• The Korean Journal of Applied Statistics
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• v.5 no.2
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• pp.181-192
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• 1992

We consider the estimation of the regression surface in generalized linear models based on tensor-product B-splines in a data-dependent way. Our approach is to use maximum likelihood method to estimate the regression function by a function from a space of tensor-product B-splines that have a finite number of knots and are linear in the tails. The knots are placed at selected order statistics of each coordinate of the sample data. The number of knots is determined by minimizing a variant of AIC. A numerical example is used to illustrate the performance of the tensor spline estimates.

• Journal of Ship and Ocean Technology
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• v.10 no.2
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• pp.24-36
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• 2006

Ship hullform is usually designed with a curve network, and smooth hullform surfaces are supposed to be generated by filling in (or interpolating) the curve network with appropriate surface patches. Tensor-product surfaces such as B-spline and $B\'{e}zier$ patches are typical representations to this interpolating problem. However, they have difficulties in representing the surfaces of irregular topological type which are frequently appeared in the fore- and after-body of ship hullform curve network. In this paper, we proposed a method that can automatically generate discrete $G^1$ continuous B-spline surfaces interpolating given curve network of ship hullform. This method consists of three steps. In the first step, given curve network is reorganized to be of two types: boundary curves and reference curves of surface patches. Especially, the boundary curves are specified for their surface patches to be rectangular or triangular topological type that can be represented with tensor-product (or degenerate) B-spline surface patches. In the second step, surface fitting points and cross boundary derivatives are estimated by constructing virtual iso-parametric curves at discrete parameters. In the last step, discrete $G^1$ continuous B-spline surfaces are generated by surface fitting algorithm. Finally, several examples of resulting smooth hullform surfaces generated from the curve network data of actual ship hullform are included to demonstrate the quality of the proposed method.

• Structural Engineering and Mechanics
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• v.25 no.5
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• pp.613-629
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• 2007

A finite element method (FEM) of B-spline wavelet on the interval (BSWI) is used in this paper to solve the static and vibration problems of thin plate. Instead of traditional polynomial interpolation, the scaling functions of two-dimensional tensor product BSWI are employed to construct the transverse displacements field. The method combines the accuracy of B-spline functions approximation and various basis functions for structural analysis. Some numerical examples are studied to demonstrate the proposed method and the numerical results presented are in good agreement with the solutions of other methods.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.429-436
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• 2003

A new linkage framework between elastic shell element with finite rotation and computar-aided geometric design (CAGD) (or surface is developed in the present study. The framework of shell finite element is based on the generalized curved two-parametric coordinate system. To represent free-form surface, cubic B-spline tensor-product functions are used. Thus the present finite element can be directly linked into the geometric modeling produced by surface generation tool in CAD software. The efficiency and accuracy of the Previously developed linear elements hold for the nonlinear element with finite rotations. To handle the finite rotation behavior of shells, exponential mapping in the SO(3) group is employed to allow the large incremental step size. The integrated frameworks of shell geometric design and nonlinear computational analysis can serve as an efficient tool in shape and topological design of surfaces with large deformations.

• Journal of Ocean Engineering and Technology
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• v.31 no.3
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• pp.189-195
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• 2017

A three-dimensional higher order boundary element method based on the B-spline is presented. The method accurately models piecewise continuous bodies and induced velocity potentials using B-spline tensor product representations, and it is capable of obtaining accurate pointwise values for the potential and its derivatives, especially in the trailing edge and tip region of the lift generating body, which may be difficult or impossible to evaluate with constant panel methods. In addition, we implement a wake roll-up and examine the tip vortex formation in the near wake region. The results are compared with existing numerical results and the results of experiments performed out at the cavitation tunnel of Chungnam National University.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.8
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• pp.1007-1013
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• 2010

A new local refinement scheme for spline finite element method has been proposed; this scheme involves the use of hierarchical B-spline. NURBS has been widely used in CAD; however, the local refinement of NURBS is difficult due to its tensor-product property. In this study, we attempted to use hierarchical B-splines as local refinement strategy in spline FEM. The regions of high gradients are overlapped by hierarchically-created local meshes. Knot vectors and control points in local meshes are extracted from global meshes, and they are refined using specific schemes. Proper compatibility conditions are imposed between global and local meshes. The effectiveness of the proposed method is verified on the basis of numerical results. Further, it is shown that by using a proposed local refinement scheme, the accuracy of the solution can be improved and it could be higher than that of the solution of a conventional spline FEM with relatively lower degrees of freedom.

• Structural Engineering and Mechanics
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• v.38 no.6
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• pp.733-751
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• 2011

In the present study, a new kind of multivariable Reissner-Mindlin plate elements with two kinds of variables based on B-spline wavelet on the interval (BSWI) is constructed to solve the static and vibration problems of a square Reissner-Mindlin plate, a skew Reissner-Mindlin plate, and a Reissner-Mindlin plate on an elastic foundation. Based on generalized variational principle, finite element formulations are derived from generalized potential energy functional. The two-dimensional tensor product BSWI is employed to form the shape functions and construct multivariable BSWI elements. The multivariable wavelet finite element method proposed here can improve the solving accuracy apparently because generalized stress and strain are interpolated separately. In addition, compared with commonly used Daubechies wavelet finite element method, BSWI has explicit expression and a very good approximation property which guarantee the satisfying results. The efficiency of the proposed multivariable Reissner-Mindlin plate elements are verified through some numerical examples in the end.

• The Korean Journal of Applied Statistics
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• v.13 no.2
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• pp.489-503
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• 2000

Data mining means data analysis and model selection using various types of data in order to explore useful information and knowledge for making decisions. Examples of data mining include scoring for credit analysis of a new customer and scoring for churn management, where the customers with high scores are given special attention. In this paper, scoring is interpreted as a modeling process of the conditional probability and polyclass scoring method is described. German credit data, a PC communication company data and a mobile communication company data are used to compare the performance of polyclass scoring method with that of the scoring method based on a tree model.