• 제목/요약/키워드: gradient estimate

검색결과 265건 처리시간 0.037초

QUALITATIVE PROPERTIES OF WEAK SOLUTIONS FOR p-LAPLACIAN EQUATIONS WITH NONLOCAL SOURCE AND GRADIENT ABSORPTION

  • Chaouai, Zakariya;El Hachimi, Abderrahmane
    • Bulletin of the Korean Mathematical Society
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    • 제57권4호
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    • pp.1003-1031
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    • 2020
  • We consider the following Dirichlet initial boundary value problem with a gradient absorption and a nonlocal source $$\frac{{\partial}u}{{\partial}t}-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)={\lambda}u^k{\displaystyle\smashmargin{2}{\int\nolimits_{\Omega}}}u^sdx-{\mu}u^l{\mid}{\nabla}u{\mid}^q$$ in a bounded domain Ω ⊂ ℝN, where p > 1, the parameters k, s, l, q, λ > 0 and µ ≥ 0. Firstly, we establish local existence for weak solutions; the aim of this part is to prove a crucial priori estimate on |∇u|. Then, we give appropriate conditions in order to have existence and uniqueness or nonexistence of a global solution in time. Finally, depending on the choices of the initial data, ranges of the coefficients and exponents and measure of the domain, we show that the non-negative global weak solution, when it exists, must extinct after a finite time.

Process Design of the Hot Pipe Bending Process Using High Frequency Induction Heating (고주파 유도가열을 이용한 열간 파이프 벤딩 공정 설계)

  • Ryu, Gyeong-Hui;Lee, Dong-Ju;Kim, Dong-Jin;Kim, Byeong-Min;Kim, Gwang-Ho
    • Journal of the Korean Society for Precision Engineering
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    • 제18권9호
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    • pp.110-121
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    • 2001
  • During hot pipe bending using induction heating, the wall of bending outside is thinned by tensile stress. In design requirement, the reduction of wall thickness is not allowed to exceed 12.5%. So in this study, two methods of bending, one is loading of reverse moment and the other is loading of temperature gradient, have been investigated to design pipe bending process that satisfy design requirements. For this purpose, finite element analysis with a bending radius 2Do(outer diameter of pipe) has been performed to calculate proper reverse moment and temperature gradient to be applied. Induction heating process has been analyzed to estimate influence of heating process parameters on heating characteristic by finite difference method. Then pipe bending experiments have been performed for verification of finite element and finite difference analysis results. Experimental results are in good agreement with the results of simulations.

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Evaluation of Regression Models with various Criteria and Optimization Methods for Pollutant Load Estimations (다양한 평가 지표와 최적화 기법을 통한 오염부하 산정 회귀 모형 평가)

  • Kim, Jonggun;Lim, Kyoung Jae;Park, Youn Shik
    • Proceedings of the Korea Water Resources Association Conference
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    • 한국수자원학회 2018년도 학술발표회
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    • pp.448-448
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    • 2018
  • In this study, the regression models (Load ESTimator and eight-parameter model) were evaluated to estimate instantaneous pollutant loads under various criteria and optimization methods. As shown in the results, LOADEST commonly used in interpolating pollutant loads could not necessarily provide the best results with the automatic selected regression model. It is inferred that the various regression models in LOADEST need to be considered to find the best solution based on the characteristics of watersheds applied. The recently developed eight-parameter model integrated with Genetic Algorithm (GA) and Gradient Descent Method (GDM) were also compared with LOADEST indicating that the eight-parameter model performed better than LOADEST, but it showed different behaviors in calibration and validation. The eight-parameter model with GDM could reproduce the nitrogen loads properly outside of calibration period (validation). Furthermore, the accuracy and precision of model estimations were evaluated using various criteria (e.g., $R^2$ and gradient and constant of linear regression line). The results showed higher precisions with the $R^2$ values closed to 1.0 in LOADEST and better accuracy with the constants (in linear regression line) closed to 0.0 in the eight-parameter model with GDM. In hence, based on these finding we recommend that users need to evaluate the regression models under various criteria and calibration methods to provide the more accurate and precise results for pollutant load estimations.

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A Variable Window Method for Three-Dimensional Structure Reconstruction in Stereo Vision (삼차원 구조 복원을 위한 스테레오 비전의 가변윈도우법)

  • 김경범
    • Journal of the Korean Society for Precision Engineering
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    • 제20권7호
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    • pp.138-146
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    • 2003
  • A critical issue in area-based stereo matching lies in selecting a fixed rectangular window size. Previous stereo methods doesn't deal effectively with occluding boundary due to inevitable window-based problems, and so give inaccurate and noisy matching results in areas with steep disparity variations. In this paper, a variable window approach is presented to estimate accurate, detailed and smooth disparities for three-dimensional structure reconstruction. It makes the smoothing of depth discontinuity reduced by evaluating corresponding correlation values and intensity gradient-based similarity in the three-dimensional disparity space. In addition, it investigates maximum connected match candidate points and then devise the novel arbitrarily shaped variable window representative of a same disparity to treat with disparity variations of various structure shapes. We demonstrate the performance of the proposed variable window method with synthetic images, and show how our results improve on those of closely related techniques for accuracy, robustness, matching density and computing speed.

A Variable Window Method with Three-Dimensional Disparity Space (삼차원 변이 공간을 이용한 가변윈도우법)

  • 김경범;이홍서
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 한국정밀공학회 2003년도 춘계학술대회 논문집
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    • pp.284-287
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    • 2003
  • Previous stereo methods doesn't deal effectively with depth discontinuity due to inevitable window-based problems, and so give inaccurate and noisy matching results in areas with steep disparity variations. In this paper. a variable window approach is presented to estimate accurate, detailed and smooth disparities with three-dimensional disparity space. It makes the smoothing of depth discontinuity reduced by evaluating corresponding correlation values and intensity gradient-based similarity in the space. In addition, it devises the novel arbitrarily-shaped variable window to treat with disparity variations of various structure shapes. We show how our results improve on those of closely related techniques for accuracy, robustness. matching density and computing speed.

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Ultrasonic NDE Classifications with the Gradient Descent Method and Synthetic Aperture Focusing Technique

  • Kim, Dae-Won
    • Journal of the Korean Society for Nondestructive Testing
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    • 제25권3호
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    • pp.189-200
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    • 2005
  • Ultrasonic inspection methods are widely used for detecting flaws in materials. One of the more popular methods involves the extraction of an appropriate set of features followed by the use of a neural network for the classification of the signals in the feature space. This paper describes an approach which uses LMS method to determine the coordinates of the ultrasonic probe followed by the use of SAFT to estimate the location of the ultrasonic reflector The method is employed for classifying NDE signals from the steam generator tubes in a nuclear power plant. The classification results using this scheme for the ultrasonic signals from cracks and deposits within steam generator tubes are presented.

A Theoretical Approach on the Turbulence Intensity of the Carrier Fluid in Two-phase Particle-laden Flows (고체입자가 부상된 이상유동에서 운반유체의 난류강도에 대한 해석적 접근)

  • Kim, Se-Yun;Lee, Chung-Gu;Lee, Kye-Bock
    • Transactions of the Korean Society of Mechanical Engineers B
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    • 제27권6호
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    • pp.813-820
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    • 2003
  • The purpose of this research is to develop the model of turbulence modulation due to the presence of particles in various types of particle-laden flows Available experimental data are surveyed and the dependence of turbulence modulation of carrier-phase on particle size, concentration and. particle Reynolds number are examined. This study takes into account the effect of wake produced by particle, the drag between phases and the velocity gradient in the wake to estimate the production of turbulence. The model of turbulence modulation using the mixing length theory under the assumption of equilibrium flow is proposed. Numerical results show that the model is successful in predicting the characteristics of the particle-laden in various flow conditions both qualitatively and quantitatively.

Grid Voltage-sensorless Current Control of LCL-filtered Grid-connected Inverter based on Gradient Steepest Descent Observer

  • Tran, Thuy Vi;Kim, Kyeong-Hwa
    • Proceedings of the KIPE Conference
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    • 전력전자학회 2019년도 전력전자학술대회
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    • pp.380-381
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    • 2019
  • This paper presents a grid voltage-sensorless current control design for an LCL-filtered grid-connected inverter with the purpose of enhancing the reliability and reducing the total cost of system. A disturbance observer based on the gradient steepest descent method is adopted to estimate the grid voltages with high accuracy and light computational burden even under distorted grid conditions. The grid fundamental components are effectively extracted from the estimated gird voltages by means of a least-squares algorithm to facilitate the synchronization process without using the conventional phase-locked loop. Finally, the estimated states of inverter system obtained by a discrete current-type full state observer are utilized in the state feedback current controller to realize a stable voltage-sensorless current control scheme. The effectiveness of the proposed scheme is validated through the simulation results.

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L1-penalized AUC-optimization with a surrogate loss

  • Hyungwoo Kim;Seung Jun Shin
    • Communications for Statistical Applications and Methods
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    • 제31권2호
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    • pp.203-212
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    • 2024
  • The area under the ROC curve (AUC) is one of the most common criteria used to measure the overall performance of binary classifiers for a wide range of machine learning problems. In this article, we propose a L1-penalized AUC-optimization classifier that directly maximizes the AUC for high-dimensional data. Toward this, we employ the AUC-consistent surrogate loss function and combine the L1-norm penalty which enables us to estimate coefficients and select informative variables simultaneously. In addition, we develop an efficient optimization algorithm by adopting k-means clustering and proximal gradient descent which enjoys computational advantages to obtain solutions for the proposed method. Numerical simulation studies demonstrate that the proposed method shows promising performance in terms of prediction accuracy, variable selectivity, and computational costs.

Effect on the Fuel Economy by Gradient in Automobile Driveway (자동차 전용도로에서 경사가 연비에 미치는 영향)

  • Choi, Seong-Cheol;Oh, Tae-Il
    • Journal of the Korea Academia-Industrial cooperation Society
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    • 제12권7호
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    • pp.2925-2930
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    • 2011
  • A vehicle fuel economy is very important issue in the view of fuel cost and environmental regulation. The fuel economy is much improved according to the development of electric, electronic and mechanical technology, but up to now the measurement of it tests the given mode(LA-4, FTP-75, etc) within computer simulation program and engine dynamometer. This fuel economy is different with it of real road. The one of main reason is not considered the gradient of the road. To estimate the effects of fuel economy at highway with gradient in this paper, we measure the amount of fuel consumption and calculate the fuel economy of it with running the Youngdong highway with high gradient. Also this paper analysis and compares the fuel economy with gradient and without gradient when the vehicle runs the same driveway. Then we calculate the total energy created the difference of fuel consumption amount of the two cases and calculate the consumpted energy by tire driving force from the torque and power of engine in the simulation. This paper verifies the relation of the driving force and the total energy by creating the difference of fuel consumption amount. This paper also proposes the method of fuel economy improvement despite of gradient at the result.