• Title/Summary/Keyword: Newton-Raphson procedure

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Variance function estimation with LS-SVM for replicated data

  • Shim, Joo-Yong;Park, Hye-Jung;Seok, Kyung-Ha
    • Journal of the Korean Data and Information Science Society
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    • v.20 no.5
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    • pp.925-931
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    • 2009
  • In this paper we propose a variance function estimation method for replicated data based on averages of squared residuals obtained from estimated mean function by the least squares support vector machine. Newton-Raphson method is used to obtain associated parameter vector for the variance function estimation. Furthermore, the cross validation functions are introduced to select the hyper-parameters which affect the performance of the proposed estimation method. Experimental results are then presented which illustrate the performance of the proposed procedure.

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A study on improving efficiency in computational procedure of finite element nonlinear analysis of plane frame structures (평면 프레임 구조물의 유한요소 비선형 해석을 위한 효율적인 수치해석 방법에 관한 연구)

  • 구정서;이병채;곽병만
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.12 no.4
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    • pp.631-641
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    • 1988
  • Computational procedures associated with finite element nonlinear analysis of plane frame structures were examined and new solution schemes were suggested. Element stiffness matrix was derived from the principle of virtual displacements. Geometric and material nonlinearities were considered in the formulation. Solution method was based upon the constant displacement length method in conjunction with the Newton-Raphson method. New solution schemes were introduced in determining the initial load increment and the sign of load increments and predicting the length of displacement increment to improve user convenience, efficiency and stability. Numerical experiments were performed for several typical problems and suggested schemes were found efficient and convenient for analyzing nonlinear frame structures.

Estimating Variance Function with Kernel Machine

  • Kim, Jong-Tae;Hwang, Chang-Ha;Park, Hye-Jung;Shim, Joo-Yong
    • Communications for Statistical Applications and Methods
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    • v.16 no.2
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    • pp.383-388
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    • 2009
  • In this paper we propose a variance function estimation method based on kernel trick for replicated data or data consisted of sample variances. Newton-Raphson method is used to obtain associated parameter vector. Furthermore, the generalized approximate cross validation function is introduced to select the hyper-parameters which affect the performance of the proposed variance function estimation method. Experimental results are then presented which illustrate the performance of the proposed procedure.

Computations of Line Reactor Parameters and DC Bus Capacitance for Inverter (인버터의 선형 리액터 파라미터와 DC 버스 용량 계산)

  • Chen, Dezhi;Chai, Wenping;Kwon, Byung-il
    • Proceedings of the KIEE Conference
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    • 2015.07a
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    • pp.968-969
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    • 2015
  • This paper proposes a novel analysis method for calculating inverter DC bus capacitance and line reactor parameters. In the realization process, DC bus capacitance parameter, and ripple current, life of DC bus capacitor, interaction between DC bus capacitance can be calculated by using Newton-Raphson procedure. The design scheme of DC bus capacitor and line reactor, specific parameters such as capacitance, loss, ripple current, central average temperature, life, ripple current, loss, size, central temperature of the reactor were given. Simulation results show that this scheme can accurately calculate the DC bus capacitance and line reactor parameters. Compared with calculation result of references, cost and volume are half. The indicators meet the demand of practical engineering. It had affirmed precision of the analytical method and verified correctness and feasibility of this method.

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Real-Time Forward Kinematics of the 6-6 Stewart Platform with One Extra Linear Sensor (한 개의 선형 여유센서를 갖는 스튜어트 플랫폼의 실시간 순기구학)

  • Lee, Tae-Young;Shim, Jae-Kyung
    • Proceedings of the KSME Conference
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    • 2000.11a
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    • pp.541-547
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    • 2000
  • This paper presents the closed-form forward kinematics of the 6-6 Stewart platform of planar base and moving platform. Based on algebraic elimination method and with one extra linear sensor, it first derives an 8th-degree univariate equation and then finds tentative solution sets out of which the actual solution is to be selected. In order to provide more exact solution despite the error between measured sensor value and the theoretical one, a correction method is also used. The overall procedure requires so little computation time that it can be efficiently used for realtime applications. In addition, unlike the iterative schemes e.g. Newton-Raphson, the algorithm does not require initial estimates of solution and is free of the problems that it does not converge to actual solution within limited time. The presented method has been implemented in C language and a numerical example is given to confirm the effectiveness and accuracy of the developed algorithm.

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Response prediction of a 50 m guyed mast under typhoon conditions

  • Law, S.S.;Bu, J.Q.;Zhu, X.Q.;Chan, S.L.
    • Wind and Structures
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    • v.9 no.5
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    • pp.397-412
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    • 2006
  • This paper presents the wind excited acceleration responses of a 50 m guyed mast under the action of Typhoon Dujuan. The response of the structure is reconstructed from using a full finite element model and an equivalent beam-column model. The wind load is modelled based on the measured wind speed and recommendations for high-rise structures. The nonlinear time response analysis is conducted using the Newton Raphson iteration procedure. Comparative studies on the measured and computed frequencies and acceleration responses show that the torsional vibration of the structure is significant particularly in the higher vibration modes after the first few bending modes. The equivalent model, in general, gives less accurate amplitude predictions than the full model because of the omission of torsional stiffness of the mast in the vibration analysis, but the root-mean-square value is close to the measured value in general with an error of less than 10%.

On an improved numerical method to solve the equilibrium problems of solids with bounded tensile strength that are subjected to thermal strain

  • Pimpinelli, Giovanni
    • Structural Engineering and Mechanics
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    • v.15 no.4
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    • pp.395-414
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    • 2003
  • In this paper we recall briefly the constitutive equations for solids subjected to thermal strain taking in account the bounded tensile stress of the material. In view to solve the equilibrium problem via the finite element method using the Newton Raphson procedure, we show that the tangent elasticity tensor is semi-definite positive. Therefore, in order to obtain a convergent numerical method, the constitutive equation needs to be modified. Specifically, the dependency of the stress by the anelastic deformation is made explicit by means of a parameter ${\delta}$, varying from 0 to 1, that factorizes the elastic tensor. This parameterization, for ${\delta}$ near to 0, assures the positiveness of the tangent elasticity tensor and enforces the convergence of the numerical method. Some numerical examples are illustrated.

Large strain analysis of two-dimensional frames by the normal flow algorithm

  • Tabatabaei, R.;Saffari, H.
    • Structural Engineering and Mechanics
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    • v.36 no.5
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    • pp.529-544
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    • 2010
  • Nonlinear equations of structures are generally solved numerically by the iterative solution of linear equations. However, this iterative procedure diverges when the tangent stiffness is ill-conditioned which occurs near limit points. In other words, a major challenge with simple iterative methods is failure caused by a singular or near singular Jacobian matrix. In this paper, using the Newton-Raphson algorithm based on Davidenko's equations, the iterations can traverse the limit point without difficulty. It is argued that the propose algorithm may be both more computationally efficient and more robust compared to the other algorithm when tracing path through severe nonlinearities such as those associated with structural collapse. Two frames are analyzed using the proposed algorithm and the results are compared with the previous methods. The ability of the proposed method, particularly for tracing the limit points, is demonstrated by those numerical examples.

On-Line Calculation of the Critical Point of Voltage Collapse Based on Multiple Load Flow Solutions (다중조류계산을 이용한 전압붕괴 임계점의 On-Line 계산)

  • Nam, Hae-Kon;Kim, Dong-Jun
    • Proceedings of the KIEE Conference
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    • 1993.07a
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    • pp.134-136
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    • 1993
  • This paper presents a novel and efficient method to calculate the critical point of voltage collapse. Conjugate gradient and modified Newton-Raphson methods are employed to calculate two pairs of multiple load flow solutions for two operating conditions, i.e., both +mode and -mode voltages for two loading conditions respectively. Then these four voltage magnitude-load data sets of the bus which is most susceptible to voltage collapse, are fitted to third order polynomial using Lagrangian interpolation in order to represent approximate nose curve (P-V curve). This nose curve locates first estimate of the critical point of voltage collapse. The procedure described above is repeated near the critical point and the new estimate will be very close to the critical point. The proposed method is tested for the eleven bus Klos-Kerner system, with good accuracy and fast computation time.

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An Analysis of Load Characteristics of Air-Lubricated Herringbone Groove Journal Bearing By Finite Element Method (공기윤활 빗살무늬 저널베어링의 부하특성에 대한 유한요소해석)

  • 박신욱;임윤철
    • Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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    • 2000.11a
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    • pp.353-362
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    • 2000
  • Herringbone groove journal bearing (HGJB) is developed to improve the static and dynamic performances of hydrodynamic journal bearing. In this study, static and dynamic compressible isothermal lubrication problems are analyzed by the finite element method together with the Newton-Raphson iterative procedure. This analysis is introduced for prediction of the static and dynamic characteristics of air lubricated HGJB for various bearing configurations. The bearing load characteristics and dynamic characteristics are dependent on geometric parameters such as asymmetric ratio, groove depth ratio, groove width ratio and groove angle.

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