• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.8-13
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• 2008

In this study, an adaptive node generation procedure in the radial point interpolation method is proposed. Since we set the initial configuration of nodes by subdivision of background cell, abrupt changes of inter-nodal distance between higher and lower error regions are unavoidable. This unpreferable nodal spacing induces additional errors. To obtain the smoothy nodal configuration, it's regenerated by local Delaunay triangulation algorithm This technique was originally developed to generate a set of well-shaped triangles and tetrahedra. To demonstrate the performance of proposed scheme, the results of making optimal nodal configuration with adaptive refinement method are investigated for stress concentration problems.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.951-969
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• 2012

In this paper, we propose a class of meshless collocation approaches for the solution of time dependent partial differential algebraic equations (PDAEs) in terms of a radial basis function interpolation numerical scheme. Kansa's method and the Hermite collocation method (HCM) for PDAEs are given. A sensitivity analysis of the solutions from different shape parameter c is obtained by numerical experiments. With use of the random collocation points, we have obtain the more accurate solution by the methods than those by the finite difference method for the PDAEs with index-2, i.e, we avoid the influence from an index jump of PDAEs in some degree. Several numerical experiments show that the methods are efficient.

• Structural Engineering and Mechanics
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• v.81 no.5
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• pp.607-616
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• 2022

In this work, the free vibration problem of a rotating Rayleigh beam is solved using the meshless Petrov-Galerkin method which is a truly meshless method. The Rayleigh beam includes rotatory inertia in addition to Euler-Bernoulli beam theory. The radial basis functions, which satisfy the Kronecker delta property, are used for the interpolation. The essential boundary conditions can be easily applied with radial basis functions. The results are obtained using six nodes within a subdomain. The results accurately match with the published literature. Also, the results with Euler-Bernoulli are obtained to compare the change in higher natural frequencies with change in the slenderness ratio (${\sqrt{A_0R^2/I_0}}$). The mass and stiffness matrices are derived where we get two stiffness matrices for the node and boundary respectively. The non-dimensional form is discussed as well.

• Journal of Ocean Engineering and Technology
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• v.20 no.3 s.70
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• pp.67-76
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• 2006

Three-dimensional information of submarine topography was acquired by assembling DGPS and Echo Sounder, which is mainly used in the marine survey. However, the features of submarine topography, derived according to mechanical data, were confirmed using human eyes. Because the dredging capacity using a submarine surveying data influences harbor public affairs, analysis and the process method of surveying data is a very special element in construction costs. In this study, information on submarine topography is acquired by assembling DGPS and Echo Sounder. Moreover, the dredging capacity in harbor public affairs has been analyzed by the interpolation method: inverse distance to a power, kriging, minimum curvature, nearest neighbor, and radial basis function. Also, utilization of DGPS and Echo Sounder method in calculation of the dredging capacity have been confirmed by comparing and analyzing the dredging capacity and the actual one, as per each interpolation. According to this comparison result, in the case of applying Radial basis function interpolation and Kriging, 3.94 % and 4.61 % of error rates have been shown, respectively. In the case of the study for application of the proper interpolation, as per characteristics of submarine topography, is preceded in calculation of the dredging capacity relevant to harbor public affairs, it is expected that more speedy and correct calculation for the dredging capacity can be made.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.562-567
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• 1998

This paper examined the relations among the multidimensional linear interpolation(MDI) and fuzzy reasoning , and neural networks, and showed that an showed that an MDI is a special form of Tsukamoto's fuzzy reasoning and regularization networks in the perspective of fuzzy reasoning and neural networks, respectively. For this purposes, we proposed a special Tsukamoto's membership (STM) systemand triangular basis function (TBF) networks, Also we verified the condition when our proposed TBF becomes a well-known radial basis function (RBF).

• Journal of the Korean Association of Geographic Information Studies
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• v.23 no.3
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• pp.85-99
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• 2020

Reservoir is an important infrastructure of our society because it can store immense amount of water for various usages - manufacturing, agriculture, drinking, power generation, tourism etc. For maintenance of reservoir, various efforts in administrative and technological aspects are periodically conducted and monitoring the conditions of reservoir bed is the first priority for maintenance of reservoir. To check the conditions of reservoir bed, we measured depth of reservoir by using echo sounder, which is relatively reliable, prior to discharging of stored water and surveyed topography of reservoir by using UAV after discharging of water. Then, we conducted interpolation of measured depth of water by means of inverse distance weighting interpolation, Kriging interpolation, minimum curvature interpolation and radial basis function interpolation and calculated the volume of reservoir for each interpolation method. We compared the calculated volume of reservoir with the volume of water calculated by UAV after discharging of water and found the following results: First, as results of the above processes, we found that the Kriging interpolation was 97% correct in measurement of the volume of reservoir. Second, as results of comparison of differences between topographical areas and interpolated areas after selection of cross section for comparison, Kriging interpolation was found to have the most similar configuration with the topographical configuration by showing the least difference in the area of cross section. Therefore, it is determined that the optimal modeling of reservoir bed with the water depth data measured by echo sounder shall provide basic information for efficient maintenance of reservoir.

• Structural Engineering and Mechanics
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• v.88 no.3
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• pp.239-249
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• 2023

The Radial Point Interpolation Method (RPIM) has been proposed to overcome the difficulties associated with the use of the Radial Basis Functions (RBFs). The RPIM has the following properties: Simple implementation in terms of boundary conditions as in the Finite Element Method (FEM). A less expensive CPU time compared to other collocation meshless methods such as the Moving Least Square (MLS) collocation method. In this work, we propose an adaptive high-order numerical algorithm based on RPIM to simulate the thermoviscoplastic behavior of a material mixing observed in the Friction Stir Welding (FSW) process. The proposed adaptive meshfree RPIM algorithm adapts well to the geometric and physical data by choosing a good shape parameter with a good precision. Our numerical approach combines the RPIM and the Asymptotic Numerical Method (ANM). A numerical procedure is also proposed in this work to automatically determine an improved shape parameter for the RBFs. The efficiency of the proposed algorithm is analyzed in comparison with an iterative algorithm.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.29 no.5
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• pp.543-550
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• 2011

The gravity anomaly is a basic geophysical data applied in various fields such as geophysics, geodesy and national defense. In general, the gravity anomaly is used through a interpolation process based on the constructed database. The gravity variation, however, is appeared in various shapes depending on the topography and the density of the underground structures. Therefore, the interpolation could lead to a large differences if the gravity fields do not satisfy the assumptions on the signal behavior like linear or a certain degree polynomials. Furthermore, the interpolation does not reflect the physical characteristics of the gravity such as the harmonic condition. In this study, the gravity modeling using the plane Fourier series and radial basis functions are performed to overcome the problems in the usual interpolation. The results of the modeling is analyzed for the case of the gravity referenced navigation focused on the signal characteristics. Based on the study, it was found that the results from modeling are not much different to that from the interpolation in a smoothly varied area. In case of the highly varied area, however, a large differences are appeared among the three methods. Especially, the Fourier series shows the most smooth variations in the modeled gravity values while the highest variations appeared in the interpolation. Applying to the gravity referenced navigation, it was found that the modeling is more effective in calculation cost. It is considered that the results from this study provides a basis on effective modeling of the gravity fields in terms of the signal characteristics and resolution for various application fields.

• Journal of Computing Science and Engineering
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• v.2 no.1
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• pp.98-108
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• 2008

Terrain reconstruction from images is an ill-posed, yet commonly desired Structure from Motion task when compositing visual effects into live-action photography. These surfaces are required for choreography of a scene, casting physically accurate shadows of CG elements, and occlusions. We present a novel framework for generating the geometry of landscapes from extremely noisy point cloud datasets obtained via limited resolution techniques, particularly optical flow based vision algorithms applied to live-action video plates. Our contribution is a new statistical approach to remove erroneous tracks ('outliers') by employing a unique combination of well established techniques-including Gaussian Mixture Models (GMMs) for robust parameter estimation and Radial Basis Functions (REFs) for scattered data interpolation-to exploit the natural constraints of this problem. Our algorithm offsets the tremendously laborious task of modeling these landscapes by hand, automatically generating a visually consistent, camera position dependent, thin-shell surface mesh within seconds for a typical tracking shot.

• ETRI Journal
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• v.22 no.2
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• pp.1-10
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• 2000

Pattern recognition is one of the most common problems encountered in engineering and scientific disciplines, which involves developing prediction or classification models from historic data or training samples. This paper introduces a new approach, called the Representational Capability (RC) algorithm, to handle pattern recognition problems using radial basis function (RBF) models. The RC algorithm has been developed based on the mathematical properties of the interpolation and design matrices of RBF models. The model development process based on this algorithm not only yields the best model in the sense of balancing its parsimony and generalization ability, but also provides insights into the design process by employing a design parameter (${\delta}$). We discuss the RC algorithm and its use at length via an illustrative example. In addition, RBF classification models are developed for heart disease diagnosis.