• Title/Summary/Keyword: Nonlinear equations

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Convergence Analysis of the Least Mean Fourth Adaptive Algorithm (최소평균사승 적응알고리즘의 수렴특성 분석)

  • Cho, Sung-Ho;Kim, Hyung-Jung;Lee, Jong-Won
    • The Journal of the Acoustical Society of Korea
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    • v.14 no.1E
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    • pp.56-64
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    • 1995
  • The least mean fourth (LMF) adaptive algorithm is a stochastic gradient method that minimizes the error in the mean fourth sense. Despite its potential advantages, the algorithm is much less popular than the conventional least mean square (LMS) algorithm in practice. This seems partly because the analysis of the LMF algorithm is much more difficult than that of the LMS algorithm, and thus not much still has been known about the algorithm. In this paper, we explore the statistical convergence behavior of the LMF algorithm when the input to the adaptive filter is zero-mean, wide-sense stationary, and Gaussian. Under a system idenrification mode, a set of nonlinear evolution equations that characterizes the mean and mean-squared behavior of the algorithm is derived. A condition for the conbergence is then found, and it turns out that the conbergence of the LMF algorithm strongly depends on the choice of initial conditions. Performances of the LMF algorithm are compared with those of the LMS algorithm. It is observed that the mean convergence of the LMF algorithm is much faster than that of the LMS algorithm when the two algorithms are designed to achieve the same steady-state mean-squared estimation error.

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Wave Forces Acting on Large Vertical Circular Cylinder and Consequent Wave Transformations by Full-Nonlinear Analysis Method after Wave Breaking (강비선형해석법에 의한 대형연직원주구조물에 작용하는 쇄파후의 파력 및 파랑변형)

  • Lee, Kwang-Ho;Shin, Dong-Hoon;Kim, Do-Sam
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.20 no.4
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    • pp.401-412
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    • 2008
  • Simulations of three-dimensional numerical wave tank are performed to investigate wave force acting on a large cylindrical structure and consequent wave deformation, which are induced by bore after breaking waves. The numerical model is based on the three-dimensional Navier-Stokes equations with a finite-difference method combined with a volume of fluid(VOF) method, which is capable of tracking the complex free surface, including wave breaking. In order to promote wave breaking of the incident wave, the approach slope was built seaward of the structure with a constant slope and a large cylindrical structure was installed on a flat bed. The incident waves were broken on the approach slope or flat bed by its wave height. In the present study, all waves acting on the large cylindrical structure were limited to breaking bore after wave breaking. The effects of the position of the structure and the incident wave height on the wave force and wave transformations were mainly investigated with the concern of wave breaking. Further, the relations between the variation of wave energy by wave propagation after wave breaking and wave force acting on the structure were discussed to give the understanding of the full-linear wave-structure interactions in three-dimensional wave fields.

Robust 3-D Motion Estimation Based on Stereo Vision and Kalman Filtering (스테레오 시각과 Kalman 필터링을 이용한 강인한 3차원 운동추정)

  • 계영철
    • Journal of Broadcast Engineering
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    • v.1 no.2
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    • pp.176-187
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    • 1996
  • This paper deals with the accurate estimation of 3- D pose (position and orientation) of a moving object with reference to the world frame (or robot base frame), based on a sequence of stereo images taken by cameras mounted on the end - effector of a robot manipulator. This work is an extension of the previous work[1]. Emphasis is given to the 3-D pose estimation relative to the world (or robot base) frame under the presence of not only the measurement noise in 2 - D images[ 1] but also the camera position errors due to the random noise involved in joint angles of a robot manipulator. To this end, a new set of discrete linear Kalman filter equations is derived, based on the following: 1) the orientation error of the object frame due to measurement noise in 2 - D images is modeled with reference to the camera frame by analyzing the noise propagation through 3- D reconstruction; 2) an extended Jacobian matrix is formulated by combining the result of 1) and the orientation error of the end-effector frame due to joint angle errors through robot differential kinematics; and 3) the rotational motion of an object, which is nonlinear in nature, is linearized based on quaternions. Motion parameters are computed from the estimated quaternions based on the iterated least-squares method. Simulation results show the significant reduction of estimation errors and also demonstrate an accurate convergence of the actual motion parameters to the true values.

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Generation and Growth of Long Ocean Waves along the West Coast of Korea in March 2007 (2007년 3월 한국 서해안에 발생한 해양장파의 형성과 성장과정)

  • Choi, Byoung-Ju;Park, Yong-Woo;Kwon, Kyung-Man
    • Ocean and Polar Research
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    • v.30 no.4
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    • pp.453-466
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    • 2008
  • In order to examine the generation mechanism of long ocean waves along the west coast of Korea and to understand the amplification process of the long ocean waves, sea level, atmospheric pressure and wind data observed every minute from 2007 March 29 to 2007 April 1 were analyzed and onedimensional numerical ocean model experiments were performed. An atmospheric pressure jump propagated southeastward from Backryungdo to Yeonggwang along the west coast of Korea with speed of $13{\sim}27\;m/s$ between 2007 March 30 23:00 and 2007 April 1 1:30. Average magnitude of pressure jump was 4.2 hPa. As a moving atmospheric jump propagated from north to south along the coast, long ocean waves were generated and the sea level abnormally rose or fell at Anheung, Kunsan, Wido and Yeonggwang. Average amplitude of sea level rise (or fall) was about 113.6 cm. In a one-dimensional numerical ocean model, nonlinear shallow water equations were numerically integrated and a moving atmospheric pressure jump with traveling speed of 24 m/s was used as an external force. While the atmospheric pressure jump travels over 60 m depth ocean, a long ocean wave is generated. Because the propagation speed of the atmospheric jump is almost equal to that of the long ocean wave, Proudman resonance occurs and the long ocean wave amplifies. As the atmospheric pressure jump moves into the coastal area shallower than 60 m, the speed of the long ocean wave decreases and Proudman resonance effect decreases. However, the amplitude of the long ocean wave increases and wave length becomes shorter because of shoaling effect. When the long ocean wave hits the land boundary, amplitude of the long ocean wave drastically amplifies due to reflection. Data analysis and numerical experiments suggest that the southeastward propagation of an atmospheric pressure jump over the shallow ocean, which is a necessary condition for Proudaman resonance, generated the long ocean waves along the west coast of Korea on 2007 March 31 and the ocean waves amplified due to shoaling effect in the coastal area and reflection at the shore.

Comparison of Artificial Neural Network and Empirical Models to Determine Daily Reference Evapotranspiration (기준 일증발산량 산정을 위한 인공신경망 모델과 경험모델의 적용 및 비교)

  • Choi, Yonghun;Kim, Minyoung;O'Shaughnessy, Susan;Jeon, Jonggil;Kim, Youngjin;Song, Weon Jung
    • Journal of The Korean Society of Agricultural Engineers
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    • v.60 no.6
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    • pp.43-54
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    • 2018
  • The accurate estimation of reference crop evapotranspiration ($ET_o$) is essential in irrigation water management to assess the time-dependent status of crop water use and irrigation scheduling. The importance of $ET_o$ has resulted in many direct and indirect methods to approximate its value and include pan evaporation, meteorological-based estimations, lysimetry, soil moisture depletion, and soil water balance equations. Artificial neural networks (ANNs) have been intensively implemented for process-based hydrologic modeling due to their superior performance using nonlinear modeling, pattern recognition, and classification. This study adapted two well-known ANN algorithms, Backpropagation neural network (BPNN) and Generalized regression neural network (GRNN), to evaluate their capability to accurately predict $ET_o$ using daily meteorological data. All data were obtained from two automated weather stations (Chupungryeong and Jangsu) located in the Yeongdong-gun (2002-2017) and Jangsu-gun (1988-2017), respectively. Daily $ET_o$ was calculated using the Penman-Monteith equation as the benchmark method. These calculated values of $ET_o$ and corresponding meteorological data were separated into training, validation and test datasets. The performance of each ANN algorithm was evaluated against $ET_o$ calculated from the benchmark method and multiple linear regression (MLR) model. The overall results showed that the BPNN algorithm performed best followed by the MLR and GRNN in a statistical sense and this could contribute to provide valuable information to farmers, water managers and policy makers for effective agricultural water governance.

PREDICTION OF THE SUN-GLINT LOCATIONS FOR THE COMMUNICATION, OCEAN AND METEOROLOGICAL SATELLITE (통신해양기상위성에서의 태양광 반사점(SUN-GLINT) 위치예측)

  • Park, Jae-Ik;Choil, Kyu-Hong;Payk, Sang-Young;Ryu, Joo-Hyung;Ahn, Yu-Hwan;Park, Jae-Woo;Kim, Byoung-Soo
    • Journal of Astronomy and Space Sciences
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    • v.22 no.3
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    • pp.263-272
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    • 2005
  • For the Communication, Ocean and Meteorological Satellite (COMS) which will be launched in 2008, an algorithm for finding the precise location of the sun-glint point on the ocean surface is studied. The precise locations of the sun-glint are estimated by considering azimuth and elevation angles of Sun-satellite-Earth geometric position and the law of reflection. The obtained nonlinear equations are solved by using the Newton-Raphson method. As a result, when COMS is located at $116.2^{\circ}E$ or $128.2^{\circ}E$ longitude, the sun-glint covers region of ${\pm}10^{\circ}(N-S)$ latitude and $80-150^{\circ}(E-W)$ longitude. The diurnal path of the sun-glint in the southern hemisphere is curved towards the North Pole, and the path in the northern hemisphere is forwards the south pole. The algorithm presented in this paper can be applied to predict the precise location of sun-glint region in any other geostationary satellites.

Pole Placement Method to Move a Equal Poles with Jordan Block to Two Real Poles Using LQ Control and Pole's Moving-Range (LQ 제어와 근의 이동범위를 이용한 조단 블록을 갖는 중근을 두 실근으로 이동시키는 극배치 방법)

  • Park, Minho
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.19 no.2
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    • pp.608-616
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    • 2018
  • If a general nonlinear system is linearized by the successive multiplication of the 1st and 2nd order systems, then there are four types of poles in this linearized system: the pole of the 1st order system and the equal poles, two distinct real poles, and complex conjugate pair of poles of the 2nd order system. Linear Quadratic (LQ) control is a method of designing a control law that minimizes the quadratic performance index. It has the advantage of ensuring the stability of the system and the pole placement of the root of the system by weighted matrix adjustment. LQ control by the weighted matrix can move the position of the pole of the system arbitrarily, but it is difficult to set the weighting matrix by the trial and error method. This problem can be solved using the characteristic equations of the Hamiltonian system, and if the control weighting matrix is a symmetric matrix of constants, it is possible to move several poles of the system to the desired closed loop poles by applying the control law repeatedly. The paper presents a method of calculating the state weighting matrix and the control law for moving the equal poles with Jordan blocks to two real poles using the characteristic equation of the Hamiltonian system. We express this characteristic equation with a state weighting matrix by means of a trigonometric function, and we derive the relation function (${\rho},\;{\theta}$) between the equal poles and the state weighting matrix under the condition that the two real poles are the roots of the characteristic equation. Then, we obtain the moving-range of the two real poles under the condition that the state weighting matrix becomes a positive semi-finite matrix. We calculate the state weighting matrix and the control law by substituting the two real roots selected in the moving-range into the relational function. As an example, we apply the proposed method to a simple example 3rd order system.

Study on the Applicability of a New Multi-body Dynamics Program Through the Application to the Heave Compensation System (상하동요 감쇠장치 적용을 통한 새로운 다물체동역학 프로그램의 적용성 검토)

  • Ku, Nam-Kug;Ha, Sol;Roh, Myung-Il
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.26 no.4
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    • pp.247-254
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    • 2013
  • In this paper, dynamic response analysis of a heave compensation system is performed for offshore drilling operations based on multibody dynamics. With this simulation, the efficiency of the heave compensation system can be virtually confirmed before it is applied to drilling operations. The heave compensation system installed on a semi-submersible platform consists of a passive and an active heave compensator. The passive and active heave compensator are composed of several bodies that are connected to each other with various types of joints. Therefore, to carry out the dynamic response analysis, the dynamics kernel was developed based on mutibody dynamics. To construct the equations of motion of the multibody system and to determine the unknown accelerations and constraint forces, the recursive Newton-Euler formulation was adapted. Functions of the developed dynamics kernel were verified by comparing them with other commercial dynamics kernels. The hydrostatic force with nonlinear effects, the linearized hydrodynamic force, and the pneumatic and hydraulic control forces were considered as the external forces that act on the platform of the semi-submersible rig and the heave compensation system. The dynamic simulation of the heave compensation system of the semi-submersible rig, which is available for drilling operations with a 3,600m water depth, was carried out. From the results of the simulation, the efficiency of the heave compensation system were evaluated before they were applied to the offshore drilling operations. Moreover, the calculated constraint forces could serve as reference data for the design of the mechanical system.

Flexural Strength of HSB Steel Girders Due to Inelastic Lateral-Torsional Buckling - Sections with Slender Web (HSB 강거더의 비탄성 횡비틂좌굴에 의한 휨강도 - 세장 복부판 단면)

  • Cho, Eun-Young;Shin, Dong-Ku
    • Journal of Korean Society of Steel Construction
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    • v.24 no.2
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    • pp.217-231
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    • 2012
  • The flexural behavior of HSB I-girder with a non-slender web attributed to inelastic lateral-torsional buckling under uniform bending was investigated using nonlinear finite element analysis of ABAQUS. The girder was assumed to have a compact or noncompact web in order to prevent premature bend-buckling of the web. The unbraced length of the girder was selected so that inelastic lateral-torsional buckling governs the ultimate flexural strength. The compression flange was also assumed to be either compact or noncompact to prevent local buckling of the elastic flange. Both homogeneous sections fabricated from HSB600 or HSB800 steel and hybrid sections with HSB800 flanges and SM570-TMC web were considered. In the FE analysis, the flanges and web of I-girder were modeled as thin shell elements. Initial imperfections and residual stresses were imposed on the FE model. An elasto-plastic strain hardening material was assumed for steel. After establishing the validity of the present FE analysis by comparing FE results with test results in existing literature, the effects of initial imperfection and residual stress on the inelastic lateral-torsional buckling behavior were analyzed. Finite element analysis results for 96 sections demonstrated that the current inelastic strength equations for the compression flange in AASHTO LTFD can be applied to predict the inelastic lateral torsional buckling strength of homogeneous and hybrid HSB I-girders with a non-slender web.

New Approach for Shear Capacity Prediction of High Strength Concrete Beams without Stirrups (스터럽이 없는 고강도 콘크리트 보의 전단강도 예측을 위한 새로운 예측식의 제안)

  • Choi, Jeong-Seon;Lee, Chang-Hoon;Yoon, Young-Soo
    • Journal of the Korea Concrete Institute
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    • v.18 no.5 s.95
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    • pp.611-620
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    • 2006
  • In the shear failure mechanism of a beam, beam and arch actions always exist simultaneously. According to the shear span to depth ratio, the proportion between these two actions is varied and the contribution of these actions to shear capacity is changed. Moreover, the current codes provide recommendations based on experimental results of normal strength concrete, so the application range of concrete strength must be extended. Based on this mechanism and new requirement, a simplified analytical equation for shear capacity prediction of reinforced high strength concrete beams without stirrups is proposed. To reflect the change in the contribution between these actions, stress variation in the longitudinal reinforcement along the span is considered by use of the Jenq and Shah Model. Dowel action with horizontal splitting failure and shear friction between cracks are also taken into account. ize effect is included to derive a more precise equation. Regression analysis is performed to determine each variable and simplify the equation. And, the formula derived from theoretical approaches is evaluated by comparison with numerous experimental data, which are in broad range of concrete strength(especially in high strength concrete), shear span to depth ratio, geometrical size and longitudinal steel ratio. It is shown that the proposed equation is more accurate and simpler than other empirical equations, so a wide range of a/d can be considered in one equation.