• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.435-443
• /
• 2007

An important approach towards solving the scattered data problem is by using radial basis functions. However, for a large class of smooth basis functions such as Gaussians, the existing theories guarantee the interpolant to approximate well only for a very small class of very smooth approximate which is the so-called 'native' space. The approximands f need to be extremely smooth. Hence, the purpose of this paper is to study approximation by a scattered shifts of a radial basis functions. We provide error estimates on larger spaces, especially on the homogeneous Sobolev spaces.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.58 no.6
• /
• pp.1223-1229
• /
• 2009

The performance of Radial Basis Function Neural Networks depends on setting up the Radial Basis Functions over the input space which are the important design procedure of Radial Basis Function Neural Networks. The existing method to initialize the location of the radial basis functions over the input space is to use the conditional fuzzy C-means clustering. However, the researchers which are interested in the conditional fuzzy C-means clustering cannot get as good modeling performance as they expect because the conditional fuzzy C-means clustering cannot project the information which is extracted over the output space into the input space. To compensate the above mentioned drawback of the conditional fuzzy C-means clustering, we apply a fuzzy K-nearest neighbors approach to project the auxiliary information defined over the output space into the input space without lose of the information.

• Structural Engineering and Mechanics
• /
• v.15 no.5
• /
• pp.535-550
• /
• 2003

In this paper, a boundary-type meshfree method, the boundary radial point interpolation method (BRPIM), is presented for solving boundary value problems of two-dimensional solid mechanics. In the BRPIM, the boundary of a problem domain is represented by a set of properly scattered nodes. A technique is proposed to construct shape functions using radial functions as basis functions. The shape functions so formulated are proven to possess both delta function property and partitions of unity property. Boundary conditions can be easily implemented as in the conventional Boundary Element Method (BEM). The Boundary Integral Equation (BIE) for 2-D elastostatics is discretized using the radial basis point interpolation. Some important parameters on the performance of the BRPIM are investigated thoroughly. Validity and efficiency of the present BRPIM are demonstrated through a number of numerical examples.

• The Pure and Applied Mathematics
• /
• v.17 no.4
• /
• pp.321-332
• /
• 2010

In this paper, we experiment image warping and morphing. In image warping, we use radial basis functions : Thin Plate Spline, Multi-quadratic and Gaussian. Then we obtain the fact that Thin Plate Spline interpolation of the displacement with reverse mapping is the efficient means of image warping. Reflecting the result of image warping, we generate two examples of image morphing.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2007.04a
• /
• pp.495-500
• /
• 2007

A Meshfree is a method used to establish algebraic equations of system for the whole problem domain without the use of a predefined mesh for the domain discretization. A point interpolation method is based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity. Furthermore, the interpolation function passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshfree methods based on the moving least-squares approximation. This study aims to investigate a stress analysis of structural element between a meshfree method and the finite element method. Examples on cantilever type plate and stress concentration problems show that the accuracy and convergence rate of the meshfree methods are high.

• Journal of the Korean Data and Information Science Society
• /
• v.26 no.3
• /
• pp.749-754
• /
• 2015

This article presents Bayesian approach to regression splines with knots on a grid of equally spaced sample quantiles of the independent variables under functional measurement error model.We consider small area model by using penalized splines of non-linear pattern. Specifically, in a basis functions of the regression spline, we use radial basis functions. To fit the model and estimate parameters we suggest a hierarchical Bayesian framework using Markov Chain Monte Carlo methodology. Furthermore, we illustrate the method in an application data. We check the convergence by a potential scale reduction factor and we use the posterior predictive p-value and the mean logarithmic conditional predictive ordinate to compar models.

• Interaction and multiscale mechanics
• /
• v.2 no.4
• /
• pp.333-352
• /
• 2009

We introduce a radial basis collocation method to solve axially moving beam problems which involve $2^{nd}$ order differentiation in time and $4^{th}$ order differentiation in space. The discrete equation is constructed based on the strong form of the governing equation. The employment of multiquadrics radial basis function allows approximation of higher order derivatives in the strong form. Unlike the other approximation functions used in the meshfree methods, such as the moving least-squares approximation, $4^{th}$ order derivative of multiquadrics radial basis function is straightforward. We also show that the standard weighted boundary collocation approach for imposition of boundary conditions in static problems yields significant errors in the transient problems. This inaccuracy in dynamic problems can be corrected by a statically condensed semi-discrete equation resulting from an exact imposition of boundary conditions. The effectiveness of this approach is examined in the numerical examples.

• Proceedings of the Acoustical Society of Korea Conference
• /
• 1997.06a
• /
• pp.13-16
• /
• 1997

본 논문에서는 Bayesian 결정 이론을 이용한 기존의 Radial Basis Function Networks 이되는 출력층에서 선형 조합되는 것과는 다른 형태의 방법을 제안하고자 한다. 제안하고자 하는 방법은 은닉층의 출력값과 가중치와의 곱해진 값이 출력층의 입력으로 들어오는데 이들 입력신호를 경쟁을 통하여 가장 큰 값만을 출력신호 인정하는 방법이다. 이런 경우에 파라미터 갱신을 할 때도 모든 가중치를 다 갱신하는 것이 아니라 출력되는 은닉층에 연결된 가중치만을 갱신하게된다. 이렇게 할 경우 계산량 감소뿐만 아니라 학습시간을 단축할 수 있다는 장점이 있다. 그리고 제안한 방법을 이용할 경우 비선형 분류문제에서도 우수한 성능결과를 확인 할 수 있었으며 기존의 RBFN rhk Wiener Filter와 성능을 비교하였다.

• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.200-200
• /
• 2000

Highly nonlinear dynamical systems are easily identified using neural networks. When disturbances are included in the learning data set Int system modeling, modeling process will be poorly performed. Since the radial basis functions in the radial basis function network(RBFN) are centered at the points specified by the weights, RBF networks are robust for approximating the process including the narrow-band disturbances deviating significantly from the regular signals. To exclude(filter) these disturbances, a robust algorithm for system identification, based on the RBFN, is proposed. The performance of system identification excluding disturbances is investigated and compared with the one including disturbances.

• Journal of Astronomy and Space Sciences
• /
• v.15 no.1
• /
• pp.229-234
• /
• 1998

We study on a terrain contour matching algorithm using Radial Basis Functions(RBFs) for aided inertial navigation system for position fixing aircraft, cruise missiles or re-entry vehicles. The parameter optimization technique is used for updating the parameters describing the characteristics of an area with modified Gaussian least square differential correction algorithm and the step size limitation filter according to the amount of updates. We have applied the algorithm for matching a sampled area with a target area supposed that the area data are available from Radar Terrain Sensor(RTS) and Reference Altitude Sensor(RAS)