• Title/Summary/Keyword: Small error approximation

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STOKES FLOW THROUGH A MICROCHANNEL WITH PROTUBERANCES OF STAGGERED ARRANGEMENT (엇갈린 배열의 돌출물들이 존재하는 마이크로채널 내의 스톡스 유동)

  • Son, Jeong Su;Jeong, Jae-Tack
    • Journal of computational fluids engineering
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    • v.20 no.4
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    • pp.109-115
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    • 2015
  • In this study, the Stokes flow in the microchannel is analysed where the semicircular protuberances with constant spacing are attached on the upper and lower walls with staggered arrangement. For the low Reynolds number flow in microchannel, Stokes approximation is used and the periodicity and symmetry of the flow are considered to determine the stream function and pressure distribution in the flow field by using the method of least squared error. As results, the streamline patterns and pressure distributions in the flow field are shown for some specific values of the size and spacing of the protuberances, and shear stress distributions on the surface of semicircular protuberances are plotted. Especially, for an important physical property, the average pressure gradient along the microchannel is obtained and compared with that for the case of in-phase arrangement of the upper and lower protuberances. And, for the small clearance between the protuberances of upper and lower walls or between the protuberances and the opposite wall, the average pressure gradient is derived from the lubrication theory and compared with that of the present study.

New Calibration Methods for improving the Accuracy of AFM (원자간력 현미경의 자율교정법)

  • Kweon, Hyun-Kyu;Go, Young-Chae
    • Proceedings of the KSME Conference
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    • 2001.06b
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    • pp.48-52
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    • 2001
  • In this paper presents an accurate AFM used that is free from the Z-directional distortion of a servo actuator is described. Two mathematical correction methods by the in-situ self-calibrationare employed in this AFM. One is the method by the integration, and the other is the method by inverse function of the calibration curve. The in situ self-calibration method by the integration, the derivative of the calibration curve function of the PZT actuator is calculated from the profile measurement data sets which are obtained by repeating measurements after a small Z-directional shift. Input displacement at each sampling point is approximately estimated first by using a straight calibration line. The derivative is integrated with reference to the approximate input to obtain the approximate calibration curve. Then the approximation of the input value of each sampling point is improved using the obtained calibration curve. Next the integral of the derivative is improved using the newly estimated input values. As a result of repeating these improving process, the calibration curve converges to the correct one, and the distortion of the AFM image can be corrected. In the in situ self-calibration through evaluating the inverse function of the calibration curve, the profile measurement data sets were used during the data processing technique. Principles and experimental results of the two methods are presented.

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A comparative study of low-complexity MMSE signal detection for massive MIMO systems

  • Zhao, Shufeng;Shen, Bin;Hua, Quan
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.12 no.4
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    • pp.1504-1526
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    • 2018
  • For uplink multi-user massive MIMO systems, conventional minimum mean square error (MMSE) linear detection method achieves near-optimal performance when the number of antennas at base station is much larger than that of the single-antenna users. However, MMSE detection involves complicated matrix inversion, thus making it cumbersome to be implemented cost-effectively and rapidly. In this paper, we first summarize in detail the state-of-the-art simplified MMSE detection algorithms that circumvent the complicated matrix inversion and hence reduce the computation complexity from ${\mathcal{O}}(K^3)$ to ${\mathcal{O}}(K^2)$ or ${\mathcal{O}}(NK)$ with some certain performance sacrifice. Meanwhile, we divide the simplified algorithms into two categories, namely the matrix inversion approximation and the classical iterative linear equation solving methods, and make comparisons between them in terms of detection performance and computation complexity. In order to further optimize the detection performance of the existing detection algorithms, we propose more proper solutions to set the initial values and relaxation parameters, and present a new way of reconstructing the exact effective noise variance to accelerate the convergence speed. Analysis and simulation results verify that with the help of proper initial values and parameters, the simplified matrix inversion based detection algorithms can achieve detection performance quite close to that of the ideal matrix inversion based MMSE algorithm with only a small number of series expansions or iterations.

Non-invasive hematocrit measurement (혈액중 non-invasive hematocrit 분석)

  • Yoon, Gil-Won;Jeon, Kye-Jin;Park, Kun-Kook;Lee, Jong-Youn;Hwang, Hyun-Tae;Yeo, Hyung-Seok;Kim, Hong-Sig
    • Proceedings of the Korean Society of Near Infrared Spectroscopy Conference
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    • 2002.11a
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    • pp.59-62
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    • 2002
  • Wavelength selection and prediction algorithm for determining hematocrit are investigated. A model based on the difference in optical density induced by the pulsation of heart beat is developed by taking approximation of Twersky's theory on the assumption that the variation of blood vessel size is small during arterial pulsing[1]. A device is constructed with a five-wavelength LED array as light source. The selected wavelengths are two isobestic points and three in compensation for tissue scattering. Data are collected from 549 out-patients who are randomly grouped as calibration and prediction sets. The range of percent hematocrit was 19.3∼51.8. The ratio of the variations of optical density between systole and diastole at two different wavelengths is used as a variable. We selected several such variables that show high reproducibility among all variables. Multiple linear regression analysis is made. The relative percent error is 8% and the standard deviation is 3.67 for the calibration set. The relative % error and standard deviation of the prediction set are 8.2% and 3.69 respectively. We successfully demonstrate the possibility of non-invasive hematocrit measurement, particularly, using the wavelengths below 1000nm.

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A Design of Low-power/Small-area Divider and Square-Root Circuits based on Logarithm Number System (로그수체계 기반의 저전력/저면적 제산기 및 제곱근기 회로 설계)

  • Kim, Chay-Hyeun;Kim, Jong-Hwan;Lee, Yong-Hwan;Shin, Kyung-Wook
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • v.9 no.2
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    • pp.895-898
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    • 2005
  • This paper describes a design of LNS-based divider and square-root circuits which are key arithmetic units in graphic processor and digital signal processor. To achive area-efficient and low-power that is an essential consideration for mobile environment, a fixed-point format of 16.16 is adopted instead of conventional floating-point format. The designed divider and square-root units consist of binary-to-logarithm converter, subtractor, logarithm-to-binary converter. The binary to logarithm converter is designed using combinational logic based on six regions approximation method. As a result, gate count reduction is obtained when compared with conventional lookup approack. The designed units is 3,130 gate count and 1,280 gate count. To minimize average percent error 3.8% and 4.2%. error compensation method is employed.

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Reduction of Chattering Error of Reed Switch Sensor for Remote Measurement of Water Flow Meter (리드 스위치 센서를 이용한 원격 검침용 상수도 계량기에서 채터링 오차 감소 방안 연구)

  • Ayurzana, Odgerel;Kim, Hie-Sik
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.44 no.4 s.316
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    • pp.42-47
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    • 2007
  • To reduce the chattering errors of reed switch sensors in the automatic remote measurement of water meter a reed switch sensor was analyzed and improved. The operation of reed switch sensors can be described as a mechanical contact switch by approximation of permanent magnet piece to generate an electrical pulse. The reed switch sensors are used mostly in measurement application to detect the rotational or translational displacement. To apply for water flow measurement devices, the reed switch sensors should keep high reliability. They are applied for the electronic digital type of water flow meters. The reed switch sensor is just mounted simply on the conventional mechanical type flow meter. A small magnet is attached on a pointer of the water meter counter rotor. Inside the reed sensor two steel leaf springs make mechanical contact and apart repeatedly as rotation of flow meter counter. The counting electrical contact pulses can be converted as the water flow amount. The MCU sends the digital flow rate data to the server using the wireless communication network. But the digital data is occurred difference or won by chattering noise. The reed switch sensor contains chattering error by it self at the force equivalent position. The vibrations such as passing vehicle near to the switch sensor installed location causes chattering. In order to reduce chattering error, most system uses just software methods, for example using filter algorithm and also statistical calibration methods. The chattering errors were reduced by changing leaf spring structure using mechanical characteristics.

An Analytical Solution for Regular Progressive Water Waves

  • Shin, JangRyong
    • Journal of Advanced Research in Ocean Engineering
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    • v.1 no.3
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    • pp.157-167
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    • 2015
  • In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

Validation of a CFD Analysis Model for the Calculation of CANDU6 Moderator Temperature Distribution (CANDU6 감속재 온도분포 계산을 위한 CFD 해석모델의 타당성 검토)

  • Yoon, Churl;Rhee, Bo-Wook;Min, Byung-Joo
    • Proceedings of the KSME Conference
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    • 2001.11b
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    • pp.499-504
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    • 2001
  • A validation of a 3D CFD model for predicting local subcooling of moderator in the vicinity of calandria tubes in a CANDU reactor is performed. The small scale moderator experiments performed at Sheridan Park Experimental Laboratory(SPEL) in Ontario, Canada[1] is used for the validation. Also a comparison is made between previous CFD analyses based on 2DMOTH and PHOENICS, and the current model analysis for the same SPEL experiment. For the current model, a set of grid structures for the same geometry as the experimental test section is generated and the momentum, heat and continuity equations are solved by CFX-4.3, a CFD code developed by AEA technology. The matrix of calandria tubes is simplified by the porous media approach. The standard $k-\varepsilon$ turbulence model associated with logarithmic wall treatment and SIMPLEC algorithm on the body fitted grid are used and buoyancy effects are accounted for by the Boussinesq approximation. For the test conditions simulated in this study, the flow pattern identified is a buoyancy-dominated flow, which is generated by the interaction between the dominant buoyancy force by heating and inertial momentum forces by the inlet jets. As a result, the current CFD moderator analysis model predicts the moderator temperature reasonably, and the maximum error against the experimental data is kept at less than $2.0^{\circ}C$ over the whole domain. The simulated velocity field matches with the visualization of SPEL experiments quite well.

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Multiple Regression Analysis for Piercing Punch Profile Optimization to Prevent Tearing During Tee Pipe Burring (다중 회귀 분석을 활용한 Tee-Pipe 버링 공정에서 찢어짐 방지를 위한 피어싱 펀치 형상 최적 설계)

  • Lee, Y.S.;Kim, J.Y.;Kang, J.S.;Hong, S.
    • Transactions of Materials Processing
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    • v.26 no.5
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    • pp.271-276
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    • 2017
  • A tee is the most common pipefitting used to combine or divide fluid flow. Tees can connect pipes of different diameters or change the direction of a pipe run. To manufacture tee type of stainless steel pipe, combinations of punch piercing and burr forming have been widely used in the industry. However, such method is considerably time consuming with regard to performing empirical work necessary to attain process conditions to prevent upper end tearing of the tee product and meet target tee height. Numerous experiments have shown that the piercing profile is the main cause of defects mentioned above. Furthermore, the mold design is formed through trial and error according to pipe diameters and changes in requirements. Thus, the objective of this study was to perform piercing and burring process analysis via finite element analysis using DYNAFORM to resolve problems mentioned above. An optimization design method was used to determine the piercing punch profile. Three radii of the piercing punch (i.e., large, small, and joined radii) were selected as design variables to minimize thinning of a tee pipe. Based on results of correlation and multiple regression analyses, we developed a predictive approximation model to satisfy requirements for both thickness reduction and target height. The new piercing punch profile was then applied to actual tee forming using the developed prediction equation. Model results were found to be in good agreement with experimental results.

Analysis on the Planar Bowtie Antenna for IMT-2000 Handset (IMT-2000 핸드셋용 평면형 Bowtie 안테나 해석)

  • Lee, Hee-Suk;Kim, Nam
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.11 no.5
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    • pp.681-688
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    • 2000
  • In this paper, a planar antenna that is small and light, is designed and analyzed aiming handset antenna of IMT-2000. Employing the Ensemble simulator based on a MoM, design-parameters are found to determine a resonant frequency. Therefore, it is analyzed with the Ensemble simulation and FDTD numerical for resonating at the allocated frequency for IMT-2000 in the fixed antenna dimension of 21$^{\circ}$wing angle that is a design parameter. Analyzing with FDTD method, Though the results of FDTD are very exact, this analysis introduces errors due to the staircasing approximation in the slope of bowtie. To reduce this error, it is divided to 4-ranges where the cell contains the boundary of perfect conductor/free space. Then, each range is calculated by different by different equation, which modify the H-field to add the component of the area and length of the cell filled with free space. Therefore, the modified FDTD algorithm provided with a narrow bandwidth of return loss calculated with a standard FDTD algorithm that can be extended to the desired ranges.

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