• 한국측량학회지
• /
• 제33권4호
• /
• pp.231-244
• /
• 2015

VLBI 안테나의 기준점을 정확하게 결정하는 것은 서로 다른 우주측지기술들을 연계하는 콜로케이션을 수행하기 위한 필수적인 사항이다. 본 연구에서는 VLBI 안테나의 기준점을 정확하게 산출할 수 있는 3D circle fitting 방법에 대한 비교와 분석을 수행하였다. 이를 위하여 평면상의 관측점 평행이동과 정규직교 좌표계 설정을 기반으로 하는 방법론과 unitary 좌표변환을 활용하는 방법론을 제시하고, 비교 대상 방법별로 fitting 정확도를 평가하였다. 각 방법의 3D circle fitting 정확도를 향상시키기 위하여 관측점과 fitting 모델 사이의 잔차로써 직교거리를 산출하고, 과대오차를 소거하는 반복계산 과정을 수행하였다. 연구의 결과, unitary 좌표변환을 기반으로 하는 3D circle fitting 방법론이 VLBI 안테나의 방위각과 앙각축에 대한 최적의 방정식을 결정하는데 가장 적합한 것으로 나타났다. 상기 방법으로 결정된 두 축의 교차점을 VLBI 안테나의 기준점으로써 계산하였고, 이러한 결과는 향후 VLBI 관측성과의 국가기준점 연계를 위한 다양한 연구에 활용될 수 있을 것으로 기대된다.

• 한국정보통신학회:학술대회논문집
• /
• 한국해양정보통신학회 2009년도 추계학술대회
• /
• pp.410-413
• /
• 2009

웨이퍼 Pre-Alignment는 반도체 공정에서 장비에 웨이퍼를 놓기 전에 웨이퍼의 중심 및 방향을 정확하게 정렬할 필요가 있는데, 이를 위해서 일정한 수준 이하로 중심과 방향을 찾아 Alignment 하는 방법을 말한다. 본 논문에서는 웨이퍼를 Alignment 하기 위해 기존의 Mechanical한 방법이 아닌 Area 카메라를 통한 비접촉식 방법을 이용하였다. 이 방법은 웨이퍼를 45도씩 8번씩, 한 바퀴를 회전하여 이미지를 획득한 뒤, 이미지의 웨이퍼의 에지값 들을 이용하여 Least Square Circle Fitting을 이용하여 웨이퍼의 중심과 방향을 정확하게 측정하여 Alignment를 한다.

• Journal of applied mathematics & informatics
• /
• 제7권3호
• /
• pp.983-994
• /
• 2000

We consider the problem of determining the circle of best fit to a set of data points in the plane. In [1] and [2] several algorithms already have been given for fitting a circle in least squares sense of minimizing the geometric distances to the given data points. In this paper we present another new descent algorithm which computes a parametric represented circle in order to minimize the sum of the squares of the distances to the given points. For any choice of starting values our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.

• 대한수학회논문집
• /
• 제34권3호
• /
• pp.1029-1047
• /
• 2019

We are interested in the problem of determining the best fitted circle to a set of data points in space. This can be usually obtained by minimizing the geometric distances or various approximate algebraic distances from the fitted circle to the given data points. In this paper, we propose an algorithm in such a way that the sum of the squares of the geometric distances is minimized in ${\mathbb{R}}^3$. Our algorithm is mainly based on the steepest descent method with a view of ensuring the convergence of the corresponding objective function Q(u) to a local minimum. Numerical examples are given.

• 전기전자학회논문지
• /
• 제26권1호
• /
• pp.104-110
• /
• 2022

본 논문에서는 UAV의 BLDC 모터 진단방법과 AI진단을 위한 새로운 데이터 셋을 제안하였다. BLDC모터 진단에 있어서 PVA(Park's Vector Approach)는 주파수 성분의 많은 리플로 인해 적용이 어려움이 따르나, 리플의 성분이 3조파를 띄고 있음에 따라 3조파에 뛰어난 SG(Savitzky-Golay)필터를 적용하여 Circle fitting으로 PVA를 활용하는 방법을 제안하였다. 한편, 3상에서 2상으로 변환시키는 기법인 PVA는 변환과정 중 항상 원점을 기준으로 두게 된다. 이에 Circle fitting의 적용과정에서 원점과 측정된 중심점의 오차를 측정하여 고장진단이 가능하도록 하였다. 또한, 이때 측정된 오차의 offset 데이터 기반으로 AI기술의 새로운 데이터 셋으로 활용 가능함을 실험을 통해 입증하였다.

• 한국공작기계학회논문집
• /
• 제12권4호
• /
• pp.17-22
• /
• 2003

This paper presents a new circular curve fitting approach of articulated manipulators, based on least square. The approach aims at gaining the interpolation of circle from n data points, under the condition that the fitted circle should pass both a starting point and an ending point. First a spherical fitting should be performed, using least squares. Then the circular curve fitting can be resulted from the intersection of the fitted sphere and the plane obtained from 3 points, i. e., a starting point, an ending point and the center of a sphere. The proposed algorithms are shown to be efficient by using MATLAB-based simulation.

• 한국소음진동공학회논문집
• /
• 제13권5호
• /
• pp.334-340
• /
• 2003

Exponential window function Is widely used In impact hammer testing to reduce leakage error as well as to get a good S/N ratio. The larger its decaying rate is, the more effectively the leakage errors are reduced. But if the decay rate of the exponential window is too large, the FRF is distorted. And the modal parameters of the system can not be exactly identified by modal analysis technique. Therefore, it is a difficult problem to determine proper decay rate in impact hammer testing. In this paper, amount of the FRF distortion caused by exponential window is theoretically uncovered. A new circle fitting method is also proposed so that the modal parameters are directly extracted from impulse response spectrum distorted by the exponential-windowed impulse response data. The results by the conventional and proposed circle fitting method are compared through a numerical example.

• 한국정밀공학회:학술대회논문집
• /
• 한국정밀공학회 2002년도 추계학술대회 논문집
• /
• pp.570-575
• /
• 2002

This paper presents a new circular curve fitting approach of articulated manipulators, based on pseudoinverses. The paper aims at gaining the interpolation of circle from n data points, under the condition that the fitted circle should pass both a start point and an end point. In this paper, two algorithms of circular interpolation are presented. Prior to circular interpolation, are a spherical fitting should be performed, using least squares. In the first algorithm, the relationship between point data and normal vector on the sphere is used. In the second algorithm. the equation of plane which can be obtained from 3 points, i.e., a start point, an end point, and center of a sphere. The proposed algorithms are show to be efficient by using MATLAB-based simulation.

• 대한임베디드공학회논문지
• /
• 제18권3호
• /
• pp.117-124
• /
• 2023

In the machine vision inspection equipment, diameter measurement is important process in inspection of cylindrical object. However, machine vision inspection equipment requires complex algorithm processing such as camera distortion correction and perspective distortion correction, and the increase in processing time and cost required for precise diameter measurement. In this paper, we proposed the algorithm for diameter measurement of cylindrical object using the laser displacement sensor. In order to fit circle for given four input outer points, grid search algorithms using root-mean-square error and mean-absolute error are applied and compared. To solve the limitations of the grid search algorithm, we finally apply the singular-value-decomposition based circle fitting algorithm. In order to compare the performance of the algorithms, we generated the pseudo data of the outer points of the cylindrical object and applied each algorithm. As a result of the experiment, the grid search using root-mean-square error confirmed stable measurement results, but it was confirmed that real-time processing was difficult as the execution time was 10.8059 second. The execution time of mean-absolute error algorithm was greatly improved as 0.3639 second, but there was no weight according to the distance, so the result of algorithm is abnormal. On the other hand, the singular-value-decomposition method was not affected by the grid and could not only obtain precise detection results, but also confirmed a very good execution time of 0.6 millisecond.

• 반도체디스플레이기술학회지
• /
• 제9권1호
• /
• pp.11-16
• /
• 2010

Wafer Pre-Alignment is to find the center and the orientation of a wafer and to move the wafer to the desired position and orientation. In this paper, an area camera based pre-aligning method is presented that captures 8 wafer images regularly during 360 degrees rotation. From the images, wafer edge positions are extracted and used to estimate the wafer's center and orientation using least squares circle fitting. These data are utilized for the proper alignment of the wafer. For accurate alignments, camera calibration methods using high order polynomials are used for converting pixel coordinates into real-world coordinates. A complete pre-alignment system was constructed using mechanical and optical components and tested. Experimental results show that alignment of wafer center and orientation can be done with the standard deviation of 0.002 mm and 0.028 degree, respectively.