• 제목/요약/키워드: Type of Mathematical Error

검색결과 109건 처리시간 0.023초

하수처리 프로세스의 선형 추론 퍼지 모델링 (Fuzzy Modeling of Activated Sludge Process Using Linear Reasoning Method)

  • 오성권;박종진;이성주;황희수;김현기;우광방
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 1990년도 추계학술대회 논문집 학회본부
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    • pp.417-420
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    • 1990
  • The conventional quantitative techniques of system analysis are intrinsically unsuited for dealing with humanistic systems. Therefore, the rule based modeling of fuzzy linguistic type has been developed for the analysis of humanistic systems and complex systems and it is very significant for analysis and design of fuzzy logic controller. The activated sludge process is a commonly used method for treating sewage and waste waters. A mathematical tool to build a fuzzy model of the activated sludge process where fuzzy implications and linear reasoning are used is presented in here. A root-mean square error is used as the criterion of the fuzzy model's adequacy to the A.S.P. and the least square method is used for the identification of optimum consequence parameters. A method of modeling of the activated sludge process using its input-output data and simulation results for its application are shown.

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야채음료 중 비타민 C 분석에 있어서의 측정불확도 추정 (Estimation of Measurement Uncertainty in Vitamin C Analysis from Vegetable and Fruit Juice)

  • 김영준;김현위
    • 한국식품과학회지
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    • 제35권6호
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    • pp.1053-1059
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    • 2003
  • 분석 중 소실되기 쉬운 야채음료의 비타민 C 함량을 HPLC를 이용하여 측정하였으며, 불확도인자로서 표준품의 무게, 순도, 분자량, 희석 등과 시료의 무게, 검정곡선, 회수율 및 정밀성 등이 작용하였다. 이러한 미심쩍음 정도와 더불어 계통오차와 우연오차 등 일련의 과정을 GUM(Guide to the expression of Uncertainty in Measurement)과 EURACHEM에 근거하여 수학적 처리 및 통계방법을 이용하여 측정불확도를 추정하였다. 추정방법은 각각의 인자들에 대하여 A-type또는 B-type으로 산출된 표준불확도 값을 합성하여 합성표준불확도를 산출하고, 확장불확도는 유효자유도로 산출된 포함인자를 곱하여 계산하였다. 야채와 과일이 혼합된 음료 중 비타민 C 함량은 27.53mg/100g이었으며, 포함인자(2.06)를 곱한 확장불확도는 0.63mg/100g로서 95% 신뢰도구간에서의 비타민C의 결과는 $27.53{\pm}0.63mg/100g$(95% 신뢰도 구간)과 같이 수치화하여 표현하였다. 비타민 C 분석의 경우 HPLC를 이용한 시료 분석의 회수율 및 정밀성(33%), 표준품 순도(23%), 표준용액 희석시(18%), 표준품 무게(10%), 시료 측정시(10%), 검정곡선(6%) 순으로 불확도를 추정할 수 있었다. 또한, 이를 통해서 시험원의 분석과정 중 불확도가 높게 산출된 실험과정에 대해서는 좀더 세심한 주의가 요구되며, 시료의 반복실험 시 재현성 있는 결과가 산출될 수 있도록 숙련도를 높일 필요가 있다.

수리모형을 이용한 선박 항해기기 패널의 인간공학적 배치 (The Ergonomic Layout of Ship's Bridge Panels using the Mathematical Programming)

  • 장준혁;김홍태;심정훈;이동춘
    • 대한인간공학회지
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    • 제30권1호
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    • pp.251-257
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    • 2011
  • When designing a ship, ergonomic considerations are crucial when minimizing a navigator's fatigue due to the burden of work, and to appropriately operate the navigational equipment for each given situation by helping the operator to understand the surroundings as well as the physical functions of the ship. However, insufficient consideration of ergonomic elements in the actual design of ship Bridges is lowering the performance of safe navigation and allows for the possibility of operation or readout errors. Consequently, these errors lead to an increase in maritime accidents. Therefore, this study conducted a usability evaluation on the importance of and the usage frequency of navigational equipment, their influence on actual navigation, and the possibility of error upon operation or readout between training ship officers, to derive an optimized layout that includes the consideration of ergonomic factors for on-Bridge navigational equipment, which are currently arranged differently according to their type or size. The optimized layout of on-Bridge navigational equipment was carried out based on the evaluation results, using the Lingo program. Through the process of optimization, revised layouts of on-Bridge navigational equipments(control and display device) were suggested, considering emergency situations(ship collision, stranding, fire and explosion, sinking, etc.) during navigation.

모델기반의 전기자동차용 전지 잔존용량계 개발 (Development of Model Based Battery SOC Indicator for Electric Vehicle)

  • 임영철;박종건;류영재;이흥수;변성천;김의선
    • 센서학회지
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    • 제5권6호
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    • pp.35-42
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    • 1996
  • 본 논문에서는 전기자동차에서 사용할 수 있는 모델 기반 잔존용량계(model based battery indicator)를 개발했다. 제안된 방법을 이용하면 잔존용량을 측정하는 데 전지의 전압과 전류만 측정하면 되고, 초기 잔존용량값의 영향을 받지 않으며, 전기자동차와 같이 부하가 급변하는 상태에서도 정확하게 계측할 수 있을 뿐 아니라, 그에 따라 주행 가능 거리를 계산하여 예측할 수 있다. 전지의 방전 특성 데이터를 이용해 수학적인 모델링을 한 후, 전압과 전류를 검출하여 이를 모델링한 식에 대입하면, 추정된 전지 전압을 얻을 수 있다. 이 추정 전압과 측정 전압의 차이가 최소가 되도록 하는 잔존용량의 반화량을 이용히여 잔존용량을 추정한다. 실험에서는 제작한 충방전장치와 PC를 이용하여 전지의 전압과 전류를 계측하여 수학적으로 모델링을 하고, 실제의 전기자동차에 탑재 가능한 스탠드 얼론(stand alone)타입의 마이크로 콘트롤러에 모델식 및 알고리즘을 장착하여 모델 기반 잔존용량계를 실제 검증하여 그 유용성을 입증하였다.

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전염병 구획 모형에 대한 시스템다이내믹스 접근법: 국내 MERS 전염 SEIR 모형의 해석 및 변환 (System Dynamics Approach to Epidemic Compartment Model: Translating SEIR Model for MERS Transmission in South Korea)

  • 정재운
    • 디지털융복합연구
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    • 제16권7호
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    • pp.259-265
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    • 2018
  • 수학모형의 한 유형인 구획모형은 전염병의 확산처럼 순차적인 이벤트나 프로세스로 구성된 동적 시스템의 변화를 분석하는 데 폭넓게 활용되어 왔다. 구획모형은 상자와 화살표로 표현되는 구획과 구획 간 관계로 구성된다. 이러한 원리는 stock과 flow로 구성되는 시스템다이내믹스(SD)의 모델링 원리와 비슷하다. 두 모형 모두 미분방정식을 이용하여 구조화된다. 이와 같은 두 모형 간 변환 가능성을 이용하여 국내 MERS 전염의 특징을 분석한 최근 연구의 SEIR 참조모형을 SD 관점에서 해석 변환한다. 변환된 SEIR 모형(Model 2)은 참조모형(Model 1)의 재현 결과와 비교하여 동일한 시뮬레이션 결과를 나타내었다. 본 연구는 전염병 구획모형의 구축에 도식과 미분방정식을 이용한 SD 방법론의 활용에 대한 인사이트를 제공하며, 변환된 SD 모형은 다른 전염병을 위한 참조모형으로 활용 가능하다.

관계적 이해를 위한 수업 도구로서의 소프트웨어 활용에 관한 사례 연구 - 고등학교 1학년 함수 단원을 중심으로 - (Using computer software as an instructional tool for enhancing relational understanding of function concept : three case studies)

  • 최윤녕;권오남;황혜정
    • 대한수학교육학회지:학교수학
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    • 제1권2호
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    • pp.637-660
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    • 1999
  • Although ‘to understand mathematics’ is an important educational purpose, most student do not have a relational understanding of the basic concept of mathematics but have a instrumental understanding. This paper will investigate the possibility of using computers for enhancing relational understanding. In the ‘Qualitative case study’, three students who are in the first grade at E-High school took part in 7 activities during four weeks, and were later interviewed and engaged in informal discussion and were observed. This is the result of this study. 1. The three students were passive participants in mathematics problem solving situation at school. Therefore, student B just applied formulas which she had memorized, and student C would forgot the formulas occasionally. These common students needed to participate actively in doing mathematics. 2. The activities utilized two software healing with connection between graphs and function, giving the students the opportunity to plan, practice, and test by themselves. As a result, they understood the mathematical formulas and rules more deeply through their own trial and error, and then they gained thinking abilities necessary for doing mathematics. In addition, the activities boosted their confidence. 3. The understanding type of students was slightly different. Student A who received a high score, understood the most relationally, but student B who received a very high score, understood instrumentally and so couldn't app1y her knowledge to solving problems related to function concept. Student C who received a middle score lacked knowledge of mathematics but thought more creatively. The result is that students need an opportunity to think rotationally regardless of score. Therefore, this study concludes that using computer software will provide a positive effect for relational understanding in loaming function concept.

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토양수분함량 예측 및 계획관개 모의 모형 개발에 관한 연구(I) (A Study on the Development of a Simulation Model for Predicting Soil Moisture Content and Scheduling Irrigation)

  • 김철회;고재군
    • 한국농공학회지
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    • 제19권1호
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    • pp.4279-4295
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    • 1977
  • Two types of model were established in order to product the soil moisture content by which information on irrigation could be obtained. Model-I was to represent the soil moisture depletion and was established based on the concept of water balance in a given soil profile. Model-II was a mathematical model derived from the analysis of soil moisture variation curves which were drawn from the observed data. In establishing the Model-I, the method and procedure to estimate parameters for the determination of the variables such as evapotranspirations, effective rainfalls, and drainage amounts were discussed. Empirical equations representing soil moisture variation curves were derived from the observed data as the Model-II. The procedure for forecasting timing and amounts of irrigation under the given soil moisture content was discussed. The established models were checked by comparing the observed data with those predicted by the model. Obtained results are summarized as follows: 1. As a water balance model of a given soil profile, the soil moisture depletion D, could be represented as the equation(2). 2. Among the various empirical formulae for potential evapotranspiration (Etp), Penman's formula was best fit to the data observed with the evaporation pans and tanks in Suweon area. High degree of positive correlation between Penman's predicted data and observed data with a large evaporation pan was confirmed. and the regression enquation was Y=0.7436X+17.2918, where Y represents evaporation rate from large evaporation pan, in mm/10days, and X represents potential evapotranspiration rate estimated by use of Penman's formula. 3. Evapotranspiration, Et, could be estimated from the potential evapotranspiration, Etp, by introducing the consumptive use coefficient, Kc, which was repre sensed by the following relationship: Kc=Kco$.$Ka+Ks‥‥‥(Eq. 6) where Kco : crop coefficient Ka : coefficient depending on the soil moisture content Ks : correction coefficient a. Crop coefficient. Kco. Crop coefficients of barley, bean, and wheat for each growth stage were found to be dependent on the crop. b. Coefficient depending on the soil moisture content, Ka. The values of Ka for clay loam, sandy loam, and loamy sand revealed a similar tendency to those of Pierce type. c. Correction coefficent, Ks. Following relationships were established to estimate Ks values: Ks=Kc-Kco$.$Ka, where Ks=0 if Kc,=Kco$.$K0$\geq$1.0, otherwise Ks=1-Kco$.$Ka 4. Effective rainfall, Re, was estimated by using following relationships : Re=D, if R-D$\geq$0, otherwise, Re=R 5. The difference between rainfall, R, and the soil moisture depletion D, was taken as drainage amount, Wd. {{{{D= SUM from { {i }=1} to n (Et-Re-I+Wd)}}}} if Wd=0, otherwise, {{{{D= SUM from { {i }=tf} to n (Et-Re-I+Wd)}}}} where tf=2∼3 days. 6. The curves and their corresponding empirical equations for the variation of soil moisture depending on the soil types, soil depths are shown on Fig. 8 (a,b.c,d). The general mathematical model on soil moisture variation depending on seasons, weather, and soil types were as follow: {{{{SMC= SUM ( { C}_{i }Exp( { - lambda }_{i } { t}_{i } )+ { Re}_{i } - { Excess}_{i } )}}}} where SMC : soil moisture content C : constant depending on an initial soil moisture content $\lambda$ : constant depending on season t : time Re : effective rainfall Excess : drainage and excess soil moisture other than drainage. The values of $\lambda$ are shown on Table 1. 7. The timing and amount of irrigation could be predicted by the equation (9-a) and (9-b,c), respectively. 8. Under the given conditions, the model for scheduling irrigation was completed. Fig. 9 show computer flow charts of the model. a. To estimate a potential evapotranspiration, Penman's equation was used if a complete observed meteorological data were available, and Jensen-Haise's equation was used if a forecasted meteorological data were available, However none of the observed or forecasted data were available, the equation (15) was used. b. As an input time data, a crop carlender was used, which was made based on the time when the growth stage of the crop shows it's maximum effective leaf coverage. 9. For the purpose of validation of the models, observed data of soil moiture content under various conditions from May, 1975 to July, 1975 were compared to the data predicted by Model-I and Model-II. Model-I shows the relative error of 4.6 to 14.3 percent which is an acceptable range of error in view of engineering purpose. Model-II shows 3 to 16.7 percent of relative error which is a little larger than the one from the Model-I. 10. Comparing two models, the followings are concluded: Model-I established on the theoretical background can predict with a satisfiable reliability far practical use provided that forecasted meteorological data are available. On the other hand, Model-II was superior to Model-I in it's simplicity, but it needs long period and wide scope of observed data to predict acceptable soil moisture content. Further studies are needed on the Model-II to make it acceptable in practical use.

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Evaluation of a Nutrition Model in Predicting Performance of Vietnamese Cattle

  • Parsons, David;Van, Nguyen Huu;Malau-Aduli, Aduli E.O.;Ba, Nguyen Xuan;Phung, Le Dinh;Lane, Peter A.;Ngoan, Le Duc;Tedeschi, Luis O.
    • Asian-Australasian Journal of Animal Sciences
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    • 제25권9호
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    • pp.1237-1247
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    • 2012
  • The objective of this study was to evaluate the predictions of dry matter intake (DMI) and average daily gain (ADG) of Vietnamese Yellow (Vang) purebred and crossbred (Vang with Red Sindhi or Brahman) bulls fed under Vietnamese conditions using two levels of solution (1 and 2) of the large ruminant nutrition system (LRNS) model. Animal information and feed chemical characterization were obtained from five studies. The initial mean body weight (BW) of the animals was 186, with standard deviation ${\pm}33.2$ kg. Animals were fed ad libitum commonly available feedstuffs, including cassava powder, corn grain, Napier grass, rice straw and bran, and minerals and vitamins, for 50 to 80 d. Adequacy of the predictions was assessed with the Model Evaluation System using the root of mean square error of prediction (RMSEP), accuracy (Cb), coefficient of determination ($r^2$), and mean bias (MB). When all treatment means were used, both levels of solution predicted DMI similarly with low precision ($r^2$ of 0.389 and 0.45 for level 1 and 2, respectively) and medium accuracy (Cb of 0.827 and 0.859, respectively). The LRNS clearly over-predicted the intake of one study. When this study was removed from the comparison, the precision and accuracy considerably increased for the level 1 solution. Metabolisable protein was limiting ADG for more than 68% of the treatment averages. Both levels differed regarding precision and accuracy. While level 1 solution had the least MB compared with level 2 (0.058 and 0.159 kg/d, respectively), the precision was greater for level 2 than level 1 (0.89 and 0.70, respectively). The accuracy (Cb) was similar between level 1 and level 2 (p = 0.8997; 0.977 and 0.871, respectively). The RMSEP indicated that both levels were on average under-or over-predicted by about 190 g/d, suggesting that even though the accuracy (Cb) was greater for level 1 compared to level 2, both levels are likely to wrongly predict ADG by the same amount. Our analyses indicated that the level 1 solution can predict DMI reasonably well for this type of animal, but it was not entirely clear if animals consumed at their voluntary intake and/or if the roughness of the diet decreased DMI. A deficit of ruminally-undegradable protein and/or a lack of microbial protein may have limited the performance of these animals. Based on these evaluations, the LRNS level 1 solution may be an alternative to predict animal performance when, under specific circumstances, the fractional degradation rates of the carbohydrate and protein fractions are not known.

반사 타겟의 관측 오차 특성 분석 - 세종 VLBI IVP 결합 측량 (Characteristics of Measurement Errors due to Reflective Sheet Targets - Surveying for Sejong VLBI IVP Estimation)

  • 홍창기;배태석
    • 한국측량학회지
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    • 제40권4호
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    • pp.325-332
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    • 2022
  • 우주 측지 기술 사이의 상대적인 위치 관계를 설명하는 벡터를 결정하기 위해서는 VLBI IVP (Very Long Baseline Interferometry Invariant Point)의 위치를 정밀하게 계산하여야 한다. 이를 위해 일반적으로 VLBI 안테나에 반사 타겟을 부착한 후 필라들로부터 경사 거리, 수평각, 수직각을 관측한다. 그 다음 단계에서는 관측값과 미지수를 연결하는 수학 모델을 이용하여 조정 계산을 수행하게 된다. 따라서 계산된 미지수는 관측값의 정밀도에 영향을 받게 된다. 이때 특히 문제가 되는 것은 반사 타켓이 일반적인 측량 정밀도를 확보하기 어려운 곳에 위치하고 있다는 점이다. 즉, 반사 타겟의 방향을 조정하여 측량 기기에 정확하게 맞출 수 없다는 것이다. 따라서 이러한 부분은 관측 오차에 또 다른 형태로 나타날 것이며 조정 계산 시 오차 모델링에 오류를 발생시킬 수도 있다. 본 연구에서는 조정 계산 후 계산된 잔차의 특성에 대한 분석을 수행하였다. 먼저 관측 타입별 통계 분석을 통해 정규성을 검정하였으며 분산에 차이가 있는 지에 대한 검정도 실시하였다. 관측 타입별로 등분산 검정을 한 경우 분산이 서로 다른 것으로 나타났다. 각 필라에 대해 관측 타입별 등분산 검정을 했을 때 경사 거리와 수평 및 수직각 사이에는 분산에 차이가 있는 것으로 나타났다. 따라서 결합 측량으로부터 최적의 결과를 얻기 위해서는 관측 오차에 대해 보다 세분화된 모델링이 필요한 것으로 나타났다.