‐resolution grid DEM, and that these networks can be used as bases for terrain partitioning. The slopeline network connecting grid cell centers is used to identify ridge points as those grid cell border midpoints and vertices that are not crossed by slopelines. From each ridge point, the average length of the two slopelines extending on the opposite slopes of the ridge until they rejoin is then computed. Based on these lengths, exorheic and endorheic basins are identified. Thalwegs of exorheic and endorheic basins are finally connected through spilling saddles to form the thalweg network. The related ridge network is identified based on neighboring relationships between ridge points. Thalweg and ridge networks are hierarchized using the well‐known concept of drainage area and an extended concept of dispersal area to inform terrain partitioning at any level of detail. Observed topographic features are well reproduced by extracted networks. The impact of preserving depressions over mountain areas is evaluated, and the benefits from unstructured terrain partitioning based on thalweg and ridge networks in the description of flood plain inundation are illustrated.

An improved adaptive triangular mesh-based image warping method.

It is of vital importance to stitch the two images into a panorama in many computer vision applications of motion detection and tracking and virtual reality, panoramic photography, and virtual tours. To preserve more local details and with few artifacts in panoramas, this article presents an improved mesh-based joint optimization image stitching model. Since the uniform vertices are usually used in mesh-based warps, we consider the matched feature points and uniform points as grid vertices to strengthen constraints on deformed vertices. Simultaneously, we define an improved energy function and add a color similarity term to perform the alignment. In addition to good alignment and minimal local distortion, a regularization parameter strategy of combining our method with an as-projective-as-possible (APAP) warp is introduced. Then, controlling the proportion of each part by calculating the distance between the vertex and the nearest matched feature point to the vertex. This ensures a more natural stitching effect in non-overlapping areas. A comprehensive evaluation shows that the proposed method achieves more accurate image stitching, with significantly reduced ghosting effects in the overlapping regions and more natural results in the other areas. The comparative experiments demonstrate that the proposed method outperforms the state-of-the-art image stitching warps and achieves higher precision panorama stitching and less distortion in the overlapping. The proposed algorithm illustrates great application potential in image stitching, which can achieve higher precision panoramic image stitching.

A Non-Rigid Hierarchical Discrete Grid Structure and Its Application to UAVs Conflict Detection and Path Planning

<p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Following the development of the unmanned aerial vehicle (UAV) industry, the number of UAVs has increased significantly, and higher expectations regarding the effect of spatial path planning have been expressed. Traditional coordinate-based conflict detection and path planning methods of UAVs are highly complex and have low computational efficiency. While the conflict detection method based on the grid system can improve efficiency, the rigid grid structure of the existing local grid system or discrete global grid system is insufficient. Since the rigid structure only encodes grid cells, multiple or different size grids are required to identify UAVs in motion, further complicating path planning. The main contributions of this article are as follows. First, we proposed a nonrigid hierarchical discrete grid structure and coding method for spatial three-dimensional grids and grid data model. This method can accomplish the aggregation of any adjacent eight grids to form multiple nonrigid structures, making the original fixed relationship between parent and child grids more flexible. Second, the nonrigid grid structure optimizes the identification ability of grid vertices, grid edges, and grid faces. It has eight times the identification ability of the rigid grid structure. We exploited this structure for UAV identification with the same size grid at any position of the grid structure. Third, based on the nonrigid grid structure, an improved UAV conflict detection method and path planning method are designed. Experimental results indicate that, on an average, the efficiency of the improved conflict detection is an order of magnitude higher than that of the traditional computational detection method. The improved path planning method reduces the path length by an average of 11% compared to the single-grid planning method, and is 3.85 times more efficient than the multi-grid buffer planning method.

A point cloud deep neural network metamodel method for aerodynamic prediction

Aiming to reduce the high expense of 3-Dimensional (3D) aerodynamics numerical simulations and overcome the limitations of the traditional parametric learning methods, a point cloud deep learning non-parametric metamodel method is proposed in this paper. The 3D geometric data, corresponding to the object boundaries, are chosen as point clouds and a deep learning neural network metamodel fed by the point clouds is further established based on the PointNet architecture. This network can learn an end-to-end mapping between spatial positions of the object surface and CFD numerical quantities. With the proposed aerodynamic metamodel approach, the point clouds are constructed by collecting the coordinates of grid vertices on the object surface in a CFD domain, which can maintain the boundary smoothness and allow the network to detect small changes between geometries. Moreover, the point clouds are easily accessible from 3D sensors. The point cloud deep learning neural network, which employs re-sampling technique, the spatial transformer network and the fully connected layer, is developed to predict the aerodynamic characteristics of 3D geometry. The effectiveness of the proposed metamodel method is further verified by aerodynamic prediction and robust shape optimization of the ONERA M6 wing. The results show that the proposed method can achieve more satisfactory agreement with the experimental measurements compared to the parametric-learning-based deep neural network.

Object extraction from image with big size based on bilateral grid

Currently image with big size segmentation suffers from low efficiency and inaccurate results, in this paper a novel object extraction approach from image with big size based on the application of a bilateral grid is proposed. Firstly, the bilateral grid is constructed according to the spatial ratio and color sampling ratios, which are determined by both image size and color range. Then, the big image data is splatted into the bilateral grid, the sampled data among the grid vertices are assigned by the nearest vertex data, and all grid vertices are assigned the object label via random forest classification. Finally, the segmentation is reconstructed from the grid data by interpolation. Experiment results show that the proposed algorithm could effectively improve the big image segmentation efficiency, and achieve the better segmentation results than state-of-the-art methods.

Arbitrary pattern formation on infinite regular tessellation graphs

Given a set R of robots, each one located at a different vertex of an infinite regular tessellation graph, we aim to explore the Arbitrary Pattern Formation (APF) problem. Given a multiset F of grid vertices such that |R|=|F|, APF asks for a distributed algorithm that moves robots so as to reach a configuration similar to F. Similarity means that robots must be disposed as F regardless of translations, rotations, reflections.So far, as possible graph discretizing the Euclidean plane only the standard square grid has been considered in the context of the classical OBLOT model. However, it is natural to consider also the other regular tessellation graphs, that are triangular and hexagonal grids. In particular, the former can be considered as the most general in terms of possible symmetries and trajectories.We provide a resolution algorithm for APF when the initial configuration is asymmetric and the considered topology is any regular tessellation graph. The algorithm and its correctness are based on a rigorous methodology.

Error-Correcting Neural Networks for Two-Dimensional Curvature Computation in the Level-set Method

We present an error-neural-modeling-based strategy for approximating two-dimensional curvature in the level-set method. Our main contribution is a redesigned hybrid solver [Larios-C\'ardenas and Gibou, J. Comput. Phys. (May 2022), 10.1016/j.jcp.2022.111291] that relies on numerical schemes to enable machine-learning operations on demand. In particular, our routine features double predicting to harness curvature symmetry invariance in favor of precision and stability. The core of this solver is a multilayer perceptron trained on circular- and sinusoidal-interface samples. Its role is to quantify the error in numerical curvature approximations and emit corrected estimates for select grid vertices along the free boundary. These corrections arise in response to preprocessed context level-set, curvature, and gradient data. To promote neural capacity, we have adopted sample negative-curvature normalization, reorientation, and reflection-based augmentation. In the same manner, our system incorporates dimensionality reduction, well-balancedness, and regularization to minimize outlying effects. Our training approach is likewise scalable across mesh sizes. For this purpose, we have introduced dimensionless parametrization and probabilistic subsampling during data production. Together, all these elements have improved the accuracy and efficiency of curvature calculations around under-resolved regions. In most experiments, our strategy has outperformed the numerical baseline at twice the number of redistancing steps while requiring only a fraction of the cost.

Optimizing Anchor Node Deployment for Fingerprint Localization With Low-Cost and Coarse-Grained Communication Chips

A part of off-the-shelf wireless communication chips can only provide very coarse-grained information of the distance range between the transmitter and receiver. Exploiting such chips for precise wireless indoor positioning (WIP) becomes very valuable since their costs are comparatively low. For the WIP systems built on the coarse-grained communication chips, this article discusses the optimal anchor node deployment problem for fingerprint localization. The problem is very challenging since it implies three particularly important requirements of adaptive localization precision, unique fingerprint, and a minimum number of anchor nodes. To minimize the required number of anchor nodes while satisfying the three requirements, we propose two anchor node deployment algorithms, namely, ANDAs and WANDA, both of which are developed for mediate and large-area deployment, respectively. We first prove the effectiveness of the chip in maintaining robust fingerprints and formulate the deployment optimization problem as a minimum attribute reduction problem. Then, to deal with the high computational complexity involved, ANDA is proposed by significantly reducing the search space of the optimization problem. To practically address the combination explosion problem for large-area deployment, the idea of area partitioning is adopted. Investigating anchor nodes at different grid vertices in subareas that may have different sharing degrees, WANDA is proposed to achieve an overall anchor node deployment optimization. Simulation and experimental results demonstrate the validity and the superiority of ANDA and WANDA over counterparts. For large-area deployment, compared to ANDA, WANDA can further decrease the total amount of anchor nodes by 17%.

Integrated graph deep learning framework for flow field reconstruction and performance prediction of turbomachinery

The performance and reliability of turbomachinery directly affect the efficiency and safety of energy conversion systems. A dual graph neural network (DGNN) for turbomachinery flow field reconstruction and performance prediction is proposed, which utilizes flow field data at grid vertices and characterizes the neighborhood relationships of grids through the adjacency matrix. Different from previous work, this work extends deep learning methods to the reconstruction of global turbomachinery fields defined on arbitrary structured/unstructured grids. The flow field reconstruction and performance prediction of low aspect ratio rotors are used to verify the generalizability of DGNN. The proposed method can not only accurately predict performance parameters, but also achieve excellent performance in flow field reconstruction. The superiority of DGNN over the artificial neural network (ANN) in flow field reconstruction is clarified. The optimal GNN operator with the highest accuracy and lowest computation costs is obtained as SAGE. A well-trained DGNN can give the flow field distribution as well as the performance of turbines within 0.05 s. The proposed approach could be a real-time simulation and analysis approach to assist turbomachinery design and optimization. It may provide an efficient solution for establishing the digital twin system of turbomachinery in the future.

Improvement of unresolved CFD-DEM by velocity field reconstruction on unstructured grids

For conventional unresolved CFD-DEM, the accurate Lagrangian tracking of the dispersed particles requires the interpolation of cell-centered fluid velocity to the particle position instead of equally treating every particle in the same cell. However, the interpolation on unstructured grids and the systematic investigations about the influence of interpolation on the simulation results are rarely reported. This study adopted gradient-based interpolation to reconstruct the velocity field on unstructured grids considering efficiency and precision. Three gradient limit strategies were introduced into the unresolved CFD-DEM to constrain the gradient determined by the weighted least-square method because gradient-based interpolation may bring about unwanted extrema that will distort the results. The influence of gradient-based interpolation, as well as three gradient limit strategies on the simulation results, were estimated by comparing the simulation results with experimental measurements in a spouted bed with a conical base. The bubble behaviors demonstrated that the reconstruction of the velocity field was of crucial significance to the improvement of unresolved CFD-DEM. Besides, the pressure drops of experiments coincided with that of simulations except for the case using the limit strategy that constrained the extrema at face centroids. Considering the bubble behaviors and pressure drops, the limit strategy that constrained the extrema at grid vertices was the most recommended.

DUT: Learning Video Stabilization by Simply Watching Unstable Videos.

Previous deep learning-based video stabilizers require a large scale of paired unstable and stable videos for training, which are difficult to collect. Traditional trajectory-based stabilizers, on the other hand, divide the task into several sub-tasks and tackle them subsequently, which are fragile in textureless and occluded regions regarding the usage of hand-crafted features. In this paper, we attempt to tackle the video stabilization problem in a deep unsupervised learning manner, which borrows the divide-and-conquer idea from traditional stabilizers while leveraging the representation power of DNNs to handle the challenges in real-world scenarios. Technically, DUT is composed of a trajectory estimation stage and a trajectory smoothing stage. In the trajectory estimation stage, we first estimate the motion of keypoints, initialize and refine the motion of grids via a novel multi-homography estimation strategy and a motion refinement network, respectively, and get the grid-based trajectories via temporal association. In the trajectory smoothing stage, we devise a novel network to predict dynamic smoothing kernels for trajectory smoothing, which can well adapt to trajectories with different dynamic patterns. We exploit the spatial and temporal coherence of keypoints and grid vertices to formulate the training objectives, resulting in an unsupervised training scheme. Experiment results on public benchmarks show that DUT outperforms state-of-the-art methods both qualitatively and quantitatively. The source code is available at https://github.com/Annbless/DUTCode.

Pose error compensation based on joint space division for 6-DOF robot manipulators

This paper introduces a pose error compensation method performed in joint space to improve both position and orientation accuracy of industrial robots. Joint space division is proposed to achieve dimension reduction to reduce the workload of pose error sampling. The six-dimensional joint space is divided into two three-dimensional subspaces by the wrist center. Each subspace is discretized by a sequence of grid elements of which grid vertices are considered as sample points. Based on point set registration, two spatial databases of pose errors are built in the two subspaces respectively using a laser tracker. For a given robot posture, the pose errors generated in the two subspaces can be separately estimated using spatial interpolation based on inverse distance weighting algorithm. Formed by the estimated values, two transformation error matrices are introduced to compensate for the pose errors of the two subspaces. A Comau NJ370–3.0 manipulator was employed as an experimental platform to evaluate the effectiveness of the proposed method. Experimental results demonstrated the maximum position error was reduced by 96.06% to below 0.334 mm, and the maximum orientation errors have decreased to below 0.027° after compensation was performed.

Digital and automatic design of free-form single-layer grid structures

Grid shells have been widely used in various long-span public buildings, and many of them are defined over free-form surfaces with complex boundaries. This emphasizes the importance of general and digitalised grid generation and optimization methods in the initial design stage to achieve visually sound grid shells. In this paper, a framework is presented for the development of a digital tool and to generate regular and fluent grids for structural design over free-form surfaces, especially those with complex boundaries. Both triangular and quadrilateral grid generation are addressed. To generate regular and fluent grids for free-form surfaces, a simple yet practical framework is proposed based on a spring-mass model. Firstly, an initial casual quadrilateral grid is tiled on the surface based on surface discretization and mesh parameterization. Secondly, the distribution of the initial grid vertices is adjusted by a dynamic relaxation procedure, assuming the grid as a spring-mass system. Thirdly, the grid vertices corresponding to the adjusted particles in the equilibrium state are then reconnected to produce a grid with a predefined pattern (triangular or quadrilateral). Finally, the generated grid is relaxed with the spring-mass model, alongside additional geometric operations including grid size adjustment and filtering techniques, to further improve the grid regularity and fluency. As part of its contribution, this paper also broadens the application scope of the fluency index, which can be used to quantitatively evaluate the suitability of a given triangular or quadrilateral grid for architectural and structural expression. Examples are presented and show that the proposed framework is effective for the triangular and quadrilateral grid generation over various surfaces and to optimize the resulted grids along complex boundaries. The method proposed can be useful for rapid design and performance evaluation of free-form grid structures.

A point-cloud deep learning framework for prediction of fluid flow fields on irregular geometries

We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics (CFD) domain are viewed as point clouds and used as inputs to a neural network based on the PointNet architecture, which learns an end-to-end mapping between spatial positions and CFD quantities. Using our approach, (i) the network inherits desirable features of unstructured meshes (e.g., fine and coarse point spacing near the object surface and in the far field, respectively), which minimizes network training cost; (ii) object geometry is accurately represented through vertices located on object boundaries, which maintains boundary smoothness and allows the network to detect small changes between geometries and (iii) no data interpolation is utilized for creating training data; thus accuracy of the CFD data is preserved. None of these features are achievable by extant methods based on projecting scattered CFD data into Cartesian grids and then using regular convolutional neural networks. Incompressible laminar steady flow past a cylinder with various shapes for its cross section is considered. The mass and momentum of predicted fields are conserved. We test the generalizability of our network by predicting the flow around multiple objects as well as an airfoil, even though only single objects and no airfoils are observed during training. The network predicts the flow fields hundreds of times faster than our conventional CFD solver, while maintaining excellent to reasonable accuracy.

A high-order vertex-centered quasi-Lagrangian discontinuous Galerkin method for compressible Euler equations in two-dimensions

This article introduces a new vertex-centered quasi-Lagrangian discontinuous Galerkin method for two-dimensional compressible flows that is third-order accurate both in space and time. The computational domain is divided into structured quadrilateral cells with straight edges. Nodal control volumes with curved edges are constructed surrounding the grid vertices. The Euler equations in arbitrary Lagrangian-Eulerian (ALE) form are discretized on these nodal control volumes using a discontinuous Galerkin method. The time marching is implemented by the third-order strong-stability-preserving Runge-Kutta method. A compact HWENO reconstruction algorithm is used as limiter to eliminate spurious oscillations near discontinuities. The polynomial expression of fluid velocity defined in a nodal control volume is also obtained from the reconstruction procedure, and is used to calculate the moving velocity of corresponding grid vertex. In this way, the grid vertices are moved in a rigorously Lagrangian manner, although there are still mass fluxes between neighbouring nodal control volumes. Therefore the scheme is called as a quasi-Lagrangian one. The scheme is conservative for mass, momentum and total energy. Some numerical tests are carried out to demonstrate the accuracy and robustness of the scheme. It has a favorable qualitative behavior for discontinuous problems and optimal convergence rates for smooth problems.

Dynamically Optimized Unstructured Grid (DOUG) for Analog Ensemble of numerical weather predictions using evolutionary algorithms

The Analog Ensemble is a statistical technique that generates probabilistic forecasts using a current deterministic prediction, a set of historical predictions, and the associated observations. It generates ensemble forecasts by first identifying the most similar past predictions to the current one, and then summarizing the corresponding observations. This is a computationally efficient solution for ensemble modeling because it does not require multiple numerical weather prediction simulations, but a single model realization.Despite this intrinsic computational efficiency, the required computation can grow very large because atmospheric models are routinely run with increasing resolutions. For example, the North American Mesoscale forecast system contains over 262 792 grid points to generate a 12 km prediction. The North American Mesoscale model generally uses a structured grid to represent the domain, despite the fact that certain physical changes occur non-uniformly across space and time. For example, temperature changes tend to occur more rapidly in mountains than plains.An evolutionary algorithm is proposed to dynamically and automatically learn the optimal unstructured grid pattern. This iterative evolutionary algorithm is guided by Darwinian evolutionary rule generation and instantiation to identify grid vertices. Analog computations are performed only at vertices. Therefore, minimizing the number of vertices and identifying their locations are paramount to optimizing the available computational resources, minimizing queue time, and ultimately achieving better results. The optimal unstructured grid is then reused to guide the predictions for a variety of applications like temperature and wind speed.

Research on 3D Human Body Deformation Based on BiharmonicWeights and Skeleton Skin

A new 3D human body deformation algorithm based on bounded biharmonic weights and skeleton skinning algorithm is proposed to improve the defects in traditional Laplace algorithm and contour-driven algorithm, such as the detail distortion and the topological structure change in 3D human body deformation. The deformation is a process from local to global. Firstly, the standard human model is bound to the annular skeleton, and then the local mesh deformation is implemented on the standard human body model based on the bounded biharmonic weights, and then we use the 3D human body proportion measured before to adjusts the position of the skeleton point, finally the 3D human mesh model can be quickly edited with the effect of the skeleton skinning algorithm. The experimental shows that the algorithm can not only maintain the topological structure of the local grid effectively, but also achieve faster 3D model mesh editing compared with directly working on all grid vertices.

Probabilistic Asymptotic Decider for Topological Ambiguity Resolution in Level-Set Extraction for Uncertain 2D Data.

We present a framework for the analysis of uncertainty in isocontour extraction. The marching squares (MS) algorithm for isocontour reconstruction generates a linear topology that is consistent with hyperbolic curves of a piecewise bilinear interpolation. The saddle points of the bilinear interpolant cause topological ambiguity in isocontour extraction. The midpoint decider and the asymptotic decider are well-known mathematical techniques for resolving topological ambiguities. The latter technique investigates the data values at the cell saddle points for ambiguity resolution. The uncertainty in data, however, leads to uncertainty in underlying bilinear interpolation functions for the MS algorithm, and hence, their saddle points. In our work, we study the behavior of the asymptotic decider when data at grid vertices is uncertain. First, we derive closed-form distributions characterizing variations in the saddle point values for uncertain bilinear interpolants. The derivation assumes uniform and nonparametric noise models, and it exploits the concept of ratio distribution for analytic formulations. Next, the probabilistic asymptotic decider is devised for ambiguity resolution in uncertain data using distributions of the saddle point values derived in the first step. Finally, the confidence in probabilistic topological decisions is visualized using a colormapping technique. We demonstrate the higher accuracy and stability of the probabilistic asymptotic decider in uncertain data with regard to existing decision frameworks, such as deciders in the mean field and the probabilistic midpoint decider, through the isocontour visualization of synthetic and real datasets.