Natural Neighbor Interpolation Method Research Articles

ROTI maps of Greenland using kriging

Abstract GNSS satellite signals are affected by the media when traversing Earth’s atmosphere, and the performance of GNSS based positioning and navigation is correlated with these effects. In the ionosphere, the signals are affected by the number of electrons along the signal path which can be quantified by the total electron content. The focus of this article is scintillation effects caused by electrons in the Arctic ionosphere, and the rate of the total electron content index, the ROTI, is used as a measure of the scintillation. Data from permanent GNSS reference stations in Greenland is used to generate maps of the ROTI in Greenland, and the novelty of the work in this paper is the application of the ordinary kriging method as the basis for ROTI maps in the Arctic. Further, the choice of satellite constellations as well as the elevation mask used in the data analyses are analyzed and discussed. Also, the performance of using ordinary kriging for ROTI maps during times with both a low and a very high geomagnetic activity are discussed. The results show that ordinary kriging performs well during high geomagnetic activity, while during low activity the natural neighbor interpolation method is a better choice for the Arctic.

Sand barrier morphological evolution based on time series remote sensing images: a case study of Anhaiao, Pingtan

The morphological evolution of the sand barrier in the Anhaiao coastal zone of Pingtan from 1996 to 2018 was studied. Tidal correction was used to refine the location of the coastline. A standard deviation ellipse method was applied to further analyze the movement of the barrier head with the axis and rotation angle. A natural neighbor interpolation (NNI) method was carried out to calculate the terrain of the intertidal area, and the erosion and deposition characteristics were illustrated based on the terrain. The results showed that the northern part of the sand barrier facing the lagoon area was deposited over the whole studied period, while erosion has always occurred in the southern part of the sand barrier facing the open sea. The erosion and deposition were slightly different on both sides of the barrier head due to hydrodynamic turbulence. The middle sand barrier moved 102.60 m away from its original location in 1996, and the end of the barrier moved 65.45 m. The head of the sand barrier continued moving 379 m to the northwest. Consequently, the preliminary morphological evolution of the sand barrier corresponding to the distance and direction of movement was detected.

Turbulence-preserving interpolation of aero-optical wavefront data using radial basis functions: application and fractal analysis

Spatial interpolation using radial basis functions (RBFs) is compared with standard natural neighbor interpolation for the purpose of populating dead zones in optical path difference (OPD) wavefront data collected through aero-optics turbulence. Both methods, and some other commonly used basis functions, are described in detail. These candidates are applied to experimental subscale turbulent wind tunnel data collected with a conformal window hemispherical turret over a range of turret look-back angles spanning 60 deg to 135 deg. Interpolation performance is evaluated using both OPD magnitude and fractal (Hurst exponent) analysis. Interpolating aero-optical OPDs using the thin-plate RBF reduces the symmetric mean absolute percent error of the OPD magnitude and the Hurst exponent by an average of 28% and 50%, respectively, compared with the natural neighbor interpolation method. The improved interpolation accuracy should likewise increase the quality of subsequent postprocessing analysis requiring uniformly populated rectangular regions as inputs, such as optical flow algorithms. A MATLAB implementation of the pseudocubic spline RBF is provided.

A three-dimensional stratigraphic model of the Mississippi River Delta, USA: implications for river deltaic hydrogeology

A three-dimensional stratigraphic model was constructed of the upper 50 m of the Mississippi River Delta, southeastern USA. The model is used to understand hydrogeological connections among the Mississippi River, adjacent interdistributary bays and groundwater systems, and to understand how stratigraphic settings affect potential anthropically induced subsidence and erosion in the region. This study uses 619 geotechnical borings throughout the area along with the multiple-indicator natural neighbor (MINN) interpolation method to construct the model. Based on available data, the study focused on the Mississippi River reach from Head of Passes (river mouth) to Jesuit Bend (108 km upstream), covering an area of approximately 1,800 km2 and ranging in elevation from 3 to −46 m. The model shows typical basal coarse-grained sand bodies overlain by 10-m-thick blanket clay, which is interbedded frequently with silty and sandy sediments and occasionally with peat and organic clay. Sands are most abundant between elevations −10 and −35 m. The Mississippi River main channel incises the underlying sands, thereby providing pathways for river–groundwater exchange. Increased hydrologic loads may propagate along the flow paths potentially giving rise to high pore-water pressure and a resultant increase in land subsidence and thus local erosion of natural and local flood-control levees. This method of analysis may apply to other deltaic regions similarly subject to anthropically accelerated subsidence and erosion.

HUBUNGAN SPASIAL TRANSAKSI TANAH DENGAN PERKEMBANGAN WILAYAH DI KABUPATEN CIREBON, JAWA BARAT

The big potential of Cirebon Regency with good transportation access and demography bonus is able to promote its regional development. Not all of the potential has been optimized to invite investment in Cirebon Regency. One of the causes is some of the lands haven't been registered, so that obstructs investment that requires land. We explore the spatial relationship between the regional development level and land transaction pattern. We calculate the entropy diversification index to see the level of regional development. We also interpolate the land transaction to see the spatial pattern. The natural neighbor interpolation method was used to show spatial patterns of land transactions. Then, we overlay the map of the entropy index and land transaction pattern map to see the relationship spatially. Land transactions in Cirebon Regency gathered in a very developed and developing region. Districts of Palimanan, Depok, Plumbon, Weru, and Plered that are categorized very developed have more quantity of transactions and land transaction value than the undeveloped area. Pasaleman district has Kecamatan Depok, has the smallest entropy index, and categorized as undeveloped has a lower number and value of land transactions. We found a similar spatial pattern between the regional level of development and land transaction interpolation.

Research on shallow sea multiple ocean bottom seismometer positioning with GNSS/acoustic technique and echo sounder

Abstract: The Global Navigation Satellite System (GNSS) combined with acoustic technique has achieved significant economic benefits in oil exploration. During positioning of ocean bottom seismometers, hundreds of underwater transponders attached to seismometers are typically deployed. In order to improve the positioning accuracy of multi-sensor in shallow water, this paper analyses the ship GNSS data, Long baseline system (LBL) and single-beam bathymetric data, and presents the solution method of multi-target underwater acoustic positioning in shallow water with the depth constraints. Combined with the Natural Neighbor Interpolation (NNI) method, the regional elevation model is constructed, and the transponders elevation interpolation is performed in the horizontal position of robust estimation solution. According to the symmetry observation and the smooth terrain of the construction sea area, the bending error of the sound line is further eliminated by using the new piecewise incident model of the sound line bending to improve the plane positioning accuracy of the multi-target underwater in shallow water. Experiments in the South China Sea show that the new method model is more stable, has better anti-gross error performance, and effectively improves the accuracy of positioning under the condition of inaccurate sound velocity measurements and more gross errors of observation data.

Mass balance analysis and calculation of wind effects on heat fluxes and water temperature in a large lake

Abstract Modeling applications often ignore the water mass balance for hydrodynamic simulations in large lakes such as the Great Lakes. However, evaluation of the water budget can be of interest, especially when water surface calculations are important, and also as it relates to the heat budget. In this study Lake Ontario is modeled using the Environmental Fluid Dynamics Code for the heating seasons in 2008–2013, with calibration focused on 2008, for which more data are available. The model is used to test both water mass and heat budgets, and various interpolation schemes for meteorological data are tested to determine the degree of sensitivity of results to the interpolation method used. The water budget incorporates flow from major tributaries and precipitation/evaporation, and it is shown that these processes alone cannot provide a balance. Missing water quantities include direct runoff and flows from smaller, probably ungauged tributaries. In 2008 the calculated quantity is 1.61 × 1010 m3 during April to September, which is equivalent to a change in water surface level of 0.7 m and represents an average flow rate of 1018 m3/s, which is larger than the inflow of any tributary to the lake except the Niagara River. Latent and sensible heat flux calculations are highly affected by wind, and interpolation of wind data is found to impact model calculations of those quantities, though different interpolation schemes do not have a strong effect on surface water temperatures. In general, the natural neighbor interpolation method is preferred over inverse distance methods.

Comparison of Inverse Distance Weighted and Natural Neighbor Interpolation Method at Air Temperature Data in Malang Region

The purpose of this study was to compare the results of Inverse Distance Weighted (IDW) and Natural Neighbor interpolation methods for spatial data of air temperature in the Malang Region. Interpolation is one way to determine a point of events from several points around the known value. Spatial interpolation can be used to estimate an area that does not have a data record using the value of its known surroundings. 38 points observation air temperature of Malang Region in 2016 is used as a sample point to interpolate the surrounding air temperature. Obtained optimum parameter power value is 2 for IDW interpolation method. The RMSE comparison results show that IDW method is better to be used than the Natural Neighbor Interpolation method with the RMSE values of 1,2292 for the IDW method and 1,6173 for the NN method.

Modeling of magneto–electro-elastic problems by a meshless local natural neighbor interpolation method

This paper presents a novel numerical procedure based on the meshless local natural neighbor interpolation (MLNNI) method for modeling two-dimensional magneto–electro-elastic solids. As a special case of the generalized meshless local Petrov–Galerkin (MLPG) method, the MLNNI method satisfies the weak form equations locally in polygonal sub-domains which surround each node. The natural neighbor interpolation is used to approximate the unknown fields in numerical simulations and thus only a set of scattered nodes are utilized to represent the problem domain. The usage of three-node triangular FEM shape functions as test functions results in the reduction of the order of integrands in domain integrals. As the constructed shape functions possess a point interpolation property, the essential boundary conditions can be imposed directly without the need of introducing special techniques. Numerical examples for magneto–electro-elastic problems are presented to demonstrate the solutions of the present MLNNI method with other available solutions.

Quasi-interpolation scheme for arbitrary dimensional scattered data approximation based on natural neighbors and RBF interpolation

A local quasi interpolation scheme is presented in the paper, which can be applied to arbitrary dimensional scattered data approximation with high accuracy, high efficiency and high stability. Under our new quasi-interpolation scheme, we treat the natural neighbor set of the point to be estimated in a given scattered node set as a local interpolation node set. Based on the local node set, a local radial basis function interpolation with algebraic precision of any degree is constructed through a modified Taylor expansion of sampled function at each natural neighbor to compute approximate values. Given the exclusion of the point to be estimated from its natural neighbor set, i.e. interpolation node set, the interpolation scheme we construct is a local quasi-interpolation scheme, and its approximation error is given. The numerical experimental results show that, when the derivative information is unavailable, our method outperforms the famous natural neighbor interpolation method in both approximation accuracy and efficiency. As algebraic precision increases, the approximation accuracy can be further improved.

Research on Natural Element Method and the application to simulate metal forming processes

Abstract Due to the special characteristics of metal forming processes (i.e., large deformations, complex nonlinear, etc.), finite element method (FEM) often encounters the mesh distortion problem in simulating large and severe deformation metal forming processes. Once meshes become severely distorted, the whole simulation process cannot be continued unless the remeshing is used. Nevertheless, remeshing usually leads to not only the deterioration of computational precision but also the increase of time-consuming. To solve the problem, a meshless method known as natural element method (NEM) is introduced to analyze metal forming processes in the paper. The shape function of NEM is constructed by employing the natural neighbor interpolation method, and it has the high accuracy of the approximation. In addition, because the shape function possesses the Kronecker δ property like the FEM, the essential boundary conditions can be imposed directly. Therefore, the paper combines NEM with rigid/visco-plastic flow theory and applies it to simulate metal forming processes. Furthermore, a numerical analysis procedure is developed. A numerical example of metal forming processes is analyzed. The validity of the numerical simulation program is evaluated by comparing simulation results with those obtained by rigid/visco-plastic finite element method.

Using Meshless Local Natural Neighbor Interpolation Method to Solve Two-Dimensional Nonlinear Problems

Based on the meshless local natural neighbor interpolation method (MLNNI), a novel solution procedure is developed for the analysis of nonlinear steady and transient heat transfer of two-dimensional structures in this paper. Nonlinearities arising from temperature dependence of material properties and nonlinear boundary conditions have been taken into account. The present method is developed based on the natural neighbor interpolation (NNI) for constructing shape functions at scattered nodes. The three-node triangular FEM shape function is employed as the test function, which reduces the orders of integrands involved in domain integrals. Due to the delta function property of the natural neighbor shape functions, there is no need to employ special techniques to enforce the essential boundary conditions. The backward difference method is employed for the time integration scheme in transient analysis and the Newton–Raphson iterative procedure is required at each time step. Three numerical examples with different geometries and boundary conditions are presented at the end to demonstrate the validity and accuracy of the proposed method for the solution of a wide class of nonlinear steady and transient heat transfer problems.

An investigation of DEM generation process based on LiDAR data filtering, decimation, and interpolation methods for an urban area

Terrain analysis is an essential step to assess landscape, spatial variability of soil and ecologic properties. An easy and effective way of this is studying with Digital Elevation Model (DEM). Traditional methods for creating DEM are very costly and time consuming because of land surveying. In time, Photogrammetry has become one of the major methods to generate DEM. Recently, airborne Light Detection and Ranging (LiDAR) system has become a powerful way to produce a DEM due to advantage of collecting three-dimensional information very effectively over a large area by means of precision and time. Airborne LiDAR system collects information not only from land surface, but also from every object between plane and terrain that can reflect the laser beam. Therefore, LiDAR data density, topographic features, and interpolation methods are the main parameters for LiDAR derived DEM accuracy.In this paper, an investigation is carried out for generating a proper DEM to analyze terrain futures. For this purpose, the DEM generation process is started with raw LiDAR data of an urban area filtering with Triangular Irregular Network (TIN) algorithm before and after for five different decimation rates. Afterward, the interpolation techniques that are the Inverse Distance Weighted (IDW), Kriging, Natural Neighbor (NN), and Topo to Raster, are used for DEM generation. According to the accuracy assessments, the TIN algorithm is very satisfactory for filtering process and the NN interpolation method is quite effective for DEM generation.

Free vibration of moderately thick functionally graded plates by a meshless local natural neighbor interpolation method

Using a meshless local natural neighbor interpolation (MLNNI) method, natural frequencies of moderately thick plates made of functionally graded materials (FGMs) are analyzed in this paper based on the first-order shear deformation theory (FSDT), which is employed to take into account the transverse shear strain and rotary inertia. The material properties of the plates are assumed to vary across the thickness direction by a simple power rule of the volume fractions of the constituents. In the present method, a set of distinct nodes are randomly distributed over the middle plane of the considered plate and each node is surrounded by a polygonal sub-domain. The trial functions are constructed by the natural neighbor interpolation, which makes the constructed shape functions possess Kronecker delta property and thus no special techniques are required to enforce the essential boundary conditions. The order of integrands involved in domain integrals is reduced due to the use of three-node triangular FEM shape functions as test functions. The natural frequencies computed by the present method are found to agree well with those reported in the literature, which demonstrates the versatility of the present method for free vibration analysis of moderately thick functionally graded plates.

WE-AB-BRA-11: Development of Physiological-Based Virtual Thorax Phantoms for Evaluation of Deformable Image Registration

Purpose: To develop a methodology of constructing physiological-based virtual thorax phantom based on hyperpolarized (HP) gas tagging MRI for evaluating deformable image registration (DIR). Methods: Three healthy subjects were imaged at both the end-of-inhalation (EOI) and the end-of-exhalation (EOE) phases using a high-resolution (2.5mm isovoxel) 3D proton MRI, as well as a hybrid MRI which combines HP gas tagging MRI and a low-resolution (4.5mm isovoxel) proton MRI. A sparse tagging displacement vector field (tDVF) was derived from the HP gas tagging MRI by tracking the displacement of tagging grids between EOI and EOE. Using the tDVF and the high-resolution MR images, we determined the motion model of the entire thorax in the following two steps: 1) the DVF inside of lungs was estimated based on the sparse tDVF using a novel multi-step natural neighbor interpolation method; 2) the DVF outside of lungs was estimated from the DIR between the EOI and EOE images (Velocity AI). The derived motion model was then applied to the high-resolution EOI image to create a deformed EOE image, forming the virtual phantom where the motion model provides the ground truth of deformation. Five DIR methods were evaluated using the developed virtual phantom. Errors in DVF magnitude (Em) and angle (Ea) were determined and compared for each DIR method. Results: Among the five DIR methods, free form deformation produced DVF results that are most closely resembling the ground truth (Em=1.04mm, Ea=6.63°). The two DIR methods based on B-spline produced comparable results (Em=2.04mm, Ea=13.66°; and Em =2.62mm, Ea=17.67°), and the two optical-flow methods produced least accurate results (Em=7.8mm; Ea=53.04°; Em=4.45mm, Ea=31.02°). Conclusion: A methodology for constructing physiological-based virtual thorax phantom based on HP gas tagging MRI has been developed. Initial evaluation demonstrated its potential as an effective tool for robust evaluation of DIR in the lung.

Natural Element Method for Material and Geometrical Bi-Nonlinear Problems

Based on the Voronoi diagram of some nodes, the natural element method (NEM) constructs the shape functions by the natural neighbor interpolation method, and its shape functions satisfy the Kronecker delta property, which makes it impose essential boundary conditions easily. Based on the geometrical nonlinear relations and material nonlinear constitutive relations, we extend the NEM to material and geometrical bi-nonlinear problems in this paper. Numerical examples show that the NEM is effective, rational and feasible in dealing with problems of both material and geometrical bi-nonlinear.

DYNAMIC ELASTOPLASTIC ANALYSIS USING THE MESHLESS LOCAL NATURAL NEIGHBOR INTERPOLATION METHOD

Dynamic elastoplastic analysis is a subject of great engineering importance and can practically be handled only by numerical methods due to its complexity. The aim of this paper is to develop the meshless local natural neighbor interpolation (MLNNI) method to perform the dynamic analysis of elastoplastic structures under plane stress or plane strain conditions. The MLNNI, as an effective truly meshless method for solving partial differential equations, employs local weak forms over a local subdomain and shape functions from the natural neighbor interpolation (NNI). The shape functions so formulated possess delta function property and, therefore, the essential boundary conditions can be implemented as ease as in the finite element method (FEM). The predictor-corrector form of the Newmark algorithm is used for the time-marching process and iterations are performed at every time step. The applied loads can have any transient time variation. Comparative results are presented at the end to illustrate the effectiveness of the proposed method and demonstrate its accuracy.

A meshless local natural neighbor interpolation method for two-dimension incompressible large deformation analysis

A meshless local natural neighbor interpolation method (MLNNIM) is utilized to build shape functions for solving elastoplastic problems in this paper. This method searches natural neighbor nodes of the given point and defines local Delaunay triangles. Total Lagrangian (TL) and Updated Lagrangian (UL) formulae have been derived and analyzed. Consideration of the constitutive law and numerical efficiency indicates that the UL formulation is more expedient and attractive in practical problems of solid mechanics. Combined with the linearized UL formulation, the MLNNIM was used to solve problems of two-dimension elastoplastic large deformation. Finally, two representative numerical examples are given to demonstrate the effectiveness and superiority of the MLNNIM combined with the UL formulation for two-dimension incompressible large deformation problems.

Geophysical parameterization and parameter structure identification using natural neighbors in groundwater inverse problems

A natural neighbor interpolation (NN) method based on Voronoi tessellation and Delaunay triangulation is developed for both parameter heterogeneity characterization and parameter structure identification in groundwater modeling. Honoring information from the natural neighboring basis points, NN generates a continuously distributed field. With NN, parameter structure identification seeks to identify the optimal parameter distribution in terms of the number, values, and locations of basis points. At each level of parameter structure complexity, the estimated distributed parameter is obtained by minimizing a regularized fitting residual. This is done sequentially, first by a genetic algorithm (GA) and then by a gradient-based algorithm (BFGS). In this study, sensitivity equations of state variables to both values and locations of basis points are developed for optimization as well as for parameter uncertainty analysis. The results obtained from numerical experiments show that, for a given set of head observations and point transmissivity measurements, the proposed inverse methodology successfully captures the variation of the true transmissivity field. The parameter structure complexity as represented by the parameter dimension is determined by considering the trade-off between the fitting residual and the parameter uncertainty error. An optimal parameter dimension is selected when the head fitting residual is close to the observation error and the uncertainty associated with identified transmissivity structure is acceptable.