• Title, Summary, Keyword: nonlinear system of polynomials

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THE SENSITIVITY OF STRUCTURAL RESPONSE USING FINITE ELEMENTS IN TIME

  • Park, Sungho;Kim, Seung-Jo
    • Journal of Theoretical and Applied Mechanics
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    • v.3 no.1
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    • pp.66-80
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    • 2002
  • The bilinear formulation proposed earlier by Peters and Izadpanah to develop finite elements in time to solve undamped linear systems, Is extended (and found to be readily amenable) to develop time finite elements to obtain transient responses of both linear and nonlinear, and damped and undamped systems. The formulation Is used in the h-, p- and hp-versions. The resulting linear and nonlinear algebraic equations are differentiated to obtain the first- and second-order sensitivities of the transient response with respect to various system parameters. The present developments were tested on a series of linear and nonlinear examples and were found to yield, when compared with results obtained using other methods, excellent results for both the transient response and Its sensitivity to system parameters. Mostly. the results were obtained using the Legendre polynomials as basis functions, though. in some cases other orthogonal polynomials namely. the Hermite. the Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of the time finite element method, and the one often overlooked in its past applications, is the ease In which the sensitivity of the transient response with respect to various system parameters can be obtained. The results of sensitivity analysis can be used for approximate schemes for efficient solution of design optimization problems. Also. the results can be applied to gradient-based parameter identification schemes.

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A multi-modal neural network using Chebyschev polynomials

  • Ikuo Yoshihara;Tomoyuki Nakagawa;Moritoshi Yasunaga;Abe, Ken-ichi
    • 제어로봇시스템학회:학술대회논문집
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    • pp.250-253
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    • 1998
  • This paper presents a multi-modal neural network composed of a preprocessing module and a multi-layer neural network module in order to enhance the nonlinear characteristics of neural network. The former module is based on spectral method using Chebyschev polynomials and transforms input data into spectra. The latter module identifies the system using the spectra generated by the preprocessing module. The omnibus numerical experiments show that the method is applicable to many a nonlinear dynamic system in the real world, and that preprocessing using Chebyschev polynomials reduces the number of neurons required for the multi-layer neural network.

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SynRM Driving CVT System Using an ARGOPNN with MPSO Control System

  • Lin, Chih-Hong;Chang, Kuo-Tsai
    • Journal of Power Electronics
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    • v.19 no.3
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    • pp.771-783
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    • 2019
  • Due to nonlinear-synthetic uncertainty including the total unknown nonlinear load torque, the total parameter variation and the fixed load torque, a synchronous reluctance motor (SynRM) driving a continuously variable transmission (CVT) system causes a lot of nonlinear effects. Linear control methods make it hard to achieve good control performance. To increase the control performance and reduce the influence of nonlinear time-synthetic uncertainty, an admixed recurrent Gegenbauer orthogonal polynomials neural network (ARGOPNN) with a modified particle swarm optimization (MPSO) control system is proposed to achieve better control performance. The ARGOPNN with a MPSO control system is composed of an observer controller, a recurrent Gegenbauer orthogonal polynomial neural network (RGOPNN) controller and a remunerated controller. To insure the stability of the control system, the RGOPNN controller with an adaptive law and the remunerated controller with a reckoned law are derived according to the Lyapunov stability theorem. In addition, the two learning rates of the weights in the RGOPNN are regulating by using the MPSO algorithm to enhance convergence. Finally, three types of experimental results with comparative studies are presented to confirm the usefulness of the proposed ARGOPNN with a MPSO control system.

An Approach to a Formal Linearization toy Time-variant Nonlinear Systems using Polynomial Approximations

  • Komatsu, Kazuo;Takata, Hitoshi
    • 제어로봇시스템학회:학술대회논문집
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    • pp.52.2-52
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    • 2002
  • In this paper we consider an approach to a formal linearization for time-variant nonlinear systems. A time-variant nonlinear sysetm is assumed to be described by a time-variant nonlinear differential equation. For this system, we introduce a coordinate transformation function which is composed of the Chebyshev polynomials. Using Chebyshev expansion to the state variable and Laguerre expansion to the time variable, the time-variant nonlinear sysetm is transformed into the time-variant linear one with respect to the above transformation function. As an application, we synthesize a time-variant nonlinear observer. Numerical experiments are included to demonstrate the validity of...

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GEGENBAUER WAVELETS OPERATIONAL MATRIX METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS

  • UR REHMAN, MUJEEB;SAEED, UMER
    • Journal of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1069-1096
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    • 2015
  • In this article we introduce a numerical method, named Gegenbauer wavelets method, which is derived from conventional Gegenbauer polynomials, for solving fractional initial and boundary value problems. The operational matrices are derived and utilized to reduce the linear fractional differential equation to a system of algebraic equations. We perform the convergence analysis for the Gegenbauer wavelets method. We also combine Gegenbauer wavelets operational matrix method with quasilinearization technique for solving fractional nonlinear differential equation. Quasilinearization technique is used to discretize the nonlinear fractional ordinary differential equation and then the Gegenbauer wavelet method is applied to discretized fractional ordinary differential equations. In each iteration of quasilinearization technique, solution is updated by the Gegenbauer wavelet method. Numerical examples are provided to illustrate the efficiency and accuracy of the methods.

Nonlinear Analysis of IPS System using the multi-noded cable element (다절점 케이블요소를 이용한 IPS 시스템의 비선형 해석)

  • Lee Jun-Seok;Kim Moon-Young;Han Man-Yop;Kim Sung-Bo;Kim Nak-Kyung
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.623-630
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    • 2006
  • In this paper, a geometric nonlinear analysis procedure of beam-column element including multi-noded cable element is presented. For this, first a stiffness matrix about beam-column element which considers the second effect of initial force supposing the curved shape at each time step with Hermitian polynomials as the shape function is derived and second, tangent stiffness matrix about multi-noded cable element being too. To verify geometric nonlinearity of this newly developed multi-noded cable-truss element, IPS(Innovative Prestressed Support) system using this theory is analysed by geometric nonlinear method and the results are compared with those by linear analysis.

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Historical analysis of System of Equations-Focused on Resultant (연립방정식 풀이의 역사발생적 고찰-종결식을 중심으로)

  • Choi, Eun Mi
    • Journal for History of Mathematics
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    • v.26 no.2_3
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    • pp.149-161
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    • 2013
  • The history of finding solutions of linear equations went back to some thousand years ago, and has been steadily developed to solve systems of higher degree polynomials. The method to eliminate variables came into use around the 17th and 18th century. This technique has been extended to the resultant theory that was laid in the 19th century by outstanding mathematicians as Euler, Sylvester, and B$\acute{e}$zout. In this paper we discuss the historical reflection about the development of solving system of polynomials. We add a special emphasis on E. B$\acute{e}$zout who gave the first account on the resultant which is a generalization of discriminant and Gauss elimination method.

A New Method of Finding Real Roots of Nonlinear System Using Extended Fixed Point Iterations (확장된 고정점이론을 이용한 비선형시스템의 근을 구하는 방법)

  • Kim, Sung-Soo;Kim, Ji-Soo
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.67 no.2
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    • pp.277-284
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    • 2018
  • In this paper, a new numerical method of finding the roots of a nonlinear system is proposed, which extends the conventional fixed point iterative method by relaxing the constraints on it. The proposed method determines the real valued roots and expands the convergence region by relaxing the constraints on the conventional fixed point iterative method, which transforms the diverging root searching iterations into the converging iterations by employing the metric induced by the geometrical characteristics of a polynomial. A metric is set to measure the distance between a point of a real-valued function and its corresponding image point of its inverse function. The proposed scheme provides the convenience in finding not only the real roots of polynomials but also the roots of the nonlinear systems in the various application areas of science and engineering.

Performance improvement of the high speed mobile communication by the predistorter (전치왜곡기로 인한 고속이동통신의 성능향상기법)

  • Lee, Kang-Mi;Shin, Duck-Ho;Kim, Bak-Hyun;Lee, Jun-Ho
    • Proceedings of the IEEK Conference
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    • pp.173-174
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    • 2006
  • High power amplifier (HPA), which is used in transmitter of wireless communication systems, usually works in near saturation point in order to achieve maximum efficiency. In this region, HPA can introduce undesirable nonlinear effects. In this paper, we present a polynomial modeling method for efficient techniques to compensate for nonlinear distortion introduced by nonlinear HPA. Proposed polynomial predistorter inverses actual amplifier. Namely, we derive polynomials of amplifiers from analytical method and the electrical parameters in the data sheet of an actual amplifier and then can derive polynomial predistorter by inversing them. It is an effective and a simple method to compensate nonlinear distortion. SSPA(Solid-state power amplifier) is considered. We also analyze the effects of predistortion on the SER performance of communication system with 16-QAM modulation format. The results have shown the efficiency of this model.

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Real-time Projectile Motion Trajectory Estimation Considering Air Resistance of Obliquely Thrown Object Using Recursive Least Squares Estimation (비스듬히 던진 물체의 공기저항을 고려한 재귀 최소 자승법 기반 실시간 포물선 운동 궤적 추정)

  • Jeong, Sangyoon;Chwa, Dongkyoung
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.67 no.3
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    • pp.427-432
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    • 2018
  • This paper uses a recursive least squares method to estimate the projectile motion trajectory of an object in real time. The equations of motion of the object are obtained considering the air resistance which occurs in the actual experiment environment. Because these equations consider air resistance, parameter estimation of nonlinear terms is required. However, nonlinear recursive least squares estimation is not suitable for estimating trajectory of projectile in that it requires a lot of computation time. Therefore, parameter estimation for real-time trajectory prediction is performed by recursive least square estimation after using Taylor series expansion to approximate nonlinear terms to polynomials. The proposed method is verified through experiments by using VICON Bonita motion capture system which can get three dimensional coordinates of projectile. The results indicate that proposed method is more accurate than linear Kalman filter method based on the equations of motion of projectile that does not consider air resistance.