• Title/Summary/Keyword: Newton-Raphson algorithm

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Parameters Estimation of Probability Distributions Using Meta-Heuristic Algorithms (Meta-Heuristic Algorithms를 이용한 확률분포의 매개변수 추정)

  • Yoon, Suk-Min;Lee, Tae-Sam;Kang, Myung-Gook;Jeong, Chang-Sam
    • Proceedings of the Korea Water Resources Association Conference
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    • 2012.05a
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    • pp.464-464
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    • 2012
  • 수문분야에 있어서 빈도해석의 목적은 특정 재현기간에 대한 발생 가능한 수문량의 규모를 파악하는데 있으며, 빈도해석의 정확도는 적합한 확률분포모형의 선택과 매개변수 추정방법에 의존하게 된다. 일반적으로 각 확률분포모형의 특성을 대표하는 매개변수를 추정하기 위해서는 모멘트 방법, 확률가중 모멘트 방법, 최대우도법 등을 이용하게 된다. 모멘트 방법에 의한 매개변수 추정은 해를 구하기 위한 과정이 단순한 반면, 비대칭형의 왜곡된 분포를 갖는 자료들에 대해서는 부정확한 결과를 나타내게 된다. 확률가중 모멘트 방법은 표본의 크기가 작거나 왜곡된 자료일 경우에도 비교적 안정적인 결과를 제공하는 반면, 확률 가중치가 정수로만 제한되는 단점을 갖고 있다. 그리고 대수 우도함수를 이용하여 매개변수를 추정하게 되는 최우도법은 가장 효율적인 매개변수 추정치를 얻을 수 있는 것으로 알려져 있으나, 비선형 연립방정식으로 표현되는 해를 구하기 위해서는 Newton-Raphson 방법을 사용하는 등 절차가 복잡하며, 때로는 수렴이 되지 않아 해룰 구하지 못하는 경우가 발생되게 된다. 이에 반해, 최근의 Genetic Algorithm, Ant Colony Optimization 및 Simulated Annealing과 같은 Meta-Heuristic Algorithm들은 복잡합 공학적 최적화 문제 있어서 효율적인 대안으로 주목받고 있으며, Hassanzadeh et al.(2011)에 의해 수문학적 빈도해석을 위한 매개변수 추정에 있어서도 그 적용성이 검증된바 있다. 본 연구의 목적은 연 최대강수 자료의 빈도해석에 적용되는 확률분포모형들의 매개변수 추정을 위해 Meta-Heuristic Algorithm을 적용하고자 함에 있다. 따라서 본 연구에서는 매개변수 추정을 위한 방법으로 Genetic Algorithm 및 Harmony Search를 적용하였고, 그 결과를 최우도법에 의한 결과와 비교하였다. GEV 분포를 이용하여 Simulation Test를 수행한 결과 Genetic Algorithm을 이용하여 추정된 매개변수들은 최우도법에 의한 결과들과 비교적 유사한 분포를 나타내었으나 과도한 계산시간이 요구되는 것으로 나타났다. 하지만 Harmony Search를 이용하여 추정된 매개변수들은 최우도법에 의한 결과들과 유사한 분포를 나타내었을 뿐만 아니라 계산시간 또한 매우 짧은 것으로 나타났다. 또한 국내 74개소의 강우관측소 자료와 Gamma, Log-normal, GEV 및 Gumbel 분포를 이용한 실증연구에 있어서도 Harmony Search를 이용한 매개변수 추정은 효율적인 매개 변수 추정치를 제공하는 것으로 나타났다.

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A Study on the Geometric Optimization of Truss Structures by Decomposition Method (분할최적화 기법에 의한 트러스 구조물의 형상최적화에 관한 연구)

  • 김성완;이규원
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.29 no.4
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    • pp.73-92
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    • 1987
  • Formulation of the geometric optimization for truss structures based on the elasticity theory turn out to be the nonlinear programming problem which has to deal with the cross-sectional area of the member and the coordinates of its nodes simultaneously. A few techniques have been proposed and adopted for the analysis of this nonlinear programming problem for the time being. These techniques, however, bear some limitations on truss shapes, loading conditions and design criteria for the practical application to real structures. A generalized algorithm for the geometric optimization of the truss structures, which can eliminate the above mentioned limitations, is developed in this study. The algorithm proposed utilizes the two-levels technique. In the first level which consists of two phases, the cross-sectional area of the truss member is optimized by transforming the nonlinear problem into SUMT, and solving SUMT utilizing the modified Newton Raphson method. In the second level, which also consists of two phases the geometric shape is optimized utillzing the unindirectional search technique of the Powell method which make it possible to minimize only the objective functlon. The algorithm proposed in this study is numerically tested for several truss structures with various shapes, loading conditions and design criteria, and compared with the results of the other algorithms to examine its applicability and stability. The numerical comparisons show that the two- levels algorithm proposed in this study is safely applicable to any design criteria, and the convergency rate is relatively fast and stable compared with other iteration methods for the geometric optimization of truss structures. It was found for the result of the shape optimization in this study to be decreased greatly in the weight of truss structures in comparison with the shape optimization of the truss utilizing the algorithm proposed with the other area optimum method.

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A Study on the Estimation of Object's Dimension based on the Vision System Model of Extended Kalman filtering (확장칼만 필터링의 비젼시스템 모델을 이용한 물체 치수 측정에 관한 연구)

  • Jang, W.S.;Ahn, H.C.;Kim, K.S.
    • Journal of the Korean Society for Nondestructive Testing
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    • v.25 no.2
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    • pp.110-116
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    • 2005
  • It is very important to reduce the computational processing time for the application of the vision system in real time such as inspection, the determination of object's dimension and welding etc, because the vision system model involves a lot of measurement data acquired by CCD camera. Also, a lot of computation time is required in estimating the parameters in the vision system model if the iterative batch estimation method such as Newton Raphson is used. Thus, the effective computation method such as the Extended Kalman Filtering(EKF) is required to solve the above problems. The EKF has much advantages in that it takes explicitly into account the measurement uncertainties, and is a simple and efficient recursive procedures. Thus, this study is to develop the EKF algorithm to compute the parameters in the vision system model in real time. This vision system model involves the six parameters to account for the cameras inner and outer parameters. Also the EKF is applied to estimate the object's dimension. Finally, practicality of the estimation scheme of the vision system based on the EKF is verified experimently by performing the estimation of object's dimension.

Evaluation of Two Robot Vision Control Algorithms Developed Based on N-R and EKF Methods for Slender Bar Placement (얇은막대 배치작업에 대한 N-R 과 EKF 방법을 이용하여 개발한 로봇 비젼 제어알고리즘의 평가)

  • Son, Jae Kyung;Jang, Wan Shik;Hong, Sung Mun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.37 no.4
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    • pp.447-459
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    • 2013
  • Many problems need to be solved before vision systems can actually be applied in industry, such as the precision of the kinematics model of the robot control algorithm based on visual information, active compensation of the camera's focal length and orientation during the movement of the robot, and understanding the mapping of the physical 3-D space into 2-D camera coordinates. An algorithm is proposed to enable robot to move actively even if the relative positions between the camera and the robot is unknown. To solve the correction problem, this study proposes vision system model with six camera parameters. To develop the robot vision control algorithm, the N-R and EKF methods are applied to the vision system model. Finally, the position accuracy and processing time of the two algorithms developed based based on the EKF and the N-R methods are compared experimentally by making the robot perform slender bar placement task.

STK Feature Tracking Using BMA for Fast Feature Displacement Convergence (빠른 피쳐변위수렴을 위한 BMA을 이용한 STK 피쳐 추적)

  • Jin, Kyung-Chan;Cho, Jin-Ho
    • Journal of the Korean Institute of Telematics and Electronics S
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    • v.36S no.8
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    • pp.81-87
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    • 1999
  • In general, feature detection and tracking algorithms is classified by EBGM using Garbor-jet, NNC-R and STK algorithm using pixel eigenvalue. In those algorithms, EBGM and NCC-R detect features with feature model, but STK algorithm has a characteristics of an automatic feature selection. In this paper, to solve the initial problem of NR tracking in STK algorithm, we detected features using STK algorithm in modelled feature region and tracked features with NR method. In tracking, to improve the tracking accuracy for features by NR method, we proposed BMA-NR method. We evaluated that BMA-NR method was superior to NBMA-NR in that feature tracking accuracy, since BMA-NR method was able to solve the local minimum problem due to search window size of NR.

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Axisymmetric large deflection analysis of fully and partially loaded shallow spherical shells

  • Altekin, Murat;Yukseler, Receb F.
    • Structural Engineering and Mechanics
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    • v.47 no.4
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    • pp.559-573
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    • 2013
  • Geometrically non-linear axisymmetric bending of a shallow spherical shell with a clamped or a simply supported edge under axisymmetric load was investigated numerically. The partial load was introduced by the Heaviside step function, and the solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for three geometrical parameters. The accuracy of the algorithm was checked by comparing the central deflection, the radial membrane stress at the edge, or the transverse shear force with the solutions of plates and shells in the literature and good agreement was obtained. The main findings of the study can be outlined as follows: (i) If the shell is fully loaded the central deflection of a clamped shell is larger than that of a simply supported shell provided that the shell is not very shallow, (ii) if the shell is partially loaded the central deflection of the shell is sensitive to the parameters of thickness, depth, and partial loading but the influence of the boundary conditions is negligible.

Design 2-Dimensional Digital Filter In Reconstruction Of EIT

  • Kang, Dong-Hoon;Kang, Byung-Chae;Kim, Ji-Hoon;Hwang, Sang-Pil;Kim, Jin-Yeop;Jang, Jae-Duck;Lee, Seung-Ha;Choi, Bong-Yeol
    • 제어로봇시스템학회:학술대회논문집
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    • 2004.08a
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    • pp.36-39
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    • 2004
  • Electrical impedance tomography (EIT) has been suffered from the severe ill-posedness which is caused by the inherent low sensitivity of boundary measurements to any changes of internal resistivity values. So, small noise occur unexpected reconstruction image. Generally in EIT system, if measured voltage includes noise, we can't find object location and resistivity values. In this paper, we propose digital filter for measured voltage in EIT. Newton-Raphson is the most..popular algorithm in EIT, but noise cause to blur image. We use Fourier transform (FT) in order to minimize the noise and design the filter. After filtering, result of reconstruction image is improved better than before filtering.

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Free vibration of thermo-electro-mechanically postbuckled FG-CNTRC beams with geometric imperfections

  • Wu, Helong;Kitipornchai, Sritawat;Yang, Jie
    • Steel and Composite Structures
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    • v.29 no.3
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    • pp.319-332
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    • 2018
  • This paper investigates the free vibration of geometrically imperfect functionally graded car-bon nanotube-reinforced composite (FG-CNTRC) beams that are integrated with two sur-face-bonded piezoelectric layers and subjected to a combined action of a uniform temperature rise, a constant actuator voltage and an in-plane force. The material properties of FG-CNTRCs are assumed to be temperature-dependent and vary continuously across the thick-ness. A generic imperfection function is employed to simulate various possible imperfections with different shapes and locations in the beam. The governing equations that account for the influence of initial geometric imperfection are derived based on the first-order shear deformation theory. The postbuckling configurations of FG-CNTRC hybrid beams are determined by the differential quadrature method combined with the modified Newton-Raphson technique, after which the fundamental frequencies of hybrid beams in the postbuckled state are obtained by a standard eigenvalue algorithm. The effects of CNT distribution pattern and volume fraction, geometric imperfection, thermo-electro-mechanical load, as well as boundary condition are examined in detail through parametric studies. The results show that the fundamental frequency of an imperfect beam is higher than that of its perfect counterpart. The influence of geometric imperfection tends to be much more pronounced around the critical buckling temperature.

Structural analysis for Riser in Floating Type for Upwelling Deep Ocean Water (해양심층수 취수를 위한 취수관의 구조해석)

  • Jeong, Dong-Ho;Kim, Hyeon-Ju;Park, Han-Il
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2003.10a
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    • pp.323-328
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    • 2003
  • A basic design on a flexible riser in a floating type development system for upwelling deep ocean water is presented. In the numerical study, an implicit finite difference algorithm is employed for three-dimensional riser equations. Fluid and geometric non-linearity and bending stiffness are considered and solved by Newton-Raphson iteration. To keep the depth of end point of a flexible and light riser is very important for upwelling deep ocean water in a floating type development system. Weight attached at the end point of the riser in order to keep its intake depth is designed under the strong surface current and the configuration of the riser is predicted. The results of this study can be contributed to the design of the development system in floating type for upwelling deep ocean water.

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Multinomial Logit Framework to Evaluate the Impact of Seating Position on Senior Occupant Injury Severity in Traffic Accidents (고령탑승자의 좌석별 상해정도에 관한 연구)

  • Choi, Jaesung
    • Journal of the Korean Society of Safety
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    • v.32 no.3
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    • pp.141-150
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    • 2017
  • A rapid increase in traffic accidents involving senior vehicle occupants has been an issue in Korea because of the aging of the population occurring at one of the fastest rates in the world; unfortunately, few studies beyond several looking at the effect of senior occupants on the level of accident injury severity can be found in the literature. A Multinomial logit model was estimated with Newton-Raphson algorithm to perform bias-reducing penalized likelihood optimization. Model covariates integral to developing the model were included, but the main focus was on the interaction of seating position and injury to senior vehicle occupants. It was found that the likelihood of an accident resulting in a fatality increased: 2.2 times for the driver seat, 2.7 times for the front passenger seat, and even 6.7 times for the rear seat. A mandatory seatbelt law to be extended to the rear seat needs to pass the assembly as soon as possible, and government, industry, and safety groups should be encouraged to join forces to strongly carry out targeted campaigns for the wearing of seatbelts in all vehicle seats to enhance the safety of senior occupants as well as other occupants who are vulnerable to road traffic accidents.