• Title/Summary/Keyword: 상태공간 방정식

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On the Study of Nonlinear Normal Mode Vibration via Poincare Map and Integral of Motion (푸앙카레 사상과 운동적분를 이용한 비선형 정규모드 진동의 연구)

  • Rhee, Huinam
    • Journal of KSNVE
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    • v.9 no.1
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    • pp.196-205
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    • 1999
  • The existence. bifurcation. and the orbital stability of periodic motions, which is called nonlinear normal mode, in a nonlinear dual mass Hamiltonian system. which has 6th order homogeneous polynomial as a nonlinear term. are studied in this paper. By direct integration of the equations of motion. Poincare Map. which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space. is obtained. And via the Birkhoff-Gustavson canonical transformation, the analytic expression of the invariant curves in the Poincare Map is derived for small value of energy. It is found that the nonlinear system. which is considered in this paper. has 2 or 4 nonlinear normal modes depending on the value of nonlinear parameter. The Poincare Map clearly shows that the bifurcation modes are stable while the mode from which they bifurcated out changes from stable to unstable.

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Mathematical Modelling and Chaotic Behavior Analysis of Cyber Addiction (사이버 중독의 수학적 모델링과 비선형 거동 해석)

  • Kim, Myung-Mi;Bae, Young-Chul
    • Journal of the Korean Institute of Intelligent Systems
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    • v.24 no.3
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    • pp.245-250
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    • 2014
  • Addiction can be largely divided into two categories. One is called medium addiction in which medium itself causes an addiction. Another is called cause addiction that brings addiction through combination of sensitive self and latent personal action. The medium addiction involves addiction phenomena directly caused by illegal drugs, alcohol and various other chemicals. The cause addiction is dependent on personal sensitivities as a sensitive problem of personal and includes cyber addictions such as shopping, work, game, internet, TV, and gambling. In this paper we propose two-dimensional addiction model that are equivalent to using an R-L-C series circuit of Electrical circuit and a Spring-Damper-mass of mechanical system. We also organize a Duffing equation that is added a nonlinear term in the proposed two-dimensional addiction model. We represent periodic motion and chaotic motion as time series and phase portrait according to parameter's variation. We confirm that among parameters chaotic motion had addicted state and periodic motion caused by change in control coefficient had pre-addiction state.

Estimation of roughness coefficient for 1D flow modeling in vegetated channel (식생하도의 1차원 흐름모의를 위한 조도계수 산정)

  • Jiwon Ryu;Un Ji;Eun-kyung Jang;Inhyeok Bae
    • Proceedings of the Korea Water Resources Association Conference
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    • 2023.05a
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    • pp.524-524
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    • 2023
  • 하천 내 식생의 분포는 흐름저항의 증가와 수위상승에 큰 영향을 미치는 요소 중 하나이다. 동일한 단면정보를 가졌더라도 식생이 분포하는 하도는 식생이 없는 하도에 비해 흐름저항으로 인해 유속이 현저히 느려져 홍수위 상승을 유발하기 때문이다. 따라서 식생의 종류, 크기, 분포 형태, 잎의 밀도 등에 따라 흐름저항계수를 정량화하며 흐름을 정확히 예측하는 것이 필요하다. 본 연구에서는 2019년 한국건설기술연구원 하천실험센터에서 진행된 식생하도에 대한 실규모 실험의 조건과 지형정보를 HEC-RAS(Hydrologic Engineering Center's River Analysis System) 1차원 수치모형에 입력하고, 식생 패치의 분포를 고려한 Manning's n의 공간적 분포 및 적용방식에 따른 수면 경사 재현 정확도에 대한 민감도 분석을 수행하였다. 실험은 상단 폭 11 m, 경사 1:2(V:H)의 사다리꼴 단면을 가진 실규모 수로에서 70 m 길이의 구간을 대상으로 진행되었다. 실험 구간 내 6개의 압력식 수위계를 설치해 수위 측정 및 수면 경사 산정을 실행하였다. 실험 조건으로 적용된 인공 식생패치의 분포 및 밀도 조건은 3가지로 큰 패치와 작은 패치로 구성된 조밀한 조건, 단일 패치로 구성된 조밀한 조건, 단일 패치로 구성된 성긴 조건이었으며, 모두 정수(emergent)상태로 진행되었다. 적용된 패치의 형상은 내성천에서 조사된 자연 형태의 식생패치 형태를 참고하였으며, 버드나무 종을 모사하였다. 실험 조건에 따라 유량은 각각 평균 1.5 cms와 2.7 cms로 공급하였으며, 평균 수심은 약 1 m로 측정되었다. 위 실험 내용을 바탕으로 수치모의를 위한 경계조건과 지형정보를 수립하였으며 모의 케이스는 크게 두 가지로, 수로 내 식생의 분포를 종방향으로 고려한 케이스와 횡방향으로 고려하여 조도계수를 적용한 케이스로 분류하였다. 모의에 적용된 조도계수는 실험에서 획득한 데이터와 베르누이 방정식을 활용하여 산정되었으며, 두 케이스에 대한 모의 결과는 실험에서 관측된 수위와 비교하였다. 본 연구에 따르면 여러 개의 식생패치가 정수상태로 존재하는 하천에 대한 1차원 수치모의 시 식생의 분포를 종방향으로 고려하여 하나의 구간조도계수를 적용하는 방식이 종횡단면의 식생패치 위치를 고려한 조도계수를 세분화하여 적용하는 방식에 비해 수위 계산 정확도가 상대적으로 높은 것으로 나타났다.

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The Roles of Wind Shadow Aspect Ratio upon the Behaviors of Transverse Dunes : A Dynamics Analysis on the Behavior Space (바람그늘의 기울기가 횡사구의 지형발달에서 담당하는 역할 -거동 공간상의 동역학적 분석을 중심으로-)

  • RHEW, Hosahng
    • Journal of the Korean association of regional geographers
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    • v.22 no.4
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    • pp.887-911
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    • 2016
  • The empirical law that transverse dunes migrate inversely with their heights leads logically to the prediction that multiple dune ridges will converse to a single huge dune by merging. This contradicts the existence of the steady state dune fields on the Earth. The recent studies have emphasized dune collisions as a key mechanism to the stability of dunefield. The roles of wind shadow aspect ratio, however, have yet to be fully explored. This research aims to investigate the potential roles of wind shadow aspect ratio in the dynamical behaviors of transverse dune field. The simplified model is established for this, based upon allometric properties of transverse dunes, wind speedup on the stoss slope and sand trapping efficiency. The derived governing equations can be transformed to the zoning criteria and vector field for dune evolution. The dynamics analysis indicates that wind shadow aspect ratios do not produce convergent areas on the behavior space; rather, they just act as one of the factors that affect the trajectories of dune evolution. Though the model cannot represent the stability of dune field, but seem to produce a reasonable exponent for dune spacing-height relations.

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One-dimensional Hydraulic Modeling of Open Channel Flow Using the Riemann Approximate Solver I : Model Development (Riemann 해법을 이용한 1차원 개수로 수리해석Ⅰ: 모형 개발)

  • Kim, Ji-Sung;Han, Kun-Yeun
    • Journal of Korea Water Resources Association
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    • v.41 no.8
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    • pp.761-772
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    • 2008
  • The object of this study is to develop the model that solves the numerically difficult problems in hydraulic engineering and to demonstrate the applicability of this model by means of various test examples, such as, verification in the gradually varied unsteady condition, three steady flow problems with the change of bottom slope with exact solution, and frictional bed with analytical solution. The governing equation of this model is the integral form of the Saint-Venant equation satisfying the conservation laws, and finite volume method with the Riemann solver is used. The evaluation of the mass and momentum flux with the HLL Riemann approximate solver is executed. MUSCL-Hancock scheme is used to achieve the second order accuracy in space and time. This study introduce the new and simple technique to discretize the source terms of gravity and hydrostatic pressure force due to longitudinal width variation for the balance of quantity between nonlinear flux and source terms. The results show that the developed model's implementation is accurate, robust and highly stable in various flow conditions with source terms, and this model is reliable for one-dimensional applications in hydraulic engineering.

Color Reproduction in DLP Projector using Hue Shift Model according to Additional White Channel (화이트 채널 추가에 따른 색상이동모델를 이용한 DLP 프로젝터의 색 재현)

  • Park, Il-Su;Ha, Ho-Gun;Ha, Yeong-Ho
    • Journal of the Institute of Electronics Engineers of Korea SP
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    • v.49 no.4
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    • pp.40-48
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    • 2012
  • This paper models the hue shift phenomenon and proposes a hue correction method to give perceptual matching between projector with and without additional white channel. To quantify the hue shift phenomenon for whole hue angle, 24 color patches with the same lightness are frist created along equally-spaced hue angle, and these are displayed one by one both displays with different luminance levels. Next, each hue value of the patches appeared on the projector with additional white channel is adjusted by observers until the hue values of patches on both displays appear the same visually. After obtaining the hue shift values from the color matching experiment, these values are piecewise fit into six polynomial functions, which approximately determine shifted hue amounts for an arbitrary hue values of each pixel in projector with additional white channel and are utilized to correct them. Actually, an input RGB image is converted to CIELAB LCH color space to get hue values of each pixel and this hue value is shifted as much as the amount calculated by the functions of hue shift model for correction. Finally, corrected image is inversely converted to an output RGB image. For an evaluation, the matching experiment with several test images and the z-score comparisons were performed.

Model - Based Sensor Fault Detection and Isolation for a Fuel Cell in an Automotive Application (모델 기반 연료전지 스택 온도 센서 고장 감지 및 판별)

  • Han, Jaeyoung;Kim, Younghyeon;Yu, Sangseok
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.41 no.11
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    • pp.735-742
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    • 2017
  • In this study, an effective model-based sensor fault detection methodology that can detect and isolate PEM temperature sensors fault is introduced. In fuel cell vehicle operation process, the stack temperature affects durability of a fuel cell. Thus, it is important for fault algorithm to detect the fault signals. The major objective of sensor fault detection is to guarantee the healthy operations of the fuel cell system and to prevent the stack from high temperature and low temperature. For the residual implementation, parity equation based on the state space is used to detect the sensors fault as stack temperature and coolant inlet temperature, and residual is compared with the healthy temperature signals. Then the residuals are evaluated by various fault scenarios that detect the presence of the sensor fault. In the result, the designed in this study fault algorithm can detect the fault signal.

Wave Attenuation due to Water-Front Vegetation (수변식생에 의한 파랑감쇠 특성)

  • Lee, Seong-Dae
    • Journal of Navigation and Port Research
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    • v.32 no.5
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    • pp.341-347
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    • 2008
  • Recently, it has been widely recognized that water-front and coastal vegetations may have great value in supporting fisheries, protecting from wave attack, stabilizing the sea bed and maintaining good scenery. Hydrodynamic factors playa major role in the functions of water quality and ecosystems. However, the studies on numerical and analytical process of wave propagation are few and far behind compared to those on the hydrodynamic roles of water-front vegetations. In this study, in order to express wave attenuation into water-front vegetation, a numerical model based on the unsteady mild slope equation is developed. This result is compared with an analytical model for describing the wave attenuation by assumed simple long wave condition. Based on both the analytical and numerical results, the physical properties of the wave attenuation are examined under various wave, geometric and vegetation conditions. Through comparisons between the analytical and numerical results, the effects of the vegetation properties, wave properties and model parameters such as the momentum exchange coefficient have been clarified.

Numerical Simulation of Gas Flow within a Radial Fracture Created by Single-Hole Blasting (단일공 발파에서 생성된 균열망에 작용하는 가스압의 수치해석적 산정)

  • Jeng, Yong-Hun;Lee, Chung-In
    • Tunnel and Underground Space
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    • v.16 no.5 s.64
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    • pp.413-421
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    • 2006
  • In order to explain entirely dynamic fracture process induced by blasting in rock mass, it needs to consider detonation pressure and gas pressure acting on blasthole wall simultaneously. In this study, prior to simulating the coupling between gas flow and rock mass, we analyzed effects of gas pressure-time history, length of cracks and equation of state adopted to calculate the gas pressure on the gas flow within a radial fracture created by single-hole blasting. The effects were investigated on two assumptions: (a) the radial fracture was composed of 5 cracks which were 0.01 m in length and 0.001 m in asperity each and (b) the PETN explosive which diameter was 36 mm was charged in a blasthole of 45 mm diameter. It was concluded that the maximum gas pressure and its travel time were dependent on characteristics of charged explosives and geometrical properties of radial fracture.

3D Optimal Layout Design of Satellite Equipment (위성 구성품의 3차원 최적 배치 설계)

  • Yeom, Seung-Yong;Kim, Hong-Rae;Chang, Young-Keun
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.43 no.10
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    • pp.875-887
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    • 2015
  • The optimal layout design is used in the development of various areas of industry. In the field of space systems, components must be placed properly in the limited space of spacecraft by considering mechanical, thermal and electrical interfaces. When applying optimal layout design, a proper, even ideal placement of components is possible in the limited space of a satellite platform. Through the optimal placement design, the minimized moment of inertia enhances efficient attitude control, rapid maneuver and mission performance of the satellite. This paper proposes 3D optimal layout design that minimizes the spacecraft's moment of inertia and effect of thermal dissipation between inner components as well as interference between inner components based on a cubic-structure satellite platform. This study proposes the new genetic algorithm for 3D optimal layout design of the satellite platform.