• Title/Summary/Keyword: Sum of squares

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Structural response analysis in time and frequency domain considering both ductility and strain rate effects under uniform and multiple-support earthquake excitations

  • Liu, Guohuan;Lian, Jijian;Liang, Chao;Zhao, Mi
    • Earthquakes and Structures
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    • v.10 no.5
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    • pp.989-1012
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    • 2016
  • The structural dynamic behavior and yield strength considering both ductility and strain rate effects are analyzed in this article. For the single-degree-of-freedom (SDOF) system, the relationship between the relative velocity and the strain rate response is deduced and the strain rate spectrum is presented. The ductility factor can be incorporated into the strain rate spectrum conveniently based on the constant-ductility velocity response spectrum. With the application of strain rate spectrum, it is convenient to consider the ductility and strain rate effects in engineering practice. The modal combination method, i.e., square root of the sum of the squares (SRSS) method, is employed to calculate the maximum strain rate of the elastoplastic multiple-degree-of-freedom (MDOF) system under uniform excitation. Considering the spatially varying ground motions, a new response spectrum method is developed by incorporating the ductility factor and strain rate into the conventional response spectrum method. In order to further analyze the effects of strain rate and ductility on structural dynamic behavior and yield strength, the cantilever beam (one-dimensional) and the triangular element (two-dimensional) are taken as numerical examples to calculate their seismic responses in time domain. Numerical results show that the permanent displacements with and without considering the strain rate effect are significantly different from each other. It is not only necessary in theory but also significant in engineering practice to take the ductility and strain rate effects into consideration.

A new method for calculating quantiles of grouped data based on the frequency polygon (집단화된 통계자료의 도수다각형에 근거한 새로운 분위수 계산법)

  • Kim, Hyuk Joo
    • Journal of the Korean Data and Information Science Society
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    • v.28 no.2
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    • pp.383-393
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    • 2017
  • When we deal with grouped statistical data, it is desirable to use a calculation method that gives as close value to the true value of a statistic as possible. In this paper, we suggested a new method to calculate the quantiles of grouped data. The main idea of the suggested method is calculating the data values by partitioning the pentagons, that correspond to the class intervals in the frequency polygon drawn according to the histogram, into parts with equal area. We compared this method with existing methods through simulations using some datasets from introductory statistics textbooks. In the simulation study, we simulated as many data values as given in each class interval using the inverse transform method, on the basis of the distribution that has the shape given by the frequency polygon. Using the sum of squares of differences from quantiles of the simulated data as a criterion, the suggested method was found to have better performance than existing methods for almost all quartiles and deciles.

Back-Analysis for Estimating Transmissivity in Riverbank Filtration (강변여과 대수층의 투수량계수 추정을 위한 역해석)

  • Park Seo-Hwa;Lee Sang-Il;Lee Sang-Sin
    • Journal of Korea Water Resources Association
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    • v.39 no.6 s.167
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    • pp.503-510
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    • 2006
  • Riverbank filtration is a natural process, using alluvial aquifers to remove contaminants and pathogens in river water for the production of drinking water. Back analysis which minimizes the objective function that is typically the sum of squares of the differences between the calculated and measured quantities is used for the estimation of aquifer parameters. In this study, transmissivity is back-analysed using the BFGS (Broyden-Fletcher-Goldfarb-Shanno) scheme for optimization. MOC is used to obtain calculated groundwater level. The developed inverse model was applied to Dae-san, Chang-won city where riverbank filtration is being undertaken. The model showed good convergence behavior for different groundwater conditions. The performance of the model was better than a widely-used commercial software package in terms of error between calculated and observed groundwater level.

Exploring the Limit of Natural Number Sequences Using Spreadsheet (스프레드시트에 기초한 자연수 수열의 극한 연구)

  • Kim, Jin-Hwan
    • Communications of Mathematical Education
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    • v.26 no.2
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    • pp.205-220
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    • 2012
  • In this article convergent sequences with natural number terms are investigated and the behaviors of tails and limits of these natural number sequences are explored. Firstly this study showed how the pre-service teachers response to the intuitive limit definition using "getting closer" for constant sequences. As a case of convergent natural sequences, the sequences in which the latter term is determined by the sum of digit squares of the former term are considered. To exploring these sequences the computational and charting capabilities of spreadsheets are utilized and some mathematical findings are obtained. Spreadsheet can be instrumentalized by teachers or students to provide a laboratory-like environment to explore a mathematical problem.

Study of Tolerance Suitability of Door Operation Mechanism on Mobile Air Handing Unit Using 3-DCS Analysis (3-DCS를 이용한 자동차 공기 분배장치의 도아 구동 기구의 공차 적합성 분석에 대한 연구)

  • Kim, Jongsu;Lee, Daewoong
    • Transactions of the Korean Society of Automotive Engineers
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    • v.24 no.5
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    • pp.527-537
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    • 2016
  • Recent automakers are trying to be more precise with the dimension check and moving parts to guarantee high quality and satisfy customer requirements. The aim of this paper is to investigate the design tolerance suitability of door operating mechanism linked arms, lever, and cam-shaft in a mobile air handling unit. These parts are complicated because doors, arms, lever and cam-shaft are connected nonlinearly in 3D. The current tolerance analysis method poses problems in design analysis because the moving doors are reasonably suitable for the AHU function. The 3-DCS analysis method provided useful results not only in establishing the inspection criteria for the quality control of products but also in enabling economical production. As a result, the vent door had $1.62^{\circ}{\sim}1.72^{\circ}$ and the defrost door had $0.84^{\circ}{\sim}0.9^{\circ}$ for the directly connected arms operating-type. For the lever connected arm operating-type, the foot door had $2.0^{\circ}{\sim}2.24^{\circ}$ tolerance, while the tolerance values satisfied the air flow volume distribution rate criteria in the AHU. Finally, the results have confirmed the design's tolerance suitability by using 3-DCS analysis at the early design stages. Reliability can be achieved by analyzing accumulated tolerance during the sub-parts assembly process and the moving mechanism linked especially by arms, lever, and cam-shaft.

Automatic Object Recognition in 3D Measuring Data (3차원 측정점으로부터의 객체 자동인식)

  • Ahn, Sung-Joon
    • The KIPS Transactions:PartB
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    • v.16B no.1
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    • pp.47-54
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    • 2009
  • Automatic object recognition in 3D measuring data is of great interest in many application fields e.g. computer vision, reverse engineering and digital factory. In this paper we present a software tool for a fully automatic object detection and parameter estimation in unordered and noisy point clouds with a large number of data points. The software consists of three interactive modules each for model selection, point segmentation and model fitting, in which the orthogonal distance fitting (ODF) plays an important role. The ODF algorithms estimate model parameters by minimizing the square sum of the shortest distances between model feature and measurement points. The local quadric surface fitted through ODF to a randomly touched small initial patch of the point cloud provides the necessary initial information for the overall procedures of model selection, point segmentation and model fitting. The performance of the presented software tool will be demonstrated by applying to point clouds.

Evaluation of Sustainable Yield for a Small Rural Watershed (농촌 소유역의 지하수 지속가능개발량 평가)

  • Park, Ki-Jung;Chung, Sang-Ok
    • Journal of Korea Water Resources Association
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    • v.37 no.7
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    • pp.581-587
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    • 2004
  • An experimental watershed was selected and sustainable yield was evaluated. The study area(3.89$\textrm{km}^2$) was located in Kyungpook Sangju Yangchon-dong. The visual MODFLOW was verified by comparing the observed and estimated groundwater table. The analysis of the observed and estimated groundwater table from 19 March 2003 to 18 March 2004 showed that the average error was 0.0009m, the error sum of squares 7.245$m^2$, absolute mean error 0.094 m, root mean square error 0.141m, and the model efficiency was 92%. The normal, 10- and 30- year drought frequency years were selected and sustainable yield was evaluated in these periods. Ratios of sustainable yield to the annual infiltration were 14.5% for the normal year(1992), 15.1% for the 10-year(1994), and 15.2% for the 30-year drought frequency year(1982). The results of this study can be used as a basic information for groundwater development and management planning considering regional characteristics.

심근조영심초음파에서 심장의 움직임을 보정한 비침습적 심근관류모델의 정량적 평가

  • 이재훈;김희중;정남식;임세중;김기황
    • Proceedings of the Korean Society of Medical Physics Conference
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    • 2003.09a
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    • pp.49-49
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    • 2003
  • 목적 : 심초음파는 비침습적이므로 반복적으로 정확히 심질환의 경과를 관찰하여 치료효과 및 수술시기를 정할 수 있는 검사로서 임상적으로 매우 유용하다. 실시간 심근조영심초음파에 의한 time intensity 평가는 부위별로 수행됨으로 연속적으로 위치하는 관심영역이 intensity에 있어 심장의 움직임 변화에 영향을 받는다. Time intensity 곡선의 최적의 곡선맞춤을 위해 주기적인 심장 운동 매개변수를 조합해 기존의 모델을 보정한 안정적인 측정방법을 제시한다. 방법 : 심장의 운동에 의한 특징적인 정보를 설명하기 위해 기존의 문헌에 제시된 지수 함수에 주어진 심박수로 만들어진 시간에 관한 일반적인 정형파 함수를 추가한다. C(t) = A[1 - exp($\beta$t)] + Dsine(2$\pi$ft + $\theta$) C(t): videointensity A: plateau videointensity (blood volume) $\beta$: capillary blood velocity (rate constant of rise in videointensity) t: pulsing interval (ms) D: displacement from the periodic variance of the curve (estimated motion field from the ejection point for the ratio between systole and diastole) f: heart rate $\theta$: transit time issue A $\times$ $\beta$ : myocardial blood flow 관상동맥의 관류 데이터에 대한 실험이 펄스간격에 대한 비디오 세기로 수행되었다. 그리고 이러한 결과들이 the sum of squares due to error, R square, root mean squared error로 평가되었다. 결과 : 실험결과, 주기적인 심장의 움직임과 심박출 시점으로부터의 변위를 잘 기술하고 곡선에서의 측정 점들이 예측된 심장 움직임에 따라 성공적으로 표시되었다. 뿐만 아니라 보정된 모델이 현저한 적합도의 향상을 보여주었다. 결론 : 제시된 접근방법은 각각의 측정에서 심장 운동 영역의 변화에 독립적이며 측정 시점에 의해 영향받지 않고 심근 관류의 안정적인 측정이 가능하다. 심장의 움직임에 관한 매개변수를 조합한 모델로 곡선접합을 수행함으로써 관류의 정량적 정보를 좀더 정확하게 얻을 수 있으며 임상적 이용을 가능하게 할 것으로 기대된다.

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Genotype x Environment Interaction and Stability Analysis for Potato Performance and Glycoalkaloid Content in Korea (유전형과 재배환경의 상호작용에 따른 감자 수량성과 글리코알카로이드 함량 변화)

  • Kim, Su Jeong;Sohn, Hwang Bae;Lee, Yu Young;Park, Min Woo;Chang, Dong Chil;Kwon, Oh Keun;Park, Young Eun;Hong, Su Young;Suh, Jong Taek;Nam, Jung Hwan;Jeong, Jin Cheol;Koo, Bon Cheol;Kim, Yul Ho
    • KOREAN JOURNAL OF CROP SCIENCE
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    • v.62 no.4
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    • pp.333-345
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    • 2017
  • The potato tuber is known as a rich source of essential nutrients, used throughout the world. Although potato-breeding programs share some priorities, the major objective is to increase the genetic potential for yield through breeding or to eliminate hazards that reduce yield. Glycoalkaloids, which are considered a serious hazard to human health, accumulate naturally in potatoes during growth, harvesting, transportation, and storage. Here, we used the AMMI (additive main effects and multiplicative interaction) and GGE (Genotype main effect and genotype by environment interaction) biplot model, to evaluate tuber yield stability and glycoalkaloid content in six potato cultivars across three locations during 2012/2013. The environment on tuber yield had the greatest effect and accounted for 33.0% of the total sum squares; genotypes accounted for 3.8% and $G{\times}E$ interaction accounted for 11.1% which is the nest highest contribution. Conversely, the genotype on glycoalkaloid had the greatest effect and accounted for 82.4% of the total sum squares), whereas environment and $G{\times}E$ effects on this trait accounted for only 0.4% and 3.7%, respectively. Furthermore, potato genotype 'Superior', which covers most of the cultivated area, exhibited high yield performance with stability. 'Goun', which showed lower glycoalkaloid content, was the most suitable and desirable genotype. Results showed that, while tuber yield was more affected by the environment, glycoalkaloid content was more dependent on genotype. Further, the use of the AMMI and GGE biplot model generated more interactive visuals, facilitated the identification of superior genotypes, and suggested decisions on a variety of recommendations for specific environments.

Seismic Design of Columns in Inverted V-braced Steel Frames Considering Brace Buckling (가새좌굴을 고려한 역 V형 가새골조의 기둥부재 내진설계법)

  • Cho, Chun-Hee;Kim, Jung-Jae;Lee, Cheol-Ho
    • Journal of Korean Society of Steel Construction
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    • v.22 no.1
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    • pp.1-12
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    • 2010
  • According to the capacity design concept which forms the basis of the current steel seismic codes, the braces in concentrically braced frames (CBFs) should dissipate seismic energy through cyclic tension yielding and cyclic compression buckling while the beams and the columns should remain elastic. Brace buckling in inverted V-braced frames induces unbalanced vertical forces which, in turn, impose the additional beam moments and column axial forces. However, due to difficulty in predicting the location of buckling stories, the most conservative approach implied in the design code is to estimate the column axial forces by adding all the unbalanced vertical forces in the upper stories. One alternative approach, less conservative and recommended by the current code, is to estimate the column axial forces based on the amplified seismic load expected at the mechanism-level response. Both are either too conservative or lacking technical foundation. In this paper, three combination rules for a rational estimation of the column axial forces were proposed. The idea central to the three methods is to detect the stories of high buckling potential based on pushover analysis and dynamic behavior. The unbalanced vertical forces in the stories detected as high buckling potential are summed in a linear manner while those in other stories are combined by following the SRSS(square root of sum of squares) rule. The accuracy and design advantage of the three methods were validated by comparing extensive inelastic dynamic analysis results. The mode-shape based method(MSBM), which is both simple and accurate, is recommended as the method of choice for practicing engineers among the three.