• 제목/요약/키워드: mathematical errors

검색결과 449건 처리시간 0.027초

선형 Model에 의한 소류역에 있어서의 무차원 단위도 유도에 관한 연구 (A study on the derivation of Dimensionless Unit Hydrographs by the Linear model in the small watersheds)

  • 이순혁;한중석
    • 한국농공학회지
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    • 제23권3호
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    • pp.78-87
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    • 1981
  • This study was attempted to get dimensionless unit hydrograph by linear model which can be used to the estimation of flood for the development of Agricultural water resources and laid emphasis on the application of dimensionless unit hydrographs for the ungaged watersheds by applying linear model. The results summarized through this study are as follows. 1.Peak discharge is found to be Qp= CAR (C =0. 895A-o.145) having high significance between peak discharge, Qp and effective rainfall, R within the range of small watershed area, 84 to 470km2. consequently, linearity was acknowledged between rainfall and runoff. Reasonability is confirmed for the derivation of dimensionless unit hydrograph by linear model. 2.Through mathematical analysis, formula for the derivation of dimensionless unit hydrograph was derived. qp--p=(tp--t)n-1[e-(n-1)](tp--t-1) 3.Moment method was used for the evaluation of storage constant, K and shape parameter, n for the derivation of dimensionless unit hydrograph. Storage constant, K is more closely related with the such watershed characteristics as length of main stream and slopes. On the other hand, the shape parameter, n was derived with such watershed characteristics as watershed area, river length, centroid distance of the basin and slopes. 4.Time to peak discharge, Tp could be expressed as Tp=1. 25 (√s/L)0.76 having a high significance. 5.Dimensionless unit hydrographs by linear model stood more closely to the observe dimensionless unit hydrographs On the contrary, dimensionless unit hydrographs by S.C. S. method has much difference in comparison with linear model at the falling limb of hydrographs. 6.Relative errors in the q/qp at the point of 0.8 and 1.2 for the dimensionles ratio by linear model and S. C. S. method showed to be 2.41, 1.57 and 4.0, 3.19 percent respectively to the q/qp of observed dimensionless unit hydrographs. 7.Derivation of dimensionless unit hydrograph by linear model can be accomplished by linking the two empirical formulars for storage constant, K, and shape parameter, n with derivation formular for dimensionless unit hydrograph for the ungaged small watersheds.

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안정화된 딥 네트워크 구조를 위한 다항식 신경회로망의 연구 (A Study on Polynomial Neural Networks for Stabilized Deep Networks Structure)

  • 전필한;김은후;오성권
    • 전기학회논문지
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    • 제66권12호
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    • pp.1772-1781
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    • 2017
  • In this study, the design methodology for alleviating the overfitting problem of Polynomial Neural Networks(PNN) is realized with the aid of two kinds techniques such as L2 regularization and Sum of Squared Coefficients (SSC). The PNN is widely used as a kind of mathematical modeling methods such as the identification of linear system by input/output data and the regression analysis modeling method for prediction problem. PNN is an algorithm that obtains preferred network structure by generating consecutive layers as well as nodes by using a multivariate polynomial subexpression. It has much fewer nodes and more flexible adaptability than existing neural network algorithms. However, such algorithms lead to overfitting problems due to noise sensitivity as well as excessive trainning while generation of successive network layers. To alleviate such overfitting problem and also effectively design its ensuing deep network structure, two techniques are introduced. That is we use the two techniques of both SSC(Sum of Squared Coefficients) and $L_2$ regularization for consecutive generation of each layer's nodes as well as each layer in order to construct the deep PNN structure. The technique of $L_2$ regularization is used for the minimum coefficient estimation by adding penalty term to cost function. $L_2$ regularization is a kind of representative methods of reducing the influence of noise by flattening the solution space and also lessening coefficient size. The technique for the SSC is implemented for the minimization of Sum of Squared Coefficients of polynomial instead of using the square of errors. In the sequel, the overfitting problem of the deep PNN structure is stabilized by the proposed method. This study leads to the possibility of deep network structure design as well as big data processing and also the superiority of the network performance through experiments is shown.

자동차 변속기용 정밀 부품의 용접변형 감소화에 관한 연구 (A Study on the Mitigation of Welding Distortion of a Precision Component for Automobile Transmission)

  • 정회윤;김재웅;윤석철
    • Journal of Welding and Joining
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    • 제30권4호
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    • pp.31-37
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    • 2012
  • In recent years, a demand for precision-welding is increasing in wide industrial fields for getting a high quality welded structures. Although laser welding is commonly used for precision-welding, gas tungsten arc (GTA) welding is also attempted as a precision-welding due to the cost benefit. However, welding heat causes an uneven temperature distribution leading to welding deformation. Since it causes geometric errors and degrades product quality, welding distortion recently rises as an important issue in the field of automobile parts. To control welding deformation, it is needed to design in shapes that can maximize stiffness against deformation during welding; control the welding sequence; minimize heat input; and weld allowing reverse deformation; etc. Thus it is necessary to find the one, among such approaches, that can minimize the deformation range by mathematical analysis and understand how effective it would be when it is actually used in industrial fields. This study performs analyses by numerical calculations and experiments for the De-Tent Lever, one of transmission part that requires precision the most among automobile parts, as the subject of experiment. Decrease in welding deformation is required for this part, since there is currently a trouble in guaranteeing precision due to angular deformation by welding between boss and plate. Finally the ways to minimize welding deformation has been suggested in this study through analyses on it.

Forecasting of the COVID-19 pandemic situation of Korea

  • Goo, Taewan;Apio, Catherine;Heo, Gyujin;Lee, Doeun;Lee, Jong Hyeok;Lim, Jisun;Han, Kyulhee;Park, Taesung
    • Genomics & Informatics
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    • 제19권1호
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    • pp.11.1-11.8
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    • 2021
  • For the novel coronavirus disease 2019 (COVID-19), predictive modeling, in the literature, uses broadly susceptible exposed infected recoverd (SEIR)/SIR, agent-based, curve-fitting models. Governments and legislative bodies rely on insights from prediction models to suggest new policies and to assess the effectiveness of enforced policies. Therefore, access to accurate outbreak prediction models is essential to obtain insights into the likely spread and consequences of infectious diseases. The objective of this study is to predict the future COVID-19 situation of Korea. Here, we employed 5 models for this analysis; SEIR, local linear regression (LLR), negative binomial (NB) regression, segment Poisson, deep-learning based long short-term memory models (LSTM) and tree based gradient boosting machine (GBM). After prediction, model performance comparison was evelauated using relative mean squared errors (RMSE) for two sets of train (January 20, 2020-December 31, 2020 and January 20, 2020-January 31, 2021) and testing data (January 1, 2021-February 28, 2021 and February 1, 2021-February 28, 2021) . Except for segmented Poisson model, the other models predicted a decline in the daily confirmed cases in the country for the coming future. RMSE values' comparison showed that LLR, GBM, SEIR, NB, and LSTM respectively, performed well in the forecasting of the pandemic situation of the country. A good understanding of the epidemic dynamics would greatly enhance the control and prevention of COVID-19 and other infectious diseases. Therefore, with increasing daily confirmed cases since this year, these results could help in the pandemic response by informing decisions about planning, resource allocation, and decision concerning social distancing policies.

횡방향 거동 특성을 고려한 부하모사 시스템 해석 (Analysis of Load Simulating System Considering Lateral Behavior of a Vehicle)

  • 김효준
    • 한국산학기술학회논문지
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    • 제20권5호
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    • pp.621-626
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    • 2019
  • 자동차의 과도한 차체 운동과 조종 불안정성을 유발하는 대표적인 외란 입력으로는 운전자에 의해 가해지는 조향 핸들 조작이다. 급격하고 과도한 핸들 조작은 SUV 차량처럼 기하학적 및 동역학적 특성에 따라 차량 전복 현상도 발생시킬 수 있다. 본 연구에서는 이에 대응할 수 있는 제어 시스템의 구조화에 대하여 다음과 같이 기초 연구를 수행하였다. 운전자 조종으로 유발되는 횡방향 거동에 대한 수학적 모델링을 수행하고, 이를 토대로 차체 운동을 제어할 수 있는 제어기를 설계하였다. 파라미터 불확실성으로 인한 모델링 오차에 대해 강건한 제어 성능을 확보하기 위하여 $H_{\infty}$ 알고리즘을 적용하였다. 비 연성화된 1/4 차량을 기반으로, 차체에 작용하는 모우멘트에 상응하는 동적 부하를 모사할 수 있는 모델을 제시하였다. 동적 시뮬레이션을 수행하여 부하 모사 모델의 타당성을 파악하였다. 차체- 차축- 서스펜션- 타이어로 조합되는 1/4 실험 차량 장치와 부하 모사 모듈, 서스펜션 제어 모듈 및 Hils 기술을 적용하는 차체 거동 제어 시스템에 대한 프레임워크를 제안하였다.

스마트폰 내장 가속도계와 카메라를 이용한 케이블 장력 추정에 관한 연구 (A Study on Cable Tension Estimation Using Smartphone Built-in Accelerometer and Camera)

  • 이형진
    • 한국산업융합학회 논문집
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    • 제25권5호
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    • pp.773-782
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    • 2022
  • Estimation of cable tension through proper measurements is one of the essential tasks in evaluating the safety of cable structures. In this paper, a study on cable tension estimation using the built-in accelerometer and camera in a smartphone was conducted. For the experimental study, visual displacement measurement using a smartphone camera and acceleration measurement using a built-in accelerometer were performed in the cable-stayed bridge model. The estimated natural frequencies and transformed tensions from these measurements were compared with the theoretical values and results from the normal visual displacement method. Through comparison, it can be seen that the error between the method using the smartphone and the normal visual displacement is sufficiently small to be acceptable. It has also been shown that those errors are much smaller than the difference between the values calculated by the theoretical model. These results show that the deviation according to the type of measurement method is not large and it is rather important to use an appropriate mathematical model. In conclusion, in the case of cable tension estimation, it can be said that the visual displacement measurement and acceleration using a smartphone can be a sufficiently applicable method, just like the normal visual displacement method. It is also noteworthy that the smartphone accelerometer has a larger magnitude error and has more limitations such as high-frequency sampling instability compared to the visual displacement method, but shows almost the same performance as the visual displacement method in this cable tension estimation.

열경화성 수지 재료를 이용한 광학 렌즈 제조공정에서 렌즈 변형에 대한 수축률이 영향에 관한 연구 (A Study on the Effect of Shrinkage on Lens Deformation in Optical Lens Manufacturing Process Using Thermosetting Resin Material)

  • 박시환
    • Design & Manufacturing
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    • 제16권3호
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    • pp.9-15
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    • 2022
  • In order to reduce the manufacturing costs of the glass lens, it is necessary to manufacture a lens using a UV curable resin or a thermosetting resin, which is a curable material, in order to replace a glass lens. In the case of forming a lens using a thermosetting material, it is necessary to form several lenses at once using the wafer-level lens manufacturing technologies due to the long curing time of the material. When a lens is manufactured using a curable material, an error in the shape of the lens due to the shrinkage of the material during the curing process is an important cause of defects. The major factors for these shape errors and deformations are the shrinkage and the change of mechanical properties in the process of changing from a liquid material during curing to a solid state after complete curing. Therefore, it is necessary to understand the curing process of the material and to examine the shrinkage rate and change of physical properties according to the degree cure. In addition, it is necessary to proceed with CAE for lens molding using these and to review problems in lens manufacturing in advance. In this study, the viscoelastic properties of the material were measured during the curing process using a rheometer. Using the results, Rheological investigation of cure kinetics was performed. At the same time, The shrinkage of the material was measured and simple mathematical models were created. And using the results, the molding process of a single lens was analyzed using Comsol, a commercial S/W. In addition, the experiment was conducted to compare and verify the CAE results. As a result, it was confirmed that the shrinkage rate of the material had a great influence on the shape precision of the final product.

유리차수 적분을 이용한 전동기 속도제어 (Motor Speed Control Using the Fractional Order Integral)

  • 전용호;강정욱
    • 한국전자통신학회논문지
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    • 제16권3호
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    • pp.503-510
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    • 2021
  • 본 연구는 유리 차수 미분의 수학적인 방법을 시스템의 응답을 제어하는 제어기에 적용하고자 한다. 따라서 제어기로 구성하기 위해서는 유리수 지수에 대한 적분기를 이산시간으로 변환하여 설계한다. IP 제어기는 오차에 대한 적분제어기를 구성하고 비례제어기는 시스템 출력만 적용하는 구조이다. 유리 차수 적분기를 IP 제어기의 적분제어기에 활용함으로 제어기를 설계한다. 먼저 PI 제어기와 IP 제어기의 성능을 비교하고, 설계된 제어기를 전동기의 속도 제어에 적용한다. 그 결과 전동기의 출력상태인 속도가 균일하며 정밀한 제어 성능을 얻을 수 있었다. 정상상태의 속도오차가 0.1 [%] 이내 이고, 오버슈트가 없는 정밀하며 균일한 속도 제어 성능을 가짐을 확인할 수 있었다.

A three-region movable-boundary helical coil once-through steam generator model for dynamic simulation and controller design

  • Shifa Wu;Zehua Li;Pengfei Wang;G.H. Su;Jiashuang Wan
    • Nuclear Engineering and Technology
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    • 제55권2호
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    • pp.460-474
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    • 2023
  • A simple but accurate mathematical model is crucial for dynamic simulations and controller design of helical coil once-through steam generator (OTSG). This paper presents a three-region movable boundary dynamic model of the helical coil OTSG. Based on the secondary side fluid conditions, the OTSG is divided into subcooled region (two control volumes), two-phase region (two control volumes) and superheated region (three control volumes) with movable boiling boundaries between each region. The nonlinear dynamic model is derived based on mass, energy and momentum conservation equations. And the linear model is obtained by using the transfer function and state space transformation, which is a 37-order model of five input and three output. Validations are made under full-power steady-state condition and four transient conditions. Results show good agreements among the nonlinear model, linear model and the RELAP5 model, with acceptable errors. This model can be applied to dynamic simulations and controller design of helical coil OTSG with constant primary-side flow rate.

Study on three-dimensional numerical simulation of shell and tube heat exchanger of the surface ship under marine conditions

  • Yi Liao;Qi Cai;Shaopeng He;Mingjun Wang;Hongguang Xiao;Zili Gong;Cong Wang;Zhen Jia;Tangtao Feng;Suizheng Qiu
    • Nuclear Engineering and Technology
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    • 제55권4호
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    • pp.1233-1243
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    • 2023
  • Shell-and-tube heat exchanger (STHX) is widely used by virtue of its simple structure and high reliability, especially in a space-constrained surface ship. For the STHX of the surface ship, roll, pitch and other motion of the ship will affect the heat transfer performance, resistance characteristics and structural strength of the heat exchanger. Therefore, it is urgent to carry out numerical simulation research on three-dimensional thermal hydraulic characteristics of surface ship STHX under the marine conditions. In this paper, the numerical simulation of marine shell and tube heat exchanger of surface ship was carried out using the porous media model. Firstly, the mathematical physical model and numerical method are validated based on the experimental data of a marine engine cooling water shell and tube heat exchanger. The simulation results are in good agreement with the experimental results. The prediction errors of pressure drop and heat transfer are less than 10% and 1% respectively. The effect of marine conditions on the heat transfer characteristics of the heat exchanger is investigated by introducing the additional force model of marine condition to evaluate the effect of different motion parameters on the heat transfer performance of the heat exchanger. This study could provide a reference for the optimization of marine heat exchanger design.