Global Interpolation Method Research Articles

AN METHOD FOR CREATING GEOINFORMATION 3D-MODEL OF AN AERODROME USING A DIGITAL TERRAIN MODEL

The creation of a three-dimensional geoinformation model of aerodrome is considered. An approach is proposed, consisting in supplementing a two-dimensional vector map with the values of the third coordinate, which are calculated using data from a digital terrain model. To implement this approach, the problem of interpolation of a function of two variables with a large number of nodal points is solved. The number of nodes where elevation values are set in a digital terrain model can be several thousand for each dimension. In this case, the use of global interpolation methods, for example, splines, in which function values at all nodal points are used to determine the values of a function at a given point falling into a grid cell, is computationally inefficient, since it requires a lot of machine time. It seems more promising to use a local approach to the interpolation problem. In this approach, the value of the function at an arbitrary point is determined by the values of the function at the nodal points of the grid closest to the specified point. Finite formulas are obtained that do not require solving equations, and allow interpolating functions for cases of linear and smooth approximation. An algorithm and a calculation program have been developed for a regular two-dimensional grid of nodes of a digital terrain model using the publicly available SRTM database. The results of numerical calculations of test cases with a comparison of linear and smooth approximations are presented. Using the proposed approach, a three-dimensional model of the Sochi aerodrome was created to simulate the movement of aircraft on its surface. The proposed approach and the interpolation method can be used to calculate the elevation of given points and to create three-dimensional cartographic models of the earth's surface.

Compaction quality assessment of highway using roller-integrated positive maximum kinetic energy increment detection technique

During conventional highway construction, quality control and acceptance (QC/QA) are based on limited spot tests of material density at random locations which may not comprehensively represent the entire compacted area and are vulnerable to potential biases. Based on roller-integrated positive maximum kinetic energy increment detection technique with real-time kinematic global positioning systems, this research adopted kinetic energy compaction value (KECV) as a real-time monitoring index for the highway compaction quality, and subsequently proposed an KECV-based assessment method to estimate the compaction quality of subgrade and pavement materials. Additionally, a global interpolation method (Green spline) was adopted to obtain estimates for both KECVs and compaction quality at any location on the work area, enabling the analysis of the passing rate of compaction quality for the entire work area. A case study on the Hengyong highway project in China indicates a highly linear correlation between the KECV and the compaction parameters, the compactness of LLL silt, and the relative density of cement-stabilized macadam; therefore, it can serve as a reliable index for monitoring compaction quality. Assessment of compaction quality on the entire work area can be fast and continuously achieved using the proposed method, which can effectively overcome the above limitation of conventional testing, timely feedback compaction information to avoid quality defects, and availably improve the construction quality of highways.

Technology for restoring functional dependencies to determine reliability parameters

The problem of determining the properties of the object by analyzing the numerical and qualitative characteristics of a discrete sample is considered. A method has been developed to determine the probability of trouble-free operation of electronic systems for the case if the interpolation fields are different between several interpolation nodes. A method has been developed to determine the probability of trouble-free operation if the interpolation polynomial is the same for the entire interpolation domain. It is shown that local interpolation methods give more accurate results, in contrast to global interpolation methods. It is shown that in the case of global interpolation it is possible to determine the value of the function outside the given values by extrapolation methods, which makes it possible to predict the probability of failure. It is shown that the use of approximation methods to determine the probability of trouble-free operation reduces the error of the second kind. A method for analyzing the qualitative characteristics of functional dependences has been developed, which allows us to choose the optimal interpolation polynomial. With sufficient statistics, using the criteria of consent, it is possible to build mathematical models for the analysis of failure statistics of electronic equipment. Provided that the volume of statistics is not large, such statistics may not be sufficient and the application of consent criteria will lead to unsatisfactory results. Another approach is to use an approximation method that is applied to statistical material that was collected during testing or controlled operation. In this regard, it is extremely important to develop a method for determining the reliability of electronic systems in case of insufficiency of the collected statistics of failures of electronic equipment.

A local-optimizing surface reconstruction method based on point cloud data

Surface reconstruction based on discrete point cloud data is a frequently encountered problem in the field of CAD/CAGD and computer graphics. In this paper, a local-optimizing surface reconstruction method based on discrete point cloud data is proposed. Firstly, the moving least square method is used to fit the discrete point cloud data to generate a gridded point clouds. Then the global interpolation method is used to generate the initial NURBS surface based on the gridded point clouds. Additionally, the knots are inserted into the regions with excessive errors. Ultimately, a multi-objective optimization function is established to optimize the regions with excessive errors and their neighbourhoods simultaneously. Compared with the existing methods, the proposed method can improve the fitting accuracy of the reconstructed surface locally and has higher efficiency.

Distributed Self-Optimization of Modular Production Units: A State-Based Potential Game Approach.

This article presents a novel approach for distributed optimization of production units based on potential game (PG) theory and machine learning. The core of our approach is split into two parts: the first part concentrates on the conceptual treatment of modular installed production units in terms of a PG scenario. The second part focuses on the development and incorporation of suitable learning algorithms to finally form an intelligent autonomous system. In this context, we model the production environment as a state-based PG where each actuator of each module has the role of an agent in the game aiming to maximize its utility value by learning the optimal process behavior. The benefit of the additional state information is visible in the performance of the algorithm making the environment dynamic and serving as a connector between the players. We propose a novel learning algorithm based on a global interpolation method that is applied to a laboratory scale modular bulk good system. The thorough analysis of the encouraging results yields to highly interesting insights into the learning dynamics and the process itself. The benefits of our distributed optimization approach are the plug-and-play functionality, the online capability, fast adaption to changing production requirements, and the possibility of an IEC 61131 conforming to PLC implementation.

Precipitation imputation with probability space-based weighting methods

Euclidean distance-based spatial interpolation methods that are conceptually simple are commonly used for the imputation of missing precipitation and other hydroclimatic variable datasets. Improved variants of these methods are essential as Euclidean distance will not always serve as an appropriate surrogate that can quantify the inter-gauge relationships in all hydroclimatic and topographical settings. Probability space-based error measure (linear error in probability space (LEPS)) and three distribution similarity hypothesis test statistic values are proposed as surrogates for distances in weighting methods to address this limitation. A k-fold cross-validation exercise of the imputation of precipitation data at 22 rain gauges in a temperate climatic region is used for the evaluation of methods. Improved imputation of missing data was noted from proposed methods compared to that from a distance-based method and is confirmed with statistical inference testing of multiple error and performance measures. Also, the LEPS-based method provided performance measures that are as good as those from a nonlinear optimization method. A local spatial interpolation approach that uses LEPS and two-sample Kolmogorov-Smirnov hypothesis test results quantified as binary outcomes for objective selection of rain gauges are also evaluated. Better estimates of missing data are obtained using this approach compared to those from a Euclidean distance-based global interpolation method. The proposed new probability space-based distances are conceptually superior alternatives to Euclidean distances when used in weighting methods for spatial interpolation.

A Fast Global Interpolation Method for Digital Terrain Model Generation from Large LiDAR-Derived Data

Airborne light detection and ranging (LiDAR) datasets with a large volume pose a great challenge to the traditional interpolation methods for the production of digital terrain models (DTMs). Thus, a fast, global interpolation method based on thin plate spline (TPS) is proposed in this paper. In the methodology, a weighted version of finite difference TPS is first developed to deal with the problem of missing data in the grid-based surface construction. Then, the interpolation matrix of the weighted TPS is deduced and found to be largely sparse. Furthermore, the values and positions of each nonzero element in the matrix are analytically determined. Finally, to make full use of the sparseness of the interpolation matrix, the linear system is solved with an iterative manner. These make the new method not only fast, but also require less random-access memory. Tests on six simulated datasets indicate that compared to recently developed discrete cosine transformation (DCT)-based TPS, the proposed method has a higher speed and accuracy, lower memory requirement, and less sensitivity to the smoothing parameter. Real-world examples on 10 public and 1 private dataset demonstrate that compared to the DCT-based TPS and the locally weighted interpolation methods, such as linear, natural neighbor (NN), inverse distance weighting (IDW), and ordinary kriging (OK), the proposed method produces visually good surfaces, which overcome the problems of peak-cutting, coarseness, and discontinuity of the aforementioned interpolators. More importantly, the proposed method has a similar performance to the simple interpolation methods (e.g., IDW and NN) with respect to computing time and memory cost, and significantly outperforms OK. Overall, the proposed method with low memory requirement and computing cost offers great potential for the derivation of DTMs from large-scale LiDAR datasets.

Assessment of a localized deterministic spatial interpolation method in generating an indoor radiofrequency radiation map

Picocell antennas are used to improve wireless communication coverage inside an area. More picocell antennas are being used to cover small areas, thus, increasing the radiofrequency radiation (RFR) levels in an indoor environment. One method in estimating the radiofrequency radiation is by using spatial interpolation techniques. This study assessed the robustness of a localized deterministic spatial interpolation method compared to its global interpolation counterpart used in generating a radiofrequency radiation map. This was investigated to speed up the data analysis by taking a smaller number of samples. An omnidirectional picocell antenna located in an office lobby area was chosen. The NARDA Selective Radiation Meter SRM-3000TM with tri-axis antenna was used to check the central frequency and average power density emitted by the antenna. A radiofrequency map was generated using a small sample size in a grid pattern. The local Shepard interpolation method with a radius of influence of 100 cm and a power factor of 1 gives a result with a mean absolute difference lower than the global interpolation method. Thus, error contribution in RFR map generation can be minimized by considering a smaller region of samples in the interpolation.

Creating an advanced backpropagation neural network toolbox within GIS software

An artificial neural network (ANN) toolbox is created within GIS software for spatial interpolation, which will help GIS users to train and test ANNs, perform spatial analysis, and display results as a single process. The performance is compared to that of the open source Fast Artificial Neural Network library and conventional interpolation methods by creating digital elevation models (DEMs) given that nearly exact solutions exist. Simulation results show that the advanced backpropagations such as iRprop speed up the learning, while they can get stuck in a local minimum depending on initial weight sets. Besides, the division of input–output examples into training and test data affects the accuracy, particularly when the distribution of the examples is skewed and peaked, and the number of data is small. ANNs, however, show the similar performance to inversed distance weighted or kriging and outperform polynomial interpolations as a global interpolation method in high-dimensional data. In addition, the neural network residual kriging (NNRK) model, which combines the ANN toolbox and kriging within GIS software, is performed. The NNRK outperforms conventional methods and well captures global trends and local variations. A key outcome of this work is that the ANN toolbox created within the de facto standard GIS software is applicable to various spatial analysis including hazard risk assessment over a large area, in particular when there are multiple potential causes, the relationship between risk factors and hazard events is not clear, and the number of available data is small given its performance for DEM generation.

Impact of spatial rainfall variability on hydrology and nonpoint source pollution modeling

Rainfall is regarded as the most important input for the hydrology and nonpoint source (H/NPS) models and uncertainty related to rainfall is generally recognized as a major challenge in watershed modeling. In this paper, we focus on the impact of spatial rainfall variability on H/NPS modeling of a large watershed. The uncertainty introduced by spatial rainfall variability was determined using a number of commonly-used interpolation methods: (1) the Centroid method; (2) the Thiessen Polygon method; (3) the Inverse Distance Weighted (IDW) method; (4) the Dis-Kriging method; and (5) the Co-Kriging method. The Soil and Water Assessment tool (SWAT) was used to quantify the effect of rainfall spatial variability on watershed H/NPS modeling of the Daning watershed in China. Results indicated that these interpolation methods could contribute significant uncertainty in spatial rainfall variability and the carry-magnify effect caused even larger uncertainty in the H/NPS modeling. This uncertainty was magnified from hydrology modeling (stream flow) into NPS modeling (sediment, TP, organic nitrogen (N) and dissolved N). This study further suggested that H/NPS prediction uncertainty relating to spatial rainfall variability was scale-dependent due to the averaging effect of spatial heterogeneity. From a practical point of view, a global interpolation method, such as IDW and Kriging, as well as elevation data derived from a digital elevation model (DEM), should be included into the H/NPS models for reliable predictions in larger watersheds.

Estimating colony and breeding population size for nocturnal burrow-nesting seabirds

MEPS Marine Ecology Progress Series Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsTheme Sections MEPS 454:83-90 (2012) - DOI: https://doi.org/10.3354/meps09663 Estimating colony and breeding population size for nocturnal burrow-nesting seabirds Heather L. Major1,2,*, Alex M. Chubaty2 1Centre for Wildlife Ecology and 2Evolutionary and Behavioural Ecology Research Group; Department of Biological Sciences, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia V5A 1S6, Canada *Email: heather.major3@gmail.com ABSTRACT: Estimating colony areas, locations, population sizes, and trends are all important aspects of managing animal populations. The ability to assess population trends and delineate important wildlife areas remains a top priority for managers and conservation biologists. Yet, outdated laborious estimation methods remain in high use. By simulating known populations on known island sizes and using established transect and quadrat survey methods, we asked whether using inverse distance weighting (IDW) interpolations in ArcGIS improved estimates of colony area and population size for nocturnal burrow-nesting seabirds over conventional global interpolation methods. We performed 100 simulations for each of 3 population sizes (500, 1000, and 50000 breeding pairs) on 3 island sizes (10, 50, and 500 ha), excluding the largest population size on the smallest island size, for a total of 800 simulated islands. We estimated colony area and population size for each simulated island using both IDW interpolations and an established global interpolation method, and the accuracy of each estimate was then calculated. Using an information theory approach, we found that IDW interpolation estimates were overall more accurate when estimating population size, but we found no difference in colony area accuracy between interpolation methods. We recommend using IDW interpolations to estimate colony area and population size along with consistency in survey structure both among study sites and years. We also recommend maintaining a consistent transect length whenever possible to ensure that observer bias does not influence areas surveyed. KEY WORDS: Colony size · Interpolation · Line transects · Population size · Seabird Full text in pdf format PreviousNextCite this article as: Major HL, Chubaty AM (2012) Estimating colony and breeding population size for nocturnal burrow-nesting seabirds. Mar Ecol Prog Ser 454:83-90. https://doi.org/10.3354/meps09663 Export citation RSS - Facebook - Tweet - linkedIn Cited by Published in MEPS Vol. 454. Online publication date: May 21, 2012 Print ISSN: 0171-8630; Online ISSN: 1616-1599 Copyright © 2012 Inter-Research.

Temperature interpolation based on local information: the example of France

AbstractMethods of interpolation, whether based on regressions or on kriging, are global methods in which all the available data for a given study area are used. But the quality of results is affected when the study area is spatially very heterogeneous. To overcome this difficulty, a method of local interpolation is proposed and tested here with temperature in France. Starting from a set of weather stations spread across the country and digitized as 250 m‐sided cells, the method consists in modelling local spatial variations in temperature by considering each point of the grid and the n weather stations that are its nearest neighbours. The procedure entails a series of steps: recognition of the n stations closest to the cell to be evaluated and subdivision of the study area into polygons defined by a neighbourhood rule, elaboration of a local model by multiple regression for each polygon, and application of the parameter estimate from the regression to obtain a predicted value of temperature at each point of the polygon under consideration.These results are compared with results from three global interpolation methods: (1) regression, (2) ordinary kriging, and (3) regression with kriging of residuals. We then develop the original results from local interpolation such as mapping of the coefficients of determination and of the parameter estimate related to altitude and to distance to the sea. These developments highlight the processes that dictate the spatial variation of climate. Copyright © 2010 Royal Meteorological Society

The first-order approximation of non-Kirchhoff-Love theory for elastic circular plate with fixed boundary under uniform surface loading (III)—Numerical results

Based upon the differential equations and their related boundary conditions given in the previous papers[1, 2], using a global interpolation method, this paper presents a numerical solution to the axisymmetric bending problem of non-Kirchhoff-Love theory for circular plate with fixed boundary under uniform surface loading. All the numerical results obtained in this paper are compared with that of Kirchhoff-Love classical theory[3] and E. Reissner's modified theory[4].

Getting better contour plots with S and GCVPACK

We show how to obtain esthetically pleasing contour plots using New S and GCVPACK. With these codes, thin plate splines can easily be used to interpolate “exact” data, and to produce smoothly varying contour plots, with none of the jagged corners that plague many other interpolation methods. It is noted that GCVPACK can also be used to interpolate data on the sphere and in Euclidean three space. We observe that a larger class of global interpolation methods (including the thin plate spline) have a Bayesian interpolation, and GCVPACK can be used to compute them.

Numerical Procedures for Surface Fitting of Scattered Data by Radial Functions

In many applications one encounters the problem of approximating surfaces from data given on a set of scattered points in a two-dimensional domain. The global interpolation methods with Duchon's “thin plate splines” and Hardy's multiquadrics are considered to be of high quality; however, their application is limited, due to computational difficulties, to $ \sim 150$ data points. In this work we develop some efficient iterative schemes for computing global approximation surfaces interpolating a given smooth data. The suggested iterative procedures can, in principle, handle any number of data points, according to computer capacity. These procedures are extensions of a previous work by Dyn and Levin on iterative methods for computing thin-plate spline interpolants for data given on a square grid. Here the procedures are improved significantly and generalized to the case of data given in a general configuration.The major theme of this work is the development of an iterative scheme for the construction of a smooth surface, presented by global basis functions, which approximates only the smooth components of a set of scattered noisy data. The novelty in the suggested method is in the construction of an iterative procedure for low-pass filtering based on detailed spectral properties of a preconditioned matrix. The general concepts of this approach can also be used in designing iterative computation procedures for many other problems.The interpolation and smoothing procedures are tested, and the theoretical results are verified, by many numerical experiments.

Numerical Procedures for Surface Fitting of Scattered Data by Radial Functions

In many applications one encounters the problem of approximating surfaces from data given on a set of scattered points in a two-dimensional domain. The global interpolation methods with Duchon's “t...