Convergence Rate of a Quasi-Newton-Raphson Method with Parameter Ortogonality

Lee, Kwan Jeh,Ko, Kwang Yee 高麗大學校 統計硏究所 1997 應用統計 Vol.12 No.-

통계석 추정에서 가장 많이 사용되고 있는 추정량 중의 하나가 최우추성량이다. 그러나, 우도 함수가 복잡한 경우나 모수의 개수가 많은 경우에는 직접 최우추정량을 구할 수가 없디. 이와 같이 경우에, 가장 널리 사용되는 반복법 중의 하나기 Newton-Raphson법이다. 모수가 여러 개인 경우에, Newton-Raphson법에서는 관찰 정보행렬의 역행렬의 계산에 따른 가중한 계산 시간을 요구하는 경우도 있다. 본 논문에서는 모수들의 직교화에 의해서 정보 행렬을 대각 행렬이 되어지도록 모수들을 재 변환하였다. 이러한 모수들간의 직교성을 만족할 경우에는 Newton -Raphson법을 적용하기 용이할뿐만 아니라 계산 시간을 감소시킬 수 있다. 또한, 모수들 중에서 특별한 관심 대상의 모수와 관심의 대상이 아닌 모수들을 장애모수로 구별하여, 이 두 모수간에 직교화를 만족시키면 특정 관심모수의 추정에서 장애의수의 영향을 감소 또는 제거하는 효과에 의해서 보다 효율적인 관심 모수의 추정은 기대할 수 있다. 이와 같이 모수의 직교화에 의한 수정 Newton-Raphson법의 수렴 비율은 본래의 Newton-Raphson법의 수렴 비율과 동일함을 보였으며, 이 때, 직교화에 따른 효율성의 감소는 나타나지 않는다. We consider convergence rate of a version of Newton-Raphson method which has a simpler form than the original Newton-Raphson Method. The first step to implement the method is to reparameterization in order to make the parameter orthogonal, And the second step is to put zeros in the off-diagonal terms of the observed information matrix. Then the suggested method has the same convergence rate as that of the Newton-Raphson method and there is no loss of asymptotic efficiency.

風力驅動 自己勵磁 誘導發電機의 解析 : Newton Raphson法과 正割法의 比較 Comparison of Newton Raphson and secant method

左宗根 濟州大學校工科大學産業技術硏究所 1996 尖端技術硏究所論文集 Vol.7 No.1

The Newton Paphson method and the secant method for the steady state analysis of a wind driven self-excited induction generator are presented and compared in this paper. The nodal admittance method which involves simple algebraic calculations is used for this analysis. Very good agreement between the two numerical methods has been obtained on several load conditions, but it is found that the secant method is better than the Newton Raphson method in the number of iteration and the length of program.

뉴턴랩슨법을 통한 조류해석에서 스코트 변압기의 모델링과 해석

김도훈(DoHun Kim),김인수(Insu Kim) 대한전기학회 2021 전기학회논문지 Vol.70 No.12

Power flow analysis is typically used for power system operation and planning. The Newton-Raphson method among power flow analysis methods is a strong and reliable method. Three-phase transformers indispensable for voltage regulation must be modeled for reliable power system operating and planning. In this paper, we enhance the Newton-Raphson method for analyzing unbalanced power systems, including Scott or T connection transformers. For this purpose, this paper proposes the universal nodal admittance matrix for correct transformer modeling. For verification, the known IEEE test systems are used and the accuracy of the proposed method is verified by comparing the percentage error. The verified transformer modeling method and proposed Newton-Raphson method can contribute to the correct modeling of unbalanced three-phase Scott or T connection transformers so that it can be used for planning and operating power systems, including Scott or T connection transformers.

Newton Raphson Method를 이용한 도파관 안테나 슬롯 파라메터 추출

배민지 한국정보기술학회 2014 한국정보기술학회논문지 Vol. No.

This paper proposes new method (ABCD method) for slot parameters extraction for waveguide antennas which are broad wall series slots. These parameters was extracted by Electromagnetic Wave simulator. Using the slot parameters as initial values, computation of slot parameters for the waveguide antennas are performed using the Newton Raphson method to solve Elliott’s equations. The slot parameters are verified by comparison of ideal values so that make small errors. With the improvement of the computational capability of the computer and Electromagnetic wave simulator, extraction of slot parameters for waveguide antennas can be achieved easily. By this approach, designing slot radiating board can be simple and easy. 본 논문에서는 넓은면 공진타입의 도파관 안테나의 설계를 위한 슬롯 파라메터 추출 방식(ABCD method)을 새롭게 제시하고, 전자기파 해석툴을 이용하여 슬롯파라메터를 추출하는 방법을 제안한다. 도파관 안테나 복사평판 설계 이론으로 Elliott이 제안한 수식을 기반으로 슬롯파라메터를 계산하는 프로그램을 작성하였으며, 비선형방정식의 해를 구하기 위한 수치해석 기법으로 Newton Raphson Method를 사용하였다. 수치해석 프로그램으로 얻은 슬롯 파라메터 해가 원하는 값에 수렴하는지 여부를 오차율로 검증하였다. 본 논문은 향상된 컴퓨터 계산능력과 전자파해석 시뮬레이터를 활용, Elliott의 안테나 설계 이론과 접목하여 프로그램 작성만으로 손쉽게 도파관 안테나의 복사평판 설계할 수 있다는 것에 의미가 있다.

풍력구동 자기여자 유도발전기의 해석 : Newton Raphson법과 정할법의 비교

좌종근 濟州大學校 産業技術硏究所 1996 산업기술연구소논문집 Vol.7 No.1

The Newton Raphson method and the secant method for the steady state analysis of a wind driven self-excited induction generator are presented and compared in this paper. The nodal admittance method which involves simple algebraic calculations is used for this analysis. Very good agreement between the two numerical methods has been obtained on several load conditions, but it is found that the secant method is better than the Newton Raphson method in the number of iteration and the length of program.

Improved Method for Shape Finding of Long-Span Suspension Bridges

Chaolin Song,Ru-Cheng Xiao,Bin Sun 한국강구조학회 2020 International Journal of Steel Structures Vol.20 No.1

In recent years, many long-span suspension bridges have been constructed and the shape fi nding is a key issue in the design stage. This paper presents an improved shape-fi nding method which can overcome the shortcomings of the previous shapefi nding method. The improved method is based on the common fi nite element analysis and convenient to be widely used in normal engineering practice. The main step can be summarized as follows. First, the vertical force components of the hangers are determined according to the construction method. Second, in the midspan, the initial equilibrium state of the main cable is calculated iteratively based on the Newton–Raphson method. Third, in the side span, the shape fi nding for the main cable is executed according to the horizontal force equilibrium of the pylon. Finally, the full-bridge model is obtained and examined carefully. The improved method is demonstrated through one suspension bridge with a planar cable system and one with a spatial cable system. The results show that the improved method is more effi cient and accurate compared with the previous shape-fi nding method.

Application of Cubic Spline on Large Deformation Analysis of Structures

H. Saffari,S. Shojaee,S. Rostami,M. Malekinejad 한국강구조학회 2014 International Journal of Steel Structures Vol.14 No.1

This paper presents a new method for non-linear analysis of structures using an iterative method originated from quadraturerule based on spline function. At first, the above-mentioned method is developed for solving systems of non-linear algebraicequations and then it is implemented on structural problems. In this procedure like many other state of the art methods, thenon-linear equations are linearized by evaluating the non-linear terms with the known solution from the preceding iteration. Theproposed method is constructed as a predictor–corrector one, must frequently taking Newton's method in the first iteration. Forthis method, a simple step-by-step algorithm was implemented and presented to calculate non-linear analysis of structures. Itshould be noted that currently, the proposed method is incapable of tracing the equilibrium curve after passing the limit points. The presented method incorporates the known information at each stage of the loading process to determine the subsequentunknown variables. Compared with the classic Newton–Raphson algorithm and a recently proposed two-point method, it offersa strategy that can be deployed to reduce the number of the iterations to trace the equilibrium path in non-linear analysis ofstructures.

Newton-Raphson법 기반의 적응 망각율을 갖는 RLS 알고리즘에 의한 원격센서시스템의 시변파라메타 추정

김경엽(Kyung-Yup Kim),이준탁(Joon-Tark Lee) 한국지능시스템학회 2007 한국지능시스템학회 학술발표 논문집 Vol.17 No.1

This paper deals with RLS algorithm using Newton-Raphson method based adaptive forgetting factor for a passive telemetry RF sensor system in order to estimate the time variant parameter to be included in RF sensor model. For this estimation with RLS algorithm, phasor typed RF sensor system modelled with inductive coupling principle is used. Instead of applying constant forgetting factor to estimate time variant parameter, the adaptive forgetting factor based on Newton-Raphson method is applied to RLS algorithm without constant forgetting factor to be determined intuitively. Finally, we provide numerical examples to evaluate the feasibility and generality of the proposed method in this paper.

A New Concept of Power Flow Analysis

Hyungchul Kim,Nader Samann,Donggeun Shin,Byeonghun Ko,Gilsoo Jang,Junmin Cha 대한전기학회 2007 Journal of Electrical Engineering & Technology Vol.2 No.3

The solution of the power flow is one of the most important problems in electrical power systems. These traditional methods such as Gauss-Seidel method and Newton-Raphson (NR) method have had drawbacks up to now such as initial values, abnormal operating solutions and divergences in heavy loads. In order to overcome theses problems, the power flow solution incorporating genetic algorithm (GA) is introduced in this paper. General operator of genetic algorithm, arithmetic crossover, and non-uniform mutation operator of GA are suggested to solve the power flow problem. While abnormal solution cannot be obtained by a NR method, multiple power flow solution can be obtained by a GA method. With a heavy load, both normal solution and abnormal solution can be obtained by a proposed method. In this paper, a floating number representation instead of the binary number representation is introduced for accuracy. Simulation results have been compared with traditional methods.

A New Concept of Power Flow Analysis

Kim, Hyung-Chul,Samann, Nader,Shin, Dong-Geun,Ko, Byeong-Hun,Jang, Gil-Soo,Cha, Jun-Min The Korean Institute of Electrical Engineers 2007 Journal of Electrical Engineering & Technology Vol.2 No.3

The solution of the power flow is one of the most important problems in electrical power systems. These traditional methods such as Gauss-Seidel method and Newton-Raphson (NR) method have had drawbacks up to now such as initial values, abnormal operating solutions and divergences in heavy loads. In order to overcome theses problems, the power flow solution incorporating genetic algorithm (GA) is introduced in this paper. General operator of genetic algorithm, arithmetic crossover, and non-uniform mutation operator of GA are suggested to solve the power flow problem. While abnormal solution cannot be obtained by a NR method, multiple power flow solution can be obtained by a GA method. With a heavy load, both normal solution and abnormal solution can be obtained by a proposed method. In this paper, a floating number representation instead of the binary number representation is introduced for accuracy. Simulation results have been compared with traditional methods.