• Title/Summary/Keyword: Linear system of equations

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A Numerical Model for Analysis of Groundwater Flow with Heat Flow in Steady-State (열(熱)흐름을 동반(同伴)한 정상지하수(定常地下水)의 흐름해석(解析) 수치모형(數値模型))

  • Wang, Soo Kyun;Cho, Won Cheol;Lee, Won Hwan
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.11 no.4
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    • pp.103-112
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    • 1991
  • In this study, a numerical model was established and applied to simulate the steady-state groundwater and heat flow in an isotropic, heterogeneous, three dimensional aquifer system with uniform thermal properties and no change of state. This model was developed as an aid in screening large groundwater-flow systems as prospects for underground waste storage. Driving forces on the system are external hydrologic conditions of recharge from precipitation and fixed hydraulic head boundaries. Heat flux includes geothermal heat-flow, conduction to the land surface, advection from recharge, and advection to or from fixed-head boundaries. The model uses an iterative procedure that alternately solves the groundwater-flow and heat-flow equations, updating advective flux after solution of the groundwater-flow equation, and updating hydraulic conductivity after solution of the heat-flow equation. Dierect solution is used for each equation. Travel time is determined by particle tracking through the modeled space. Velocities within blocks are linear interpolations of velocities at block faces. Applying this model to the groundwater-flow system located in Jigyung-ri. Songla-myun, Youngil-gun. Kyungsangbuk-do, the groundwater-flow system including distribution of head, temperature and travel time and flow line, is analyzed.

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Minimizing Estimation Errors of a Wind Velocity Forecasting Technique That Functions as an Early Warning System in the Agricultural Sector (농업기상재해 조기경보시스템의 풍속 예측 기법 개선 연구)

  • Kim, Soo-ock;Park, Joo-Hyeon;Hwang, Kyu-Hong
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.24 no.2
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    • pp.63-77
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    • 2022
  • Our aim was to reduce estimation errors of a wind velocity model used as an early warning system for weather risk management in the agricultural sector. The Rural Development Administration (RDA) agricultural weather observation network's wind velocity data and its corresponding estimated data from January to December 2020 were used to calculate linear regression equations (Y = aX + b). In each linear regression, the wind estimation error at 87 points and eight time slots per day (00:00, 03:00, 06:00, 09.00, 12.00, 15.00, 18.00, and 21:00) is the dependent variable (Y), while the estimated wind velocity is the independent variable (X). When the correlation coefficient exceeded 0.5, the regression equation was used as the wind velocity correction equation. In contrast, when the correlation coefficient was less than 0.5, the mean error (ME) at the corresponding points and time slots was substituted as the correction value instead of the regression equation. To enable the use of wind velocity model at a national scale, a distribution map with a grid resolution of 250 m was created. This objective was achieved b y performing a spatial interpolation with an inverse distance weighted (IDW) technique using the regression coefficients (a and b), the correlation coefficient (R), and the ME values for the 87 points and eight time slots. Interpolated grid values for 13 weather observation points in rural areas were then extracted. The wind velocity estimation errors for 13 points from January to December 2019 were corrected and compared with the system's values. After correction, the mean ME of the wind velocities reduced from 0.68 m/s to 0.45 m/s, while the mean RMSE reduced from 1.30 m/s to 1.05 m/s. In conclusion, the system's wind velocities were overestimated across all time slots; however, after the correction model was applied, the overestimation reduced in all time slots, except for 15:00. The ME and RMSE improved b y 33% and 19.2%, respectively. In our system, the warning for wind damage risk to crops is driven by the daily maximum wind speed derived from the daily mean wind speed obtained eight times per day. This approach is expected to reduce false alarms within the context of strong wind risk, by reducing the overestimation of wind velocities.

Development of Optimal Chlorination Model and Parameter Studies (최적 염소 소독 모형의 개발 및 파라미터 연구)

  • Kim, Joonhyun;Ahn, Sooyoung;Park, Minwoo
    • Journal of Environmental Impact Assessment
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    • v.29 no.6
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    • pp.403-413
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    • 2020
  • A mathematical model comprised with eight simultaneous quasi-linear partial differential equations was suggested to provide optimal chlorination strategy. Upstream weighted finite element method was employed to construct multidimensional numerical code. The code was verified against measured concentrations in three type of reactors. Boundary conditions and reaction rate were calibrated for the sixteen cases of experimental results to regenerate the measured values. Eight reaction rate coefficients were estimated from the modeling result. The reaction rate coefficients were expressed in terms of pH and temperature. Automatic optimal algorithm was invented to estimate the reaction rate coefficients by minimizing the sum of squares of the numerical errors and combined with the model. In order to minimize the concentration of chlorine and pollutants at the final usage sites, a real-time predictive control system is imperative which can predict the water quality variables from the chlorine disinfection process at the water purification plant to the customer by means of a model and operate the disinfection process according to the influent water quality. This model can be used to build such a system in water treatment plants.

Growth Model of Common Ice Plant (Mesembryanthemum crystallinum L.) Using Expolinear Functions in a Closed-type Plant Production System (완전제어형 식물 생산 시스템에서 선형 지수 함수를 이용한 Common Ice Plant의 생육 모델)

  • Cha, Mi-Kyung;Kim, Ju-Sung;Cho, Young-Yeol
    • Horticultural Science & Technology
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    • v.32 no.4
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    • pp.493-498
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    • 2014
  • The objective of this study was to make growth and yield models for common ice plant (Mesembryanthemum crystallinum L.) using expolinear functional equations in a closed-type plant production system. Three-band radiation type fluorescent lamps with a 12-hours photoperiod were used, and the light intensity was $200{\mu}mol{\cdot}m^{-2}{\cdot}s^{-1}$. Nutrient film systems with three layers were used for plant growth. Environmental conditions, such as air temperature, relative humidity and $CO_2$ concentration were controlled by an ON/OFF operation. Leaf area, shoot fresh and dry weights, light use efficiency of common ice plant as function of days after transplanting, accumulative temperature and accumulative radiation were analyzed. Leaf area, shoot fresh and dry weights per area were described using an expolinear equation. A linear relationship between shoot dry and fresh weights was observed. Light use efficiency of common ice plant was $3.3g{\cdot}MJ^{-1}$ at 30 days after transplanting. It is concluded that the expolinear growth model can be a useful tool for quantifying the growth and yield of common ice plant in a closed plant production system.

Kinetic Behavior of Immobilized Tyrosinase on Carbon in a Simulated Packed-Bed Reactor (충전층에서 탄소에 고정시킨 Tyrosinase의 반응속도에 관한 연구)

  • Shin, Sun Kyoung;Kim, Kyeo-Keun
    • Analytical Science and Technology
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    • v.10 no.1
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    • pp.66-74
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    • 1997
  • Influence of the axial dispersion on immobilized enzyme catalytic bed was investigated in order to examine the kinetic behavior of the biocatalysis. The enzyme employed in this study was the tyrosinase(EC 1.14.18.1) immobilized on carbon support : this system requires two substrates of phenol and oxygen. This enzyme has potential application for phenol degradation in waste water. A simulated reactor was a packed-bed reactor of 2.54cm in diameter and 10cm long, loaded with the immobilized carbon particle with an average diameter of $550{\mu}m$. A phenol feed in the strength of 55.5mM(5220ppm) was used to observe the behavior of the immobilized enzyme column at three different dissolved oxygen levels of 0.08445mM(2.7ppm), 0.1689mM(5.4ppm) and 0.3378mM(9.5ppm) with the flow rates in the range of 60(1mL/s) to 180mL/min(3mL/s). Examination of the Biot number and Damkolher numbers of the immobilized system enables us to eliminate the contribution of external mass transfer to set of differential equations derived from the dispersion model. Solution of the equation was finally obtained numerically with the application of the Danckwert boundary conditions and the assumed zero-and first order rates on the non-linear two substrate enzyme kinetics. Higher conversion of phenol was observed at the low flow rates and at the higher oxygen concentration. Comparison of axial dispersion and plug flow model showed that no detectable difference was observed in the column outlet conversion between the axial and the plug flow models which was in complete agreement with the previous studies.

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Methodology to Predict Service Lives of Pavement Marking Materials (도로 차선 재료의 공용수명 예측방법)

  • Oh, Heung-Un;Lee, Hyun-Seock;Jang, Jung-Hwa;Kang, Jai-Soo
    • International Journal of Highway Engineering
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    • v.10 no.4
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    • pp.151-159
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    • 2008
  • Performances of retroreflectivity vary place to place, according to traffic volumes and time lengths after striping, depending on pavement marking materials and colors. The present paper uses the nation wide data of retroreflectivity, which has been collected from freeways and then tries to develop the regression curve setting traffic volume and service life as independent variables and retroreflectivities as dependent variables. The DB system includes two year's measurement in $2005{\sim}2006$ over Korean freeway pavement marking at an interval of three months for the period. The mobile measurement system, a laserlux, was employed for the purpose. The DB has provided a lot of information about materials and performance of the specific pavement marking such as geometric features, traffic volumes, material characteristics and the installation date. This study provides the comparison of pavement marking performances under diversified conditions. Based on accumulated pavement marking performances, this study provides performance curves based on the diversified factors. The goal of the retroreflectivity modeling is to develop equations that can be used to estimate an average retroreflectivity of pavement markings as a function time since application and traffic volume. After representing the variation of retroreflectivities and estimating regression curves by linear, exponential, logarithmic and power function, the regression curve which had the highest coefficient of determination and the value similar to the last field measurement was regarded as the retroreflectivity decay model. As a result of verification, the decay model showed the signification within the 90% confidence level and especially showed the clear relation with field data according to increase of cumulative vehicle exposure. Accordingly, these models can be used to determine service lives, retroreflectivity degradation rates, and retroreflectivity of new markings.

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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.

Performance Comparison of the Batch Filter Based on the Unscented Transformation and Other Batch Filters for Satellite Orbit Determination (인공위성 궤도결정을 위한 Unscented 변환 기반의 배치필터와 다른 배치필터들과의 성능비교)

  • Park, Eun-Seo;Park, Sang-Young;Choi, Kyu-Hong
    • Journal of Astronomy and Space Sciences
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    • v.26 no.1
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    • pp.75-88
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    • 2009
  • The main purpose of the current research is to introduce the alternative algorithm of the non-recursive batch filter based on the unscented transformation in which the linearization process is unnecessary. The presented algorithm is applied to the orbit determination of a low earth orbiting satellite and compared its results with those of the well-known Bayesian batch least squares estimation and the iterative UKF smoother (IUKS). The system dynamic equations consist of the Earth's geo-potential, the atmospheric drag, solar radiation pressure and the lunar/solar gravitational perturbations. The range, azimuth and elevation angles of the satellite measured from ground stations are used for orbit determination. The characteristics of the non recursive unscented batch filter are analyzed for various aspects, including accuracy of the determined orbit, sensitivity to the initial uncertainty, measurement noise and stability performance in a realistic dynamic system and measurement model. As a result, under large non-linear conditions, the presented non-recursive batch filter yields more accurate results than the other batch filters about 5% for initial uncertainty test and 12% for measurement noise test. Moreover, the presented filter exhibits better convergence reliability than the Bayesian least squares. Hence, it is concluded that the non-recursive batch filter based on the unscented transformation is effectively applicable for highly nonlinear batch estimation problems.

Experimental Evaluation of Levitation and Imbalance Compensation for the Magnetic Bearing System Using Discrete Time Q-Parameterization Control (이산시간 Q 매개변수화 제어를 이용한 자기축수 시스템에 대한 부상과 불평형보정의 실험적 평가)

  • ;Fumio Matsumura
    • Journal of KSNVE
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    • v.8 no.5
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    • pp.964-973
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    • 1998
  • In this paper we propose a levitation and imbalance compensation controller design methodology of magnetic bearing system. In order to achieve levitation and elimination of unbalance vibartion in some operation speed we use the discrete-time Q-parameterization control. When rotor speed p = 0 there are no rotor unbalance, with frequency equals to the rotational speed. So in order to make levitatiom we choose the Q-parameterization controller free parameter Q such that the controller has poles on the unit circle at z = 1. However, when rotor speed p $\neq$ 0 there exist sinusoidal disturbance forces, with frequency equals to the rotational speed. So in order to achieve asymptotic rejection of these disturbance forces, the Q-parameterization controller free parameter Q is chosen such that the controller has poles on the unit circle at z = $exp^{ipTs}$ for a certain speed of rotation p ( $T_s$ is the sampling period). First, we introduce the experimental setup employed in this research. Second, we give a mathematical model for the magnetic bearing in difference equation form. Third, we explain the proposed discrete-time Q-parameterization controller design methodology. The controller free parameter Q is assumed to be a proper stable transfer function. Fourth, we show that the controller free parameter which satisfies the design objectives can be obtained by simply solving a set of linear equations rather than solving a complicated optimization problem. Finally, several simulation and experimental results are obtained to evaluate the proposed controller. The results obtained show the effectiveness of the proposed controller in eliminating the unbalance vibrations at the design speed of rotation.

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Establishment of Waste Collection and Transportation System for Composting I. Estimation of Unit Garbage Generation (퇴비화촉진을 위한 쓰레기 수거체계의 확립 I. 음식물찌꺼기 원단위 발생량의 산정)

  • Shin, H.S.;Hwang, E.J.;Kang, H.;Lee, S.J.;Jang, W.
    • Journal of the Korea Organic Resources Recycling Association
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    • v.3 no.2
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    • pp.25-36
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    • 1995
  • It is important to separate the compostables from waste for successful operation of composting plant, since various compositions are mixed in it. For the separation of compostables, it is necessary to estimate total amounts of compostables from several sources. Based on it, required capacity and number of composting plant as well as proper waste collection and transportation system can be determined. So, amounts of garbage, major target material for composting. were estimated in this study. In survey of unit garbage generation(UGG). different estimation results would be obtained depending on the basis of its measurement. However, previous researches did not consider it. In this paper, the correlations between area and the number of user of garbage source were analyzed to find the related equations which were apllyed to estimation of total generation. Obtained results are as the following. Relative variations of measured UGG based on area and custumer are 62.5 and 52.8, respectively. In linear regression, related equation between area and custumer was Y=0.244X+59.0 (X=area, Y=custumer). The correlation factor r is 0.904. Equation Y=616.5X/(X+1215.4) was also obtained from linear regression using Monod equation (r=0.720). From the first order equation and measured data of UGG based on custumer, amounts of garbage generation from restaurant in Seoul and the whole country were calculated to 2043.9 ton/d and 9014.0 ton/d, respectively. But, the values calculated from measured data of UGG based on area were as low as 821.3 ton/d Cin Seoul) and 3821.0 ton/d(in the whole country). Consequently, the measurement of unit garbage generation based on the number of custumer was more favorable to lessen the points of survey and to guarantee the representative values. Especially, it would fit well on restaurant having statistics of area.

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