• Title/Summary/Keyword: eigenvalue technique

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Natural Frequency Characteristics of Vertically Loaded Barrettes (수직하중을 받는 Barrette 말뚝의 고유진동수 특성)

  • Lee, Joon Kyu;Ko, Jun Young;Choi, Yong Hyuk;Park, Ku Byoung;Kim, Jae Young
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.41 no.1
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    • pp.39-48
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    • 2021
  • In this paper, an analytical model is proposed for assessing the natural frequency of barrettes subjected to vertical loading. The differential equation governing the free vibration of rectangular friction piles embedded in inhomogeneous soil is derived. The governing equation is numerically integrated by Runge-Kutta technique and the eigenvalue of natural frequency is computed by Regula-Falsi method. The numerical solutions for the natural frequency of barrettes compare well with those obtained from finite element analysis. Illustrated examples show that the natural frequencies increase with an increase of the cross-sectional aspect ratio, the friction resistance ratio and the soil stiffness ratio, and decrease with an increase of the friction aspect ratio, the slenderness ratio and the load factor, respectively.

Dislocation in Semi-infinite Half Plane Subject to Adhesive Complete Contact with Square Wedge: Part II - Approximation and Application of Corrective Functions (직각 쐐기와 응착접촉 하는 반무한 평판 내 전위: 제2부 - 보정 함수의 근사 및 응용)

  • Kim, Hyung-Kyu
    • Tribology and Lubricants
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    • v.38 no.3
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    • pp.84-92
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    • 2022
  • In Part I, developed was a method to obtain the stress field due to an edge dislocation that locates in an elastic half plane beneath the contact edge of an elastically similar square wedge. Essential result was the corrective functions which incorporate a traction free condition of the free surfaces. In the sequel to Part I, features of the corrective functions, Fkij,(k = x, y;i,j = x,y) are investigated in this Part II at first. It is found that Fxxx(ŷ) = Fxyx(ŷ) where ŷ = y/η and η being the location of an edge dislocation on the y axis. When compared with the corrective functions derived for the case of an edge dislocation at x = ξ, analogy is found when the indices of y and x are exchanged with each other as can be readily expected. The corrective functions are curve fitted by using the scatter data generated using a numerical technique. The algebraic form for the curve fitting is designed as Fkij(ŷ) = $\frac{1}{\hat{y}^{1-{\lambda}}I+yp}$$\sum_{q=0}^{m}{\left}$$\left[A_q\left(\frac{\hat{y}}{1+\hat{y}} \right)^q \right]$ where λI=0.5445, the eigenvalue of the adhesive complete contact problem introduced in Part I. To investigate the exponent of Fkij, i.e.(1 - λI) and p, Log|Fkij|(ŷ)-Log|(ŷ)| is plotted and investigated. All the coefficients and powers in the algebraic form of the corrective functions are obtained using Mathematica. Method of analyzing a surface perpendicular crack emanated from the complete contact edge is explained as an application of the curve-fitted corrective functions.

Application of data-driven model reduction techniques in reactor neutron field calculations

  • Zhaocai Xiang;Qiafeng Chen;Pengcheng Zhao
    • Nuclear Engineering and Technology
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    • v.56 no.8
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    • pp.2948-2957
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    • 2024
  • High-order harmonic techniques can be used to recreate neutron flux distributions in reactor cores using the neutron diffusion equation. However, traditional source iteration and source correction iteration techniques have sluggish convergence rates and protracted calculation periods. The correctness of the implicitly restarted Arnoldi method (IRAM) in resolving the eigenvalue problems of the one-dimensional and two-dimensional neutron diffusion equations was confirmed by computing the benchmark problems SLAB_1D_1G and two-dimensional steady-state TWIGL using IRAM. By integrating Galerkin projection with Proper Orthogonal Decomposition (POD) techniques, a POD-Galerkin reduced-order model was developed and the IRAM model was used as the full-order model. For 14 macroscopic cross-section values, the TWIGL benchmark problem was perturbed within a 20% range. We extracted 100 sample points using the Latin hypercube sampling method, and 70% of the samples were used as the testing set to assess the performance of the reduced-order model The remaining 30% were utilized as the training set to develop the reduced-order model, which was employed to rebuild the TWIGL benchmark problem. The reduced-order model demonstrates good flexibility and can efficiently and accurately forecast the effective multiplication factor and neutron flux distribution in the core. The reduced-order model predicts keff and neutron flux distribution with a high degree of agreement compared to the full-order model. Additionally, the reduced-order model's computation time is only 10.18% of that required by the full-order model.The neutron flux distribution of the steady-state TWIGL benchmark was recreated using the reduced-order model. The obtained results indicate that the reduced-order model can accurately predict the keff and neutron flux distribution of the steady-state TWIGL benchmark.Overall, the proposed technique not only has the potential to accurately project neutron flux distributions in transient settings, but is also relevant for reconstructing neutron flux distributions in steady-state conditions; thus, its applicability is bound to increase in the future.

A Symbolic Manipulation Computer Program for Structural Analysis (구조해석(構造解析)을 위한 Symbolic Manipulation Program)

  • Shim, Jae Soo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.3 no.4
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    • pp.95-107
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    • 1983
  • The general purpose programs are in their fixed algorithm and theory of mechanics which can not be altered without painful program modifications. Users are usually guided by user's manual for data input. The several symbolic manipulation programs for structural analysis are introduced recently. These programs allow users to include a wide class of solution algorithm and to specify, by means of some symbolic manipulation, a combination of analytical steps to suit a particular problem. As they can solve a single domain problem, a large computer is usually needed. The scope of this study is to develop an efficient symbolic manipulation program with space beam element, plate bending element and eigen value routines. The incorporated Substructure capability and generation capability of finite element characteristic arrays (e.g., stiffness matrix, mass matrix) enables users to analyse multidomain problem with small computer. The program consists of modulized independent processors, each having its own specific function and is easily modified, eliminated and added. The processors are efficiently handling data by the Data base approach which is the concept of integrated program network(IPN).

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Development of a groundwater contamination potential evaluation technique by improving DRASTIC Index for a tunnel excavation area (개선된 DRASTIC 기법을 이용한 터널굴착 예정지역의 지하수 오염 가능성 평가기법 개발에 관한 연구)

  • Park, Jun-Kyung;Park, Young-Jin;Wye, Yong-Gon;Choi, Young-Tae;Lee, Han-Min
    • Journal of Korean Tunnelling and Underground Space Association
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    • v.5 no.1
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    • pp.71-88
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    • 2003
  • The DRASTIC system is widely used for assessing regional groundwater pollution susceptibility by using hydrogeological factors such as depth to water, net recharge, aquifer media, soil media, topography, vadose zone media, hydraulic conductivity. This study is providing Modified Drastic Model to which lineament density, land use, influence of groundwater drawdown caused by tunnel excavation are added as additional factors using geographic information system, and then to evaluate groundwater contamination potential of ${\bigcirc}{\bigcirc}$ area. For statistical analysis, vector coverage per each factor is converted to grid layer and after each correlation coefficient between factors, covariance, variance, eigenvalue and eigenvector by principal component analysis of 3 direction, are calculated, correlation between factors is analyzed. Also after correlation coefficients between general DRASTIC layer and rated lineament density layer, between general DRASTIC layer and rated land use layer, between general DRASTIC layer and rated tunnel excavation influence layer are calculated, final modified DRASTIC model is constructed by using them with each weighting. When modified DRASTIC model was compared with general DRASTIC model, contamination potential in modified DRASTIC model is fairly detailed and consequently, vulnerable area which has high contamination potential could be presented concretly.

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Groundwater Flow Model for the Pollutant Transport in Subsurface Porous Media Theory and Modeling (지하다공질(地下多孔質) 매체(媒體)속에서의 오염물질이동(汚染物質移動) 해석(解析)을 위한 지하수(地下水)흐름 모형(模型))

  • Cho, Won Cheal
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.9 no.3
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    • pp.97-106
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    • 1989
  • This paper is on the modeling of two-dimensional groundwater flow, which is the first step of the development of Dynamic System Model for groundwater flow and pollutant transport in subsurface porous media. The particular features of the model are its versatility and flexibility to deal with as many real-world problems as possible. Points as well as distributed sources/sinks are included to represent recharges/pumping and rainfall infiltrations. All sources/sinks can be transient or steady state. Prescribed hydraulic head on the Dirichlet boundaries and fluxes on Neumann or Cauchy boundaries can be time-dependent or constant. Sources/sinks strength over each element and node, hydraulic head at each Dirichlet boundary node and flux at each boundary segment can vary independently of each other. Either completely confined or completely unconfined aquifers, or partially confined and partially unconfined aquifers can be dealt with effectively. Discretization of a compound region with very irregular curved boundaries is made easy by including both quadrilateral and triangular elements in the formulation. Large-field problems can be solved efficiently by including a pointwise iterative solution strategy as an optional alternative to the direct elimination solution methed for the matrix equation approximating the partial differential equation of groundwater flow. The model also includes transient flow through confining leaky aquifers lying above and/or below the aquifer of interest. The model is verified against three simple cases to which analytical solutions are available. The groundwater flow model shall be combined with the model of pollutant transport in subsurface porous media. Then the combined model, with the applications of the Eigenvalue technique and the Dynamic system theory, shall be improved to the Dynamic System Model which can simulate the real groundwater flow and the pollutant transport accurately and effectively for the analyses and predictions.

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Extraction of Important Areas Using Feature Feedback Based on PCA (PCA 기반 특징 되먹임을 이용한 중요 영역 추출)

  • Lee, Seung-Hyeon;Kim, Do-Yun;Choi, Sang-Il;Jeong, Gu-Min
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.13 no.6
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    • pp.461-469
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    • 2020
  • In this paper, we propose a PCA-based feature feedback method for extracting important areas of handwritten numeric data sets and face data sets. A PCA-based feature feedback method is proposed by extending the previous LDA-based feature feedback method. In the proposed method, the data is reduced to important feature dimensions by applying the PCA technique, one of the dimension reduction machine learning algorithms. Through the weights derived during the dimensional reduction process, the important points of data in each reduced dimensional axis are identified. Each dimension axis has a different weight in the total data according to the size of the eigenvalue of the axis. Accordingly, a weight proportional to the size of the eigenvalues of each dimension axis is given, and an operation process is performed to add important points of data in each dimension axis. The critical area of the data is calculated by applying a threshold to the data obtained through the calculation process. After that, induces reverse mapping to the original data in the important area of the derived data, and selects the important area in the original data space. The results of the experiment on the MNIST dataset are checked, and the effectiveness and possibility of the pattern recognition method based on PCA-based feature feedback are verified by comparing the results with the existing LDA-based feature feedback method.