Inverse Distance Weighting Algorithm Research Articles

Advanced geospatial modeling and statistical evaluation of heterogenous geotechnical facets at multiple depths using the improved formulation of modified Shepard IDW algorithm

A formidable challenge in geology and geotechnics is the significant spatial heterogeneity in the subsoil characteristics in fine-scale grids. To mitigate this problem, geotechnical data is integrated as geotechnical soil maps (GSMs), which uses sophisticated interpolation techniques and provides an advanced understanding and accurate depiction of subsurface variability. This study uses an improved formulation of inverse distance weighting (IDW) algorithm based on modified Shepard method, integrated with the Google Earth Engine platform. The prediction efficiencies of GSMs and traditional IDW algorithm are statistically evaluated and compared, considering heterogeneous geotechnical facets at multiple depths in an unexplored region. Pertinent geotechnical properties including soil type, plasticity index, and standard penetration test were considered to evaluate the algorithm performance based on critical performance metrics. The results demonstrate that the improved formulation of the IDW algorithm is more relevant to field values and tends to align with Tobler's first law of geography by inducing a smooth transition rather than a disruptive trend owing to high geotechnical variability. The prediction accuracy increased by 10 – 20% compared to the traditional IDW algorithm. This study demonstrates and promotes the use of an improved formulation of the modified IDW algorithm considering its better accuracy and relevance to field value

Reconstruction of γ Dose Rate Field and Algorithm Validation Based on Inverse Distance Weight Interpolation

The inverse distance weighting (IDW) interpolation algorithm is used to reconstruct the γ radiation field. The traditional IDW interpolation algorithm is improved. The power exponent of distance P in the IDW for each interpolation point is not fixed and varies from one point to the other point. A fitting expression of P is obtained, which is a function of the coordinates of each point and can minimize the interpolation error when the number of sampling points is specified. Afterward, the improved algorithm is used to reconstruct a γ radiation field of a single source, and the theoretic results are compared with the results from Geant4, yielding an average relative error of 7.50%. The interpolated results from the experimental measurements align well with the actual data, with an average relative error of only 0.12%. The P derived from the interpolated experimental measurement data shows an error of 2.0% compared to the power exponent obtained from the Geant4 data interpolation. Then we set up a double-source γ radiation scene experiment and measured the count rate data at the grid points. At the same time, the experiment scene was simulated by Geant4. The improved IDW algorithm could not reconstruct the double-source γ radiation field well, thus further improvement is needed.

Robot joint space grid error compensation based on three-dimensional discrete point space circular fitting

The poor absolute positioning accuracy of industrial robots has limited their application in fields such as aerospace manufacturing. To address this issue, the spatial grid compensation method has been proposed as an effective solution. In this paper, we propose a sampling method based on three-dimensional discrete point space circular fitting for grid points to significantly reduce the sampling workload and improve compensation accuracy compared to traditional joint space grid compensation methods. Additionally, we use the Kriging interpolation algorithm instead of the inverse distance weighting (IDW) algorithm for spatial interpolation prediction of pose error. Based on this, the proposed sampling and interpolation prediction method in this paper was verified on a Comau NJ500–2.7 manipulator equipped with a fiber-laying end effector. The experimental results demonstrate that using our proposed sampling method yields pose data of grid points that have only a small deviation from directly sampled results and are only slightly higher than the robot's repeat positioning accuracy. Moreover, our proposed method can significantly reduce the sampling workload by 60% under the experimental conditions of this study (sampling 10 groups of data within 90 degrees range), with increasing sampling range leading to more obvious efficiency improvements. Finally, we show that compared to the IDW algorithm, the Kriging interpolation algorithm yields better results and improves the mean absolute positioning accuracy of robots after compensation by 30%.

Development of daily gridded Penman-Monteith reference crop evapotranspiration data for Karnataka State, India

ABSTRACT Reference crop evapotranspiration (ET0) estimates are often unavailable at fine spatial resolutions due to the lack of dense climatic networks. The present study was taken up to develop a methodology for obtaining a gridded Penman-Monteith (PM) ET0 dataset for Karnataka State, India, through spatial interpolation of estimates obtained at climate stations. Three interpolation techniques, Inverse Distance Weighted (IDW), Kriging, and Point-Based Sentinel Hospitals Area Distance (P-BSHADE), were employed to derive PM ET0 estimates. Considering the historical climate records of 67 stations located in Karnataka State for the period of 2006–2016, the interpolation methodologies were evaluated using a cross-validation procedure. Results showed that the performance of IDW was better with significant error reduction at validation sites. Subsequently, the IDW algorithm was used to derive daily PM ET0 values at 0.25° × 0.25° grids over the Karnataka State, India. Finally, the comparative analysis of developed PM ET0 gridded data product against three global ET0 products indicated the developed gridded ET0 to be most accurate across different agroclimatic zones. Web links of the developed product have been created in an effort to share the data on ET0, which is a critical input in a variety of studies in earth sciences.

Optimized inverse distance weighted interpolation algorithm for γ radiation field reconstruction

The inversion of radiation field distribution is of great significance in the decommissioning sites of nuclear facilities. However, the radiation fields often contain multiple mixtures of radionuclides, making the inversion extremely difficult and posing a huge challenge. Many radiation field reconstruction methods, such as Kriging algorithm and neural network, can not solve this problem perfectly. To address this issue, this paper proposes an optimized inverse distance weighted (IDW) interpolation algorithm for reconstructing the gamma radiation field. The algorithm corrects the difference between the experimental and simulated scenarios, and the data is preprocessed with normalization to improve accuracy. The experiment involves setting up gamma radiation fields of three Co-60 radioactive sources and verifying them by using the optimized IDW algorithm. The results show that the mean absolute percentage error (MAPE) of the reconstruction result obtained by using the optimized IDW algorithm is 16.0%, which is significantly better than the results obtained by using the Kriging method. Importantly, the optimized IDW algorithm is suitable for radiation scenarios with multiple radioactive sources, providing an effective method for obtaining radiation field distribution in nuclear facility decommissioning engineering.

Novel application of Google earth engine interpolation algorithm for the development of geotechnical soil maps: a case study of mega-district

This article explores the novel application of the Google Earth Engine (GEE) platform using the inverse distance weighting (IDW) interpolation technique based on an improved version of the modified Shephard method for the development of specialized geotechnical soil maps (GSMs) for mega-district Lahore. The study area was assessed at multiple depths in terms of key geotechnical properties. The result depicts a predominance of fine-grained soil at a shallow depth of 3 m exhibiting low to moderate soil stiffness, consistency and activity along with a few zones of problematic soil with adverse geotechnical characteristics which require due attention. Whereas beyond 3 m the study area exhibits higher bearing values, low plasticity and non-active soil. Besides, the chemical content level was within permissible limits except for a few spots. The comprehensive statistical evaluation based on key performance indices indicates the efficient performance of the novel GEE-based IDW algorithm to yield significantly accurate maps.

Reconstruction of Rainfall Field Using Earth–Space Links Network: A Compressed Sensing Approach

High-precision rainfall information is of great importance for the improvement of the accuracy of numerical weather prediction and the monitoring of floods and mudslides that affect human life. With the rapid development of satellite constellation networks, there is great potential for reconstructing high-precision rainfall fields in large areas by using widely distributed Earth–space link (ESL) networks. In this paper, we have carried out research on reconstructing high-precision rainfall fields using an ESL network with the compressed sensing (CS) method in the case of a sparse distribution of the ESLs. Firstly, ESL networks with different densities are designed using the K-means clustering algorithm. The real rainfall fields are then reconstructed using the designed ESL networks with CS, and the reconstructed results are compared with that of the inverse distance weighting (IDW) algorithm. The results show that the root mean square error (RMSE) and correlation coefficient (CC) of the reconstructed rainfall fields using the ESL network with CS are lower than 0.15 mm/h and higher than 0.999, respectively, when the density is 0.05 links per square kilometer, indicating that the ESL network with CS is capable of reconstructing the high-precision rainfall fields under sparse sampling. Additionally, the performance of reconstructing the rainfall fields using the ESL networks with CS is superior compared to the reconstructed results of the IDW algorithm.

Spatial variation of sub-surface heterogenieties within the dyke swarm of Nandurbar region, Maharashtra, India, for groundwater exploration using Inverse Distance Weighted technique

To understand the protective capacity of aquifers, anisotropic nature and fracture geometry of dyke infested terrain in parts of Nandurbar region, Maharashtra, data from 39 vertical electrical soundings using Schlumberger configuration were acquired. Analysis suggests 3–5 layered structure in the study area. Further, the Dar-Zarrouk and other geoelectric indices were computed utilizing resistivity and layer thickness at each station. The Inverse Distance Weighted (IDW) algorithm was used to interpolate data spatially. Longitudinal conductance values suggest that the area has poor to moderate aquifer protective capacity, indicating that weaker zones may be prone to infiltrating contaminants. The high electrical anisotropy (λ) signifies EW and NS oriented dykes, suggesting heterogeneous and anisotropic nature of the subsurface. A direct relationship involving λ and fracture porosity indicate porous medium. The IDW algorithm, used for the first time in this region, provided an accurate and reliable estimate of spatial distribution and the underlying heterogeneities.

一种基于反距离权重法修正CMM体积误差的方法

一种基于反距离权重法修正CMM体积误差的方法

Multiplanar reconstruction with incomplete data via enhanced fuzzy radial basis function neural networks

Slice images based on a single slicing direction often contain incomplete data and cannot be used by clinicians for diagnosis or observation. It is thus necessary to reconstruct the slices using multiplanar reconstruction technology. In the case of complete data, it is not difficult to obtain a series of clear images from other slicing directions. In the case of incomplete data, interpolation methods are commonly employed on reconstructed images to compensate for the missing information. However, such results are often not ideal. In this study, we propose a new method based on an enhanced fuzzy radial basis function neural network. First, a series of incomplete transverse section images that have been accurately registered are adopted. Then, we superpose the sequence images to obtain the three-dimensional data volume. Thereafter, we can acquire the coronal or sagittal images by reformatting this data volume. For a reconstructed image, the proposed system was applied to compensate for the lost data. We used 15 sets of proposed neural networks to obtain 15 sets of output data, with the final output data acquired via the inverse distance-weighted algorithm. We trained the system via a gravitational search algorithm. Finally, we repaired all the interpolated data. In this experiment, we used two types of datasets, i.e., images obtained via brain magnetic resonance imaging and abdominal computed tomography. Subjective observations and objective evaluations confirm the superiority and effectiveness of the proposed method compared to other state-of-the-art methods.

Haemodialysis services in the northeastern region of Iran.

Chronic kidney disease is growing and the current estimated global prevalence exceeds 13%. As the use of haemodialysis machines for patients with end stage renal disease increases survival considerably, it is critical to plan correctly for the allocation of these machines. This study aimed to develop a geographical information systems (GIS)-based approach to predict the need for this service in the northeastern region of Iran taking into account where patients live and where haemodialysis is the most needed and identifying areas with poor access to haemodialysis centres. Patients were interviewed to obtain self-reported actual travel time and the inverse distance-weighting algorithm was used to determine access in each area. The prediction is based on the domestic growth rate for haemodialysis services and the estimated active hours of machine use for the next five years. We estimate that six new haemodialysis machines are required in northeastern Iran at the present time with 50 machines required over the next five years. Ashkhane City was identified to have the least access to haemodialysis centres in the study area. Our GIS-based model can be used to investigate not only the need for new haemodialysis machines but also to examine geographic disparities in the allocation of haemodialysis centres and to identify areas most in need of this service. It is important that policymakers consider both spatial and non-spatial dimensions of access to enable better allocation of haemodialysis services ensuring they are targeted to reach those in need.

An Overview of Equal Educational Opportunities in Turkey: A Spatial Analysis of Classrooms in Rural and Urban Primary Schools

The number of students in a class is a primary factor affecting the quality of education. Therefore, this study examines the distribution of the number of students per class in rural and urban primary schools in Turkey, and efforts have been made to specify classroom needs. Statistical data was obtained from the Turkish Institute of Statistics and the Ministry of National Education. In order to better interpret data, graphs and maps were prepared with the help of GIS. The MapInfo 12.0 program was used for map drawing. The data was mapped using the Inverse Distance Weighted Algorithm. Whether there was global clustering regarding the distribution of the number of students per class in both rural and urban primary schools in Turkey was investigated using Moran I. In addition, local Moran I maps were employed to identify whether or not there was local clustering or neighboring interaction. At the end of the research, a variety of findings and results were obtained regarding the condition of primary school classes in Turkey. In conclusion, it has been determined that there is a need for more classes in certain regions, while they are urgently needed in others.

Machine Learning on Spark for the Optimal IDW-based Spatiotemporal Interpolation

GIScience 2016 Short Paper Proceedings Machine Learning on Spark for the Optimal IDW-based Spatiotemporal Interpolation Weitian Tong 1 , Jason Franklin 1 , Xiaolu Zhou 2 , Lixin Li 1* , Gina Besenyi 3 Department of Computer Sciences, Department of Geology and Geography, Georgia Southern University, P.O. Box 7997, Statesboro, GA 30460, USA Emails: {wtong; jf00936; xzhou; lli}@georgiasouthern.edu Clinical and Digital Health Sciences, CAHS, Augusta University, Augusta, GA 30912, USA Email: gbesenyi@augusta.edu Abstract To improve current spatiotemporal interpolation methods for public health applications (Li et al., 2010), we combine the extension approach (Li and Revesz, 2004) with machine learning methods, employ the efficient k-d tree structure to store data, and implement our method on Apache Spark (Spark, 2016). Preliminary results demonstrate the computational power of our method, which outperforms the previous work in terms of speed and generates comparable results in terms of accuracy (Li et al., 2014). Future research will continue exploring this method to improve the interpolation accuracy and efficiency, with the long term objective of establishing associations between air pollution exposure and adverse health effects. 1. Introduction To implement the spatiotemporal interpolation method, Li and Revesz (2004) proposed an extension approach, which resolves the spatiotemporal interpolation into a higher-dimensional spatial interpolation by treating time as an asymmetric dimension in space. Unfortunately, modern work on spatiotemporal interpolation (Pebesma, 2012; Graler et al., 2013; Losser et al., 2014; Li et al., 2014, etc) utilizes simplistic methods to scale the range of the time dimension. In recent work, Li et al. (2014) extended the inverse distance weighted (IDW) method (Shepard, 1968) to model the PM 2.5 exposure risk by scaling the time domain with a parameter !, which is a similar concept to the spatiotemporal anisotropy parameter (Graler et al., 2014). In applying the extension approach to the spatial IDW method to interpolate the spatiotemporal data, we arrived at the following formulae where #, %, !& represents the unknown value to be calculated at the un-sampled location (#, %) and time instance t, ! is the spatiotemporal anisotropy parameter, 6 is the exponent that influences the weighting of ) , and n is the number of nearest neighbors. Applying k-fold cross validation (k-CV) to the training set can discover the optimal parameters !, 6 and 7 for this data set in order to estimate the daily PM 2.5 concentration values at unknown points. Building upon this work, our method parallelizes the implementation of the original IDW algorithm using Correspondence Author

Parallel Algorithms for Spatial Rainfall Distribution

This paper proposes parallel algorithms for precipitation of flood modelling, especially applied in spatial rainfall distribution. As an important input in flood modelling, spatial distribution of rainfall is always needed as a pre-conditioned model. In this paper two interpolation methods, Inverse distance weighting (IDW) and Ordinary kriging (OK) are discussed. Both are developed in parallel algorithms in order to reduce the computational time. To measure the computation efficiency, the performance of the parallel algorithms are compared to the serial algorithms for both methods. Findings indicate that: (1) the computation time of OK algorithm is up to 23% longer than IDW; (2) the computation time of OK and IDW algorithms is linearly increasing with the number of cells/ points; (3) the computation time of the parallel algorithms for both methods is exponentially decaying with the number of processors. The parallel algorithm of IDW gives a decay factor of 0.52, while OK gives 0.53; (4) The parallel algorithms perform near ideal speed-up.