• Title/Summary/Keyword: Least squares approximation

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Reaction process in electrochromism of tungsten oxide thin films

  • An, Il-Sin;Lee, Chang-Hyo;Lim, Won-Taeg
    • Journal of Korean Vacuum Science & Technology
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    • v.2 no.2
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    • pp.85-91
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    • 1998
  • The electrochromic behaviors of de-magnetron sputtered tungsten oxide thin films were investigated during coloration and bleach cycles using in situ real-time spectroscopic ellipsometry. Effective medium approximation and least-squares regression analyses were employed to investigate the electrochromic process. The optical properties of the tungsten oxide film were analyzed using the oscillator model and the evolution of the process using a reaction-limited model. In these analyses, we found that two different reaction rates were associated with the process. We ascribe this behavior to the microstructure of this films.

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Analysis of Stress Concentration Problems Using Moving Least Squares Finite Difference Method(I) : Formulation for Solid Mechanics Problem (이동최소제곱 유한차분법을 이용한 응력집중문제 해석(I) : 고체문제의 정식화)

  • Yoon, Young-Cheol;Kim, Hyo-Jin;Kim, Dong-Jo;Liu, Wing Kam;Belytschko, Ted;Lee, Sang-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.20 no.4
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    • pp.493-499
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    • 2007
  • The Taylor expansion expresses a differentiable function and its coefficients provide good approximations for the given function and its derivatives. In this study, m-th order Taylor Polynomial is constructed and the coefficients are computed by the Moving Least Squares method. The coefficients are applied to the governing partial differential equation for solid problems including crack problems. The discrete system of difference equations are set up based on the concept of point collocation. The developed method effectively overcomes the shortcomings of the finite difference method which is dependent of the grid structure and has no approximation function, and the Galerkin-based meshfree method which involves time-consuming integration of weak form and differentiation of the shape function and cumbersome treatment of essential boundary.

Analysis of Dynamic Crack Propagation using MLS Difference Method (MLS 차분법을 이용한 동적균열전파 해석)

  • Yoon, Young-Cheol;Kim, Kyeong-Hwan;Lee, Sang-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.27 no.1
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    • pp.17-26
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    • 2014
  • This paper presents a dynamic crack propagation algorithm based on the Moving Least Squares(MLS) difference method. The derivative approximation for the MLS difference method is derived by Taylor expansion and moving least squares procedure. The method can analyze dynamic crack problems using only node model, which is completely free from the constraint of grid or mesh structure. The dynamic equilibrium equation is integrated by the Newmark method. When a crack propagates, the MLS difference method does not need the reconstruction of mode model at every time step, instead, partial revision of nodal arrangement near the new crack tip is carried out. A crack is modeled by the visibility criterion and dynamic energy release rate is evaluated to decide the onset of crack growth together with the corresponding growth angle. Mode I and mixed mode crack propagation problems are numerically simulated and the accuracy and stability of the proposed algorithm are successfully verified through the comparison with the analytical solutions and the Element-Free Galerkin method results.

Moving Least Squares Difference Method for the Analysis of 2-D Melting Problem (2차원 융해문제의 해석을 위한 이동최소제곱 차분법)

  • Yoon, Young-Cheol
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.26 no.1
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    • pp.39-48
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    • 2013
  • This paper develops a 2-D moving least squares(MLS) difference method for Stefan problem by extending the 1-D version of the conventional method. Unlike to 1-D interfacial modeling, the complex topology change in 2-D domain due to arbitrarily moving boundary is successfully modelled. The MLS derivative approximation that drives the kinetics of moving boundary is derived while the strong merit of MLS Difference Method that utilizes only nodal computation is effectively conserved. The governing equations are differentiated by an implicit scheme for achieving numerical stability and the moving boundary is updated by an explicit scheme for maximizing numerical efficiency. Numerical experiments prove that the MLS Difference Method shows very good accuracy and efficiency in solving complex 2-D Stefan problems.

A Gridless Finite Difference Method for Elastic Crack Analysis (탄성균열해석을 위한 그리드 없는 유한차분법)

  • Yoon, Young-Cheol;Kim, Dong-Jo;Lee, Sang-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.20 no.3
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    • pp.321-327
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    • 2007
  • This study presents a new gridless finite difference method for solving elastic crack problems. The method constructs the Taylor expansion based on the MLS(Moving Least Squares) method and effectively calculates the approximation and its derivatives without differentiation process. Since no connectivity between nodes is required, the modeling of discontinuity embedded in the domain is very convenient and discontinuity effect due to crack is naturally implemented in the construction of difference equations. Direct discretization of the governing partial differential equations makes solution process faster than other numerical schemes using numerical integration. Numerical results for mode I and II crack problems demonstrates that the proposed method accurately and efficiently evaluates the stress intensity factors.

Study of Reliability-Based Robust Design Optimization Using Conservative Approximate Meta-Models (보수적 근사모델을 적용한 신뢰성 기반 강건 최적설계 방법)

  • Sim, Hyoung Min;Song, Chang Yong;Lee, Jongsoo;Choi, Ha-Young
    • Journal of Ocean Engineering and Technology
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    • v.26 no.6
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    • pp.80-85
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    • 2012
  • The methods of robust design optimization (RDO) and reliability-based robust design optimization (RBRDO) were implemented in the present study. RBRDO is an integrated method that accounts for the design robustness of an objective function and for the reliability of constraints. The objective function in RBRDO is expressed in terms of the mean and standard deviation of an original objective function. Thus, a multi-objective formulation is employed. The regressive approximate models are generated via the moving least squares method (MLSM) and constraint-feasible moving least squares method (CF-MLSM), which make it possible to realize the feasibility regardless of the multimodality/nonlinearity of the constraint function during the approximate optimization processes. The regression model based RBRDO is newly devised and its numerical characteristics are explored using the design of an actively controlled ten bar truss structure.

Visualization of 4-Dimensional Scattered Data Linear Interpolation Based on Data Dependent Tetrahedrization (4차원 산포된 자료 선형 보간의 가시화 -자료 값을 고려한 사면체 분할법에 의한-)

  • Lee, Kun
    • The Transactions of the Korea Information Processing Society
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    • v.3 no.6
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    • pp.1553-1567
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    • 1996
  • The numerous applications surface interpolation include the modeling and visualization phenomena. A tetrahedrization is one of pre-processing steps for 4-D space interpolation. The quality of a piecewise linear interpolation 4-D space depends not only on the distribution of the data points in $R^2$, but also on the data values. We show that the quality of approximation can be improved by data dependent tetraheadrization through visualization of 4-D space. This paper discusses Delaunary tetrahedrization method(sphere criterion) and one of the data dependent tetrahedrization methods(least squares fitting criterion). This paper also discusses new data dependent criteria:1) gradient difference, and 2) jump in normal direction derivative.

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Ellipse detection based on RANSAC algorithm (RANSAC 알고리듬을 적용한 타원 검출)

  • Ye, Sao-Young;Nam, Ki-Gon
    • Journal of the Institute of Convergence Signal Processing
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    • v.14 no.1
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    • pp.27-32
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    • 2013
  • It plays an important role to detect the shape of an ellipse in many application areas of image processing. But it is very difficult to detect the ellipse in the real image because the noise was involved in the image, other objects obscured the ellipse or the ellipses were overlap with each other. In this paper, we extract the boundary (edge) to detect ellipse in the image and perform the grouping process in order to reduce amount of information. As a result, the speed of the ellipse detection was improved. Also in order to the ellipse detection, we selected the five ellipse parameters at random And then to select the optimal parameters of the ellipse, the linear least-squares approximation is applied. To verify the ellipse detection, RANSAC algorithm is applied. After the algorithm proposed in this study was implemented, the results applied to the real images showed an aocuracy of 75% and speed was very fast to compared with other researches. It mean that the proposed algorithm was valuable to detect the ellipses in the image.

Analysis of Interface Problem using the MLS Difference Method with Interface Condition Embedment (계면경계조건이 매입된 이동최소제곱 차분법을 이용한 계면경계문제 해석)

  • Yoon, Young-Cheol
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.32 no.4
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    • pp.215-222
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    • 2019
  • The heat conduction problem with discontinuous material coefficients generally consists of the conservative equation, boundary condition, and interface condition, which should be additionally satisfied in the solution procedure. This feature often makes the development of new numerical schemes difficult as it induces a layered singularity in the solution fields; thus, a special approximation is required to capture the singular behavior. In addition to the approximation, the construction of a total system of equations is challenging. In this study, a wedge function is devised for enriching the approximation, and the interface condition itself is embedded in the moving least squares(MLS) derivative approximation to consistently satisfy the interface condition. The heat conduction problem is then discretized in a strong form using the developed derivative approximation, which is named as the interface immersed MLS difference method. This method is able to efficiently provide a numerical solution for such interface problems avoiding both numerical quadrature as well as extra difference equations related to the interface condition enforcement. Numerical experiments proved that the developed numerical method was highly accurate and computationally efficient at solving the heat conduction problem with interfacial jump as well as the problem with a geometrically induced interfacial singularity.

Controller Auto-tuning Scheme for Improving Feedback System Performance in Frequency Domain (주파수역에서의 피드백시스템의 성능향상을 위한 제어기 Atuo-tuning 기법)

  • 정유철;이건복
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.10 no.3
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    • pp.26-30
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    • 2001
  • Controller refinement scheme to improve the performance of a conventional system automatically in frequency domain is proposed. The controller automatic tuning method features using experimental frequency responses of the conventional closed-loop system, the conventional controller, and the improved closed-loop system, instead of poorly modeled plant due to non-linearities and disturbances. The improved closed-loop system characteristics is automatically acquired by the con-ventional closed-loop system characteristics and the proposed performance index in system bandwidth. And the proper controller is realized by least squares approximation in frequency domain. To testify the usefulness of the approach, the path tracking control of robot arm is performed. Experimental results and analytic results are well-matched.

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