• Title/Summary/Keyword: approximation theory

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Horizontal Consolidation Characteristics of Marine Clay Using Piezocone Test (Piezocone 시험을 이용한 해성점토의 수평압밀 특성 연구)

  • 이강운;윤길림;채영수
    • Journal of the Korean Geotechnical Society
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    • v.19 no.5
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    • pp.133-144
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    • 2003
  • Horizontal consolidation characteristics of Busan marine clay were investigated by computing coefficient of horizontal consolidation from Piezocone data and comparing their results with those of standard consolidation test. It is well known that current prediction models of $c_h$ for high plastic soils have large uncertainties, and show a great difference between the predicted and the measured values. However, the spherical models and expanding cavity theory of Torstensson(1977), and Burns & Mayne(1998) based on modified Cam-Clay model with critical limit state concepts have relative reliability in estimating $c_h$ and good applicability in highly plasticity soils. In this paper, a normalization technique was used to evaluate $c_h$ using the Burns and Mayne's method based on the dissipation test, and their normalized consolidation curves give 0.015 of time factor($T_{50}$) when 50% degree of consolidation is completed. Comparison study using Piezocone data obtained at other similar ground site shows 1.5 times less systematicality than that of standard consolidation test, which indicates considerable approximation with the measured values because standard consolidation test gives the difference of three to few times compared with the measured values. In addition, design chart for estimating $c_h$ based on the chart from Robertson et al.(1992) and using the other method of the direct prediction from the of dissipation test was newly proposed. It is judged that new proposed chart is very applicable to Korean marine soils, especially in very high plastic soils.

Transmitter Beamforming and Artificial Noise with Delayed Feedback: Secrecy Rate and Power Allocation

  • Yang, Yunchuan;Wang, Wenbo;Zhao, Hui;Zhao, Long
    • Journal of Communications and Networks
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    • v.14 no.4
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    • pp.374-384
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    • 2012
  • Utilizing artificial noise (AN) is a good means to guarantee security against eavesdropping in a multi-inputmulti-output system, where the AN is designed to lie in the null space of the legitimate receiver's channel direction information (CDI). However, imperfect CDI will lead to noise leakage at the legitimate receiver and cause significant loss in the achievable secrecy rate. In this paper, we consider a delayed feedback system, and investigate the impact of delayed CDI on security by using a transmit beamforming and AN scheme. By exploiting the Gauss-Markov fading spectrum to model the feedback delay, we derive a closed-form expression of the upper bound on the secrecy rate loss, where $N_t$ = 2. For a moderate number of antennas where $N_t$ > 2, two special cases, based on the first-order statistics of the noise leakage and large number theory, are explored to approximate the respective upper bounds. In addition, to maintain a constant signal-to-interferenceplus-noise ratio degradation, we analyze the corresponding delay constraint. Furthermore, based on the obtained closed-form expression of the lower bound on the achievable secrecy rate, we investigate an optimal power allocation strategy between the information signal and the AN. The analytical and numerical results obtained based on first-order statistics can be regarded as a good approximation of the capacity that can be achieved at the legitimate receiver with a certain number of antennas, $N_t$. In addition, for a given delay, we show that optimal power allocation is not sensitive to the number of antennas in a high signal-to-noise ratio regime. The simulation results further indicate that the achievable secrecy rate with optimal power allocation can be improved significantly as compared to that with fixed power allocation. In addition, as the delay increases, the ratio of power allocated to the AN should be decreased to reduce the secrecy rate degradation.

A Failure Probability Estimation Method of Nonlinear Bridge Structures using the Non-Gaussian Closure Method (Non-Gaussian Closure 기법을 적용한 비선형 교량 구조계의 파괴확률 추정 기법)

  • Hahm, Dae-Gi;Koh, Hyun-Moo;Park, Kwan-Soon
    • Journal of the Earthquake Engineering Society of Korea
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    • v.14 no.1
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    • pp.25-34
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    • 2010
  • A method is presented for evaluating the seismic failure probability of bridge structures which show a nonlinear hysteretic dynamic behavior. Bridge structures are modeled as a bilinear dynamic system with a single degree of freedom. We regarded that the failure of bridges will occur when the displacement response of a deck level firstly crosses the predefined limit state during a duration of strong motion. For the estimation of the first-crossing probability of a nonlinear structural system excited by earthquake motion, we computed the average frequency of crossings of the limit state. We presented the non-Gaussian closure method for the approximation of the joint probability density function of response and its derivative, which is required for the estimation of the average frequency of crossings. The failure probabilities are estimated according to the various artificial earthquake acceleration sets representing specific seismic characteristics. For the verification of the accuracy and efficiency of presented method, we compared the estimated failure probabilities with the results evaluated from previous methods and the exact values estimated with the crude Monte-Carlo simulation method.

ADMM algorithms in statistics and machine learning (통계적 기계학습에서의 ADMM 알고리즘의 활용)

  • Choi, Hosik;Choi, Hyunjip;Park, Sangun
    • Journal of the Korean Data and Information Science Society
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    • v.28 no.6
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    • pp.1229-1244
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    • 2017
  • In recent years, as demand for data-based analytical methodologies increases in various fields, optimization methods have been developed to handle them. In particular, various constraints required for problems in statistics and machine learning can be solved by convex optimization. Alternating direction method of multipliers (ADMM) can effectively deal with linear constraints, and it can be effectively used as a parallel optimization algorithm. ADMM is an approximation algorithm that solves complex original problems by dividing and combining the partial problems that are easier to optimize than original problems. It is useful for optimizing non-smooth or composite objective functions. It is widely used in statistical and machine learning because it can systematically construct algorithms based on dual theory and proximal operator. In this paper, we will examine applications of ADMM algorithm in various fields related to statistics, and focus on two major points: (1) splitting strategy of objective function, and (2) role of the proximal operator in explaining the Lagrangian method and its dual problem. In this case, we introduce methodologies that utilize regularization. Simulation results are presented to demonstrate effectiveness of the lasso.

Fast GPU Implementation for the Solution of Tridiagonal Matrix Systems (삼중대각행렬 시스템 풀이의 빠른 GPU 구현)

  • Kim, Yong-Hee;Lee, Sung-Kee
    • Journal of KIISE:Computer Systems and Theory
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    • v.32 no.11_12
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    • pp.692-704
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    • 2005
  • With the improvement of computer hardware, GPUs(Graphics Processor Units) have tremendous memory bandwidth and computation power. This leads GPUs to use in general purpose computation. Especially, GPU implementation of compute-intensive physics based simulations is actively studied. In the solution of differential equations which are base of physics simulations, tridiagonal matrix systems occur repeatedly by finite-difference approximation. From the point of view of physics based simulations, fast solution of tridiagonal matrix system is important research field. We propose a fast GPU implementation for the solution of tridiagonal matrix systems. In this paper, we implement the cyclic reduction(also known as odd-even reduction) algorithm which is a popular choice for vector processors. We obtained a considerable performance improvement for solving tridiagonal matrix systems over Thomas method and conjugate gradient method. Thomas method is well known as a method for solving tridiagonal matrix systems on CPU and conjugate gradient method has shown good results on GPU. We experimented our proposed method by applying it to heat conduction, advection-diffusion, and shallow water simulations. The results of these simulations have shown a remarkable performance of over 35 frame-per-second on the 1024x1024 grid.

Animation Generation for Chinese Character Learning on Mobile Devices (모바일 한자 학습 애니메이션 생성)

  • Koo, Sang-Ok;Jang, Hyun-Gyu;Jung, Soon-Ki
    • Journal of KIISE:Computer Systems and Theory
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    • v.33 no.12
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    • pp.894-906
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    • 2006
  • There are many difficulties to develop a mobile contents due to many constraints on mobile environments. It is difficult to make a good mobile contents with only visual reduction of existing contents on wire Internet. Therefore, it is essential to devise the data representation and to develop the authoring tool to meet the needs of the mobile contents market. We suggest the compact mobile contents to learn Chinese characters and developed its authoring tool. The animation which our system produces is realistic as if someone writes letters with pen or brush. Moreover, our authoring tool makes a user generate a Chinese character animation easily and rapidly although she or he has not many knowledge in computer graphics, mobile programming or Chinese characters. The method to generate the stroke animation is following: We take basic character shape information represented with several contours from TTF(TrueType Font) and get the information for the stroke segmentation and stroke ordering from simple user input. And then, we decompose whole character shape into some strokes by using polygonal approximation technique. Next, the stroke animation for each stroke is automatically generated by the scan line algorithm ordered by the stroke direction. Finally, the ordered scan lines are compressed into some integers by reducing coordinate redundancy As a result, the stroke animation of our system is even smaller than GIF animation. Our method can be extended to rendering and animation of Hangul or general 2D shape based on vector graphics. We have the plan to find the method to automate the stroke segmentation and ordering without user input.

Stereo Image-based 3D Modelling Algorithm through Efficient Extraction of Depth Feature (효율적인 깊이 특징 추출을 이용한 스테레오 영상 기반의 3차원 모델링 기법)

  • Ha, Young-Su;Lee, Heng-Suk;Han, Kyu-Phil
    • Journal of KIISE:Computer Systems and Theory
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    • v.32 no.10
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    • pp.520-529
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    • 2005
  • A feature-based 3D modeling algorithm is presented in this paper. Since conventional methods use depth-based techniques, they need much time for the image matching to extract depth information. Even feature-based methods have less computation load than that of depth-based ones, the calculation of modeling error about whole pixels within a triangle is needed in feature-based algorithms. It also increase the computation time. Therefore, the proposed algorithm consists of three phases, which are an initial 3D model generation, model evaluation, and model refinement phases, in order to acquire an efficient 3D model. Intensity gradients and incremental Delaunay triangulation are used in the Initial model generation. In this phase, a morphological edge operator is adopted for a fast edge filtering, and the incremental Delaunay triangulation is modified to decrease the computation time by avoiding the calculation errors of whole pixels and selecting a vertex at the near of the centroid within the previous triangle. After the model generation, sparse vertices are matched, then the faces are evaluated with the size, approximation error, and disparity fluctuation of the face in evaluation stage. Thereafter, the faces which have a large error are selectively refined into smaller faces. Experimental results showed that the proposed algorithm could acquire an adaptive model with less modeling errors for both smooth and abrupt areas and could remarkably reduce the model acquisition time.

Evaluations of the Equations of State and Thermodynamic Quantities of Fluid Metal at High Temperatures and Densities

  • Shin, Hyun-Joon;Hong, Jong-Ha;Oh, Byung-Wan
    • Nuclear Engineering and Technology
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    • v.10 no.3
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    • pp.127-136
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    • 1978
  • We have applied the temperature dependent Thomas-Fermi theory to evaluate the equations of state, chemical potentials, entropies, % ionizations, total energies and kinetic energies of an atom, and seveal thermodynamic quantifies of one of metallic substance, Na, for a density range of 0.1$\rho$$_{0}$ ~ 10$\rho$$_{0}$, where $\rho$$_{0}$ is the normal density of Na at its melting point, and for a temperature range of 60.88Ryd. ~0.0216 Ryd., where the system is expected to be in a gaseous or liquid state. The main interest of present work lies in physical quantities at high temperatures and high densities, however, we have included those quantities of Na at sufficiently low temperatures and low densities to show that the approximation is not so crude as one might expect. Particularly, at high temperatures, the calculated equations of state, kinetic energies of an atom, chemical potentials and entropies are compared with those, of an ideal Fermi gas. The results show that, at high temperatures, the agreement seems good for chemical Potentials. However, the differences in, entropy, kinetic energy of an atom, and equation of state are not negligible even at such high temperature as $textsc{k}$T=60.88Ryd.

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Study of the Molecular Reorientation in Ammonium Sulfate by Neutron Scattering

  • Kim, Huhn-Jun
    • Nuclear Engineering and Technology
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    • v.4 no.4
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    • pp.306-321
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    • 1972
  • Molecular reorientation in (NH$_4$)$_2$SO$_4$, has been studied by cold neutron scattering. For T=300$^{\circ}$K data, the isolated quasielastic spectra and form-factors at various scattering angles are compared with four reorientational models based on SKOLD theory. Front these, it is concluded that the NH$_4$ions are performing either 3-fold four axes or 2-fold three axes reorientation with $\tau$$_{c}$=2.0$\times$10$^{-11}$ sec. The temperature dependence of f. is studied over 100$^{\circ}$K-413$^{\circ}$K and for the high-temperature phase, the widths of composite spectra are compared with the results from NMR relaxation measurements. All the results have shown that the neutron scattering method is capable of giving detalis of the reorientational modes in solids and therefore some discussions are given on the application of this method. A study of the form-factor is applied for NH$_4$I (Phase I) by comparing the measurement with the calculation based on free rotation approximation and proposed a reorientation model of NH$_4$ ions in the octahedral potential cage with $\tau$$_{c}$$\leq$10$^{-12}$ sec. Also a brief theoretical prediction for the effect of reorientational motions on the inelastic spectrum is discussed.sed.

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A Finite Element Simulation of Cancellous Bone Remodeling Based on Volumetric Strain (스폰지 뼈의 Remodeling 예측을 위한 체적 변형률을 이용한 유한요소 알고리즘)

  • Kim, Young;Vanderby, Ray
    • Journal of Biomedical Engineering Research
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    • v.21 no.4
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    • pp.373-384
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    • 2000
  • The goal of this paper is to develop a computational method to predict cancellous bone density distributions based upon continuum levels of volumetric strain. Volumetric strain is defined as the summation of normal strains, excluding shear strains, within an elastic range of loadings. Volumetric strain at a particular location in a cancellous structure changes with changes of the boundary conditions (prescribed displacements, tractions, and pressure). This change in the volumetric strain is postulated to predict the adaptive change in the bone apparent density. This bone remodeling theory based on volumetric strain is then used with the finite element method to compute the apparent density distribution for cancellous bone in both lumbar spine and proximal femur using an iterative algorithm, considering the dead zone of strain stimuli. The apparent density distribution of cancellous bone predicted by this method has the same pattern as experimental data reported in the literature (Wolff 1892, Keller et al. 1989, Cody et al. 1992). The resulting bone apparent density distributions predict Young's modulus and strength distributions throughout cancellous bone in agreement with the literature (Keller et al. 1989, Carter and Hayes 1977). The method was convergent and sensitive to changes in boundary conditions. Therefore, the computational algorithm of the present study appears to be a useful approach to predict the apparent density distribution of cancellous bone (i.e. a numerical approximation for Wolff's Law)

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