• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.11-18
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• 2004

In this paper, an efficient model reduction scheme is presented for large scale dynamic systems. The method is founded on a modal analysis in which optimal eigenvalue is extracted from time samples of the given system response. The techniques we discuss are based on classical theory such as the Karhunen-Loeve expansion. Only recently has it been applied to structural dynamics problems. It consists in obtaining a set of orthogonal eigenfunctions where the dynamics is to be projected. Practically, one constructs a spatial autocorrelation tensor and then performs its spectral decomposition. The resulting eigenfunctions will provide the required proper orthogonal modes(POMs) or empirical eigenmodes and the correspondent empirical eigenvalues (or proper orthogonal values, POVs) represent the mean energy contained in that projection. The purpose of this paper is to compare the reduced order model using Karhunen-Loeve expansion with the full model analysis. A cantilever beam and a simply supported plate subjected to sinusoidal force demonstrated the validity and efficiency of the reduced order technique by K-L method.

• Korean Journal of Computational Design and Engineering
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• v.14 no.1
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• pp.10-17
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• 2009

Surface detection and parameter estimation in point cloud is a relevant subject in CAD/CAM, reverse engineering, computer vision, coordinate metrology and digital factory. In this paper we present a software for a fully automatic surface detection and parameter estimation in unordered, incomplete and error-contaminated point cloud with a large number of data points. The software consists of three algorithmic modules each for object identification, point segmentation, and model fitting, which work interactively. Our newly developed algorithms for orthogonal distance fitting(ODF) play a fundamental role in each of the three modules. The ODF algorithms estimate the model parameters by minimizing the square sum of the shortest distances between the model feature and the measurement points. We demonstrate the performance of the software on a variety of point clouds generated by laser radar, computer tomography, and stripe-projection method.

• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.423-429
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• 2014

This paper discusses a method for getting Type I sums of squares by projections under a two-way fixed-effects model when variances of errors are not equal. The method of weighted least squares is used to estimate the parameters of the assumed model. The model is fitted to the data in a sequential manner by using the model comparison technique. The vector space generated by the model matrix can be composed of orthogonal vector subspaces spanned by submatrices consisting of column vectors related to the parameters. It is discussed how to get the Type I sums of squares by using the projections into the orthogonal vector subspaces.

• Nuclear Engineering and Technology
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• v.55 no.8
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• pp.2835-2843
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• 2023

After an emergency shutdown of a lead-bismuth fast reactor, thermal stratification occurs in the upper Plenum, which negatively impacts the integrity of the reactor structure and the residual heat removal capacity of natural circulation flow. The research on thermal stratification of reactors has mainly been conducted using an experimental method, a system program, and computational fluid dynamics (CFD). However, the equipment required for the experimental method is expensive, accuracy of the system program is unpredictable, and resources and time required for the CFD approach are extensive. To overcome the defects of thermal stratification analysis, a high-precision full-order thermal stratification model based on CFD technology is prepared in this study. Furthermore, a reduced-order model has been developed by combining proper orthogonal decomposition (POD) with Galerkin projection. A comparative analysis of thermal stratification with the proposed full-order model reveals that the reduced-order thermal stratification model can well simulate the temperature distribution in the upper plenum and rapidly elucidate the thermal stratification interface characteristics during the lead-bismuth fast reactor accident. Overall, this study provides an analytical tool for determining the thermal stratification mechanism and reducing thermal stratification.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.7
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• pp.157-165
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• 1989

To recover three dimensional information in Shape from Texture, the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts. In this paper, we show an approximated maximum likelihood estimation method in which we find surface orientation of the visible surface (hemisphere) in gaussian sphere using local analysis of the texture. In addition, assuming that an orthogonal projection and a circle is an image formation system and a texel (texture element) respectively, we drive the surface orientation from the distribution of variation by means of orthogonal projection of a tangent direction which exists regularly in the arc length of a circle. We present the orientation parameters of textured surface with slant and tilt in gradient space, and also the surface normal of the resulted surface orientationas as needle map. This algorithm is applied to geographic contour (artificially generated chejudo) and synthetic texture.

• Journal of Korea Multimedia Society
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• v.7 no.12
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• pp.1680-1691
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• 2004

One of the representative methods of optical flow is a gradient method which estimates the movement of an object based on the differential of image brightness. However, the method is ineffective for large displacement of the object and many improved methods have been proposed to copy with such limitations. One of these improved techniques is the multigrid processing, which is used in many optical flow algorithms. As an alternative novel technique we have been proposing an orthogonal functional expansion method, where whole displacements are expanded from low frequency terms. This method is expected to be applicable to flow estimation with large displacement and deformation including expansion and contraction, which are difficult to cope with by conventional optical flow methods. In the orthogonal functional expansion method, the apparent displacement field is calculated iteratively by a projection method which utilizes derivatives of the invariant constraint equations of brightness constancy. One feature of this method is that differentiation of the input image is not necessary, thereby reducing sensitivity to noise. In this paper, we apply our method to several real images in which the objects undergo large displacement and/or deformation including expansion. We demonstrate the effectiveness of the orthogonal functional expansion method by comparing with conventional methods including our optimally scaled multigrid optical flow algorithm.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.7
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• pp.1407-1413
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• 1994

To obtain accurate target information in a radar system, clutter or interference signals must first be effectively removed for target detection. In this paper, the signal is projected onto a constrained orthogonal subspace, so that a minimum variance optimal detector is transformed into an unconstrained detector. The proposed algorithm is equivalent to the conventional optimal detector algorithm, and th algorithm structure shows that the Gram-Schmidt orthogonalization can be achieved to obtain the fast convergence. The performance of the proposed method was observed by simulation experiments.

• Korean Management Science Review
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• v.21 no.2
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• pp.43-60
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• 2004

Every iteration of interior-point methods of large scale optimization requires computing at least one orthogonal projection. In the practice, symmetric variants of the Gaussian elimination such as Cholesky factorization are accepted as the most efficient and sufficiently stable method. In this paper several specific implementation issues of the symmetric factorization that can be applied for solving such equations are discussed. The code called McSML being the result of this work is shown to produce comparably sparse factors as another implementations in the $MATLAB^{***}$ environment. It has been used for computing projections in an efficient implementation of self-regular based interior-point methods, McIPM. Although primary aim of developing McSML was to embed it into an interior-point methods optimizer, the code may equally well be used to solve general large sparse systems arising in different applications.

• Proceedings of the IEEK Conference
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• 2000.07a
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• pp.62-65
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• 2000

In this paper we propose skewed angle detection methods for images that contain text that is not aligned horizontally. In most images text areas are aligned along the horizontal axis, however there are many occasions when the text may be at a skewed angle (denoted by 0 < ${\theta}\;{\leq}\;{\pi}$). In the work described, we adapt the Hough transform, Shadow and Threshold Projection methods to detect the skewed angle of text in an input image using the orthogonal angle view property. The results of this method are a primary text skewed angle, which allows us to rotate the original input image into an image with horizontally aligned text. This utilizes document image processing prior to the recognition stage.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.327-342
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• 2021

We consider a generalization of the L^q-spectrum with respect to two Borel probability measures on ℝⁿ having the same compact support, and also study their behavior under orthogonal projections of measures onto an m-dimensional subspace. In particular, we try to improve the main result of Bahroun and Bhouri [4]. In addition, we are interested in studying the behavior of the generalized lower and upper L^q-spectrum with respect to two measures on "sliced" measures in an (n - m)-dimensional linear subspace. The results in this article establish relations with the L^q-spectrum with respect to two Borel probability measures and its projections and generalize some well-known results.