• Title/Summary/Keyword: Least Square Solution

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Design of Fuzzy Models with the Aid of an Improved Differential Evolution (개선된 미분 진화 알고리즘에 의한 퍼지 모델의 설계)

  • Kim, Hyun-Ki;Oh, Sung-Kwun
    • Journal of the Korean Institute of Intelligent Systems
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    • v.22 no.4
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    • pp.399-404
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    • 2012
  • Evolutionary algorithms such as genetic algorithm (GA) have been proven their effectiveness when applying to the design of fuzzy models. However, it tends to suffer from computationally expensWive due to the slow convergence speed. In this study, we propose an approach to develop fuzzy models by means of an improved differential evolution (IDE) to overcome this limitation. The improved differential evolution (IDE) is realized by means of an orthogonal approach and differential evolution. With the invoking orthogonal method, the IDE can search the solution space more efficiently. In the design of fuzzy models, we concern two mechanisms, namely structure identification and parameter estimation. The structure identification is supported by the IDE and C-Means while the parameter estimation is realized via IDE and a standard least square error method. Experimental studies demonstrate that the proposed model leads to improved performance. The proposed model is also contrasted with the quality of some fuzzy models already reported in the literature.

Development of Computer Program for Solving Astronomical Ship Position Based on Circle of Equal Altitude Equation and SVD-Least Square Algorithm

  • Nguyen, Van-Suong;Im, Namkyun
    • Journal of Navigation and Port Research
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    • v.38 no.2
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    • pp.89-96
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    • 2014
  • This paper presents an improvement for calculating method of astronomical ship position based on circle of equal altitude equation. In addition, to enhance the accuracy of ship position achieved from solving equation system, the authors used singular value decomposition (SVD) in least square method instead of normal decomposition. In maths, the SVD was proved more numerically stable than normal decomposition. Therefore, the solution of equation system will be more efficient and the result would be more accurate than previous methods. By proposal algorithm, a computer program have been developed to help the navigators in calculating directly ship position when the modern equipment has failure. Finally, some of experiments are carried out to verify effectiveness of proposed algorithm, the results show that the accuracy of ship position based on new method is better than the intercept method.

Application SVD-Least Square Algorithm for solving astronomical ship position basing on circle of equal altitude equation

  • Nguyen, Van Suong;Im, Namkyun
    • Proceedings of the Korean Institute of Navigation and Port Research Conference
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    • 2013.10a
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    • pp.130-132
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    • 2013
  • This paper presents an improvement for calculating method of astronomical vessel position with circle of equal altitude equation based on using a virtual object in sun and two stars observation. In addition, to enhance the accuracy of ship position achieved from solving linear matrix system, and surmount the disadvantages on rank deficient matrices situation, the authors used singular value decomposition (SVD) in least square method instead of normal equation and QR decomposition, so, the solution of matrix system will be available in all situation. As proposal algorithm, astronomical ship position will give more accuracy than previous methods.

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Development of a meshless finite mixture (MFM) method

  • Cheng, J.Q.;Lee, H.P.;Li, Hua
    • Structural Engineering and Mechanics
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    • v.17 no.5
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    • pp.671-690
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    • 2004
  • A meshless method with novel variation of point collocation by finite mixture approximation is developed in this paper, termed the meshless finite mixture (MFM) method. It is based on the finite mixture theorem and consists of two or more existing meshless techniques for exploitation of their respective merits for the numerical solution of partial differential boundary value (PDBV) problems. In this representation, the classical reproducing kernel particle and differential quadrature techniques are mixed in a point collocation framework. The least-square method is used to optimize the value of the weight coefficient to construct the final finite mixture approximation with higher accuracy and numerical stability. In order to validate the developed MFM method, several one- and two-dimensional PDBV problems are studied with different mixed boundary conditions. From the numerical results, it is observed that the optimized MFM weight coefficient can improve significantly the numerical stability and accuracy of the newly developed MFM method for the various PDBV problems.

Quantitative Analysis of Indomethacin by the Portable Near-Infrared (NIR) System (근적외분광분석법을 이용한 인도메타신의 정량분석)

  • 김도형;우영아;김효진
    • YAKHAK HOEJI
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    • v.47 no.5
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    • pp.261-265
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    • 2003
  • Near-infrared (NIR) system was used to determine rapidly and simply indomethacin in buffer solution for a dissolution test of tablets and capsules. Indomethacin standards were prepared ranging from 10 to 50 ppm using the mixture of phosphate buffer (pH 7.2) and water (1 : 4). The near-infrared (NIR) transmittance spectra of indomethacin standard solutions were collected by using a quartz cell in 1 mm and 2 mm pathlength. Partial least square regression (PLSR) was explored to develop calibration models over the spectral range 1100∼1700 nm. The model using 1 mm quartz cell was better than that using 2 mm quartz cell. The PLSR models developed gave standard error of prediction (SEP) of 0.858 ppm. In order to validate the developed calibration model, routine analysis was performed using another standard solutions. The NIR routine analysis showed good correlation with actual values. Standard error of prediction (SEP) is 1.414 ppm for 7 indomethacin samples in routine analysis and its error was permeable in the regulation of Korean Pharmacopoeia (VII). These results show the potential use of the real time monitoring for indomethacin during a dissolution test.

Unoccluded Cylindrical Object Pose Measurement Using Least Square Method (최소자승법을 이용한 가려지지 않은 원통형 물체의 자세측정)

  • 주기세
    • Journal of the Korean Society for Precision Engineering
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    • v.15 no.7
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    • pp.167-174
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    • 1998
  • This paper presents an unoccluded cylindrical object pose measurement using a slit beam laser in which a robot recognizes all of the unoccluded objects from the top of jumbled objects, and picks them up one by one. The elliptical equation parameters of a projected curve edge on a slice are calculated using LSM. The coefficients of standard elliptical equation are compared with these parameters to estimate the object pose. The hamming distances between the estimated coordinates and the calculated ones are extracted as measures to evaluate a local constraint and a smoothing surface curvature. The edges between slices are linked using error function based on the edge types and the hamming distances. The linked edges on slices are compared with the model object's length to recognize the unoccluded object. This proposed method may provide a solution to the automation of part handling in manufacturing environments such as punch press operation or part assembly.

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ANALYSIS OF A MESHFREE METHOD FOR THE COMPRESSIBLE EULER EQUATIONS

  • Kim, Yong-Sik;Pahk, Dae-Hyeon
    • Journal of the Korean Mathematical Society
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    • v.43 no.5
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    • pp.1081-1098
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    • 2006
  • Mathematical analysis is made on a mesh free method for the compressible Euler equations. In particular, the Moving Least Square Reproducing Kernel (MLSRK) method is employed for space approximation. With the backward-Euler method used for time discretization, existence of discrete solution and it's $L^2-error$ estimate are obtained under a regularity assumption of the continuous solution. The result of numerical experiment made on the biconvex airfoil is presented.

Extension of shuster's algorithm for spin-axis attitude and sensor bias determination (위성 회전축 및 센서 바이어스 결정을 위한 확장 Shuster 알고리즘에 관한 연구)

  • 노태수
    • 제어로봇시스템학회:학술대회논문집
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    • 1994.10a
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    • pp.238-242
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    • 1994
  • Shuster's algorithm for spin-axis determination is extended to include sensor bias and mounting angle as its solve-for parameters. The relation between direct and derived measurements bias is obtained by linearizing their kinematic equations. A one-step least-square estimation technique referred to as the 'closed form' solution is used, and the solution provides a more refined and decent initial guess for the subsequent filtering process contained within the differential correction module. The modified algorithm is applied for attitude determination of a GEO communication satellite in transfer orbit, and its results are presented.

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A solution to the inverse kinematic by using neural network (신경회로망을 사용한 역운동학 해)

  • 안덕환;이종용;양태규;이상효
    • 제어로봇시스템학회:학술대회논문집
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    • 1989.10a
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    • pp.124-126
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    • 1989
  • Inverse kinematic problem is a crucial point for robot manipulator control. In this paper, to implement the Jacobian control technique we used the Hopfield(Tank)'s neural network. The states of neurons represent joint veocities, and the connection weights are determined from the current value of the Jacobian matrix. The network energy function is constructed so that its minimum corresponds to the minimum least square error. At each sampling time, connection weights and neuron states are updated according to current joint position. Inverse kinematic solution to the planar redundant manipulator is solved by computer simulation.

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Stress Recovery Technique by Ordinary Kriging Interpolation in p-Adaptive Finite Element Method (적응적 p-Version 유한요소법에서 정규 크리깅에 의한 응력복구기법)

  • Woo, Kwang Sung;Jo, Jun Hyung;Lee, Dong Jin
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.26 no.4A
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    • pp.677-687
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    • 2006
  • Kriging interpolation is one of the generally used interpolation techniques in Geostatistics field. This technique includes the experimental and theoretical variograms and the formulation of kriging interpolation. In contrast to the conventional least square method for stress recovery, kriging interpolation is based on the weighted least square method to obtain the estimated exact solution from the stress data at the Gauss points. The weight factor is determined by variogram modeling for interpolation of stress data apart from the conventional interpolation methods that use an equal weight factor. In addition to this, the p-level is increased non-uniformly or selectively through a posteriori error estimation based on SPR (superconvergent patch recovery) technique, proposed by Zienkiewicz and Zhu, by auto mesh p-refinement. The cut-out plate problem under tension has been tested to validate this approach. It also provides validity of kriging interpolation through comparing to existing least square method.