Natural Neighbor Research Articles

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.

One shape fits all, but only in the aggregate: Diversity in sub‐stand scale diameter distributions

AbstractQuestionsTo what extent are the sub‐stand size class distributions at the neighbourhood patch scale masked at the stand level via spatial smoothing? What are the implications for naturalness assessment of obscuring, at the stand level, structures that arise from endogenous processes at the neighbourhood scale?LocationElborz Mountains, south of the Caspian Sea, Iran.MethodsNatural uneven‐aged old‐growth Oriental beech (Fagus orientalis) forest subject to fine‐scale disturbances was stem‐mapped in a 1.2‐ha plot of live trees >7.5 cm DBH; neighbourhoods were delineated across multiple scales using the tree‐centred floating neighbourhood approach of spatial tessellation to connect trees to their natural neighbours. Cluster analysis was used to identify an optimal number of recurring diameter distribution types (DDT) based on the proportion of trees in each of the five size classes. The richness of DDTs was assessed and the extent of DDTs was modelled as a function of tree size.ResultsThe number of member trees and spatial extent increased with neighbourhood scale. While the stand‐level tree size class distribution exhibited a rotated sigmoid shape, the nine most distinct DDTs were characterized by four different distribution shapes (negative exponential, increasing‐q, rotated sigmoid and unimodal) and varied considerably in the abundance of trees in different size classes. Each individual tree contributed to at least three of the nine DDTs, which were nonetheless spatially distinct and varied in extent with size class composition. As expected, all metrics exhibited spatial smoothing (i.e., increasing homogeneity with increasing scale) as small, heterogeneous tree neighbourhoods were expanded into larger neighbourhoods with more similar average composition, which converged on a rotated sigmoid shape at the broadest scale.ConclusionsThe stand‐level rotated sigmoid distribution reflected spatial smoothing across more heterogeneous fine‐scale tree neighbourhood patches. Further studies are needed to assess if a better measure of natural forest structure may be the diversity of sub‐stand structures and the contribution of individual trees to that diversity, rather than an aggregated metric that averages across the hallmark heterogeneity of neighbourhood dynamics.

Least Squares Compactly Supported Radial Basis Function for Digital Terrain Model Interpolation from Airborne Lidar Point Clouds

To overcome the huge volume problem of light detection and ranging (LiDAR) data for the derivation of digital terrain models (DTMs), a least squares compactly supported radial basis function (CSRBF) interpolation method is proposed in this paper. The proposed method has a limited support radius and fewer RBF centers than the sample points, selected by a newly developed surface variation-based algorithm. Those make the linear system of the proposed method not only much sparser but also efficiently solvable. Tests on a synthetic dataset demonstrate that the proposed method is comparable to the smoothing RBF, and far superior to the exact RBF. Moreover, the first is much faster than the others. The proposed method with the RBF centers selected by the surface variation-based algorithm obviously outperforms that with the random selection of equal number. Real-world examples on one private and ten public datasets show that the surfaces of simple interpolation methods including inverse distance weighting, natural neighbor, linear and bicubic suffer from the problems of roughness, peak-cutting, discontinuity and subtle terrain feature loss, respectively. By contrast, the proposed method produces visually appealing results, keeping a good tradeoff between noise removal and terrain feature preservation. Additionally, the new method compares favorably with ordinary kriging (OK) for the generation of high-resolution DTMs in terms of interpolation accuracy, yet the former is much more robust to spatial resolution variation and terrain characteristics than the latter. More importantly, our method is about 4 times faster than OK. In conclusion, the proposed method has high potential for the interpolation of a large LiDAR dataset, especially when both interpolation accuracy and computational cost are taken into account.

Compact tension fracture specimen: Experimental and computational implementations on stress intensity factor

This work concentrates on the characterization of the stress intensity factor range for a compact tension specimen tested under a uniaxial tensile fatigue loading condition. The experimental solution is obtained using a three-dimensional full-field optical technique, digital image correlation. The deformation field is measured and documented for distinct crack lengths. As a relevant fracture parameter, stress intensity factor is thus experimentally measured combined with a computational overdeterministic algorithm for different crack lengths. Moreover, to verify the performance of the proposed fracture model, the cracked compact tension specimen is elasto-statically resolved using advanced discretization techniques, such as the finite element method, the meshless radial point interpolation method and the meshless natural neighbour radial point interpolation method. The finite element method model is thereby analysed with ABAQUS©to enable computation of mode I stress intensity factor results based on strain energy release rate criterion for different crack measurements in addition to strain contours. Likewise, the resolution pattern is repeated for meshless methods, and analogous numerical solutions are thus obtained. Overall, the experimental and numerical stress intensity factor results are compared with an available solution (ASTM E647) exhibiting a reasonable agreement. The novelty of this investigation is the amalgamation of an experimental digital image correlation procedure with a computational overdeterministic algorithm and, most importantly, the meshless formulation performance in the linear elastic fracture mechanics.

Extending radial point interpolating meshless methods to the elasto-plastic analysis of aluminium alloys

This study performs an elasto-plastic numerical analysis of an aluminium alloy using two efficient meshless methods. The obtained numerical solutions are validated using experimental results due to the lack of a suitable elasto-plastic analytical solution. Thus, an experimental test was performed in order to obtain the force/displacement curve and the corresponding mechanical properties by means of Digital Image Correlation (DIC). In this work, two advanced discretization techniques, the Radial Point Interpolation Meshless Method (RPIM) and Natural Neighbour Radial Point Interpolation Meshless Method (NNRPIM), were extended to elasto-plasticity. In order to assess the performance of the numerical methods, the problem was additionally solved with the Finite Element Method (FEM) formulation in ABAQUS©. The success of the obtained numerical results validates the experimental solution contributing to accomplish the study objectives. Additionally, meshless methods produce accurate results compared to the experimental solution and FEM, proving that the presented methodology is feasible and robust.

Comparative Study of Interpolation Methods in Development of Local Geoid

The main aims of the research are to estimate the efficiency of different methods of interpolation (Natural Neighbour, Inverse Distance Weighting, Kriging and Topo to Raster) for the normal height determination by comparing with heights anomalies determined by using GPS-leveling and global gravitational model EGM2008. The discrepancies between the calculated and interpolated heights were analyzed and discussed for Fergana valley located within in Republic of Uzbekistan. Comparison of the results with the data of global gravimetric model EGM 2008 showed that the best interpolation surface demonstrated Natural Neighbour and Topo to Raster methods for considered region.

Adaptive analysis of plates and laminates using natural neighbor Galerkin meshless method

In this paper, natural neighbor Galerkin meshless method is employed for adaptive analysis of plates and laminates. The displacement field and strain field of plate are based on Reissner–Mindlin plate theory. The interpolation functions employed here were developed by Sibson and based on natural neighbor coordinates. An adaptive refinement strategy based on recovery energy norm which is in turn based on natural neighbors is employed for analysis of plates. The present adaptive procedure is applied to classical plate problems subjected to in-plane loads. In addition to that the laminated composite plates with cutouts subjected to transverse loads are investigated. Influence of the location of the cutout and the boundary conditions of the plate on the results have been studied. The results obtained with present adaptive analysis are accurate at lower computational effort when compare to that of no adaptivity. Further, the adaptive analysis provided accurate magnitude of maximum stresses and their locations in the laminate plates with and without cutout subjected to transverse loads. Additionally, failure prone areas in the geometry of the plates subjected to loads are revealed with the adaptive analysis.

Effect of Pinus ponderosa afforestation on soilborne Frankia and saprophytic Actinobacteria in Northwest Patagonia, Argentina

Large areas in the extra-Andean region in the forest - steppe ecotone in “Northwestern Argentinean Patagonia” have been replaced by plantations of the exotic conifer Pinus ponderosa which modify soils physical and chemical factors and alter the biodiversity. Considering that in the region occur saprophytic soilborne actinobacteria that play important role as the fixation of atmospheric nitrogen (N2) in symbiosis with native plant species and the production of bioactive molecules in plants rhizosphere, we aimed to study the effect of the plantation on the abundance of the N2 fixer Frankia and on the genus diversity of cultivable rhizospheric actinobacteria. The study was performed with soils of six paired sites with pine plantations and natural neighbor areas (including steppes or shrublands). Abundance of infective Frankia was estimated by evaluating the nodulation capacity of soils, through a plant bioassay using Ochetophila trinervis as trap plant. Isolation trials for saprophytic actinobacteria were performed by applying chemotactic and successive soils dilutions methods. We concluded that P. ponderosa afforestation affect soil actinobacteria. This was mainly evidenced by a decrease in the Frankia nodulation capacity in O. trinervis, which was related to plantation age, to lower soil carbon and nitrogen content, higher available phosphorus, and to a slight decrease in soils pH. Pine plantation influence on the cultivable saprophytic actinobacteria was less clear. The study highlights the importance of soils as source of Frankia and rhizospheric actinobacteria in relation to disturbance caused by pine plantation in natural environments with native actinorhizal plant species.

Cross-comparison and evaluation of air pollution field estimation methods

Accurate estimates of human exposure is critical for air pollution health studies and a variety of methods are currently being used to assign pollutant concentrations to populations. Results from these methods may differ substantially, which can affect the outcomes of health impact assessments. Here, we applied 14 methods for developing spatiotemporal air pollutant concentration fields of eight pollutants to the Atlanta, Georgia region. These methods include eight methods relying mostly on air quality observations (CM: central monitor; SA: spatial average; IDW: inverse distance weighting; KRIG: kriging; TESS-D: discontinuous tessellation; TESS-NN: natural neighbor tessellation with interpolation; LUR: land use regression; AOD: downscaled satellite-derived aerosol optical depth), one using the RLINE dispersion model, and five methods using a chemical transport model (CMAQ), with and without using observational data to constrain results. The derived fields were evaluated and compared. Overall, all methods generally perform better at urban than rural area, and for secondary than primary pollutants. We found the CM and SA methods may be appropriate only for small domains, and for secondary pollutants, though the SA method lead to large negative spatial correlations when using data withholding for PM2.5 (spatial correlation coefficient R = −0.81). The TESS-D method was found to have major limitations. Results of the IDW, KRIG and TESS-NN methods are similar. They are found to be better suited for secondary pollutants because of their satisfactory temporal performance (e.g. average temporal R2 > 0.85 for PM2.5 but less than 0.35 for primary pollutant NO2). In addition, they are suitable for areas with relatively dense monitoring networks due to their inability to capture spatial concentration variabilities, as indicated by the negative spatial R (lower than −0.2 for PM2.5 when assessed using data withholding). The performance of LUR and AOD methods were similar to kriging. Using RLINE and CMAQ fields without fusing observational data led to substantial errors and biases, though the CMAQ model captured spatial gradients reasonably well (spatial R = 0.45 for PM2.5). Two unique tests conducted here included quantifying autocorrelation of method biases (which can be important in time series analyses) and how well the methods capture the observed interspecies correlations (which would be of particular importance in multipollutant health assessments). Autocorrelation of method biases lasted longest and interspecies correlations of primary pollutants was higher than observations when air quality models were used without data fusing. Use of hybrid methods that combine air quality model outputs with observational data overcome some of these limitations and is better suited for health studies. Results from this study contribute to better understanding the strengths and weaknesses of different methods for estimating human exposures.

Floating neighborhoods reveal contribution of individual trees to high sub-stand scale heterogeneity

Abstract Forest structure is typically characterized using approaches that fail to capture the sub-stand heterogeneity reflecting the processes shaping stand structure at neighborhood patch scales. We propose a focal-tree based approach that flexibly scales across natural tree neighborhoods and demonstrate it by quantifying small-scale structural heterogeneity using diameter distributions across multiple scales in an old-growth mixed conifer forest in western Oregon exhibiting a rotated sigmoid shape. Tree-centered delineation of neighborhoods via Delaunay triangulation (spatial tessellation) was used to connect natural tree neighbors. At the First-order neighborhood scale, each tree was connected to an average of 6 neighbors in 75 m2 of convex hull area, which increased to 118 neighbors covering 2542 m2 by the Fifth-order scale. Agglomerative clustering identified the ten most prevalent sub-stand diameter distribution types (DDTs). At the smallest scale, these ten DDTs were characterized by four different distribution shapes (negative exponential, concave, rotated sigmoid, and unimodal) and varied considerably in the abundance of trees in different size classes and species composition (Douglas-fir composing the larger trees and western hemlock and western redcedar the smaller). On average, each individual tree contributed to over 3 different DDTs at any given scale. Small-scale tree neighborhoods were tremendously heterogeneous, such that the stand-level diameter distribution represented an aggregation across extremely disparate sub-stand distributions. As expected, these distributions exhibited spatial smoothing (i.e., increasing homogeneity with increasing scale) as small, heterogeneous tree neighborhoods were expanded into larger neighborhoods with more similar average composition, which converged on a rotated-sigmoid shape by the Fifth-order scale. Structural complexity in the demonstration stand likely owes more to shade-tolerant ingrowth below residual trees than to gap processes. The diversity of structural contribution (e.g., the number of DDTs to which a tree contributes) may be a more informative measure of structural complexity than indices based on a fixed spatial perspective. The floating neighborhood delineation and scaling approach allows for the identification of natural neighborhoods, permits the assessment of multiple conditions for any given tree, and provides of a logical mechanism for exploring scale-dependent ecological phenomena.

The free vibrations analysis of the cupula in the inner ear using a natural neighbor meshless method

The cupula is a part of the inner ear semi-circular canals that plays an important role in the maintenance of the human balance. In order to understand the dynamic response of the cupula, first it is necessary to obtain its vibration frequencies. A two-dimensional and three-dimensional geometrical model of the cupula was built. Then, a free vibration analysis was performed using two distinct numerical techniques, the finite element method (FEM) and the natural neighbor radial point interpolation method (NNRPIM). Besides the fundamental analysis, other scenarios were studied, aiming to analyze the environment of the cupula (in healthy and pathologic scenarios). The results obtained with the geometrical models show that NNRPIM is capable to deliver results very close with the FEM. Additionally, the NNRPIM formulation possesses a high convergence and acceptable computational costs.This work presents for the first time a computational study on the free vibration analysis of the cupula and shows an alternative numerical technique to calculate with precision the natural frequency of the cupula. The outcomes of this work will allow the development of alternative therapies for cupulolithiasis, which causes severe dizziness.

Mechanical bone remodelling: Comparative study of distinct numerical approaches

Bone is a complex living structure. Induced by its biomechanical environment, bone constantly adapts its internal and external structure, altering its mass and morphology. In this work, three distinct discretization techniques are combined with a mechanologic bone tissue remodelling algorithm, which describes the remodelling process by minimizing the strain energy density (SED) field. During an iterative remodelling process, bone tissue's mechanical properties are recurrently correlated with bone apparent density through a phenomenological law. The purpose of this study is to compare bone tissue remodelling solutions obtained with the Finite Element Method (FEM), the Radial Point Interpolation Method (RPIM) and the Natural Neighbour RPIM (NNRPIM). Thus, two numerical examples were analysed, namely a benchmark bone patch and a femur. On both examples, regardless the discretization technique, it was possible to accurately reproduce the trabecular bone architecture. Additionally, a comparison between each numerical method was performed. The model shown high adaptability, since, for every method, successful performances were obtained. Nevertheless, meshless solutions produced smoother and more accurate results, closer to real X-ray images.

Homogenization technique for heterogeneous composite materials using meshless methods

Due to its random fibre distribution across the cross-section and their anisotropic and heterogeneous characteristic, the prediction of the mechanical behaviour of fibre composite materials is complex. Multi-scale approaches have been proposed in the literature to more accurately predict their mechanical properties using computational homogenization procedures.This work is based on existing multi-scale numerical transition techniques suitable for simulating heterogeneous materials and makes use of two meshless methods—the Radial Point Interpolation Method (RPIM) and the Natural Neighbour Radial Point Interpolation Method (NNRPIM)—and the Finite Element Method (FEM). Representative volume elements (RVEs) are modelled and discretized using the three numerical methods. Prescribed microscopic displacements are imposed on different RVEs whose boundaries are periodic and, from the obtained stress field, the average stresses are determined. Consequentially, the effective elastic properties of a heterogeneous material are obtained for different fibre volume fractions. In the end, the numerical solutions are compared with the solutions proposed in the literature and it is proved that the NNRPIM achieve more accurate solutions than the RPIM and the FEM.

Об одном методе оценки многомерной плотности на основеближайших соседей

A method of multivariate density estimation based on the reweighted nearest neighbours,mimicking the natural neighbours techniques, is presented. Estimation of multivariate densityis important for machine learning, astronomy, biology, physics and econometrics. A 2-additivefuzzy measure is constructed based on proxies for pairwise interaction indices. The neighboursof a point lying in nearly the same direction are treated as redundant, and the contributionof the farthest neighbour is transferred to the nearer neighbour. The calculation of the localpoint density estimate is performed by the discrete Choquet integral, so that the contributionsof the neighbours all around that point are accounted for. This way an approximation to theSibson’s natural neighbours is computed. The method relieves the computational burden of theDelaunay tessellation-based natural neighbours approach in higher dimensions, whose complexityis exponential in the dimension of the data. This method is suitable for density estimates ofstructured data (possibly lying on lower dimensional manifolds), as the nearest neighbours differsignificantly from the natural neighbours in this case.

Ocena točnosti in primerjava metod interpolacij modelov geoida

In this paper the accuracy of 6 spatial interpolation methods on geoid grid models are tested and compared: Inverse Distance Weighting, Kriging, Minimum Curvature, Natural Neighbour, Radial Basis Function and Moving Average. Grid models are derived from three global geopotential models: EGM2008, EIGEN-6C4 and GECO. Totally 18 geoid models in forms of equiangular grid models are created in GoldenSoftware Surfer 13 for this purpose, by combining 6 methods of interpolation and 3 global models, whose size and position cover a wide area of Croatia with parts of neighbouring countries. Default interpolation parameters were kept during the process. Models were created in a way that modelled values of geoid undulations can be subtracted from undulations of independent models in equal points. Residuals calculated in this way served as a base for quality assessment. Comparative analysis of quality indicators, statistics and graphical indicators of residuals led to a conclusion that the best-fitted methods of interpolation for this specific case are Radial Basis Function, Kriging, and Natural Neighbour, in that order.

AQUA Satellite Data and Imputation of Geopotential Height: A Case Study for Pakistan

In current study an attempt is carried out by filling missing data of geopotiential height over Pakistan and identifying the optimum method for interpolation. In last thirteen years geopotential height values over were missing over Pakistan. These gaps are tried to be filled by interpolation Techniques. The techniques for interpolations included Bilinear interpolations [BI], Nearest Neighbor [NN], Natural [NI] and Inverse distance weighting [IDW]. These imputations were judged on the basis of performance parameters which include Root Mean Square Error [RMSE], Mean Absolute Error [MAE], Correlation Coefficient [Corr] and Coefficient of Determination [R2]. The NN and IDW interpolation Imputations were not precise and accurate. The Natural Neighbors and Bilinear interpolations immaculately fitted to the data set. A good correlation was found for Natural Neighbor interpolation imputations and perfectly fit to the surface of geopotential height. The root mean square error [maximum and minimum] values were ranges from ±5.10 to ±2.28 m respectively. However mean absolute error was near to 1. The validation of imputation revealed that NN interpolation produced more accurate results than BI. It can be concluded that Natural Interpolation was the best suited interpolation technique for filling missing data sets from AQUA satellite for geopotential height.

Accurate Imputation for Relative Humidity over Pakistan Gathered from AQUA Satellite

The relative humidity in the atmosphere captured by AQUA satellite contains missing matrices. In order to fill such missing values four very popular imputation techniques: Bilinear, Inverse Distance Weighting, Natural Neighbor and Nearest Interpolations were tested. Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Coefficient of Determination (R2) and Correlation Coefficient (Corr), were used to check the accuracy of these interpolations. It was found that the Inverse Distance Weighting and Nearest Interpolation were proved not to be suited. Natural interpolation gave accurate results than the aforementioned two interpolations. Missing values of relative humidity were accurately refilled with Bilinear Interpolation. This interpolation produced RMSE of ±0.543 for relative humidity over 100, 150, 200, 250, 300, 400, 500 hPa while for 600, 700, 850 and 925 hPa RMSE remainnear to 1. A perfect fit to the surface and very strong correlation (value near to 0.99) was found between actual and imputed relative humidity data through Bilinear Interpolation. Therefore it was concluded that the Bilinear Interpolation is the most accurate and best imputation for missing values of relative humidity form 100 to 1000 hPa levels.

Preliminary Evaluation of the Earthquake Hazard for Underground Electric Facility Lines in Pohang City based on ArcGIS

Pohang, a big city of Gyeongbuk province, South Korea, is developing rapidly in every aspect, containing many important infrastructures such as seaports, industrial factories, commercial centers, and underground electric facility systems that play an integral part in the contribution of electricity stemming from nuclear power plants. The main purpose of this research is a preliminary assessment of the earthquake hazard for underground electric facility lines (UEFL) located beneath Pohang city by using ArcGIS program. About 1000 drilling boreholes were collected as a database. All of the data were processed by filtering with respect to the depths, then the SPT-N values of unknown points were estimated by interpolation. Four interpolation methods (e.g., Inverse Distance Weighting (IDW), Kriging, Natural Neighbor, and Spline) were evaluated to find the method which gives the best representation of the SPT-N value for unknown points. The IDW method was finally selected. Afterwards, the border surface between soft- and hard-soil layers, the ground rock zonation map, the dramatic change of soil condition, and the depth of structure were determined as important scales to evaluate primarily whether the structures might be in danger or not when an earthquake occurs. In this way, proposed method can be applied to whole South Korea with over 100,000 available borehole data.

Mapping of Soil Properties Using Geographical Information System (GIS): A Case Study of Hassan Usman Katsina Polytechnic

GIS relates and integrates spatial data from various sources, for storage, retrieval, analyses and display. This paper presents the analysis and mapping of Geotechnical data using natural neighbour interpolation tool of GIS. The Campus of Hassan Usman Katsina Polytechnic Nigeria was as the study area, and Arc GIS 10.2.1 was used to perform the analyses. The study used soils samples from ten trial pit distributed within the study area and subjected to various laboratory tests. Index and engineering properties of the samples were determined. Map database developed in a GIS environment and the result of the laboratory tests stored, were analysed and displayed using GIS. The research results show maps of various soil properties. The research result provides estimated data for preliminary designing of engineering infrastructures in the area.

Geospatial Suitability Mapping of Climate-based Disease Transmission using Fuzzy Logic for Central India

Geographic Information System (GIS) today supports health and disease mapping in diverse ways. Present study divulges geographic dimensions of malaria disease in Madhya Pradesh and Chhattisgarh states located in Central India. Chhattisgarh is second and Madhya Pradesh is the third most malarious states after Odisha in India. In the present study, an attempt is made to map climate-based malaria transmission suitability using fuzzy logic for Central India. Temperature and relative humidity were selected as the two indicators for malaria transmission suitability analysis. District wise meteorological data for 2008 was used for the present study. Monthly temperature and relative humidity interpolation maps were generated using ‘Natural Neighbor’ interpolation algorithm. For both the indicators trapezoidal membership function was selected. Arc GIS software and its FUZZY tool were used to generate ‘climate suitability map’ for malaria transmission depicting the spatial distribution of Transmission Window length (in months) across the region. The findings illustrate that most districts of Chattisgarh and very few districts of Madhya Pradesh have transmission window open for more than 10 months and are identified as ‘High Endemic Regions’. Compared to Chhattisgarh, Madhya Pradesh experiences more numbers of least suitable months i.e. February, March, April and May. The study aims to benefit judicious decision making for efficient intervention implementation.