Frozen Landweber Iteration for Nonlinear Ill-Posed Problems
Institute of Scientific and Technical Information of China (English)
J.Xu; B.Han; L.Li
2007-01-01
In this paper we propose a modification of the Landweber iteration termed frozen Landweber iteration for nonlinear ill-posed problems.A convergence analysis for this iteration is presented.The numerical performance of this frozen Landweber iteration for a nonlinear Hammerstein integral equation is compared with that of the Landweber iteration.We obtain a shorter running time of the frozen Landweber iteration based on the same convergence accuracy.
SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS
Desmal, Abdulla
2015-07-29
A scheme for efficiently solving the nonlinear electromagnetic inverse scattering problem on sparse investigation domains is described. The proposed scheme reconstructs the (complex) dielectric permittivity of an investigation domain from fields measured away from the domain itself. Least-squares data misfit between the computed scattered fields, which are expressed as a nonlinear function of the permittivity, and the measured fields is constrained by the L0/L1-norm of the solution. The resulting minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two-dimensional problems, where the ``measured\\'\\' fields are synthetically generated or obtained from actual experiments. These numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed scheme in reconstructing sparse profiles with high permittivity values.
Landweber-Kaczmarz method in Banach spaces with inexact inner solvers
Jin, Qinian
2016-10-01
In recent years the Landweber-Kaczmarz method has been proposed for solving nonlinear ill-posed inverse problems in Banach spaces using general convex penalty functions. The implementation of this method involves solving a (nonsmooth) convex minimization problem at each iteration step and the existing theory requires its exact resolution which in general is impossible in practical applications. In this paper we propose a version of the Landweber-Kaczmarz method in Banach spaces in which the minimization problem involved in each iteration step is solved inexactly. Based on the \\varepsilon -subdifferential calculus we give a convergence analysis of our method. Furthermore, using Nesterov's strategy, we propose a possible accelerated version of the Landweber-Kaczmarz method. Numerical results on computed tomography and parameter identification in partial differential equations are provided to support our theoretical results and to demonstrate our accelerated method.
Landweber Iterative Methods for Angle-limited Image Reconstruction
Institute of Scientific and Technical Information of China (English)
Gang-rong Qu; Ming Jiang
2009-01-01
We introduce a general itcrative scheme for angle-limited image reconstruction based on Landwe-ber's method. We derive a representation formula for this scheme and consequently establish its convergence conditions. Our results suggest certain relaxation strategies for an accelerated convergcnce for angle-limited im-age reconstruction in L2-norm comparing with alternative projection methods. The convolution-backprojection algorithm is given for this iterative process.
A sparse electromagnetic imaging scheme using nonlinear landweber iterations
Desmal, Abdulla
2015-10-26
Development and use of electromagnetic inverse scattering techniques for imagining sparse domains have been on the rise following the recent advancements in solving sparse optimization problems. Existing techniques rely on iteratively converting the nonlinear forward scattering operator into a sequence of linear ill-posed operations (for example using the Born iterative method) and applying sparsity constraints to the linear minimization problem of each iteration through the use of L0/L1-norm penalty term (A. Desmal and H. Bagci, IEEE Trans. Antennas Propag, 7, 3878–3884, 2014, and IEEE Trans. Geosci. Remote Sens., 3, 532–536, 2015). It has been shown that these techniques produce more accurate and sharper images than their counterparts which solve a minimization problem constrained with smoothness promoting L2-norm penalty term. But these existing techniques are only applicable to investigation domains involving weak scatterers because the linearization process breaks down for high values of dielectric permittivity.
On Landweber-Kaczmarz methods for regularizing systems of ill-posed equations in Banach spaces
Leitão, A.; Marques Alves, M.
2012-10-01
In this paper, iterative regularization methods of Landweber-Kaczmarz type are considered for solving systems of ill-posed equations modeled (finitely many) by operators acting between Banach spaces. Using assumptions of uniform convexity and smoothness on the parameter space, we are able to prove a monotony result for the proposed method, as well as to establish convergence (for exact data) and stability results (in the noisy data case).
Modified Landweber Algorithm for Solving the Inverse Problem in EIT
Institute of Scientific and Technical Information of China (English)
WANGChao; WANGHuaxiang
2005-01-01
This paper analyses the Landweber iteration method and demonstrates that Landweber method is a modified of the generalized inverse constructed using the iteration solution. The phenomenon is explained that the image reconstructed using Landweber iteration algorithm through a large numbers of iteration steps is similar tothe minimum norm solution of the generalized inverse. A new reconstruction algorithm called the modified Landweber method is proposed, which divides the image reconstruction process into two steps， off-line pre-iteration and on-line one-step reconstruction. The reconstruction speed is markedly improved.
Vogelgesang, Jonas; Schorr, Christian
2016-12-01
We present a semi-discrete Landweber-Kaczmarz method for solving linear ill-posed problems and its application to Cone Beam tomography and laminography. Using a basis function-type discretization in the image domain, we derive a semi-discrete model of the underlying scanning system. Based on this model, the proposed method provides an approximate solution of the reconstruction problem, i.e. reconstructing the density function of a given object from its projections, in suitable subspaces equipped with basis function-dependent weights. This approach intuitively allows the incorporation of additional information about the inspected object leading to a more accurate model of the X-rays through the object. Also, physical conditions of the scanning geometry, like flat detectors in computerized tomography as used in non-destructive testing applications as well as non-regular scanning curves e.g. appearing in computed laminography (CL) applications, are directly taken into account during the modeling process. Finally, numerical experiments of a typical CL application in three dimensions are provided to verify the proposed method. The introduction of geometric prior information leads to a significantly increased image quality and superior reconstructions compared to standard iterative methods.
Iterative regularization methods for nonlinear ill-posed problems
Scherzer, Otmar; Kaltenbacher, Barbara
2008-01-01
Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.
Landweber iterative regularization for nearfield acoustic holography
Institute of Scientific and Technical Information of China (English)
BI Chuanxing; CHEN Xinzhao; ZHOU Rong; CHEN Jian
2006-01-01
On the basis of the distributed source boundary point method (DSBPM)-based nearfield acoustic holography (NAH), Landweber iterative regularization method is proposed to stabilize the NAH reconstruction process, control the influence of measurement errors on the reconstructed results and ensure the validity of the reconstructed results. And a new method, the auxiliary surface method, is proposed to determine the optimal iterative number for optimizing the regularization effect. Here, the optimal number is determined by minimizing the relative error between the calculated pressure on the auxiliary surface corresponding to each iterative number and the measured pressure. An experiment on a speaker is investigated to demonstrate the high sensitivity of the reconstructed results to measurement errors and to validate the chosen method of the optimal iterative number and the Landweber iterative regularization method for controlling the influence of measurement errors on the reconstructed results.
Enhanced Landweber algorithm via Bregman iterations for bioluminescence tomography
Xia, Yi; Zhang, Meng
2014-09-01
Bioluminescence tomography (BLT) is an important optical molecular imaging modality aimed at visualizing physiological and pathological processes at cellular and molecular levels. While the forward process of light propagation is described by the diffusion approximation to radiative transfer equation, BLT is the inverse problem to reconstruct the 3D localization and quantification of internal bioluminescent sources distribution. Due to the inherent ill-posedness of the BLT problem, regularization is generally indispensable to obtain more favorable reconstruction. In particular, total variation (TV) regularization is known to be effective for piecewise-constant source distribution which can permit sharp discontinuities and preserve edges. However, total variation regularization generally suffers from the unsatisfactory staircasing effect. In this work, we introduce the Bregman iterative regularization to alleviate this degeneration and enhance the numerical reconstruction of BLT. Based on the existing Landweber method (LM), we put forward the Bregman-LM-TV algorithm for BLT. Numerical experiments are carried out and preliminary simulation results are reported to evaluate the proposed algorithms. It is found that Bregman-LM-TV can significantly outperform the individual Landweber method for BLT when the source distribution is piecewise-constant.
A preconditioned inexact newton method for nonlinear sparse electromagnetic imaging
Desmal, Abdulla
2015-03-01
A nonlinear inversion scheme for the electromagnetic microwave imaging of domains with sparse content is proposed. Scattering equations are constructed using a contrast-source (CS) formulation. The proposed method uses an inexact Newton (IN) scheme to tackle the nonlinearity of these equations. At every IN iteration, a system of equations, which involves the Frechet derivative (FD) matrix of the CS operator, is solved for the IN step. A sparsity constraint is enforced on the solution via thresholded Landweber iterations, and the convergence is significantly increased using a preconditioner that levels the FD matrix\\'s singular values associated with contrast and equivalent currents. To increase the accuracy, the weight of the regularization\\'s penalty term is reduced during the IN iterations consistently with the scheme\\'s quadratic convergence. At the end of each IN iteration, an additional thresholding, which removes small \\'ripples\\' that are produced by the IN step, is applied to maintain the solution\\'s sparsity. Numerical results demonstrate the applicability of the proposed method in recovering sparse and discontinuous dielectric profiles with high contrast values.
Improved nonlinear prediction method
Adenan, Nur Hamiza; Md Noorani, Mohd Salmi
2014-06-01
The analysis and prediction of time series data have been addressed by researchers. Many techniques have been developed to be applied in various areas, such as weather forecasting, financial markets and hydrological phenomena involving data that are contaminated by noise. Therefore, various techniques to improve the method have been introduced to analyze and predict time series data. In respect of the importance of analysis and the accuracy of the prediction result, a study was undertaken to test the effectiveness of the improved nonlinear prediction method for data that contain noise. The improved nonlinear prediction method involves the formation of composite serial data based on the successive differences of the time series. Then, the phase space reconstruction was performed on the composite data (one-dimensional) to reconstruct a number of space dimensions. Finally the local linear approximation method was employed to make a prediction based on the phase space. This improved method was tested with data series Logistics that contain 0%, 5%, 10%, 20% and 30% of noise. The results show that by using the improved method, the predictions were found to be in close agreement with the observed ones. The correlation coefficient was close to one when the improved method was applied on data with up to 10% noise. Thus, an improvement to analyze data with noise without involving any noise reduction method was introduced to predict the time series data.
Sparse electromagnetic imaging using nonlinear iterative shrinkage thresholding
Desmal, Abdulla
2015-04-13
A sparse nonlinear electromagnetic imaging scheme is proposed for reconstructing dielectric contrast of investigation domains from measured fields. The proposed approach constructs the optimization problem by introducing the sparsity constraint to the data misfit between the scattered fields expressed as a nonlinear function of the contrast and the measured fields and solves it using the nonlinear iterative shrinkage thresholding algorithm. The thresholding is applied to the result of every nonlinear Landweber iteration to enforce the sparsity constraint. Numerical results demonstrate the accuracy and efficiency of the proposed method in reconstructing sparse dielectric profiles.
Nonlinear Multiantenna Detection Methods
Directory of Open Access Journals (Sweden)
Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
Gorban, A. N.; Karlin, I.V.
2003-01-01
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation, Phenomenology and Quasi-chemical representation of the Boltzmann equation, Kinetic models, Discrete velocity models, Direct simulation, Lattice Gas and Lattice Boltzmann models, Minimal Boltzmann models for flows at low Knudsen number, Other kinetic equati...
A filtered backprojection algorithm with characteristics of the iterative landweber algorithm
L. Zeng, Gengsheng
2012-01-01
Purpose: In order to eventually develop an analytical algorithm with noise characteristics of an iterative algorithm, this technical note develops a window function for the filtered backprojection (FBP) algorithm in tomography that behaves as an iterative Landweber algorithm.
Nonlinear programming analysis and methods
Avriel, Mordecai
2012-01-01
This text provides an excellent bridge between principal theories and concepts and their practical implementation. Topics include convex programming, duality, generalized convexity, analysis of selected nonlinear programs, techniques for numerical solutions, and unconstrained optimization methods.
Nonlinear programming analysis and methods
Avriel, Mordecai
2003-01-01
Comprehensive and complete, this overview provides a single-volume treatment of key algorithms and theories. The author provides clear explanations of all theoretical aspects, with rigorous proof of most results. The two-part treatment begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs. The second part concerns techniques for numerical solutions and unconstrained optimization methods, and it presents commonly used algorithms for constrained nonlinear optimization problems. This g
V S, Unni; Mishra, Deepak; Subrahmanyam, G R K S
2016-12-01
The need for image fusion in current image processing systems is increasing mainly due to the increased number and variety of image acquisition techniques. Image fusion is the process of combining substantial information from several sensors using mathematical techniques in order to create a single composite image that will be more comprehensive and thus more useful for a human operator or other computer vision tasks. This paper presents a new approach to multifocus image fusion based on sparse signal representation. Block-based compressive sensing integrated with a projection-driven compressive sensing (CS) recovery that encourages sparsity in the wavelet domain is used as a method to get the focused image from a set of out-of-focus images. Compression is achieved during the image acquisition process using a block compressive sensing method. An adaptive thresholding technique within the smoothed projected Landweber recovery process reconstructs high-resolution focused images from low-dimensional CS measurements of out-of-focus images. Discrete wavelet transform and dual-tree complex wavelet transform are used as the sparsifying basis for the proposed fusion. The main finding lies in the fact that sparsification enables a better selection of the fusion coefficients and hence better fusion. A Laplacian mixture model fit is done in the wavelet domain and estimation of the probability density function (pdf) parameters by expectation maximization leads us to the proper selection of the coefficients of the fused image. Using the proposed method compared with the fusion scheme without employing the projected Landweber (PL) scheme and the other existing CS-based fusion approaches, it is observed that with fewer samples itself, the proposed method outperforms other approaches.
Statistical methods in nonlinear dynamics
Indian Academy of Sciences (India)
K P N Murthy; R Harish; S V M Satyanarayana
2005-03-01
Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical methods employed in the study of deterministic and stochastic dynamical systems. These include power spectral analysis and aliasing, extreme value statistics and order statistics, recurrence time statistics, the characterization of intermittency in the Sinai disorder problem, random walk analysis of diffusion in the chaotic pendulum, and long-range correlations in stochastic sequences of symbols.
Nonlinear structural analysis using integrated force method
Indian Academy of Sciences (India)
N R B Krishnam Raju; J Nagabhushanam
2000-08-01
Though the use of the integrated force method for linear investigations is well-recognised, no efforts were made to extend this method to nonlinear structural analysis. This paper presents the attempts to use this method for analysing nonlinear structures. General formulation of nonlinear structural analysis is given. Typically highly nonlinear bench-mark problems are considered. The characteristic matrices of the elements used in these problems are developed and later these structures are analysed. The results of the analysis are compared with the results of the displacement method. It has been demonstrated that the integrated force method is equally viable and efficient as compared to the displacement method.
Some geometrical iteration methods for nonlinear equations
Institute of Scientific and Technical Information of China (English)
LU Xing-jiang; QIAN Chun
2008-01-01
This paper describes geometrical essentials of some iteration methods (e.g. Newton iteration,secant line method,etc.) for solving nonlinear equations and advances some geomet-rical methods of iteration that are flexible and efficient.
Convergence of some asynchronous nonlinear multisplitting methods
Szyld, Daniel B.; Xu, Jian-Jun
2000-09-01
Frommer's nonlinear multisplitting methods for solving nonlinear systems of equations are extended to the asynchronous setting. Block methods are extended to include overlap as well. Several specific cases are discussed. Sufficient conditions to guarantee their local convergence are given. A numerical example is presented illustrating the performance of the new approach.
TAYLOR EXPANSION METHOD FOR NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
HE Yin-nian
2005-01-01
A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0-th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1-st order modified Taylor expansion method. Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example,namely, the two-dimensional Navier-Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.
ACCELERATION METHODS OF NONLINEAR ITERATION FOR NONLINEAR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
Guang-wei Yuan; Xu-deng Hang
2006-01-01
This paper discusses the accelerating iterative methods for solving the implicit scheme of nonlinear parabolic equations. Two new nonlinear iterative methods named by the implicit-explicit quasi-Newton (IEQN) method and the derivative free implicit-explicit quasi-Newton (DFIEQN) method are introduced, in which the resulting linear equations from the linearization can preserve the parabolic characteristics of the original partial differential equations. It is proved that the iterative sequence of the iteration method can converge to the solution of the implicit scheme quadratically. Moreover, compared with the Jacobian Free Newton-Krylov (JFNK) method, the DFIEQN method has some advantages, e.g., its implementation is easy, and it gives a linear algebraic system with an explicit coefficient matrix, so that the linear (inner) iteration is not restricted to the Krylov method. Computational results by the IEQN, DFIEQN, JFNK and Picard iteration meth-ods are presented in confirmation of the theory and comparison of the performance of these methods.
Control methods for localization of nonlinear waves
Porubov, Alexey; Andrievsky, Boris
2017-03-01
A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions. This article is part of the themed issue 'Horizons of cybernetical physics'.
Iterative total variation schemes for nonlinear inverse problems
Bachmayr, Markus; Burger, Martin
2009-10-01
In this paper we discuss the construction, analysis and implementation of iterative schemes for the solution of inverse problems based on total variation regularization. Via different approximations of the nonlinearity we derive three different schemes resembling three well-known methods for nonlinear inverse problems in Hilbert spaces, namely iterated Tikhonov, Levenberg-Marquardt and Landweber. These methods can be set up such that all arising subproblems are convex optimization problems, analogous to those appearing in image denoising or deblurring. We provide a detailed convergence analysis and appropriate stopping rules in the presence of data noise. Moreover, we discuss the implementation of the schemes and the application to distributed parameter estimation in elliptic partial differential equations.
LINEARIZATION AND CORRECTION METHOD FOR NONLINEAR PROBLEMS
Institute of Scientific and Technical Information of China (English)
何吉欢
2002-01-01
A new perturbation-like technique called linearization and correction method is proposed. Contrary to the traditional perturbation techniques, the present theory does not assume that the solution is expressed in the form of a power series of small parameter. To obtain an asymptotic solution of nonlinear system, the technique first searched for a solution for the linearized system, then a correction was added to the linearized solution. So the obtained results are uniformly valid for both weakly and strongly nonlinear equations.
Method for conducting nonlinear electrochemical impedance spectroscopy
Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.
2015-06-02
A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.
Method for conducting nonlinear electrochemical impedance spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.
2015-06-02
A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.
Advances in iterative methods for nonlinear equations
Busquier, Sonia
2016-01-01
This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations...
Entropy viscosity method for nonlinear conservation laws
Guermond, Jean-Luc
2011-05-01
A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.
Numerical methods for nonlinear partial differential equations
Bartels, Sören
2015-01-01
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Monotone method for nonlinear nonlocal hyperbolic problems
Directory of Open Access Journals (Sweden)
Azmy S. Ackleh
2003-02-01
Full Text Available We present recent results concerning the application of the monotone method for studying existence and uniqueness of solutions to general first-order nonlinear nonlocal hyperbolic problems. The limitations of comparison principles for such nonlocal problems are discussed. To overcome these limitations, we introduce new definitions for upper and lower solutions.
Review of Nonlinear Methods and Modelling
Borg, F G
2005-01-01
The first part of this Review describes a few of the main methods that have been employed in non-linear time series analysis with special reference to biological applications (biomechanics). The second part treats the physical basis of posturogram data (human balance) and EMG (electromyography, a measure of muscle activity).
Nonlinear system compound inverse control method
Institute of Scientific and Technical Information of China (English)
Yan ZHANG; Zengqiang CHEN; Peng YANG; Zhuzhi YUAN
2005-01-01
A compound neural network is utilized to identify the dynamic nonlinear system.This network is composed of two parts: one is a linear neural network,and the other is a recurrent neural network.Based on the inverse theory a compound inverse control method is proposed.The controller has also two parts:a linear controller and a nonlinear neural network controller.The stability condition of the closed-loop neural network-based compound inverse control system is demonstrated based on the Lyapunov theory.Simulation studies have shown that this scheme is simple and has good control accuracy and robustness.
Multigrid Methods for Nonlinear Problems: An Overview
Energy Technology Data Exchange (ETDEWEB)
Henson, V E
2002-12-23
Since their early application to elliptic partial differential equations, multigrid methods have been applied successfully to a large and growing class of problems, from elasticity and computational fluid dynamics to geodetics and molecular structures. Classical multigrid begins with a two-grid process. First, iterative relaxation is applied, whose effect is to smooth the error. Then a coarse-grid correction is applied, in which the smooth error is determined on a coarser grid. This error is interpolated to the fine grid and used to correct the fine-grid approximation. Applying this method recursively to solve the coarse-grid problem leads to multigrid. The coarse-grid correction works because the residual equation is linear. But this is not the case for nonlinear problems, and different strategies must be employed. In this presentation we describe how to apply multigrid to nonlinear problems. There are two basic approaches. The first is to apply a linearization scheme, such as the Newton's method, and to employ multigrid for the solution of the Jacobian system in each iteration. The second is to apply multigrid directly to the nonlinear problem by employing the so-called Full Approximation Scheme (FAS). In FAS a nonlinear iteration is applied to smooth the error. The full equation is solved on the coarse grid, after which the coarse-grid error is extracted from the solution. This correction is then interpolated and applied to the fine grid approximation. We describe these methods in detail, and present numerical experiments that indicate the efficacy of them.
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Directory of Open Access Journals (Sweden)
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
Nonlinear ordinary differential equations analytical approximation and numerical methods
Hermann, Martin
2016-01-01
The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...
A NUMERICAL METHOD FOR NONLINEAR WATER WAVES
Institute of Scientific and Technical Information of China (English)
ZHAO Xi-zeng; SUN Zhao-chen; LIANG Shu-xiu; HU Chang-hong
2009-01-01
This article presents a numerical method for modeling nonlinear water waves based on the High Order Spectral (HOS) method proposed by Dommermuth and Yue and West et al., involving Taylor expansion of the Dirichlet problem and the Fast Fourier Transform (FFT) algorithm. The validation and efficiency of the numerical scheme is illustrated by a number of case studies on wave and wave train configuration including the evolution of fifth-order Stokes waves, wave dispersive focusing and the instability of Stokes wave with finite slope. The results agree well with those obtained by other studies.
Nonlinear modal methods for crack localization
Sutin, Alexander; Ostrovsky, Lev; Lebedev, Andrey
2003-10-01
A nonlinear method for locating defects in solid materials is discussed that is relevant to nonlinear modal tomography based on the signal cross-modulation. The scheme is illustrated by a theoretical model in which a thin plate or bar with a single crack is excited by a strong low-frequency wave and a high-frequency probing wave (ultrasound). A crack is considered as a small contact-type defect which does not perturb the modal structure of sound in linear approximation but creates combinational-frequency components whose amplitudes depend on their closeness to a resonance and crack position. Using different crack models, including the hysteretic ones, the nonlinear part of its volume variations under the given stress and then the combinational wave components in the bar can be determined. Evidently, their amplitude depends strongly on the crack position with respect to the peaks or nodes of the corresponding linear signals which can be used for localization of the crack position. Exciting the sample by sweeping ultrasound frequencies through several resonances (modes) reduces the ambiguity in the localization. Some aspects of inverse problem solution are also discussed, and preliminary experimental results are presented.
Nonlinear calculating method of pile settlement
Institute of Scientific and Technical Information of China (English)
贺炜; 王桂尧; 王泓华
2008-01-01
To study calculating method of settlement on top of extra-long large-diameter pile, the relevant research results were summarized. The hyperbola model, a nonlinear load transfer function, was introduced to establish the basic differential equation with load transfer method. Assumed that the displacement of pile shaft was the high order power series of buried depth, through merging the same orthometric items and arranging the relevant coefficients, the solution which could take the nonlinear pile-soil interaction and stratum properties of soil into account was solved by power series. On the basis of the solution, by determining the load transfer depth with criterion of settlement on pile tip, the method by making boundary conditions compatible was advised to solve the load-settlement curve of pile. The relevant flow chart and mathematic expressions of boundary conditions were also listed. Lastly, the load transfer methods based on both two-broken-line model and hyperbola model were applied to analyzing a real project. The related coefficients of fitting curves by hyperbola were not less than 0.96, which shows that the hyperbola model is truthfulness, and is propitious to avoid personal error. The calculating value of load-settlement curve agrees well with the measured one, which indicates that it can be applied in engineering practice and making the theory that limits the design bearing capacity by settlement on pile top comes true.
Identification methods for nonlinear stochastic systems.
Fullana, Jose-Maria; Rossi, Maurice
2002-03-01
Model identifications based on orbit tracking methods are here extended to stochastic differential equations. In the present approach, deterministic and statistical features are introduced via the time evolution of ensemble averages and variances. The aforementioned quantities are shown to follow deterministic equations, which are explicitly written within a linear as well as a weakly nonlinear approximation. Based on such equations and the observed time series, a cost function is defined. Its minimization by simulated annealing or backpropagation algorithms then yields a set of best-fit parameters. This procedure is successfully applied for various sampling time intervals, on a stochastic Lorenz system.
Optimal Variational Method for Truly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Vasile Marinca
2013-01-01
Full Text Available The Optimal Variational Method (OVM is introduced and applied for calculating approximate periodic solutions of “truly nonlinear oscillators”. The main advantage of this procedure consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary. This approach does not depend upon any small or large parameters. A very good agreement was found between approximate and numerical solution, which proves that OVM is very efficient and accurate.
NONLINEAR DATA RECONCILIATION METHOD BASED ON KERNEL PRINCIPAL COMPONENT ANALYSIS
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
In the industrial process situation, principal component analysis (PCA) is a general method in data reconciliation.However, PCA sometime is unfeasible to nonlinear feature analysis and limited in application to nonlinear industrial process.Kernel PCA (KPCA) is extension of PCA and can be used for nonlinear feature analysis.A nonlinear data reconciliation method based on KPCA is proposed.The basic idea of this method is that firstly original data are mapped to high dimensional feature space by nonlinear function, and PCA is implemented in the feature space.Then nonlinear feature analysis is implemented and data are reconstructed by using the kernel.The data reconciliation method based on KPCA is applied to ternary distillation column.Simulation results show that this method can filter the noise in measurements of nonlinear process and reconciliated data can represent the true information of nonlinear process.
A simplified NARMAX method using nonlinear input-output data
Institute of Scientific and Technical Information of China (English)
Jie CHEN; Sheng FENG
2007-01-01
A system identification method for nonlinear systems with unknown structure is presented using short input-output data. The method simplifies the original NARMAX method. It introduces more general model structures for nonlinear systems. The group method of data handling (GMDH) method is employed to obtain the model terms and parameters. Effectiveness of the proposed method is illustrated by a typical nonlinear system with unknown structure and deficient input-output data.
Adaptive explicit Magnus numerical method for nonlinear dynamical systems
Institute of Scientific and Technical Information of China (English)
LI Wen-cheng; DENG Zi-chen
2008-01-01
Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group,an efficient numerical method is proposed for nonlinear dynamical systems.To improve computational efficiency,the integration step size can be adaptively controlled.Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system,the van der Pol system with strong stiffness,and the nonlinear Hamiltonian pendulum system.
Scalable nonlinear iterative methods for partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Cai, X-C
2000-10-29
We conducted a six-month investigation of the design, analysis, and software implementation of a class of singularity-insensitive, scalable, parallel nonlinear iterative methods for the numerical solution of nonlinear partial differential equations. The solutions of nonlinear PDEs are often nonsmooth and have local singularities, such as sharp fronts. Traditional nonlinear iterative methods, such as Newton-like methods, are capable of reducing the global smooth nonlinearities at a nearly quadratic convergence rate but may become very slow once the local singularities appear somewhere in the computational domain. Even with global strategies such as line search or trust region the methods often stagnate at local minima of {parallel}F{parallel}, especially for problems with unbalanced nonlinearities, because the methods do not have built-in machinery to deal with the unbalanced nonlinearities. To find the same solution u* of F(u) = 0, we solve, instead, an equivalent nonlinearly preconditioned system G(F(u*)) = 0 whose nonlinearities are more balanced. In this project, we proposed and studied a nonlinear additive Schwarz based parallel nonlinear preconditioner and showed numerically that the new method converges well even for some difficult problems, such as high Reynolds number flows, when a traditional inexact Newton method fails.
μ Synthesis Method for Robust Control of Uncertain Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
μ synthesis method for robust control of uncertain nonlinear systems is propored, which is based on feedback linearization. First, nonlinear systems are linearized as controllable linear systems by I/O linearization,such that uncertain nonlinear systems are expressed as the linear fractional transformations (LFTs) on the generalized linearized plants and uncertainty.Then,linear robust controllers are obtained for the LFTs usingμsynthesis method based on H∞ optimization.Finally,the nonlinear robust controllers are constructed by combining the linear robust controllers and the nonlinear feedback.An example is given to illustrate the design.
Comparative study of homotopy continuation methods for nonlinear algebraic equations
Nor, Hafizudin Mohamad; Ismail, Ahmad Izani Md.; Majid, Ahmad Abd.
2014-07-01
We compare some recent homotopy continuation methods to see which method has greater applicability and greater accuracy. We test the methods on systems of nonlinear algebraic equations. The results obtained indicate the superior accuracy of Newton Homotopy Continuation Method (NHCM).
Nonlinear generalization of Den Hartog's equal-peak method
Habib, G.; Detroux, T.; Viguié, R.; Kerschen, G.
2015-02-01
This study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog's equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments.
Vibrations of Nonlinear Systems. The Method of Integral Equations,
Many diverse applied methods of investigating oscillations of nonlinear systems often in different mathematical formulations and outwardly not...parameter classical methods and the methods of investigating nonlinear systems of automatic control based on the so-called filter hypothesis, and to
Nonlinear Ultrasonic Characterization Using the Noncollinear Method
Croxford, A. J.; Drinkwater, B. W.; Wilcox, P. D.
2011-06-01
The measurement of material non-linearity using ultrasound is an attractive concept, offering the potential to detect fatigue damage earlier than is possible with conventional techniques. Despite this advantage and much work in the field the currently developed approaches are primarily limited to the lab environment. This is due to the difficulty in separating the material nonlinearity from that generated by equipment. This paper reports on an approach that eliminates this problem. When two shear waves interact a third wave is generated due to the material nonlinearity. This paper shows how this interaction can be used to measure material properties in damaged specimens. It goes on to show that this approach can be used to make measurements of material non-linearity both across a specimen.
Institute of Scientific and Technical Information of China (English)
杨真真; 杨震; 李雷
2012-01-01
The basic theory of reconstruction signals is that the signals are sparse or approximate sparse in a transform domain. Based on the approximate sparsity of speech signal in the DCT domain, compressed sensing theory is applied to reconstruct speech signal: The iterative hard thresholding (IHT) algorithm with good performances is widely used to reconstruct signals, however, its convergence speed is too slow. How to improve the convergence speed of the iterative hard thresholding algorithm has been a hot topic. The accelerated Landweber iterative hard thresholding ( A1IHT) algorithm in the DCT domain for speech reconstruction is proposed to solve the problem that the convergence speed is too slow when the iterative hard thresholding algorithm is applied to the compressed sensing. The accelerated Landweber iterative hard thresholding algorithm firstly transforms the original speech signal to its DCT domain, and then speeds up the convergence speed by discomposing the each one step of the Landweber iteration in the iterative hard thresholding algorithm into two steps as the matrix computation and solution in the DCT domain, and modifying the matrix computation step. The experimental simulations show that the accelerated Landweber iterative hard thresholding algorithm increases convergence speed and reduces the calculation measures.%重构信号的最基本理论依据是该信号在某个变换域是稀疏的或近似稀疏的.基于语音信号在DCT域的 近似稀疏性,可以采用压缩感知(Compressed Sensing,CS)理论对其进行重构.压缩感知理论中的迭代硬阈值(Iterative hard thresholding,IHT)算法以其较好的性能被广泛用来重构信号,但其收敛速度比较慢,如何提高收敛速度,一直是迭代硬阈值算法研究的重点之一.针对压缩感知理论中的IHT算法收敛速度相当慢的问题,提出了语音重构的DCT域加速Landweber迭代硬阈值(Accelerated Landweber iterative hard thresholding,ALIHT)算法.该算
A Hybrid of DL and WYL Nonlinear Conjugate Gradient Methods
Directory of Open Access Journals (Sweden)
Shengwei Yao
2014-01-01
Full Text Available The conjugate gradient method is an efficient method for solving large-scale nonlinear optimization problems. In this paper, we propose a nonlinear conjugate gradient method which can be considered as a hybrid of DL and WYL conjugate gradient methods. The given method possesses the sufficient descent condition under the Wolfe-Powell line search and is globally convergent for general functions. Our numerical results show that the proposed method is very robust and efficient for the test problems.
Auxiliary equation method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Sirendaoreji,; Jiong, Sun
2003-03-31
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation.
Nonlinear fault diagnosis method based on kernel principal component analysis
Institute of Scientific and Technical Information of China (English)
Yan Weiwu; Zhang Chunkai; Shao Huihe
2005-01-01
To ensure the system run under working order, detection and diagnosis of faults play an important role in industrial process. This paper proposed a nonlinear fault diagnosis method based on kernel principal component analysis (KPCA). In proposed method, using essential information of nonlinear system extracted by KPCA, we constructed KPCA model of nonlinear system under normal working condition. Then new data were projected onto the KPCA model. When new data are incompatible with the KPCA model, it can be concluded that the nonlinear system isout of normal working condition. Proposed method was applied to fault diagnosison rolling bearings. Simulation results show proposed method provides an effective method for fault detection and diagnosis of nonlinear system.
Energy Method to Obtain Approximate Solutions of Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
Full Text Available We introduce a nonlinearization procedure that replaces the system potential energy by an equivalent representation form that is used to derive analytical solutions of strongly nonlinear conservative oscillators. We illustrate the applicability of this method by finding the approximate solutions of two strongly nonlinear oscillators and show that this procedure provides solutions that follow well the numerical integration solutions of the corresponding equations of motion.
Dynamic decoupling nonlinear control method for aircraft gust alleviation
Lv, Yang; Wan, Xiaopeng; Li, Aijun
2008-10-01
A dynamic decoupling nonlinear control method for MIMO system is presented in this paper. The dynamic inversion method is used to decouple the multivariable system. The nonlinear control method is used to overcome the poor decoupling effect when the system model is inaccurate. The nonlinear control method has correcting function and is expressed in analytic form, it is easy to adjust the parameters of the controller and optimize the design of the control system. The method is used to design vertical transition mode of active control aircraft for gust alleviation. Simulation results show that the designed vertical transition mode improves the gust alleviation effect about 34% comparing with the normal aircraft.
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
Numerical Methods for Nonlinear PDEs in Finance
DEFF Research Database (Denmark)
Mashayekhi, Sima
Nonlinear Black-Scholes equations arise from considering parameters such as feedback and illiquid markets eects or large investor preferences, volatile portfolio and nontrivial transaction costs into option pricing models to have more accurate option price. Here some nite dierence schemes have been...
Nonlinear modal method of crack localization
Ostrovsky, Lev; Sutin, Alexander; Lebedev, Andrey
2004-05-01
A simple scheme for crack localization is discussed that is relevant to nonlinear modal tomography based on the cross-modulation of two signals at different frequencies. The scheme is illustrated by a theoretical model, in which a thin plate or bar with a single crack is excited by a strong low-frequency wave and a high-frequency probing wave (ultrasound). The crack is assumed to be small relative to all wavelengths. Nonlinear scattering from the crack is studied using a general matrix approach as well as simplified models allowing one to find the nonlinear part of crack volume variations under the given stress and then the combinational wave components in the tested material. The nonlinear response strongly depends on the crack position with respect to the peaks or nodes of the corresponding interacting signals which can be used for determination of the crack position. Juxtaposing various resonant modes interacting at the crack it is possible to retrieve both crack location and orientation. Some aspects of inverse problem solutions are also discussed, and preliminary experimental results are presented.
Numerical Methods for Nonlinear PDEs in Finance
DEFF Research Database (Denmark)
Mashayekhi, Sima
Nonlinear Black-Scholes equations arise from considering parameters such as feedback and illiquid markets eects or large investor preferences, volatile portfolio and nontrivial transaction costs into option pricing models to have more accurate option price. Here some nite dierence schemes have be...
Modified Homotopy Analysis Method for Nonlinear Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
D. Ziane
2017-05-01
Full Text Available In this paper, a combined form of natural transform with homotopy analysis method is proposed to solve nonlinear fractional partial differential equations. This method is called the fractional homotopy analysis natural transform method (FHANTM. The FHANTM can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. The results show that the FHANTM is an appropriate method for solving nonlinear fractional partial differentia equation.
Reproducing Kernel Particle Method for Non-Linear Fracture Analysis
Institute of Scientific and Technical Information of China (English)
Cao Zhongqing; Zhou Benkuan; Chen Dapeng
2006-01-01
To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method (RKPM). Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method.
Online Fault Diagnosis Method Based on Nonlinear Spectral Analysis
Institute of Scientific and Technical Information of China (English)
WEI Rui-xuan; WU Li-xun; WANG Yong-chang; HAN Chong-zhao
2005-01-01
The fault diagnosis based on nonlinear spectral analysis is a new technique for the nonlinear fault diagnosis, but its online application could be limited because of the enormous compution requirements for the estimation of general frequency response functions. Based on the fully decoupled Volterra identification algorithm, a new online fault diagnosis method based on nonlinear spectral analysis is presented, which can availably reduce the online compution requirements of general frequency response functions. The composition and working principle of the method are described, the test experiments have been done for damping spring of a vehicle suspension system by utilizing the new method, and the results indicate that the method is efficient.
Hyperbolic function method for solving nonlinear differential-different equations
Institute of Scientific and Technical Information of China (English)
Zhu Jia-Min
2005-01-01
An algorithm is devised to obtained exact travelling wave solutions of differential-different equations by means of hyperbolic function. For illustration, we apply the method to solve the discrete nonlinear (2+1)-dimensional Toda lattice equation and the discretized nonlinear mKdV lattice equation, and successfully constructed some explicit and exact travelling wave solutions.
GHM method for obtaining rationalsolutions of nonlinear differential equations.
Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo
2015-01-01
In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.
On filter-successive linearization methods for nonlinear semidefinite programming
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially effcient.
On filter-successive linearization methods for nonlinear semidefinite programming
Institute of Scientific and Technical Information of China (English)
LI ChengJin; SUN WenYui
2009-01-01
In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially efficient.
Directory of Open Access Journals (Sweden)
E. M. E. Zayed
2014-01-01
Full Text Available We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
Bifurcation methods of dynamical systems for handling nonlinear wave equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-05-01
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U
Energy Technology Data Exchange (ETDEWEB)
Sun, Y.; Borland, Michael
2017-06-25
Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.
A Numerical Embedding Method for Solving the Nonlinear Optimization Problem
Institute of Scientific and Technical Information of China (English)
田保锋; 戴云仙; 孟泽红; 张建军
2003-01-01
A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theory, the existence and the continuation of the following path for the corresponding homotopy equations were proved. Therefore the basic theory for the algorithm of the numerical embedding method for solving the non-linear optimization problem was established. Based on the theoretical results, a numerical embedding algorithm was designed for solving the nonlinear optimization problem, and prove its convergence carefully. Numerical experiments show that the algorithm is effective.
A granular computing method for nonlinear convection-diffusion equation
Directory of Open Access Journals (Sweden)
Tian Ya Lan
2016-01-01
Full Text Available This paper introduces a method of solving nonlinear convection-diffusion equation (NCDE, based on the combination of granular computing (GrC and characteristics finite element method (CFEM. The key idea of the proposed method (denoted as GrC-CFEM is to reconstruct the solution from coarse-grained layer to fine-grained layer. It first gets the nonlinear solution on the coarse-grained layer, and then the function (Taylor expansion is applied to linearize the NCDE on the fine-grained layer. Switch to the fine-grained layer, the linear solution is directly derived from the nonlinear solution. The full nonlinear problem is solved only on the coarse-grained layer. Numerical experiments show that the GrC-CFEM can accelerate the convergence and improve the computational efficiency without sacrificing the accuracy.
A Hybrid Method for Nonlinear Least Squares Problems
Institute of Scientific and Technical Information of China (English)
Zhongyi Liu; Linping Sun
2007-01-01
A negative curvature method is applied to nonlinear least squares problems with indefinite Hessian approximation matrices. With the special structure of the method,a new switch is proposed to form a hybrid method. Numerical experiments show that this method is feasible and effective for zero-residual,small-residual and large-residual problems.
Nonlinear Dimensionality Reduction Methods in Climate Data Analysis
Ross, Ian
2008-01-01
Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be appropriate for the analysis of data arising from nonlinear processes occurring in the climate system. Numerous techniques for nonlinear dimensionality reduction have been developed recently that may provide a potentially useful tool for the identification of low-dimensional manifolds in climate data sets arising from nonlinear dynamics. In this thesis I apply three such techniques to the study of El Nino/Southern Oscillation variability in tropical Pacific sea surface temperatures and thermocline depth, comparing observational data with simulations from coupled atmosphere-ocean general circulation models from the CMIP3 multi-model ensemble. The three methods used here are a nonlinear principal component analysis (NLPCA) approach based on neural networks, the Isomap isometric mappin...
NOLB: Nonlinear Rigid Block Normal Mode Analysis Method
Hoffmann, Alexandre; Grudinin, Sergei
2017-01-01
International audience; We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velo...
LIMITED MEMORY BFGS METHOD FOR NONLINEAR MONOTONE EQUATIONS
Institute of Scientific and Technical Information of China (English)
Weijun Zhou; Donghui Li
2007-01-01
In this paper, we propose an algorithm for solving nonlinear monotone equations by combining the limited memory BFGS method (L-BFGS) with a projection method. We show that the method is globally convergent if the equation involves a Lipschitz continuous monotone function. We also present some preliminary numerical results.
A simple harmonic balance method for solving strongly nonlinear oscillators
Directory of Open Access Journals (Sweden)
Md. Abdur Razzak
2016-10-01
Full Text Available In this paper, a simple harmonic balance method (HBM is proposed to obtain higher-order approximate periodic solutions of strongly nonlinear oscillator systems having a rational and an irrational force. With the proposed procedure, the approximate frequencies and the corresponding periodic solutions can be easily determined. It gives high accuracy for both small and large amplitudes of oscillations and better result than those obtained by other existing results. The main advantage of the present method is that its simplicity and the second-order approximate solutions almost coincide with the corresponding numerical solutions (considered to be exact. The method is illustrated by examples. The present method is very effective and convenient method for solving strongly nonlinear oscillator systems arising in nonlinear science and engineering.
CONVERGENCE OF NONLINEAR CONJUGATE GRADIENT METHODS
Institute of Scientific and Technical Information of China (English)
Yu-hong Dai
2001-01-01
This paper proves that a simplified Armijo-type line search can ensure the global con vergences of the Fletcher-Reeves method and the Polak-Ribiére-Polyak method for un constrained optimization. Although it seems not possible to verify that the PRP method using the generalized Armijo line search converges globally for generally problems, it can be shown that in this case the PRP method always solves uniformly convex problems.
Improved HPC method for nonlinear wave tank
DEFF Research Database (Denmark)
Zhu, Wenbo; Greco, Marilena; Shao, Yanlin
2017-01-01
The recently developed Harmonic Polynomial Cell (HPC) method has been proved to be a promising choice for solving potential-flow Boundary Value Problem (BVP). In this paper, a flux method is proposed to consistently deal with the Neumann boundary condition of the original HPC method and enhance...
Nonlinear Methods in Riemannian and Kählerian Geometry
Jost, Jürgen
1991-01-01
In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps ...
Adaptive control method for nonlinear time-delay processes
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Two complex properties,varying time-delay and block-oriented nonlinearity,are very common in chemical engineering processes and not easy to be controlled by routine control methods.Aimed at these two complex properties,a novel adaptive control algorithm the basis of nonlinear OFS(orthonormal functional series) model is proposed.First,the hybrid model which combines OFS and Volterra series is introduced.Then,a stable state feedback strategy is used to construct a nonlinear adaptive control algorithm that can guarantee the closed-loop stability and can track the set point curve without steady-state errors.Finally,control simulations and experiments on a nonlinear process with varying time-delay are presented.A number of experimental results validate the efficiency and superiority of this algorithm.
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.
Baranwal, Vipul K; Pandey, Ram K; Singh, Om P
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.
Extended Trial Equation Method for Nonlinear Partial Differential Equations
Gepreel, Khaled A.; Nofal, Taher A.
2015-04-01
The main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber-Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.
The optical nonlinearity of gold nanoparticles prepared by bioreduction method
Balbuena Ortega, A.; Arroyo Carrasco, M. L.; Gayou, V. L.; Orduña Díaz, A.; Delgado Macuil, R.; Rojas López, Marlon
2013-11-01
Nonlinear optical and electronic properties of nanosized metal particles have drawn considerable attention because of their strong and size-dependent plasmon resonance absorption. In a metal nanoparticle system such as gold dispersed in a transparent matrix, an absorption peak due to surface plasmon resonance is usually observed in the visible spectral region. Metal nanoparticles are of special interest as nonlinear materials for optical switching and computing because of their relatively large third-order nonlinearity (χ3) and ultrafast response time. The purpose of this study was to analyze the nonlinear optical properties of biosynthesized gold nanoparticles. The samples were prepared by biosynthesis method using yeast extract as reducing agent and the nonlinear optical properties of the nanoparticles were investigated using a single beam Z-scan technique with a beam power of 20 mW and operated at wavelength of 514 nm. The reaction between metal ions and yeast extracts were monitored by UV-visible spectra of Au nanoparticles in aqueous solution with different pH (3-6). The surface plasmon peak position was shifted from 528 nm to 573 nm, according to of pH variation 4 to 6. The average particle size was calculated by the absorption peak position using the Fernig method, from 42 to 103 nm. The z-scan curves showed a negative nonlocal nonlinear refractive index with a magnitude dependent on the nanoparticle size.
THE MORTAR ELEMENT METHOD FOR A NONLINEAR BIHARMONIC EQUATION
Institute of Scientific and Technical Information of China (English)
Zhong-ci Shi; Xue-jun Xu
2005-01-01
The mortar element method is a new domain decomposition method(DDM) with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and H1-norm estimates are obtained under a reasonable elliptic regularity assumption.
Direct Perturbation Method for Derivative Nonlinear Schrodinger Equation
Institute of Scientific and Technical Information of China (English)
CHENG Xue-Ping; LIN Ji; HAN Ping
2008-01-01
We extend Lou's direct perturbation method for solving the nonlinear SchrSdinger equation to the case of the derivative nonlinear Schrodinger equation (DNLSE). By applying this method, different types of perturbation solutions axe obtained. Based on these approximate solutions, the analytical forms of soliton parameters, such as the velocity, the width and the initial position, are carried out and the effects of perturbation on solitons are analyzed at the same time. A numerical simulation of perturbed DNLSE finally verifies the results of the perturbation method.
New Efficient Fourth Order Method for Solving Nonlinear Equations
Directory of Open Access Journals (Sweden)
Farooq Ahmad
2013-12-01
Full Text Available In a paper [Appl. Math. Comput., 188 (2 (2007 1587--1591], authors have suggested and analyzed a method for solving nonlinear equations. In the present work, we modified this method by using the finite difference scheme, which has a quintic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method having convergence of fourth order, is efficient.
Chaos Control in Nonlinear Systems Using the Generalized Backstopping Method
Directory of Open Access Journals (Sweden)
A. R. Sahab
2008-01-01
Full Text Available One of the most important nonlinear systems for checking the abilities of control methods is chaos. In this study chaos in Lorenz system was used for checking abilities of new control method. This new method to control nonlinear systems was called Generalized Backstepping method because of its similarity to Backstepping but its abilities to control more systems than Backstepping. This new method was applied to Lorenz system in three ways: 1.Stabilized states of equations. 2. Track step response. 3. Track sinusoidal response. In every way, simulations proved abilities of method. Comparing this new method with Backstepping showed that in this method, states stabilize at zero in shorter time than Backstepping and input control is more limited. So new method not only is used in more systems but also has better response.
APPLICATION OF MODIFIED CONVERSION METHOD TO A NONLINEAR DYNAMICAL SYSTEM
Directory of Open Access Journals (Sweden)
G.I. Melnikov
2015-01-01
Full Text Available The paper deals with a mathematical model of dynamical system with single degree of freedom, presented in the form of ordinary differential equations with nonlinear parts in the form of polynomials with constant and periodic coefficients. A modified method for the study of self-oscillations of nonlinear mechanical systems is presented. A refined method of transformation and integration of the equation, based on Poincare-Dulac normalization method has been developed. Refinement of the method lies in consideration of higher order nonlinear terms by Chebyshev economization technique that improves the accuracy of the calculations. Approximation of the higher order remainder terms by homogeneous forms of lower orders is performed; in the present case, it is done by cubic forms. An application of the modified method for the Van-der-Pol equation is considered as an example; the expressions for the amplitude and the phase of the oscillations are obtained in an analytical form. The comparison of the solution of the Van-der-Pol equation obtained by the developed method and the exact solution is performed. The error of the solution obtained by the modified method equals to 1%, which shows applicability of the developed method for analysis of self-oscillations of nonlinear dynamic systems with constant and periodic parameters.
An averaging method for nonlinear laminar Ekman layers
DEFF Research Database (Denmark)
Andersen, Anders Peter; Lautrup, B.; Bohr, T.
2003-01-01
We study steady laminar Ekman boundary layers in rotating systems using,an averaging method similar to the technique of von Karman and Pohlhausen. The method allows us to explore nonlinear corrections to the standard Ekman theory even at large Rossby numbers. We consider both the standard self...
Tensor methods for large sparse systems of nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science
1996-12-31
This paper introduces censor methods for solving, large sparse systems of nonlinear equations. Tensor methods for nonlinear equations were developed in the context of solving small to medium- sized dense problems. They base each iteration on a quadratic model of the nonlinear equations. where the second-order term is selected so that the model requires no more derivative or function information per iteration than standard linear model-based methods, and hardly more storage or arithmetic operations per iteration. Computational experiments on small to medium-sized problems have shown censor methods to be considerably more efficient than standard Newton-based methods, with a particularly large advantage on singular problems. This paper considers the extension of this approach to solve large sparse problems. The key issue that must be considered is how to make efficient use of sparsity in forming and solving the censor model problem at each iteration. Accomplishing this turns out to require an entirely new way of solving the tensor model that successfully exploits the sparsity of the Jacobian, whether the Jacobian is nonsingular or singular. We develop such an approach and, based upon it, an efficient tensor method for solving large sparse systems of nonlinear equations. Test results indicate that this tensor method is significantly more efficient and robust than an efficient sparse Newton-based method. in terms of iterations, function evaluations. and execution time.
A Spectral Element Method for Nonlinear and Dispersive Water Waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bigoni, Daniele; Eskilsson, Claes
The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...... methods is of key interest. We present a high-order general-purpose three-dimensional numerical model solving fully nonlinear and dispersive potential flow equations with a free surface.......The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...
Analysis of Nonlinear Dynamics by Square Matrix Method
Energy Technology Data Exchange (ETDEWEB)
Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II
2016-07-25
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.
Nonlinear Direct Robust Adaptive Control Using Lyapunov Method
Directory of Open Access Journals (Sweden)
Chunbo Xiu
2013-07-01
Full Text Available The problem of robust adaptive stabilization of a class of multi-input nonlinear systems with arbitrary unknown parameters and unknown structure of bounded variation have been considered. By employing the direct adaptive and control Lyapunov function method, a robust adaptive controller is designed to complete the globally adaptive stability of the system states. By employing our result, a kind of nonlinear system is analyzed, the concrete form of the control law is given and the meaningful quadratic control Lyapunov function for the system is constructed. Simulation of parallel manipulator is provided to illustrate the effectiveness of the proposed method.
Wave envelopes method for description of nonlinear acoustic wave propagation.
Wójcik, J; Nowicki, A; Lewin, P A; Bloomfield, P E; Kujawska, T; Filipczyński, L
2006-07-01
A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach
An Analytical Approximation Method for Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Wang Shimin
2012-01-01
Full Text Available An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of the spring varies with the vibration amplitude for nonstationary oscillations. The varied stiffness is constructed by means of the first and second averaged derivatives of the restoring force with respect to the displacement. Then, this stiffness gives the amplitude frequency and the phase frequency characteristics of the oscillator. Various examples show that this method can be applied extensively to oscillators with nonlinear restoring force, and that the solving process is extremely simple.
Linear Algebraic Method for Non-Linear Map Analysis
Energy Technology Data Exchange (ETDEWEB)
Yu,L.; Nash, B.
2009-05-04
We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.
Application of homotopy analysis method for solving nonlinear Cauchy problem
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V.G. Gupta
2012-11-01
Full Text Available In this paper, by means of the homotopy analysis method (HAM, the solutions of some nonlinear Cauchy problem of parabolic-hyperbolic type are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter \\hbar that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple.
An Agent Interaction Based Method for Nonlinear Process Plan Scheduling
Institute of Scientific and Technical Information of China (English)
GAO Qinglu; WU Bo; GUO Guang
2006-01-01
This article puts forward a scheduling method for nonlinear process plan shop floor. Task allocation and load balance are realized by bidding mechanism. Though the agent interaction process, the execution of tasks is determined and the coherence of manufacturing decision is verified. The employment of heuristic index can help to optimize the system performance.
Applications of non-linear methods in astronomy
Martens, P.C.H.
1984-01-01
In this review I discuss catastrophes, bifurcations and strange attractors in a non-mathematical manner by giving very simple examples that st ill contain the essence of the phenomenon. The salientresults of the applications of these non-linear methods in astrophysics are reviewed and include such d
Method for Measuring Small Nonlinearities of Electric Characteristics
DEFF Research Database (Denmark)
Guldbrandsen, Tom; Meyer, Niels I; Schjær-Jacobsen, Jørgen
1965-01-01
A method is described for measuring very small deviations from linearity in electric characteristics. The measurement is based on the harmonics generated by the nonlinear element when subjected to a sine wave signal. A special bridge circuit is used to balance out the undesired harmonics...... of the signal generator together with the first harmonic frequency. The set-up measures the small-signal value and the first and second derivative with respect to voltage. The detailed circuits are given for measuring nonlinearities in Ohmic and capacitive components. In the Ohmic case, a sensitivity...
Various Newton-type iterative methods for solving nonlinear equations
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Manoj Kumar
2013-10-01
Full Text Available The aim of the present paper is to introduce and investigate new ninth and seventh order convergent Newton-type iterative methods for solving nonlinear equations. The ninth order convergent Newton-type iterative method is made derivative free to obtain seventh-order convergent Newton-type iterative method. These new with and without derivative methods have efficiency indices 1.5518 and 1.6266, respectively. The error equations are used to establish the order of convergence of these proposed iterative methods. Finally, various numerical comparisons are implemented by MATLAB to demonstrate the performance of the developed methods.
Slope stability analysis using limit equilibrium method in nonlinear criterion.
Lin, Hang; Zhong, Wenwen; Xiong, Wei; Tang, Wenyu
2014-01-01
In slope stability analysis, the limit equilibrium method is usually used to calculate the safety factor of slope based on Mohr-Coulomb criterion. However, Mohr-Coulomb criterion is restricted to the description of rock mass. To overcome its shortcomings, this paper combined Hoek-Brown criterion and limit equilibrium method and proposed an equation for calculating the safety factor of slope with limit equilibrium method in Hoek-Brown criterion through equivalent cohesive strength and the friction angle. Moreover, this paper investigates the impact of Hoek-Brown parameters on the safety factor of slope, which reveals that there is linear relation between equivalent cohesive strength and weakening factor D. However, there are nonlinear relations between equivalent cohesive strength and Geological Strength Index (GSI), the uniaxial compressive strength of intact rock σ ci , and the parameter of intact rock m i . There is nonlinear relation between the friction angle and all Hoek-Brown parameters. With the increase of D, the safety factor of slope F decreases linearly; with the increase of GSI, F increases nonlinearly; when σ ci is relatively small, the relation between F and σ ci is nonlinear, but when σ ci is relatively large, the relation is linear; with the increase of m i , F decreases first and then increases.
Method of Conjugate Radii for Solving Linear and Nonlinear Systems
Nachtsheim, Philip R.
1999-01-01
This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.
Relaxation and decomposition methods for mixed integer nonlinear programming
Nowak, Ivo; Bank, RE
2005-01-01
This book presents a comprehensive description of efficient methods for solving nonconvex mixed integer nonlinear programs, including several numerical and theoretical results, which are presented here for the first time. It contains many illustrations and an up-to-date bibliography. Because on the emphasis on practical methods, as well as the introduction into the basic theory, the book is accessible to a wide audience. It can be used both as a research and as a graduate text.
A Filter Method for Nonlinear Semidefinite Programming with Global Convergence
Institute of Scientific and Technical Information of China (English)
Zhi Bin ZHU; Hua Li ZHU
2014-01-01
In this study, a new filter algorithm is presented for solving the nonlinear semidefinite programming. This algorithm is inspired by the classical sequential quadratic programming method. Unlike the traditional filter methods, the suffi cient descent is ensured by changing the step size instead of the trust region radius. Under some suitable conditions, the global convergence is obtained. In the end, some numerical experiments are given to show that the algorithm is eff ective.
A New Nonlinear Compound Forecasting Method Based on ANN
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper the compound-forecasting method is discussed. The compound-forecasting method is one of the hotspots in the current predication. Firstly, the compound-forecasting method is introduced and various existing compound-forecasting methods arediscussed. Secondly, the Artificial Neural Network (ANN) is brought in compound-prediction research and a nonlinear compound-prediction model based on ANN is presented. Finally, inorder to avoid irregular weight, a new method is presented which uses principal component analyses to increase the availability of compound-forecasting information. Higherforecasting precision is achieved in practice.
Perturbation and harmonic balance methods for nonlinear panel flutter.
Kuo, C.-C.; Morino, L.; Dugundji, J.
1972-01-01
A systematic way of applying both perturbation methods and harmonic balance methods to nonlinear panel flutter problems is developed here. Results obtained by both these methods for two-dimensional simply supported and three-dimensional clamped-clamped plates with six modes agree well with those obtained by the straightforward direct integration method, yet require less computer time and provide better insight into the solutions. Effects of viscoelastic structural damping on the flutter stability boundary are generally found to be destabilizing and the postflutter behavior becomes more explosive. The methods developed here may be of interest in related vibration problems.
Multi-level damage detection with nonlinear ultrasonic methods
Matlack, Kathryn H.; Kim, Jin-Yeon; Jacobs, Laurence J.; Qu, Jianmin
2013-01-01
The nonlinear ultrasonic method of second harmonic generation is used to detect multiple levels of damage on a single specimen. There is a breadth of research in the literature that measures the second harmonic and the resulting nonlinear parameter to monitor increasing amounts of uniform damage, but for this method to be applicable as an in situ technique, it must be able to scan an area of a structure with varying amounts of damage over a region. To investigate this, an aluminum alloy sample is shot-peened to two intensity levels along its length, to produce different sections of cold work and residual stress as a function of spatial location. Previous research has shown that the residual stress and cold work introduced in a material from shot peening causes an increase in the nonlinear parameter. Rayleigh waves are generated in the sample and the first and second harmonic amplitudes are measured at increasing propagation distances that encompass an undamaged section and two sections, each with different levels of shot peening. Results show that the nonlinear parameter increases as the Rayleigh wedge sensor is scanned over the shot peening sections.
Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging
Desmal, Abdulla
2016-03-01
Electromagnetic imaging is the problem of determining material properties from scattered fields measured away from the domain under investigation. Solving this inverse problem is a challenging task because (i) it is ill-posed due to the presence of (smoothing) integral operators used in the representation of scattered fields in terms of material properties, and scattered fields are obtained at a finite set of points through noisy measurements; and (ii) it is nonlinear simply due the fact that scattered fields are nonlinear functions of the material properties. The work described in this thesis tackles the ill-posedness of the electromagnetic imaging problem using sparsity-based regularization techniques, which assume that the scatterer(s) occupy only a small fraction of the investigation domain. More specifically, four novel imaging methods are formulated and implemented. (i) Sparsity-regularized Born iterative method iteratively linearizes the nonlinear inverse scattering problem and each linear problem is regularized using an improved iterative shrinkage algorithm enforcing the sparsity constraint. (ii) Sparsity-regularized nonlinear inexact Newton method calls for the solution of a linear system involving the Frechet derivative matrix of the forward scattering operator at every iteration step. For faster convergence, the solution of this matrix system is regularized under the sparsity constraint and preconditioned by leveling the matrix singular values. (iii) Sparsity-regularized nonlinear Tikhonov method directly solves the nonlinear minimization problem using Landweber iterations, where a thresholding function is applied at every iteration step to enforce the sparsity constraint. (iv) This last scheme is accelerated using a projected steepest descent method when it is applied to three-dimensional investigation domains. Projection replaces the thresholding operation and enforces the sparsity constraint. Numerical experiments, which are carried out using
Shuttle entry guidance revisited using nonlinear geometric methods
Mease, Kenneth D.; Kremer, Jean-Paul
1994-11-01
The entry guidance law for the space shuttle orbiter is revisited using nonlinear geometric methods. The shuttle guidance concept is to track a reference drag trajectory that has been designed to lead a specified range and velocity. It is shown that the approach taken in the original derivation of the shuttle entry guidance has much in common with the more recently developed feedback linearization method of differential geometric control. Using the feedback linearization method, however, an alternative, potentially superior, guidance law was formulated. Comparing the two guidance laws based performance domains in state space, taking into account the nonlinear dynamics, the alternative guidance law achieves the desired performance over larger domains in state space; the stability domain of the laws are similar. With larger operating domain for the shuttle or some other entry vehicle, the alternative guidance law should be considered.
Analysis of Nonlinear Missile Guidance Systems Through Linear Adjoint Method
Directory of Open Access Journals (Sweden)
Khaled Gamal Eltohamy
2015-12-01
Full Text Available In this paper, a linear simulation algorithm, the adjoint method, is modified and employed as an efficient tool for analyzing the contributions of system parameters to the miss - distance of a nonlinear time-varying missile guidance system model. As an example for the application of the linear adjoint method, the effect of missile flight time on the miss - distance is studied. Since the missile model is highly nonlinear and a time-varying linearized model is required to apply the adjoint method, a new technique that utilizes the time-reversed linearized coefficients of the missile as a replacement for the time-varying describing functions is applied and proven to be successful. It is found that, when compared with Monte Carlo generated results, simulation results of this linear adjoint technique provide acceptable accuracy and can be produced with much less effort.
Bayesian Methods for Nonlinear System Identification of Civil Structures
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Conte Joel P.
2015-01-01
Full Text Available This paper presents a new framework for the identification of mechanics-based nonlinear finite element (FE models of civil structures using Bayesian methods. In this approach, recursive Bayesian estimation methods are utilized to update an advanced nonlinear FE model of the structure using the input-output dynamic data recorded during an earthquake event. Capable of capturing the complex damage mechanisms and failure modes of the structural system, the updated nonlinear FE model can be used to evaluate the state of health of the structure after a damage-inducing event. To update the unknown time-invariant parameters of the FE model, three alternative stochastic filtering methods are used: the extended Kalman filter (EKF, the unscented Kalman filter (UKF, and the iterated extended Kalman filter (IEKF. For those estimation methods that require the computation of structural FE response sensitivities with respect to the unknown modeling parameters (EKF and IEKF, the accurate and computationally efficient direct differentiation method (DDM is used. A three-dimensional five-story two-by-one bay reinforced concrete (RC frame is used to illustrate the performance of the framework and compare the performance of the different filters in terms of convergence, accuracy, and robustness. Excellent estimation results are obtained with the UKF, EKF, and IEKF. Because of the analytical linearization used in the EKF and IEKF, abrupt and large jumps in the estimates of the modeling parameters are observed when using these filters. The UKF slightly outperforms the EKF and IEKF.
Institute of Scientific and Technical Information of China (English)
崔霞
2002-01-01
Alternating direction finite element (ADFE) scheme for d-dimensional nonlinear system of parabolic integro-differential equations is studied. By using a local approximation based on patches of finite elements to treat the capacity term qi(u), decomposition of the coefficient matrix is realized; by using alternating direction, the multi-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using finite element method, high accuracy for space variant is kept; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity of the coefficients and boundary conditions is treated; by introducing Ritz-Volterra projection, the difficulty coming from the memory term is solved. Finally, by using various techniques for priori estimate for differential equations, the unique resolvability and convergence properties for both FE and ADFE schemes are rigorously demonstrated, and optimal H1 and L2norm space estimates and O((△t)2) estimate for time variant are obtained.
Multi-crack imaging using nonclassical nonlinear acoustic method
Zhang, Lue; Zhang, Ying; Liu, Xiao-Zhou; Gong, Xiu-Fen
2014-10-01
Solid materials with cracks exhibit the nonclassical nonlinear acoustical behavior. The micro-defects in solid materials can be detected by nonlinear elastic wave spectroscopy (NEWS) method with a time-reversal (TR) mirror. While defects lie in viscoelastic solid material with different distances from one another, the nonlinear and hysteretic stress—strain relation is established with Preisach—Mayergoyz (PM) model in crack zone. Pulse inversion (PI) and TR methods are used in numerical simulation and defect locations can be determined from images obtained by the maximum value. Since false-positive defects might appear and degrade the imaging when the defects are located quite closely, the maximum value imaging with a time window is introduced to analyze how defects affect each other and how the fake one occurs. Furthermore, NEWS-TR-NEWS method is put forward to improve NEWS-TR scheme, with another forward propagation (NEWS) added to the existing phases (NEWS and TR). In the added phase, scanner locations are determined by locations of all defects imaged in previous phases, so that whether an imaged defect is real can be deduced. NEWS-TR-NEWS method is proved to be effective to distinguish real defects from the false-positive ones. Moreover, it is also helpful to detect the crack that is weaker than others during imaging procedure.
Condition Monitoring of Turbines Using Nonlinear Mapping Method
Institute of Scientific and Technical Information of China (English)
Liao Guang-lan; Shi Tie-lin; Jiang Nan
2004-01-01
Aiming at the non-linear nature of the signals generated from turbines, curvilinear component analysis (CCA), a novel nonlinear projection method that favors local topology conservation is presented for turbines conditions monitoring. This is accomplished in two steps. Time domain features are extracted from raw vibration signals, and then they are projected into a two-dimensional output space by using CCA method and form regions indicative of specific conditions, which helps classify and identify turbine states visually. Therefore, the variation of turbine conditions can be observed clearly with the trajectory of image points for the feature data in the two-dimensional space, and the occurrence and development of failures can be monitored in time.
Application of the homotopy perturbation method to the nonlinear pendulum
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Hernandez, A; Belendez, T; Neipp, C; Marquez, A [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-01-15
The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as high as 130{sup 0}. Another important point is that this method provides an analytical expression for the angular displacement as a function of time as the sum of an infinite number of harmonics; although for practical purposes it is sufficient to consider only a finite number of harmonics. We believe that the present study may be a suitable and fruitful exercise for teaching and better understanding perturbation techniques in advanced undergraduate courses on classical mechanics.
Lavrentiev regularization method for nonlinear ill-posed problems
Kinh, N V
2002-01-01
In this paper we shall be concerned with Lavientiev regularization method to reconstruct solutions x sub 0 of non ill-posed problems F(x)=y sub o , where instead of y sub 0 noisy data y subdelta is an element of X with absolut(y subdelta-y sub 0) X is an accretive nonlinear operator from a real reflexive Banach space X into itself. In this regularization method solutions x subalpha supdelta are obtained by solving the singularly perturbed nonlinear operator equation F(x)+alpha(x-x*)=y subdelta with some initial guess x*. Assuming certain conditions concerning the operator F and the smoothness of the element x*-x sub 0 we derive stability estimates which show that the accuracy of the regularized solutions is order optimal provided that the regularization parameter alpha has been chosen properly.
Adomian decomposition method for nonlinear Sturm-Liouville problems
Directory of Open Access Journals (Sweden)
Sennur Somali
2007-09-01
Full Text Available In this paper the Adomian decomposition method is applied to the nonlinear Sturm-Liouville problem-y" + y(tp=λy(t, y(t > 0, t ∈ I = (0, 1, y(0 = y(1 = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.
Reproducing wavelet kernel method in nonlinear system identification
Institute of Scientific and Technical Information of China (English)
WEN Xiang-jun; XU Xiao-ming; CAI Yun-ze
2008-01-01
By combining the wavelet decomposition with kernel method, a practical approach of universal multi-scale wavelet kernels constructed in reproducing kernel Hilbert space (RKHS) is discussed, and an identifica-tion scheme using wavelet support vector machines ( WSVM ) estimator is proposed for nonlinear dynamic sys-tems. The good approximating properties of wavelet kernel function enhance the generalization ability of the pro-posed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.
The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions
Directory of Open Access Journals (Sweden)
Shoukry Ibrahim Atia El-Ganaini
2013-01-01
Full Text Available The first integral method introduced by Feng is adopted for solving some important nonlinear partial differential equations, including the (2 + 1-dimensional hyperbolic nonlinear Schrodinger (HNLS equation, the generalized nonlinear Schrodinger (GNLS equation with a source, and the higher-order nonlinear Schrodinger equation in nonlinear optical fibers. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner.
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2012-01-01
Full Text Available We modified the rational Jacobi elliptic functions method to construct some new exact solutions for nonlinear differential difference equations in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, the discrete nonlinear Klein-Gordon equation, and the quintic discrete nonlinear Schrodinger equation. Some new types of the Jacobi elliptic solutions are obtained for some nonlinear differential difference equations in mathematical physics. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.
Sandhu, Ali Imran
2016-04-10
A sparsity-regularized Born iterative method (BIM) is proposed for efficiently reconstructing two-dimensional piecewise-continuous inhomogeneous dielectric profiles. Such profiles are typically not spatially sparse, which reduces the efficiency of the sparsity-promoting regularization. To overcome this problem, scattered fields are represented in terms of the spatial derivative of the dielectric profile and reconstruction is carried out over samples of the dielectric profile\\'s derivative. Then, like the conventional BIM, the nonlinear problem is iteratively converted into a sequence of linear problems (in derivative samples) and sparsity constraint is enforced on each linear problem using the thresholded Landweber iterations. Numerical results, which demonstrate the efficiency and accuracy of the proposed method in reconstructing piecewise-continuous dielectric profiles, are presented.
A mixed finite element method for nonlinear diffusion equations
Burger, Martin
2010-01-01
We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.
An hp symplectic pseudospectral method for nonlinear optimal control
Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong
2017-01-01
An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.
Mapping deformation method and its application to nonlinear equations
Institute of Scientific and Technical Information of China (English)
李画眉
2002-01-01
An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinearpartial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraicmapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein-Gordon equation. This isapplied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained,including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions.
The simplex method for nonlinear sliding mode control
Directory of Open Access Journals (Sweden)
Bartolini G.
1998-01-01
Full Text Available General nonlinear control systems described by ordinary differential equations with a prescribed sliding manifold are considered. A method of designing a feedback control law such that the state variable fulfills the sliding condition in finite time is based on the construction of a suitable simplex of vectors in the tangent space of the manifold. The convergence of the method is proved under an obtuse angle condition and a way to build the required simplex is indicated. An example of engineering interest is presented.
Method of guiding functions in problems of nonlinear analysis
Obukhovskii, Valeri; Van Loi, Nguyen; Kornev, Sergei
2013-01-01
This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations, differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis, describes the classical aspects of the method of guiding functions, and then presents recent findings only available in the research literature. It describes essential applications in control theory, the theory of bifurcations, and physics, making it a valuable resource not only for “pure” mathematicians, but also for students and researchers working in applied mathematics, the engineering sciences and physics.
High-Order Energy Balance Method to Nonlinear Oscillators
Seher Durmaz; Metin Orhan Kaya
2012-01-01
Energy balance method (EBM) is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated fo...
High-Order Energy Balance Method to Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Seher Durmaz
2012-01-01
Full Text Available Energy balance method (EBM is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated for several values of parameters of the oscillator.
The energy balance to nonlinear oscillations via Jacobi collocation method
Directory of Open Access Journals (Sweden)
M.K. Yazdi
2015-06-01
Full Text Available This study develops the energy balance based on Jacobi collocation method for accurate prediction of conservative nonlinear oscillator models with a single collocation point. The node points are taken as the roots of Jacobi orthogonal polynomials. Several examples are included to demonstrate the applicability and accuracy of the proposed algorithm, and some comparisons are made with the existing results. The method is suitable and the approximate frequencies are valid for small as well as large amplitudes of oscillation. Excellent agreement with exact ones is presented for the first order approximation.
A new method for nonlinear optimization - experimental results
Energy Technology Data Exchange (ETDEWEB)
Loskovska, S.; Percinkova, B.
1994-12-31
In this paper an application of a new method for nonlinear optimization problems suggested and presented by B. Percinkova is performed. The method is originally developed and applicated on nonlinear systems. Basis of the method is following: A system of n-nonlinear equations gives as F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) = 0; 1 = 1, 2, ..., n and solution domain x{sub pi} {<=} x{sub i} {<=} x{sub ki} i = 1, 2, ..., n is modified by introducing a new variable z. The new system is given by: F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) = z; i = 1, 2, ..., n. The system defines a curve in (n + 1) dimensional space. System`s point X = (x{sub i}, x{sub 2}, x{sub 3}, ..., x{sub n}, z) that, the solution of the system is obtained using an interative procedure moving along the curve until the point with z = 0 is reached. In order to applicate method on optimization problems, a basic optimization model given with (min, max)F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) with the following optimization space: F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) ({<=}{>=})0 : i = 1, 2, ..., n is transformed into a system equivalent to system (2) by (dF/dx{sub i}) = z; i - 1, 2, ..., n. The main purpose of this work is to make relevant evaluation of the method by standard test problems.
Pulse wave attenuation measurement by linear and nonlinear methods in nonlinearly elastic tubes.
Bertram, C D; Pythoud, F; Stergiopulos, N; Meister, J J
1999-04-01
Reasons for the continuing difficulty in making definitive measurements of pulse wave attenuation in elastic tubes and arteries in the presence of reflections are sought. The measurement techniques available were re-examined in elastic tubes mimicking the arterial compliance nonlinearity, under conditions of strong reflection. The pulse was of physiological shape, and two different pulse amplitudes in the physiological range were used. Measurements of pressure, flow-rate and diameter pulsation allowed the deployment of four of the classical linear methods of analysis. In addition, a method of separating the forward- and backward-travelling waves that does not require linearising assumptions was used, and the attenuation in the forward and reverse directions was calculated from the resulting waveforms. Overall, the results obtained here suggest that a fully satisfactory way of measuring arterial attenuation has yet to be devised. The classical linear methods all provided comparable attenuation estimates in terms of average value and degree of scatter across frequency. Increased scatter was generally found at the higher pulse amplitude. When the forward waveforms from the separation were similarly compared in terms of frequency components, the average value at energetic harmonics was similar to both the value indicated by the linear methods and the values predicted from linear theory on the basis of estimated viscous and viscoelastic parameter data. The backward waveforms indicated a physically unreasonable result, attributed as the expression for this technique of the same difficulties that normally manifest in scatter. Data in the literature suggesting that one of the classical methods, the three-point, systematically over-estimates attenuation were not supported, but it was confirmed that this method becomes prone to negative attenuation estimates at low harmonics as pulse amplitude increases. Although the goal of definitive attenuation measurement remains elusive
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper presents a method on non-linear correction of broadband LFMCW signal utilizing its relativenonlinear error. The deriving procedure and the results simulated by a computer and tested by a practical system arealso introduced. The method has two obvious advantages compared with the previous methods: (1) Correction has norelation with delay time td and sweep bandwidth B; (2) The inherent non-linear error of VCO has no influence on thecorrection and its last results.
Prediction of biodegradation kinetics using a nonlinear group contribution method
Energy Technology Data Exchange (ETDEWEB)
Tabak, H.H. (Environmental Protection Agency, Cincinnati, OH (United States)); Govind, R. (Univ. of Cincinnati, OH (United States))
1993-02-01
The fate of organic chemicals in the environment depends on their susceptibility to biodegradation. Hence, development of regulations concerning their manufacture and use requires information on the extent and rate of biodegradation. Recent studies have attempted to correlate the kinetics of biodegradation with the molecular structure of the compound. This has led to the development of structure-biodegradation relationships (SBRs) using the group contribution approach. Each defined group present in the chemical structure of the compound is assigned a unique numerical contribution toward the calculation of the biodegradation kinetic constants. In this paper, a nonlinear group contribution method has been developed using neural networks; it is trained using literature data on the first-order biodegradation kinetic rate constant for a number of priority pollutants. The trained neural network is then used to predict the biodegradation kinetic constant for a new list of compounds, and results have been compared with the experimental values and the predictions obtained from a linear group contribution method. It has been shown that the nonlinear group contribution method using neural networks is able to provide a superior fit to the training set data and test data set and produce a lower prediction error than the previous linear method.
Diagnosis of multiple sclerosis from EEG signals using nonlinear methods.
Torabi, Ali; Daliri, Mohammad Reza; Sabzposhan, Seyyed Hojjat
2017-09-08
EEG signals have essential and important information about the brain and neural diseases. The main purpose of this study is classifying two groups of healthy volunteers and Multiple Sclerosis (MS) patients using nonlinear features of EEG signals while performing cognitive tasks. EEG signals were recorded when users were doing two different attentional tasks. One of the tasks was based on detecting a desired change in color luminance and the other task was based on detecting a desired change in direction of motion. EEG signals were analyzed in two ways: EEG signals analysis without rhythms decomposition and EEG sub-bands analysis. After recording and preprocessing, time delay embedding method was used for state space reconstruction; embedding parameters were determined for original signals and their sub-bands. Afterwards nonlinear methods were used in feature extraction phase. To reduce the feature dimension, scalar feature selections were done by using T-test and Bhattacharyya criteria. Then, the data were classified using linear support vector machines (SVM) and k-nearest neighbor (KNN) method. The best combination of the criteria and classifiers was determined for each task by comparing performances. For both tasks, the best results were achieved by using T-test criterion and SVM classifier. For the direction-based and the color-luminance-based tasks, maximum classification performances were 93.08 and 79.79% respectively which were reached by using optimal set of features. Our results show that the nonlinear dynamic features of EEG signals seem to be useful and effective in MS diseases diagnosis.
Estimation methods for nonlinear state-space models in ecology
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Berg, Casper Willestofte; Thygesen, Uffe Høgsbro
2011-01-01
The use of nonlinear state-space models for analyzing ecological systems is increasing. A wide range of estimation methods for such models are available to ecologists, however it is not always clear, which is the appropriate method to choose. To this end, three approaches to estimation in the theta...... logistic model for population dynamics were benchmarked by Wang (2007). Similarly, we examine and compare the estimation performance of three alternative methods using simulated data. The first approach is to partition the state-space into a finite number of states and formulate the problem as a hidden...... Markov model (HMM). The second method uses the mixed effects modeling and fast numerical integration framework of the AD Model Builder (ADMB) open-source software. The third alternative is to use the popular Bayesian framework of BUGS. The study showed that state and parameter estimation performance...
Similar Constructive Method for Solving a nonlinearly Spherical Percolation Model
Directory of Open Access Journals (Sweden)
WANG Yong
2013-01-01
Full Text Available In the view of nonlinear spherical percolation problem of dual porosity reservoir, a mathematical model considering three types of outer boundary conditions: closed, constant pressure, infinity was established in this paper. The mathematical model was linearized by substitution of variable and became a boundary value problem of ordinary differential equation in Laplace space by Laplace transformation. It was verified that such boundary value problem with one type of outer boundary had a similar structure of solution. And a new method: Similar Constructive Method was obtained for solving such boundary value problem. By this method, solutions with similar structure in other two outer boundary conditions were obtained. The Similar Constructive Method raises efficiency of solving such percolation model.
A nonlinear analytic function expansion nodal method for transient calculations
Energy Technology Data Exchange (ETDEWEB)
Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1998-12-31
The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)
CAD—Oriented Noise Analysis Method of Nonlinear Microwave Chircuits
Institute of Scientific and Technical Information of China (English)
WANGJun; TANGGaodi; CHENHuilian
2003-01-01
A general method is introduced which is capable of making accurate,quantitative predictions about the noise of different type of nonlinear microwave circuits.This new approach also elucidates several design criteria for making it suitable to CAD-oriented analysis via identifying the mechanisms by which intrinsic device noise and external noise sources contribute to the total equivalent noise.In particular,it explains the details of how noise spectrum at the interesting port is obtained.And the theory also naturally leads to additional important design insights.In the illustrative experiments,excellent agreement among theory,simulations,and measurements is observed.
Method of the Logistic Function for Finding Analytical Solutions of Nonlinear Differential Equations
Kudryashov, N. A.
2015-01-01
The method of the logistic function is presented for finding exact solutions of nonlinear differential equations. The application of the method is illustrated by using the nonlinear ordinary differential equation of the fourth order. Analytical solutions obtained by this method are presented. These solutions are expressed via exponential functions.logistic function, nonlinear wave, nonlinear ordinary differential equation, Painlev´e test, exact solution
A modal method for ﬁnite amplitude, nonlinear sloshing
Indian Academy of Sciences (India)
P N Shankar; R Kidambi
2002-10-01
A modal method is used to calculate the two-dimensional sloshing motion of an inviscid liquid in a rectangular container. The full nonlinear problem is reduced to the solution of a system of nonlinear ordinary differential equations for the time varying coefﬁcients in the expansions of the interface and the potential. The effects of capillarity are included in the formulation. The simplicity, generality and power of the method are exhibited not only by recovering the earlier results obtained, for example, by Penney and Price [1], Tadjbakhsh and Keller [2] and Faltinsen et al [3], but also by obtaining new and interesting results of the effects of capillarity and shallow depth, which would be difﬁcult to obtain otherwise. For example, it is found that for the initial interface proﬁle considered here, parasitic capillary waves, borne by the higher number wave modes, are generated for moderate capillarity but disappear for larger values of the parameter. The method can be extended to other simple geometries.
Fast nonlinear regression method for CT brain perfusion analysis.
Bennink, Edwin; Oosterbroek, Jaap; Kudo, Kohsuke; Viergever, Max A; Velthuis, Birgitta K; de Jong, Hugo W A M
2016-04-01
Although computed tomography (CT) perfusion (CTP) imaging enables rapid diagnosis and prognosis of ischemic stroke, current CTP analysis methods have several shortcomings. We propose a fast nonlinear regression method with a box-shaped model (boxNLR) that has important advantages over the current state-of-the-art method, block-circulant singular value decomposition (bSVD). These advantages include improved robustness to attenuation curve truncation, extensibility, and unified estimation of perfusion parameters. The method is compared with bSVD and with a commercial SVD-based method. The three methods were quantitatively evaluated by means of a digital perfusion phantom, described by Kudo et al. and qualitatively with the aid of 50 clinical CTP scans. All three methods yielded high Pearson correlation coefficients ([Formula: see text]) with the ground truth in the phantom. The boxNLR perfusion maps of the clinical scans showed higher correlation with bSVD than the perfusion maps from the commercial method. Furthermore, it was shown that boxNLR estimates are robust to noise, truncation, and tracer delay. The proposed method provides a fast and reliable way of estimating perfusion parameters from CTP scans. This suggests it could be a viable alternative to current commercial and academic methods.
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.
2013-01-01
In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
Hybrid discretization method for time-delay nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zheng [Xi' an Jiaotong University, Xi' an (China); Zhang, Yuanliang; Kil Chong, To [Chonbuk National University, Jeonju (Korea, Republic of); Kostyukova, Olga [3Institute of Mathematics National Academy of Science of Belarus, Minsk (Belarus)
2010-03-15
A hybrid discretization scheme that combines the virtues of the Taylor series and Matrix exponential integration methods is proposed. In the algorithm, each sampling time interval is divided into two subintervals to be considered according to the time delay and sampling period. The algorithm is not too expensive computationally and lends itself to be easily inserted into large simulation packages. The mathematical structure of the new discretization scheme is explored and described in detail. The performance of the proposed discretization procedure is evaluated by employing case studies. Various input signals, sampling rates, and time-delay values are considered to test the proposed method. The results demonstrate that the proposed discretization scheme is better than previous Taylor series method for nonlinear time-delay systems, especially when a large sampling period is inevitable
Ultrasound Tomography in Circular Measurement Configuration using Nonlinear Reconstruction Method
Directory of Open Access Journals (Sweden)
Tran Quang-Huy
2015-12-01
Full Text Available Ultrasound tomography offers the potential for detecting of very small tumors whose sizes are smaller than the wavelength of the incident pressure wave without ionizing radiation. Based on inverse scattering technique, this imaging modality uses some material properties such as sound contrast and attenuation in order to detect small objects. One of the most commonly used methods in ultrasound tomography is the Distorted Born Iterative Method (DBIM. The compressed sensing technique was applied in the DBIM as a promising approach for the image reconstruction quality improvement. Nevertheless, the random measurement configuration of transducers in this method is very difficult to set up in practice. Therefore, in this paper, we take advantages of simpler sparse uniform measurement configuration set-up of transducers and high-quality image reconstruction of 1 non-linear regularization in sparse scattering domain. The simulation results demonstrate the high performance of the proposed approach in terms of tremendously reduced total runtime and normalized error.
Analytic treatment of nonlinear evolution equations using ﬁrst integral method
Indian Academy of Sciences (India)
Ahmet Bekir; Ömer Ünsal
2012-07-01
In this paper, we show the applicability of the ﬁrst integral method to combined KdV-mKdV equation, Pochhammer–Chree equation and coupled nonlinear evolution equations. The power of this manageable method is conﬁrmed by applying it for three selected nonlinear evolution equations. This approach can also be applied to other nonlinear differential equations.
The tanh-coth method combined with the Riccati equation for solving non-linear equation
Energy Technology Data Exchange (ETDEWEB)
Bekir, Ahmet [Dumlupinar University, Art-Science Faculty, Department of Mathematics, Kuetahya (Turkey)], E-mail: abekir@dumlupinar.edu.tr
2009-05-15
In this work, we established abundant travelling wave solutions for some non-linear evolution equations. This method was used to construct solitons and traveling wave solutions of non-linear evolution equations. The tanh-coth method combined with Riccati equation presents a wider applicability for handling non-linear wave equations.
Optimization of nonlinear structural resonance using the incremental harmonic balance method
DEFF Research Database (Denmark)
Dou, Suguang; Jensen, Jakob Søndergaard
2015-01-01
We present an optimization procedure for tailoring the nonlinear structural resonant response with time-harmonic loads. A nonlinear finite element method is used for modeling beam structures with a geometric nonlinearity and the incremental harmonic balance method is applied for accurate nonlinea...
NOLB : Non-linear rigid block normal mode analysis method.
Hoffmann, Alexandre; Grudinin, Sergei
2017-04-05
We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velocities. The key observation of our method is that the angular velocity of a rigid block can be interpreted as the result of an implicit force, such that the motion of the rigid block can be considered as a pure rotation about a certain center. We demonstrate the motions produced with the NOLB method on three different molecular systems and show that some of the lowest frequency normal modes correspond to the biologically relevant motions. For example, NOLB detects the spiral sliding motion of the TALE protein, which is capable of rapid diffusion along its target DNA. Overall, our method produces better structures compared to the standard approach, especially at large deformation amplitudes, as we demonstrate by visual inspection, energy and topology analyses, and also by the MolProbity service validation. Finally, our method is scalable and can be applied to very large molecular systems, such as ribosomes. Standalone executables of the NOLB normal mode analysis method are available at https://team.inria.fr/nano-d/software/nolb-normal-modes. A graphical user interfaces created for the SAMSON software platform will be made available at https: //www.samson-connect.net.
Pan, Shoukui; Okano, Y.; Tsunekawa, S.; Fukuda, T.
1993-03-01
The Kyropoulus method was used to grow nonlinear optical organic crystals ABP (4-aminobenzophenone). The crystals were characterized by nonlinear optical measurements and had a large effect of frequency doubling.
Finite Volume Evolution Galerkin Methods for Nonlinear Hyperbolic Systems
Lukáčová-Medvid'ová, M.; Saibertová, J.; Warnecke, G.
2002-12-01
We present new truly multidimensional schemes of higher order within the frame- work of finite volume evolution Galerkin (FVEG) methods for systems of nonlinear hyperbolic conservation laws. These methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of the multidimensional hyperbolic system, such that all of the infinitely many directions of wave propagation are taken into account. Following our previous results for the wave equation system, we derive approximate evolution operators for the linearized Euler equations. The integrals along the Mach cone and along the cell interfaces are evaluated exactly, as well as by means of numerical quadratures. The influence of these numerical quadratures will be discussed. Second-order resolution is obtained using a conservative piecewise bilinear recovery and the midpoint rule approximation for time integration. We prove error estimates for the finite volume evolution Galerkin scheme for linear systems with constant coefficients. Several numerical experiments for the nonlinear. Euler equations, which confirm the accuracy and good multidimensional behavior of the FVEG schemes, are presented as well.
Efficient computation method for two-dimensional nonlinear waves
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The theory and simulation of fully-nonlinear waves in a truncated two-dimensional wave tank in time domain are presented. A piston-type wave-maker is used to generate gravity waves into the tank field in finite water depth. A damping zone is added in front of the wave-maker which makes it become one kind of absorbing wave-maker and ensures the prescribed Neumann condition. The efficiency of nmerical tank is further enhanced by installation of a sponge layer beach (SLB) in front of downtank to absorb longer weak waves that leak through the entire wave train front. Assume potential flow, the space- periodic irrotational surface waves can be represented by mixed Euler- Lagrange particles. Solving the integral equation at each time step for new normal velocities, the instantaneous free surface is integrated following time history by use of fourth-order Runge- Kutta method. The double node technique is used to deal with geometric discontinuity at the wave- body intersections. Several precise smoothing methods have been introduced to treat surface point with high curvature. No saw-tooth like instability is observed during the total simulation.The advantage of proposed wave tank has been verified by comparing with linear theoretical solution and other nonlinear results, excellent agreement in the whole range of frequencies of interest has been obtained.
Conditions on Structural Controllability of Nonlinear Systems: Polynomial Method
Directory of Open Access Journals (Sweden)
Qiang Ma
2011-03-01
Full Text Available In this paper the structural controllability of a class of a nonlinear system is investigated. The transfer function (matrix of nonlinear systems is obtained by putting the nonlinear system model on non-commutative ring. Conditions of structural controllability of nonlinear systems are presented according to the criterion of linear systems structural controllability in frequency domain. An example is used to testify the presented conditions finally.
Simple noise-reduction method based on nonlinear forecasting
Tan, James P. L.
2017-03-01
Nonparametric detrending or noise reduction methods are often employed to separate trends from noisy time series when no satisfactory models exist to fit the data. However, conventional noise reduction methods depend on subjective choices of smoothing parameters. Here we present a simple multivariate noise reduction method based on available nonlinear forecasting techniques. These are in turn based on state-space reconstruction for which a strong theoretical justification exists for their use in nonparametric forecasting. The noise reduction method presented here is conceptually similar to Schreiber's noise reduction method using state-space reconstruction. However, we show that Schreiber's method has a minor flaw that can be overcome with forecasting. Furthermore, our method contains a simple but nontrivial extension to multivariate time series. We apply the method to multivariate time series generated from the Van der Pol oscillator, the Lorenz equations, the Hindmarsh-Rose model of neuronal spiking activity, and to two other univariate real-world data sets. It is demonstrated that noise reduction heuristics can be objectively optimized with in-sample forecasting errors that correlate well with actual noise reduction errors.
Nonlinear diffusion methods based on robust statistics for noise removal
Institute of Scientific and Technical Information of China (English)
JIA Di-ye; HUANG Feng-gang; SU Han
2007-01-01
A novel smoothness term of Bayesian regularization framework based on M-estimation of robust statistics is proposed, and from this term a class of fourth-order nonlinear diffusion methods is proposed. These methods attempt to approximate an observed image with a piecewise linear image, which looks more natural than piecewise constant image used to approximate an observed image by P-M[1] model. It is known that M-estimators and W-estimators are essentially equivalent and solve the same minimization problem. Then, we propose PL bilateral filter from equivalent W-estimator. This new model is designed for piecewise linear image filtering,which is more effective than normal bilateral filter.
A new method for parameter estimation in nonlinear dynamical equations
Wang, Liu; He, Wen-Ping; Liao, Le-Jian; Wan, Shi-Quan; He, Tao
2015-01-01
Parameter estimation is an important scientific problem in various fields such as chaos control, chaos synchronization and other mathematical models. In this paper, a new method for parameter estimation in nonlinear dynamical equations is proposed based on evolutionary modelling (EM). This will be achieved by utilizing the following characteristics of EM which includes self-organizing, adaptive and self-learning features which are inspired by biological natural selection, and mutation and genetic inheritance. The performance of the new method is demonstrated by using various numerical tests on the classic chaos model—Lorenz equation (Lorenz 1963). The results indicate that the new method can be used for fast and effective parameter estimation irrespective of whether partial parameters or all parameters are unknown in the Lorenz equation. Moreover, the new method has a good convergence rate. Noises are inevitable in observational data. The influence of observational noises on the performance of the presented method has been investigated. The results indicate that the strong noises, such as signal noise ratio (SNR) of 10 dB, have a larger influence on parameter estimation than the relatively weak noises. However, it is found that the precision of the parameter estimation remains acceptable for the relatively weak noises, e.g. SNR is 20 or 30 dB. It indicates that the presented method also has some anti-noise performance.
Elsawy, Mahmoud M R
2016-01-01
Two distinct models are developed to investigate the transverse magnetic stationary solutions propagating in one-dimensional anisotropic nonlinear plasmonic structures made from a nonlinear metamaterial core of Kerr-type embedded between two semi-infinite metal claddings. The first model is semi-analytical, in which we assumed that the anisotropic nonlinearity depends only on the transverse component of the electric field and that the nonlinear refractive index modification is small compared to the linear one. This method allows us to derive analytically the field profiles and the nonlinear dispersion relations in terms of the Jacobi elliptical functions. The second model is fully numerical, it is based on the finite-element method in which all the components of the electric field are considered in the Kerr-type nonlinearity with no presumptions on the nonlinear refractive index change. Our finite-element based model is valid beyond weak nonlinearity regime and generalize the well-known single-component fixed...
Method and system for non-linear motion estimation
Lu, Ligang (Inventor)
2011-01-01
A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.
Applications of Automation Methods for Nonlinear Fracture Test Analysis
Allen, Phillip A.; Wells, Douglas N.
2013-01-01
Using automated and standardized computer tools to calculate the pertinent test result values has several advantages such as: 1. allowing high-fidelity solutions to complex nonlinear phenomena that would be impractical to express in written equation form, 2. eliminating errors associated with the interpretation and programing of analysis procedures from the text of test standards, 3. lessening the need for expertise in the areas of solid mechanics, fracture mechanics, numerical methods, and/or finite element modeling, to achieve sound results, 4. and providing one computer tool and/or one set of solutions for all users for a more "standardized" answer. In summary, this approach allows a non-expert with rudimentary training to get the best practical solution based on the latest understanding with minimum difficulty.Other existing ASTM standards that cover complicated phenomena use standard computer programs: 1. ASTM C1340/C1340M-10- Standard Practice for Estimation of Heat Gain or Loss Through Ceilings Under Attics Containing Radiant Barriers by Use of a Computer Program 2. ASTM F 2815 - Standard Practice for Chemical Permeation through Protective Clothing Materials: Testing Data Analysis by Use of a Computer Program 3. ASTM E2807 - Standard Specification for 3D Imaging Data Exchange, Version 1.0 The verification, validation, and round-robin processes required of a computer tool closely parallel the methods that are used to ensure the solution validity for equations included in test standard. The use of automated analysis tools allows the creation and practical implementation of advanced fracture mechanics test standards that capture the physics of a nonlinear fracture mechanics problem without adding undue burden or expense to the user. The presented approach forms a bridge between the equation-based fracture testing standards of today and the next generation of standards solving complex problems through analysis automation.
Dynamic properties of the cubic nonlinear Schr(o)dinger equation by symplectic method
Institute of Scientific and Technical Information of China (English)
Liu Xue-Shen; Wei Jia-Yu; Ding Pei-Zhu
2005-01-01
The dynamic properties of a cubic nonlinear Schrodinger equation are investigated numerically by using the symplectic method with different space approximations. The behaviours of the cubic nonlinear Schrodinger equation are discussed with different cubic nonlinear parameters in the harmonically modulated initial condition. We show that the conserved quantities will be preserved for long-time computation but the system will exhibit different dynamic behaviours in space difference approximation for the strong cubic nonlinearity.
A method for generating highly nonlinear periodic waves in physical wave basins
DEFF Research Database (Denmark)
Zhang, Haiwen; Schäffer, Hemming A.; Bingham, Harry B.
2006-01-01
This abstract describes a new method for generating nonlinear waves of constant form in physical wave basins. The idea is to combine fully dispersive linear wavemaker theory with nonlinear shallow water wave generation theory; and use an exact nonlinear theory as the target. We refer to the metho...... as an ad-hoc unified wave generation theory, since there is no rigorous analysis behind the idea which is simply justified by the improved results obtained for the practical generation of steady nonlinear waves....
A MESHLESS LOCAL PETROV-GALERKIN METHOD FOR GEOMETRICALLY NONLINEAR PROBLEMS
Institute of Scientific and Technical Information of China (English)
Xiong Yuanbo; Long Shuyao; Hu De'an; Li Guangyao
2005-01-01
Nonlinear formulations of the meshless local Petrov-Galerkin (MLPG) method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation are imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.
A Non-smooth Nonlinear Conjugate Gradient Method for Interactive Contact Force Problems
DEFF Research Database (Denmark)
Silcowitz, Morten; Niebe, Sarah Maria; Erleben, Kenny
2010-01-01
of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze...
DEFF Research Database (Denmark)
Kragh, Knud Abildgaard; Thomsen, Jon Juel; Tcherniak, Dmitri
2010-01-01
exists. The present study suggests a framework for the detection of structural nonlinearities. Two methods for detection are compared, the homogeneity method and a Hilbert transform based method. Based on these two methods, a nonlinearity index is suggested. Through simulations and laboratory experiments...
Energy Technology Data Exchange (ETDEWEB)
Zhao Xiqiang [Department of Mathematics, Ocean University of China, Qingdao Shandong 266071 (China)] e-mail: zhaodss@yahoo.com.cn; Wang Limin [Shandong University of Technology, Zibo Shandong 255049 (China); Sun Weijun [Shandong University of Technology, Zibo Shandong 255049 (China)
2006-04-01
In this letter, a new method, called the repeated homogeneous balance method, is proposed for seeking the traveling wave solutions of nonlinear partial differential equations. The Burgers-KdV equation is chosen to illustrate our method. It has been confirmed that more traveling wave solutions of nonlinear partial differential equations can be effectively obtained by using the repeated homogeneous balance method.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Some theoretical methods have been reported to deal with nonlinear problems of composite materials but the accuracy is not so good. In the meantime, a lot of nonlinear problems are difficult to be managed by the theoretical methods. The present study aims to use the developed method, the random microstructure finite element method, to deal with these nonlinear problems. In this paper, the random microstructure finite element method is used to deal with all three kinds of nonlinear property problems of composite materials. The analyzed results suggest that the influences of the nonlinear phenomena on the effective properties of composite materials are significant and the random microstructure finite element method is an efficient tool to investigate the nonlinear problems.
Cigeroglu, Ender; Samandari, Hamed
2014-11-01
Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion. The effect of nonlinearities, different end conditions, initial curvature, and stiffness of the surrounding elastic medium, and vibrational modes on the nonlinear free vibration of DWCNTs is studied. Results show that it is possible to detect different vibration modes occurring at a single vibration frequency when CNTs vibrate in the out-of-phase vibration mode. Moreover, it is observed that boundary conditions have significant effect on the nonlinear natural frequencies of the DWCNT including multiple solutions.
Implementing Kernel Methods Incrementally by Incremental Nonlinear Projection Trick.
Kwak, Nojun
2016-05-20
Recently, the nonlinear projection trick (NPT) was introduced enabling direct computation of coordinates of samples in a reproducing kernel Hilbert space. With NPT, any machine learning algorithm can be extended to a kernel version without relying on the so called kernel trick. However, NPT is inherently difficult to be implemented incrementally because an ever increasing kernel matrix should be treated as additional training samples are introduced. In this paper, an incremental version of the NPT (INPT) is proposed based on the observation that the centerization step in NPT is unnecessary. Because the proposed INPT does not change the coordinates of the old data, the coordinates obtained by INPT can directly be used in any incremental methods to implement a kernel version of the incremental methods. The effectiveness of the INPT is shown by applying it to implement incremental versions of kernel methods such as, kernel singular value decomposition, kernel principal component analysis, and kernel discriminant analysis which are utilized for problems of kernel matrix reconstruction, letter classification, and face image retrieval, respectively.
Application of nonlinear methods to the study of ionospheric plasma
Chernyshov, A. A.; Mogilevsky, M. M.; Kozelov, B. V.
2015-01-01
Most of the processes taking place in the auroral region of Earth's ionosphere are reflected in a variety of dynamic forms of the aurora borealis. In order to study these processes it is necessary to consider temporary and spatial variations of the characteristics of ionospheric plasma. Most traditional methods of classical physics are applicable mainly for stationary or quasi-stationary phenomena, but dynamic regimes, transients, fluctuations, selfsimilar scaling could be considered using the methods of nonlinear dynamics. Special interest is the development of the methods for describing the spatial structure and the temporal dynamics of auroral ionosphere based on the ideas of percolation theory and fractal geometry. The fractal characteristics (the Hausdorff fractal dimension and the index of connectivity) of Hall and Pedersen conductivities are used to the description of fractal patterns in the ionosphere. To obtain the self-consistent estimates of the parameters the Hausdorff fractal dimension and the index of connectivity in the auroral zone, an additional relation describing universal behavior of the fractal geometry of percolation at the critical threshold is applied. Also, it is shown that Tsallis statistics can be used to study auroral ionosphere
Nonlinear Analysis Methods for Evaluating Seismic Performance of Multi-Story RC Buildings
Tayyebi, Saeid Moussavi
2014-01-01
ABSTRACT: A major challenge in performance-based earthquake engineering is to develop simple and practical methods for estimating capacity level and seismic demand on structures by taking into account their inelastic behavior. Researchers and engineers certainly prefer to use nonlinear static methods over complicated nonlinear time-history methods. However, in Nonlinear Static procedure both predetermined target displacement and force distribution pattern are based on a false assumption that ...
Directory of Open Access Journals (Sweden)
Elsayed Mohamed Elsayed ZAYED
2014-07-01
Full Text Available In this article, many new exact solutions of the (2+1-dimensional nonlinear Boussinesq-Kadomtsev-Petviashvili equation and the (1+1-dimensional nonlinear heat conduction equation are constructed using the Riccati equation mapping method. By means of this method, many new exact solutions are successfully obtained. This method can be applied to many other nonlinear evolution equations in mathematical physics.doi:10.14456/WJST.2014.14
Analysis and Design Methods for Nonlinear Control Systems
1990-03-01
entitled "Design of Nonlinear PID Controllers ." In this paper it is demonstrated that the extended linearization approach can be applied to standard...Sciences and Systems, Baltimore, Maryland, pp. 675-680, 1987. [3] WJ. Rugh, "Design of Nonlinear PID Controllers ," AIChE Journa Vol. 33, No. 10, pp. 1738
Hu, Juju; Hu, Haijiang; Ji, Yinghua
2010-03-15
Periodic nonlinearity that ranges from tens of nanometers to a few nanometers in heterodyne interferometer limits its use in high accuracy measurement. A novel method is studied to detect the nonlinearity errors based on the electrical subdivision and the analysis method of statistical signal in heterodyne Michelson interferometer. Under the movement of micropositioning platform with the uniform velocity, the method can detect the nonlinearity errors by using the regression analysis and Jackknife estimation. Based on the analysis of the simulations, the method can estimate the influence of nonlinearity errors and other noises for the dimensions measurement in heterodyne Michelson interferometer.
Modified extended tanh-function method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Department of Physics, Faculty of Science, Theoretical Research Group, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Department of Physics, Faculty of Science, Theoretical Research Group, Mansoura University, 35516 Mansoura (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-03-15
Based on computerized symbolic computation, modified extended tanh-method for constructing multiple travelling wave solutions of nonlinear evolution equations is presented and implemented in a computer algebraic system. Applying this method, with the aid of Maple, we consider some nonlinear evolution equations in mathematical physics such as the nonlinear partial differential equation, nonlinear Fisher-type equation, ZK-BBM equation, generalized Burgers-Fisher equation and Drinfeld-Sokolov system. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods.
Simplified Methods Applied to Nonlinear Motion of Spar Platforms
Energy Technology Data Exchange (ETDEWEB)
Haslum, Herbjoern Alf
2000-07-01
Simplified methods for prediction of motion response of spar platforms are presented. The methods are based on first and second order potential theory. Nonlinear drag loads and the effect of the pumping motion in a moon-pool are also considered. Large amplitude pitch motions coupled to extreme amplitude heave motions may arise when spar platforms are exposed to long period swell. The phenomenon is investigated theoretically and explained as a Mathieu instability. It is caused by nonlinear coupling effects between heave, surge, and pitch. It is shown that for a critical wave period, the envelope of the heave motion makes the pitch motion unstable. For the same wave period, a higher order pitch/heave coupling excites resonant heave response. This mutual interaction largely amplifies both the pitch and the heave response. As a result, the pitch/heave instability revealed in this work is more critical than the previously well known Mathieu's instability in pitch which occurs if the wave period (or the natural heave period) is half the natural pitch period. The Mathieu instability is demonstrated both by numerical simulations with a newly developed calculation tool and in model experiments. In order to learn more about the conditions for this instability to occur and also how it may be controlled, different damping configurations (heave damping disks and pitch/surge damping fins) are evaluated both in model experiments and by numerical simulations. With increased drag damping, larger wave amplitudes and more time are needed to trigger the instability. The pitch/heave instability is a low probability of occurrence phenomenon. Extreme wave periods are needed for the instability to be triggered, about 20 seconds for a typical 200m draft spar. However, it may be important to consider the phenomenon in design since the pitch/heave instability is very critical. It is also seen that when classical spar platforms (constant cylindrical cross section and about 200m draft
Application of homotopy-perturbation method to nonlinear population dynamics models
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, M.S.H. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia); Hashim, I. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)], E-mail: ishak_h@ukm.my; Abdulaziz, O. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)
2007-08-20
In this Letter, the homotopy-perturbation method (HPM) is employed to derive approximate series solutions of nonlinear population dynamics models. The nonlinear models considered are the multispecies Lotka-Volterra equations. The accuracy of this method is examined by comparison with the available exact and the fourth-order Runge-Kutta method (RK4)
Wideband nonlinear time reversal seismo-acoustic method for landmine detection.
Sutin, Alexander; Libbey, Brad; Fillinger, Laurent; Sarvazyan, Armen
2009-04-01
Acoustic and seismic waves provide a method to localize compliant mines by vibrating the top plate and a thin soil layer above the mine. This vibration is mostly linear, but also includes a small nonlinear deviation. The main goal of this paper is to introduce a method of processing that uses phase-inversion to observe nonlinear effects in a wide frequency band. The method extracts a nonlinear part of surface velocity from two similar broadcast signals of opposite sign by summing and cancelling the linear components and leaving the nonlinear components. This phase-inversion method is combined with time reversal focusing to provide increased seismic vibration and enhance the nonlinear effect. The experiments used six loudspeakers in a wood box placed over sand in which inert landmines were buried. The nonlinear surface velocity of the sand with a mine compared to the sand without a mine was greater as compared to a linear technique.
Nonlinear Circuit Analysis via Perturbation Methods and Hardware Prototyping
Directory of Open Access Journals (Sweden)
K. Odame
2010-01-01
Full Text Available Nonlinear signal processing is necessary in many emerging applications where form factor and power are at a premium. In order to make such complex computation feasible under these constraints, it is necessary to implement the signal processors as analog circuits. Since analog circuit design is largely based on a linear systems perspective, new tools are being introduced to circuit designers that allow them to understand and exploit circuit nonlinearity for useful processing. This paper discusses two such tools, which represent nonlinear circuit behavior in a graphical way, making it easy to develop a qualitative appreciation for the circuits under study.
Elsawy, Mahmoud M. R.; Renversez, Gilles
2017-07-01
Two distinct models are developed to investigate the transverse magnetic stationary solutions propagating in one-dimensional anisotropic nonlinear plasmonic structures made from a Kerr-type nonlinear metamaterial core embedded between two semi-infinite metal claddings. The first model is semi-analytical, in which we assume that the anisotropic nonlinearity depends only on the transverse component of the electric field and that the nonlinear refractive index modification is small compared to the linear one. This method allows us to derive analytically the field profiles and nonlinear dispersion relations in terms of the Jacobi elliptical functions. The second model is fully numerical and is based on the finite element method in which all the components of the electric field are considered in the Kerr-type nonlinearity, with no presumptions as to the nonlinear refractive index change. Our finite-element-based model is valid beyond the weak nonlinearity regime and generalizes the well-known single-component fixed power algorithm that is usually used. Examples of the main cases are investigated, including those with strong spatial nonlinear effects at low power. Loss issues are reduced through the use of a gain medium in the nonlinear metamaterial core. Using anisotropic nonlinear FDTD simulations, we provide some results for the properties of the main solution.
Geometric methods for nonlinear many-body quantum systems
Lewin, Mathieu
2010-01-01
Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schr\\"odinger operators. In this paper we provide a formalism which also allows to study nonlinear systems. We start by defining a weak topology on many-body states, which appropriately describes the physical behavior of the system in the case of lack of compactness, that is when some particles are lost at infinity. We provide several important properties of this topology and use them to provide a simple proof of the famous HVZ theorem in the repulsive case. In a second step we recall the method of geometric localization in Fock space as proposed by Derezi\\'nski and G\\'erard, and we relate this tool to our weak topology. We then provide several applications. We start by studying the so-called finite-rank approximation which consists in imposing that the many-body wavefunction can be expanded using finitely many one-body functions. We thereby emphasize geometric properties of Hartree-Fock states and ...
STABILITY ANALYSIS OF RUNGE-KUTTA METHODS FOR NONLINEAR SYSTEMS OF PANTOGRAPH EQUATIONS
Institute of Scientific and Technical Information of China (English)
Yue-xin Yu; Shou-fu Li
2005-01-01
This paper is concerned with numerical stability of nonlinear systems of pantograph equations. Numerical methods based on (k, l)-algebraically stable Runge-Kutta methods are suggested. Global and asymptotic stability conditions for the presented methods are derived.
LOCAL DISCONTINUOUS GALERKIN METHODS FOR THREE CLASSES OF NONLINEAR WAVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
Yan Xu; Chi-wang Shu
2004-01-01
In this paper, we further develop the local discontinuous Galerkin method to solve three classes of nonlinear wave equations formulated by the general KdV-Burgers type equations, the general fifth-order KdV type equations and the fully nonlinear K(n, n, n)equations, and prove their stability for these general classes of nonlinear equations. The schemes we present extend the previous work of Yan and Shu [30, 31] and of Levy, Shu and Yan [24] on local discontinuous Galerkin method solving partial differential equations with higher spatial derivatives. Numerical examples for nonlinear problems are shown to illustrate the accuracy and capability of the methods. The numerical experiments include stationary solitons, soliton interactions and oscillatory solitary wave solutions.The numerical experiments also include the compacton solutions of a generalized fifthorder KdV equation in which the highest order derivative term is nonlinear and the fully nonlinear K(n, n, n) equations.
Directory of Open Access Journals (Sweden)
U. Filobello-Nino
2015-01-01
Full Text Available We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM. Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.
Nonlinear generalized source method for modeling second-harmonic generation in diffraction gratings
Weismann, Martin; Panoiu, Nicolae C
2015-01-01
We introduce a versatile numerical method for modeling light diffraction in periodically patterned photonic structures containing quadratically nonlinear non-centrosymmetric optical materials. Our approach extends the generalized source method to nonlinear optical interactions by incorporating the contribution of nonlinear polarization sources to the diffracted field in the algorithm. We derive the mathematical formalism underlying the numerical method and introduce the Fourier-factorization suitable for nonlinear calculations. The numerical efficiency and runtime characteristics of the method are investigated in a set of benchmark calculations: the results corresponding to the fundamental frequency are compared to those obtained from a reference method and the beneficial effects of the modified Fourier-factorization rule on the accuracy of the nonlinear computations is demonstrated. In order to illustrate the capabilities of our method, we employ it to demonstrate strong enhancement of second-harmonic genera...
Directory of Open Access Journals (Sweden)
Md. Nur Alam
2016-06-01
Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.
Institute of Scientific and Technical Information of China (English)
Long Shuyao; Zhang Qin
2000-01-01
In this paper the dual reciprocity boundary element method is employed to solve nonlinear differential equation 2 u + u + εu3 = b. Results obtained in an example have a good agreement with those by FEM and show the applicability and simplicity of dual reciprocity method(DRM) in solving nonlinear dif ferential equations.
A new method to solve the damped nonlinear Klein-Gordon equation
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper discusses a damped nonlinear Klein-Gordon equation in the reproducing kernel space and provides a new method for solving the damped nonlinear Klein-Gordon equation based on the reproducing kernel space.Two numerical examples are given for illustrating the feasibility and accuracy of the method.
Variational iteration method for solving non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Hemeda, A.A. [Department of Mathematics, Faculty of Science, University of Tanta, Tanta (Egypt)], E-mail: aahemeda@yahoo.com
2009-02-15
In this paper, we shall use the variational iteration method to solve some problems of non-linear partial differential equations (PDEs) such as the combined KdV-MKdV equation and Camassa-Holm equation. The variational iteration method is superior than the other non-linear methods, such as the perturbation methods where this method does not depend on small parameters, such that it can fined wide application in non-linear problems without linearization or small perturbation. In this method, the problems are initially approximated with possible unknowns, then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
A SIMPLIFIED CALCULATING METHOD OF NONLINEAR FREQUENCY OF CABLE NET UNDER MEAN WIND LOAD
Institute of Scientific and Technical Information of China (English)
Feng Ruoqiang; Wu Yue; Shen Shizhao
2006-01-01
The cable net supported glass curtain wallas the most advanced technique in dot point supported glass curtain wall, is widely used in China. Because of its large deflection and high nonlinearity under wind load, the dynamic performance of the cable net is greatly different from that of the conventional linear structures. The continuous membrane theory is used to construct the nonlinear vibration differential equation of the cable net, and the harmonic balance method is used to solve the analytic formula of the nonlinear frequency. In order to verify the accuracy of the above analytic formula, the results of the formula and the nonlinear FEM time-history method are compared and found to be in good agreement. Furthermore, the nonlinear vibration differential equation and the nonlinear frequency obtained in this paper are the basis for the wind-induced response analysis of a cable net under fluctuating wind load.
Peng, Haijun; Wang, Xinwei; Zhang, Sheng; Chen, Biaosong
2017-07-01
Nonlinear state-delayed optimal control problems have complex nonlinear characters. To solve this complex nonlinear problem, an iterative symplectic pseudospectral method based on quasilinearization techniques, the dual variational principle and pseudospectral methods is proposed in this paper. First, the proposed method transforms the original nonlinear optimal control problem into a series of linear quadratic optimal control problems. Then, a symplectic pseudospectral method is developed to solve these converted linear quadratic state-delayed optimal control problems. Coefficient matrices in the proposed method are sparse and symmetric since the dual variational principle is used, which makes the proposed method highly efficient. Converged numerical solutions with high precision can be obtained after a few iterations due to the benefit of the local pseudospectral method and quasilinearization techniques. In the numerical simulations, other numerical methods were used for comparisons. The numerical simulation results show that the proposed method is highly accurate, efficient and robust.
Directory of Open Access Journals (Sweden)
Süleyman Öğrekçi
2015-01-01
Full Text Available We propose an efficient analytic method for solving nonlinear differential equations of fractional order. The fractional derivative is defined in the sense of modified Riemann-Liouville derivative. A new technique for calculating the generalized Taylor series coefficients (also known as “generalized differential transforms,” GDTs of nonlinear functions and a new approach of the generalized Taylor series method (GTSM are presented. This new method offers a simple algorithm for computing GDTs of nonlinear functions and avoids massive computational work that usually arises in the standard method. Several illustrative examples are demonstrated to show effectiveness of the proposed method.
A new method based on the harmonic balance method for nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Chen, Y.M. [Department of Mechanics, Zhongshan University, Guangzhou 510275 (China); Liu, J.K. [Department of Mechanics, Zhongshan University, Guangzhou 510275 (China)], E-mail: jikeliu@hotmail.com
2007-08-27
The harmonic balance (HB) method as an analytical approach is widely used for nonlinear oscillators, in which the initial conditions are generally simplified by setting velocity or displacement to be zero. Based on HB, we establish a new theory to address nonlinear conservative systems with arbitrary initial conditions, and deduce a set of over-determined algebraic equations. Since these deduced algebraic equations are not solved directly, a minimization problem is constructed instead and an iterative algorithm is employed to seek the minimization point. Taking Duffing and Duffing-harmonic equations as numerical examples, we find that these attained solutions are not only with high degree of accuracy, but also uniformly valid in the whole solution domain.
A Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem
Directory of Open Access Journals (Sweden)
Meixia Li
2012-01-01
Full Text Available Based on the smoothing function of penalized Fischer-Burmeister NCP-function, we propose a new smoothing inexact Newton algorithm with non-monotone line search for solving the generalized nonlinear complementarity problem. We view the smoothing parameter as an independent variable. Under suitable conditions, we show that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem. We also establish the local superlinear (quadratic convergence of the proposed algorithm under the BD-regular assumption. Preliminary numerical experiments indicate the feasibility and efficiency of the proposed algorithm.
A novel method for extracting acoustic nonlinearity parameters with diffraction corrections
Energy Technology Data Exchange (ETDEWEB)
Jeong, Hyunjo [Wonkwang University, Iksan (Korea, Republic of); Zhang, Shuzeng; Li, Xiongbing [Central South University, Changsha (China)
2016-02-15
A new method for determining the acoustic nonlinearity parameter using a nonlinear data fitting method is proposed. Based on the quasilinear theory of Westervelt's equation, the fundamental and second harmonic beam fields are expressed as a multi-Gaussian beam model that separates the attenuation and diffraction correction terms from the propagating plane waves. A nonlinear least squares curve fitting method is developed to extract the nonlinearity parameter without knowing the attenuation coefficients of the material being tested. The nonlinearity parameter of water is determined using the proposed method, and the result agrees well with the literature value. The attenuation coefficients of the fundamental and the second harmonic are also extracted and discussed.
Enokida, Ryuta; Takewaki, Izuru; Stoten, David
2014-12-01
The problem of control system design can be conceptualised as identifying an input signal to a plant (the system to be controlled) so that the corresponding output matches that of a pre-defined reference signal. Primarily, this problem is solved via well-known techniques based upon the principle of feedback design, an essential component for ensuring stability and robustness of the controlled system. However, feedforward design techniques also have a large part to play, whereby (in the absence of feedback control and assuming that the plant is stable) a model of the plant dynamics can be used to modify the reference signal so that the resultant feedforward input signal generates a plant output signal that is sufficiently close to the original reference signal. The principal objective of this paper is to introduce a new nonlinear control method, called nonlinear signal-based control (NSBC) that can be executed as an on-line technique of feedforward compensation (used synonymously here with the phrase 'input identification') and an off-line technique of feedback compensation. NSBC determines the feedforward input signal to the plant by using an error signal, determined from the difference between the output signals from a linear model of the plant and from the nonlinear plant, under the same input signal. The efficacy of NSBC is examined via numerical examples using Matlab/Simulink and compared with alternative well-known methods based upon inverse transfer function compensation and also the method of high gain feedback control. NSBC was found to provide the most accurate input identification in all the examined cases of linear or nonlinear single-input, single-output and single-input, multi-output (SIMO) systems. Furthermore, in problems of structural and earthquake engineering, NSBC was also found to be particularly effective in estimating the original ground motion from a nonlinear SIMO system and its response.
Institute of Scientific and Technical Information of China (English)
ZHANG Juliang; ZHANG Xiangsun
2001-01-01
In this paper, we use the smoothing penalty function proposed in [1] as the merit function of SQP method for nonlinear optimization with inequality constraints. The global convergence of the method is obtained.
A Direct Algebraic Method in Finding Particular Solutions to Some Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
LIUChun-Ping; CHENJian-Kang; CAIFan
2004-01-01
Firstly, a direct algebraic method and a routine way in finding traveling wave solutions to nonlinear evolution equations are explained. And then some new exact solutions for some evolution equations are obtained by using the method.
DEFF Research Database (Denmark)
Ibsen, Lars Bo; Barari, Amin; Kimiaeifar, Amin
2010-01-01
/approximate analytical solution to strong nonlinear oscillators. Furthermore, it is shown that a large class of linear or nonlinear differential equations can be solved without the tangible restriction of sensitivity to the degree of the nonlinear term, adding that the method is quite convenient due to reduction in size...
Prediction of peptide bonding affinity: kernel methods for nonlinear modeling
Bergeron, Charles; Sundling, C Matthew; Krein, Michael; Katt, Bill; Sukumar, Nagamani; Breneman, Curt M; Bennett, Kristin P
2011-01-01
This paper presents regression models obtained from a process of blind prediction of peptide binding affinity from provided descriptors for several distinct datasets as part of the 2006 Comparative Evaluation of Prediction Algorithms (COEPRA) contest. This paper finds that kernel partial least squares, a nonlinear partial least squares (PLS) algorithm, outperforms PLS, and that the incorporation of transferable atom equivalent features improves predictive capability.
Comparison of alternative improved perturbative methods for nonlinear oscillations
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico)]. E-mail: paolo@ucol.mx; Raya, Alfredo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Diag. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2005-06-06
We discuss and compare two alternative perturbation approaches for the calculation of the period of nonlinear systems based on the Lindstedt-Poincare technique. As illustrative examples we choose one-dimensional anharmonic oscillators and the Van der Pol equation. Our results show that each approach is better for just one type of model considered here.
Quantifying Poincare’s Continuation Method for Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Daniel Núñez
2015-01-01
Full Text Available In the sixties, Loud obtained interesting results of continuation on periodic solutions in driven nonlinear oscillators with small parameter (Loud, 1964. In this paper Loud’s results are extended out for periodically driven Duffing equations with odd symmetry quantifying the continuation parameter for a periodic odd solution which is elliptic and emanates from the equilibrium of the nonperturbed problem.
A Novel Method for Prediction of Nonlinear Aeroelastic Responses
2010-01-01
Brian A. Freno Graduate Student, Texas A&M University Publications Journal articles: 1. Gargoloff, J. I. and Cizmas, P. G. A., “Mesh Generation and...papers: 1. Cizmas, P. G. A., Freno , B. A., Brenner, T. A., Worley, G. D., “A High-Fidelity Nonlinear Aeroelastic Model for Aircraft with Large Wing
Applied Nonlinear Dynamics Analytical, Computational, and Experimental Methods
Nayfeh, Ali H
1995-01-01
A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.
Probabilistic methods for discrete nonlinear Schr\\"odinger equations
Chatterjee, Sourav
2010-01-01
Using techniques from probability theory, we show that the thermodynamics of the focusing cubic discrete nonlinear Schrodinger equation (NLS) are exactly solvable in dimensions three and higher. A number of explicit formulas are derived. The probabilistic results, combined with dynamical information, prove the existence and typicality of solutions to the discrete NLS with highly stable localized modes that are sometimes called discrete breathers.
DEFF Research Database (Denmark)
Rasmussen, Christian Jørgen
2001-01-01
Presents a simple and fast method for determination of the step size that exactly leads to a prescribed accuracy when signal propagation through nonlinear optical fibres is computed using the split-step Fourier method.......Presents a simple and fast method for determination of the step size that exactly leads to a prescribed accuracy when signal propagation through nonlinear optical fibres is computed using the split-step Fourier method....
A SELF-ADAPTIVE TECHNIQUE FOR A KIND OF NONLINEAR CONJUGATE GRADIENT METHODS
Institute of Scientific and Technical Information of China (English)
王丽平
2004-01-01
Conjugate gradient methods. are a class of important methods for unconstrained optimization, especially when the dimension is large. In 2001, Dai and Liao have proposed a new conjugate condition, based on it two nonlinear conjugate gradient methods are constructed. With trust region idea, this paper gives a self-adaptive technique for the two methods. The numerical results show that this technique works well for the given nonlinear optimization test problems.
A new method of determining the optimal embedding dimension based on nonlinear prediction
Institute of Scientific and Technical Information of China (English)
Meng Qing-Fang; Peng Yu-Hua; Xue Pei-Jun
2007-01-01
A new method is proposed to determine the optimal embedding dimension from a scalar time series in this paper. This method determines the optimal embedding dimension by optimizing the nonlinear autoregressive prediction model parameterized by the embedding dimension and the nonlinear degree. Simulation results show the effectiveness of this method. And this method is applicable to a short time series, stable to noise, computationally efficient, and without any purposely introduced parameters.
Analysis of factors influencing fire damage to concrete using nonlinear resonance vibration method
Energy Technology Data Exchange (ETDEWEB)
Park, Gang Kyu; Park, Sun Jong; Kwak, Hyo Gyoung [Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, KAIST, Daejeon (Korea, Republic of); Yim, Hong Jae [Dept. of Construction and Disaster Prevention Engineering, Kyungpook National University, Sangju (Korea, Republic of)
2015-04-15
In this study, the effects of different mix proportions and fire scenarios (exposure temperatures and post-fire-curing periods) on fire-damaged concrete were analyzed using a nonlinear resonance vibration method based on nonlinear acoustics. The hysteretic nonlinearity parameter was obtained, which can sensitively reflect the damage level of fire-damaged concrete. In addition, a splitting tensile strength test was performed on each fire-damaged specimen to evaluate the residual property. Using the results, a prediction model for estimating the residual strength of fire-damaged concrete was proposed on the basis of the correlation between the hysteretic nonlinearity parameter and the ratio of splitting tensile strength.
Zhao, Zhanqi; Guttmann, Josef; Möller, Knut
2012-01-01
The objective of this paper is to introduce and evaluate the adaptive SLICE method (ASM) for continuous determination of intratidal nonlinear dynamic compliance and resistance. The tidal volume is subdivided into a series of volume intervals called slices. For each slice, one compliance and one resistance are calculated by applying a least-squares-fit method. The volume window (width) covered by each slice is determined based on the confidence interval of the parameter estimation. The method was compared to the original SLICE method and evaluated using simulation and animal data. The ASM was also challenged with separate analysis of dynamic compliance during inspiration. If the signal-to-noise ratio (SNR) in the respiratory data decreased from +∞ to 10 dB, the relative errors of compliance increased from 0.1% to 22% for the ASM and from 0.2% to 227% for the SLICE method. Fewer differences were found in resistance. When the SNR was larger than 40 dB, the ASM delivered over 40 parameter estimates (42.2 ± 1.3). When analyzing the compliance during inspiration separately, the estimates calculated with the ASM were more stable. The adaptive determination of slice bounds results in consistent and reliable parameter values. Online analysis of nonlinear respiratory mechanics will profit from such an adaptive selection of interval size.
Institute of Scientific and Technical Information of China (English)
WangLin; NiQiao; HuangYuying
2003-01-01
This paper proposes a new method for investigating the Hopf bifurcation of a curved pipe conveying fluid with nonlinear spring support. The nonlinear equation of motion is derived by forces equilibrium on microelement of the system under consideration. The spatial coordinate of the system is discretized by the differential quadrature method and then the dynamic equation is solved by the Newton-Raphson method. The numerical solutions show that the inner fluid velocity of the Hopf bifurcation point of the curved pipe varies with different values of the parameter,nonlinear spring stiffness. Based on this, the cycle and divergent motions are both found to exist at specific fluid flow velocities with a given value of the nonlinear spring stiffness. The results are useful for further study of the nonlinear dynamic mechanism of the curved fluid conveying pipe.
Applications of algebraic method to exactly solve some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Darwish, A.A. [Department of Mathematics, Faculty of Science, Helwan University (Egypt)]. E-mail: profdarwish@yahoo.com; Ramady, A. [Department of Mathematics, Faculty of Science, Beni-Suef University (Egypt)]. E-mail: aramady@yahoo.com
2007-08-15
A direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear evolution equations is used and implemented in a computer algebraic system. New solutions for some nonlinear partial differential equations (NLPDE's) are obtained. Graphs of the solutions are displayed.
A NUMERICAL CALCULATION METHOD FOR EIGENVALUE PROBLEMS OF NONLINEAR INTERNAL WAVES
Institute of Scientific and Technical Information of China (English)
SHI Xin-gang; FAN Zhi-song; LIU Hai-long
2009-01-01
Generally speaking, the background shear current U(z)must be taken into account in eigenvalue problems of nonlinear internal waves in ocean, as is different from those of linear internal waves. A numerical calculation method for eigenvalue problems of nonlinear internal waves is presented in this paper on the basis of the Thompson-Haskell's calculation method. As an application of this method, at a station (21°N, 117°15′E) in the South China Sea, a modal structure and parameters of nonlinear internal waves are calculated, and the results closely agree with the calculated results based on observation by Yang et al..
Directory of Open Access Journals (Sweden)
Shaheed N. Huseen
2013-01-01
Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.
Directory of Open Access Journals (Sweden)
Hasibun Naher
2014-10-01
Full Text Available In this article, new extension of the generalized and improved (G′/G-expansion method is proposed for constructing more general and a rich class of new exact traveling wave solutions of nonlinear evolution equations. To demonstrate the novelty and motivation of the proposed method, we implement it to the Korteweg-de Vries (KdV equation. The new method is oriented toward the ease of utilize and capability of computer algebraic system and provides a more systematic, convenient handling of the solution process of nonlinear equations. Further, obtained solutions disclose a wider range of applicability for handling a large variety of nonlinear partial differential equations.
NONLINEAR GALERKIN METHOD FOR THE EXTERIOR NONSTATIONARY NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
何银年; 李开泰
2002-01-01
A new algorithm combining nonlinear Galerkin method and coupling method of finite element and boundary element is introduced to solve the exterior nonstationary Navier-Stokes equations. The regularity of the coupling variational formulation and the convergence of the approximate solution corresponding to the algorithm are proved. If the fine mesh h is choosed as coarse mesh H-sgure, the nonlinear Galerkin method, nonlinearity is only treated on the coarse grid and linearity is treated on the fine grid. Hence, the new algorithm can save a large amount of computational time.
Nonlinear time series theory, methods and applications with R examples
Douc, Randal; Stoffer, David
2014-01-01
FOUNDATIONSLinear ModelsStochastic Processes The Covariance World Linear Processes The Multivariate Cases Numerical Examples ExercisesLinear Gaussian State Space Models Model Basics Filtering, Smoothing, and Forecasting Maximum Likelihood Estimation Smoothing Splines and the Kalman Smoother Asymptotic Distribution of the MLE Missing Data Modifications Structural Component Models State-Space Models with Correlated Errors Exercises Beyond Linear ModelsNonlinear Non-Gaussian Data Volterra Series Expansion Cumulants and Higher-Order Spectra Bilinear Models Conditionally Heteroscedastic Models Thre
A NUMERICAL EMBEDDING METHOD FOR SOLVING THE NONLINEAR COMPLEMENTARITY PROBLEM(Ⅰ)--THEORY
Institute of Scientific and Technical Information of China (English)
Jian-jun Zhang; De-ren Wang
2002-01-01
In this paper, we extend the numerical embedding method for solving the smooth equations to the nonlinear complementarity problem. By using the nonsmooth theory,we prove the existence and the continuation of the following path for the corresponding homotopy equations. Therefore the basic theory of the numerical embedding method for solving the nonlinear complementarity problem is established. In part Ⅱ of this paper, we will further study the implementation of the method and give some numerical exapmles.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A trial equation method to nonlinear evolution equation with rank inhomogeneous is given. As applications, the exact traveling wave solutions to some higher-order nonlinear equations such as generalized Boussinesq equation,generalized Pochhammer-Chree equation, KdV-Burgers equation, and KS equation and so on, are obtained. Among these, some results are new. The proposed method is based on the idea of reduction of the order of ODE. Some mathematical details of the proposed method are discussed.
Institute of Scientific and Technical Information of China (English)
ZHANGJin-Liang; WANGMing-Liang
2004-01-01
The complex tanh-function expansion method was presented recently, and it can be applied to derive exact solutions to the Schroedinger-type nonlinear evolution equations directly without transformation. In this paper,the complex tanh-function expansion method is applied to derive the exact solutions to the general coupled nonlinear evolution equations. Zakharov system and a long-short-wave interaction system are considered as examples, and the new applications of the complex tanh-function expansion method are shown.
NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Cheng-jian Zhang
2002-01-01
This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDEs,are given. In particular, it is shown that the (k, l)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.
Directory of Open Access Journals (Sweden)
Sohrab Bazm
2016-11-01
Full Text Available Alternative Legendre polynomials (ALPs are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given and the efficiency and accuracy are illustrated by applying the method to some examples.
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-Liang; WANG Ming-Liang
2004-01-01
The complex tanh-function expansion method was presented recently, and it can be applied to derive exact solutions to the Schrodinger-type nonlinear evolution equations directly without transformation. In this paper,the complex tanh-function expansion method is applied to derive the exact solutions to the general coupled nonlinear evolution equations. Zakharov system and a long-short-wave interaction system are considered as examples, and the new applications of the complex tanh-function expansion method are shown.
Variational Iteration Method for the Magnetohydrodynamic Flow over a Nonlinear Stretching Sheet
Directory of Open Access Journals (Sweden)
Lan Xu
2013-01-01
Full Text Available The variational iteration method (VIM is applied to solve the boundary layer problem of magnetohydrodynamic flow over a nonlinear stretching sheet. The combination of the VIM and the Padé approximants is shown to be a powerful method for solving two-point boundary value problems consisting of systems of nonlinear differential equations. And the comparison of the obtained results with other available results shows that the method is very effective and convenient for solving boundary layer problems.
An extended harmonic balance method based on incremental nonlinear control parameters
Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.
2017-02-01
A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.
A NUMERICAL METHOD FOR SIMULATING NONLINEAR FLUID-RIGID STRUCTURE INTERACTION PROBLEMS
Institute of Scientific and Technical Information of China (English)
XingJ.T; PriceW.G; ChenY.G
2005-01-01
A numerical method for simulating nonlinear fluid-rigid structure interaction problems is developed. The structure is assumed to undergo large rigid body motions and the fluid flow is governed by nonlinear, viscous or non-viscous, field equations with nonlinear boundary conditions applied to the free surface and fluid-solid interaction interfaces. An Arbitrary-Lagrangian-Eulerian (ALE) mesh system is used to construct the numerical model. A multi-block numerical scheme of study is adopted allowing for the relative motion between moving overset grids, which are independent of one another. This provides a convenient method to overcome the difficulties in matching fluid meshes with large solid motions. Nonlinear numerical equations describing nonlinear fluid-solid interaction dynamics are derived through a numerical discretization scheme of study. A coupling iteration process is used to solve these numerical equations. Numerical examples are presented to demonstrate applications of the model developed.
Directory of Open Access Journals (Sweden)
J. Prakash
2016-03-01
Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.
Directory of Open Access Journals (Sweden)
Shadan Sadigh Behzadi
2011-12-01
Full Text Available In this paper, Adomian decomposition method (ADM and homotopy analysis method (HAM are proposed to solving the fuzzy nonlinear Volterra-Fredholm integral equation of the second kind$(FVFIE-2$. we convert a fuzzy nonlinear Volterra-Fredholm integral equation to a nonlinear system of Volterra-Fredholm integral equation in crisp case. we use ADM , HAM and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the nonlinear fuzzy Volterra-Fredholm integral equation. Also, the existence and uniqueness of the solution and convergence of the proposed methods are proved. Examples is given and the results reveal that homotopy analysis method is very effective and simple compared with the Adomian decomposition method.
Indian Academy of Sciences (India)
Zaiyun Zhang; Jianhua Huang; Juan Zhong; Sha-Sha Dou; Jiao Liu; Dan Peng; Ting Gao
2014-06-01
In this paper, we construct the travelling wave solutions to the perturbed nonlinear Schrödinger’s equation (NLSE) with Kerr law non-linearity by the extended (′/)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with Kerr law nonlinearity with arbitrary parameters. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.
Rashidi, M. M.; Erfani, E.
2009-09-01
In this study, we present a numerical comparison between the differential transform method (DTM) and the homotopy analysis method (HAM) for solving Burgers' and nonlinear heat transfer problems. The first differential equation is the Burgers' equation serves as a useful model for many interesting problems in applied mathematics. The second one is the modeling equation of a straight fin with a temperature dependent thermal conductivity. In order to show the effectiveness of the DTM, the results obtained from the DTM is compared with available solutions obtained using the HAM [M.M. Rashidi, G. Domairry, S. Dinarvand, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 708-717; G. Domairry, M. Fazeli, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 489-499] and whit exact solutions. The method can easily be applied to many linear and nonlinear problems. It illustrates the validity and the great potential of the differential transform method in solving nonlinear partial differential equations. The obtained results reveal that the technique introduced here is very effective and convenient for solving nonlinear partial differential equations and nonlinear ordinary differential equations that we are found to be in good agreement with the exact solutions.
Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems
Cerro, J. A.; Scotti, S. J.
1991-01-01
Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.
Tajaldini, Mehdi; Mat Jafri, Mohd Zubir Mat
2013-05-01
In this study, we propose a novel approach that is called nonlinear modal propagation analysis method (NMPA) in MMI coupler via the enhances of nonlinear wave propagation in terms of guided modes interferences in nonlinear regimes, such that the modal fields are measurable at any point of coupler and output facets. Then, the ultra-short MMI coupler is optimized as a building block in micro ring resonator to investigate the method efficiency against the already used method. Modeling results demonstrate more efficiency and accuracy in shorter lengths of multimode interference coupler. Therefore, NMPA can be used as a method to study the compact dimension coupler and for developing the performance in applications. Furthermore, the possibility of access tothe all-optical switching is assumed due to one continuous MMI for proof of the development of performances in nonlinear regimes.
NONLINEAR GALERKIN METHODS FOR SOLVING TWO DIMENSIONAL NEWTON-BOUSSINESQ EQUATIONS
Institute of Scientific and Technical Information of China (English)
GUOBOLING
1995-01-01
The nonlinear Galerkin methods for solving two-dimensional Newton-Boussinesq equations are proposed. The existence and uniqueness of global generalized solution of these equations,and the convergence of approximate solutions are also obtained.
On the freezing method for nonlinear nonautonomous systems with delay
Directory of Open Access Journals (Sweden)
Michael I. Gil'
2001-01-01
Full Text Available Nonlinear nonautonomous differential systems with delaying argument are considered. Explicit conditions for absolute stability are derived. The proposed approach is based on the generalization of the freezing method for ordinary differential equations.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
The Full—Discrete Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
Institute of Scientific and Technical Information of China (English)
YanpingCHEN; YunqingHUANG
1998-01-01
This article treats mixed finite element methods for second order nonlinear hyperbolic equations.A fully discrete scheme is presented and improved L2-error estimates are established.The convergence of both the function value andthe flux is demonstrated.
Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations
Institute of Scientific and Technical Information of China (English)
2007-01-01
The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.
Nonlinear Time Reversal Acoustic Method of Friction Stir Weld Assessment Project
National Aeronautics and Space Administration — The goal of the project is demonstration of the feasibility of Friction Stir Weld (FSW) assessment by novel Nonlinear Time Reversal Acoustic (TRA) method. Time...
Wang, Qing; Yao, Jing-Zheng
2010-12-01
Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.
Determining the minimum embedding dimension of nonlinear time series based on prediction method
Institute of Scientific and Technical Information of China (English)
Bian Chun-Hua; Ning Xin-Bao
2004-01-01
Determining the embedding dimension of nonlinear time series plays an important role in the reconstruction of nonlinear dynamics. The paper first summarizes the current methods for determining the embedding dimension.Then, inspired by the fact that the optimum modelling dimension of nonlinear autoregressive (NAR) prediction model can characterize the embedding feature of the dynamics, the paper presents a new idea that the optimum modelling dimension of the NAR model can be taken as the minimum embedding dimension. Some validation examples and results are given and the present method shows its advantage for short data series.
H∞ Synthesis Method for Control of Non-linear Flexible Joint Models
Axelsson, Patrik; Pipeleers, Goele; Helmersson, Anders; Norrlöf, Mikael
2014-01-01
An H∞ synthesis method for control of a flexible joint, with non-linear spring characteristic, is proposed. The first step of the synthesis method is to extend the joint model with an uncertainty description of the stiffness parameter. In the second step, a non-linear optimisation problem, based on nominal performance and robust stability requirements, has to be solved. Using the Lyapunov shaping paradigm and a change of variables, the non-linear optimisation problem can be rewritten as a con...
DEFF Research Database (Denmark)
Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari
2010-01-01
Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...... and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However...
Nonlinear dynamics of rotating shallow water methods and advances
Zeitlin, Vladimir
2007-01-01
The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wa
DOUBLE TRIALS METHOD FOR NONLINEAR PROBLEMS ARISING IN HEAT TRANSFER
Directory of Open Access Journals (Sweden)
Chun-Hui He
2011-01-01
Full Text Available According to an ancient Chinese algorithm, the Ying Buzu Shu, in about second century BC, known as the rule of double false position in West after 1202 AD, two trial roots are assumed to solve algebraic equations. The solution procedure can be extended to solve nonlinear differential equations by constructing an approximate solution with an unknown parameter, and the unknown parameter can be easily determined using the Ying Buzu Shu. An example in heat transfer is given to elucidate the solution procedure.
Indian Academy of Sciences (India)
M Mirzazadeh; M Eslami
2013-12-01
Studying compactons, solitons, solitary patterns and periodic solutions is important in nonlinear phenomena. In this paper we study nonlinear variants of the Kadomtsev–Petviashvili (KP) and the Korteweg–de Vries (KdV) equations with positive and negative exponents. The functional variable method is used to establish compactons, solitons, solitary patterns and periodic solutions for these variants. This method is a powerful tool for searching exact travelling solutions in closed form.
A Nonlinear Physics-Based Optimal Control Method for Magnetostrictive Actuators
Smith, Ralph C.
1998-01-01
This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.
In vivo characterization of skin using a Weiner nonlinear stochastic system identification method.
Chen, Yi; Hunter, Ian W
2009-01-01
This paper describes an indentometer device used to identify the linear dynamic and nonlinear properties of skin and underlying tissue using an in vivo test. The device uses a Lorentz force actuator to apply a dynamic force to the skin and measures the resulting displacement. It was found that the skin could be modeled as a Wiener system (i.e. a linear dynamic system followed by a static nonlinearity). Using a stochastic nonlinear system identification technique, the method presented in this paper was able to identify the dynamic linear and static nonlinear mechanical parameters of the indentometer-skin system within 2 to 4 seconds. The shape of the nonlinearity was found to vary depending on the area of the skin that was tested. We show that the device can repeatably distinguish between different areas of human tissue for multiple test subjects.
Directory of Open Access Journals (Sweden)
Shahriari
2017-02-01
Full Text Available In this work, the optical properties dependence of Multi-Walled Carbon Nanotubes (MWNT on concentration was discussed. MWNT samples were prepared in polypyrrole by an electrochemical polymerization of monomers, in the presence of different concentrations of MWNTs, using Sodium Dodecyl-Benzen-Sulfonate (SDBS as surfactant at room temperature. The nonlinear refractive and nonlinear absorbtion indices were measured using a low power CW laser beam operated at 532 nm using z-scan method. The results show that nonlinear refractive and nonlinear absorbtion indices tend to be increased with increasing the concentration of carbon nanotubes. Optical properties of carbone nanotubes indicate that they are good candidates for nonlinear optical devices
Investigation of nonlinear optical properties of various organic materials by the Z-scan method
Ganeev, R. A.; Boltaev, G. S.; Tugushev, R. I.; Usmanov, T.
2012-06-01
We have studied the nonlinear optical properties of various organic materials (vegetable oil, juice, wine, cognac, Coca-Cola and Fanta drinks, Nescafé coffee, tea, gasoline, clock oil, glycerol, and polyphenyl ether) that are used in everyday life. Their nonlinearities have been studied by the Z-scan method in the near-IR and visible spectral ranges. We have shown that the majority of samples possess a nonlinear absorption; however, some of the studied materials show a strong saturated absorption and nonlinear refraction. Red wine and glycerol proved to be the most interesting materials. For these samples, we have observed a change in the sign of the nonlinear absorption with increasing laser intensity, which was attributed to the competition between two-photon absorption and saturated absorption.
Analytical exploration of γ-function explicit method for pseudodynamic testing of nonlinear systems
Institute of Scientific and Technical Information of China (English)
Shuenn-Yih Chang; Yu-Chi Sung
2005-01-01
It has been well studied that the γ-function explicit method can be effective in providing favorable numerical dissipation for linear elastic systems. However, its performance for nonlinear systems is unclear due to a lack of analytical evaluation techniques. Thus, a novel technique is proposed herein to evaluate its efficiency for application to nonlinear systems by introducing two parameters to describe the stiffness change. As a result, the numerical properties and error propagation characteristics of the γ-function explicit method for the pseudodynamic testing of a nonlinear system are analytically assessed. It is found that the upper stability limit decreases as the step degree of nonlinearity increases; and it increases as the current degree of nonlinearity increases. It is also shown that this integration method provides favorable numerical dissipation not only for linear elastic systems but also for nonlinear systems. Furthermore, error propagation analysis reveals that the numerical dissipation can effectively suppress the severe error propagation of high frequency modes while the low frequency responses are almost unaffected for both linear elastic and nonlinear systems.
A FAST CONVERGENT METHOD OF ITERATED REGULARIZATION
Institute of Scientific and Technical Information of China (English)
Huang Xiaowei; Wu Chuansheng; Wu Di
2009-01-01
This article presents a fast convergent method of iterated regularization based on the idea of Landweber iterated regularization, and a method for a-posteriori choice by the Morozov discrepancy principle and the optimum asymptotic convergence order of the regularized solution is obtained. Numerical test shows that the method of iterated regu-larization can quicken the convergence speed and reduce the calculation burden efficiently.
Third-order nonlinear optical properties of acid green 25 dye by Z-scan method
Jeyaram, S.; Geethakrishnan, T.
2017-03-01
Third-order nonlinear optical (NLO) properties of aqueous solutions of an anthraquinone dye (Acid green 25 dye, color index: 61570) have been studied by Z-scan method with a 5 mW continuous wave (CW) diode laser operating at 635 nm. The nonlinear refractive index (n2) and the absorption coefficient (β) have been evaluated respectively from the closed and open aperture Z-scan data and the values of these parameters are found to increase with increase in concentration of the dye solution. The negative sign of the observed nonlinear refractive index (n2) indicates that the aqueous solution of acid green 25 dye exhibits self-defocusing type optical nonlinearity. The mechanism of the observed nonlinear absorption (NLA) and nonlinear refraction (NLR) is attributed respectively to reverse saturable absorption (RSA) and thermal nonlinear effects. The magnitudes of n2 and β are found to be of the order of 10-7 cm2/W and 10-3 cm/W respectively. With these experimental results, the authors suggest that acid green 25 dye may have potential applications in nonlinear optics.
Three-step iterative methods with eighth-order convergence for solving nonlinear equations
Directory of Open Access Journals (Sweden)
Mashallah Matinfar
2013-01-01
Full Text Available A family of eighth-order iterative methods for solution of nonlinear equations is presented. We propose an optimal three-step method with eight-order convergence for finding the simple roots of nonlinear equations by Hermite interpolation method. Per iteration of this method requires two evaluations of the function and two evaluations of its first derivative, which implies that the efficiency index of the developed methods is 1.682. Some numerical examples illustrate that the algorithms are more efficient and performs better than the other methods.
Non-linear time series analysis: methods and applications to atrial fibrillation.
Hoekstra, B P; Diks, C G; Allessie, M A; Degoede, J
2001-01-01
We apply methods from non-linear statistical time series analysis to characterize electrograms of atrial fibrillation. These are based on concepts originating from the theory of non-linear dynamical systems and use the empirical reconstruction density in reconstructed phase space. Application of these methods is not restricted to deterministic chaos but is valid in a general time series context. We illustrate this by applying three recently proposed non-linear time series methods to fibrillation electrograms: 1) a test for time reversibility in atrial electrograms during paroxysmal atrial fibrillation in patients; 2) a test to detect differences in the dynamical behaviour during the pharmacological conversion of sustained atrial fibrillation in instrumented conscious goats; 3) a test for general Granger causality to identify couplings and information transport in the atria during fibrillation. We conclude that a characterization of the dynamics via the reconstruction density offers a useful framework for the non-linear analysis of electrograms of atrial fibrillation.
Ren, Shijin
2003-01-01
Response surface models based on multiple linear regression had previously been developed for the toxicity of aromatic chemicals to Tetrahymena pyriformis. However, a nonlinear relationship between toxicity and one of the molecular descriptors in the response surface model was observed. In this study, response surface models were established using six nonlinear modeling methods to handle the nonlinearity exhibited in the aromatic chemicals data set. All models were validated using the method of cross-validation, and prediction accuracy was tested on an external data set. Results showed that response surface models based on locally weighted regression scatter plot smoothing (LOESS), multivariate adaptive regression splines (MARS), neural networks (NN), and projection pursuit regression (PPR) provided satisfactory power of model fitting and prediction and had similar applicabilities. The response surface models based on nonlinear methods were difficult to interpret and conservative in discriminating toxicity mechanisms.
Exact travelling solutions for some nonlinear physical models by (′/)-expansion method
Indian Academy of Sciences (India)
B Salim Bahrami; H Abdollahzadeh; I M Berijani; D D Ganji; M Abdollahzadeh
2011-08-01
In this paper, we establish exact solutions for some special nonlinear partial differential equations. The (′/)-expansion method is used to construct travelling wave solutions of the twodimensional sine-Gordon equation, Dodd–Bullough–Mikhailov and Schrödinger–KdV equations, which appear in many ﬁelds such as, solid-state physics, nonlinear optics, ﬂuid dynamics, ﬂuid ﬂow, quantum ﬁeld theory, electromagnetic waves and so on. In this method we take the advantage of general solutions of second-order linear ordinary differential equation (LODE) to solve many nonlinear evolution equations effectively. The (′/)-expansion method is direct, concise and elementary and can be used with a wider applicability for handling many nonlinear wave equations.
A novel order reduction method for nonlinear dynamical system under external periodic excitations
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The concept of approximate inertial manifold (AIM) is extended to develop a kind of nonlinear order reduction technique for non-autonomous nonlinear systems in second-order form in this paper.Using the modal transformation,a large nonlinear dynamical system is split into a ’master’ subsystem,a ’slave’ subsystem,and a ’negligible’ subsystem.Accordingly,a novel order reduction method (Method I) is developed to construct a low order subsystem by neglecting the ’negligible’ subsystem and slaving the ’slave’ subsystem into the ’master’ subsystem using the extended AIM.As a comparison,Method II accounting for the effects of both ’slave’ subsystem and the ’negligible’ subsystem is also applied to obtain the reduced order subsystem.Then,a typical 5-degree-of-freedom nonlinear dynamical system is given to compare the accuracy and efficiency of the traditional Galerkin truncation (ignoring the contributions of the slave and negligible subsystems),Method I and Method II.It is shown that Method I gives a considerable increase in accuracy for little computational cost in comparison with the standard Galerkin method,and produces almost the same accuracy as Method II.Finally,a 3-degree-of-freedom nonlinear dynamical system is analyzed by using the analytic method for showing predominance and convenience of Method I to obtain the analytically reduced order system.
A Family of Fifth-order Iterative Methods for Solving Nonlinear Equations
Institute of Scientific and Technical Information of China (English)
Liu Tian-Bao; Cai Hua
2013-01-01
In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order five. Numerical examples show that the new methods are comparable with the well known existing methods and give better results in many aspects.
Institute of Scientific and Technical Information of China (English)
TAO Hua-xue (陶华学); GUO Jin-yun (郭金运)
2003-01-01
Data are very important to build the digital mine. Data come from many sources, have different types and temporal states. Relations between one class of data and the other one, or between data and unknown parameters are more nonlinear. The unknown parameters are non-random or random, among which the random parameters often dynamically vary with time. Therefore it is not accurate and reliable to process the data in building the digital mine with the classical least squares method or the method of the common nonlinear least squares. So a generalized nonlinear dynamic least squares method to process data in building the digital mine is put forward. In the meantime, the corresponding mathematical model is also given. The generalized nonlinear least squares problem is more complex than the common nonlinear least squares problem and its solution is more difficultly obtained because the dimensions of data and parameters in the former are bigger. So a new solution model and the method are put forward to solve the generalized nonlinear dynamic least squares problem. In fact, the problem can be converted to two sub-problems, each of which has a single variable. That is to say, a complex problem can be separated and then solved. So the dimension of unknown parameters can be reduced to its half, which simplifies the original high dimensional equations. The method lessens the calculating load and opens up a new way to process the data in building the digital mine, which have more sources, different types and more temporal states.
Method and system for training dynamic nonlinear adaptive filters which have embedded memory
Rabinowitz, Matthew (Inventor)
2002-01-01
Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.
Directory of Open Access Journals (Sweden)
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs. The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
NONLINEAR ESTIMATION METHODS FOR AUTONOMOUS TRACKED VEHICLE WITH SLIP
Institute of Scientific and Technical Information of China (English)
ZHOU Bo; HAN Jianda
2007-01-01
In order to achieve precise, robust autonomous guidance and control of a tracked vehicle, a kinematic model with longitudinal and lateral slip is established. Four different nonlinear filters are used to estimate both state vector and time-varying parameter vector of the created model jointly. The first filter is the well-known extended Kalman filter. The second filter is an unscented version of the Kalman filter. The third one is a particle filter using the unscented Kalman filter to generate the importance proposal distribution. The last one is a novel and guaranteed filter that uses a linear set-membership estimator and can give an ellipsoid set in which the true state lies. The four different approaches have different complexities, behavior and advantages that are surveyed and compared.
Modified Semi-Classical Methods for Nonlinear Quantum Oscillations Problems
Moncrief, Vincent; Maitra, Rachel
2012-01-01
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof. Under smoothness, convexity and coercivity hypotheses on its potential energy function, we prove, using the calculus of variations together with the Banach space implicit function theorem, the existence of a global, smooth `fundamental solution'. Higher order quantum corrections, for ground and excited states, are computed through the integration of associated systems of linear transport equations, and formal expansions for the corresponding energy eigenvalues obtained by imposing smoothness on the quantum corrections to the eigenfunctions. For linear oscillators our expansions naturally truncate, reproducing the well-known solutions for the energy eigenfunctions and eigenvalues. As an application, w...
A hybrid nonlinear programming method for design optimization
Rajan, S. D.
1986-01-01
Solutions to engineering design problems formulated as nonlinear programming (NLP) problems usually require the use of more than one optimization technique. Moreover, the interaction between the user (analysis/synthesis) program and the NLP system can lead to interface, scaling, or convergence problems. An NLP solution system is presented that seeks to solve these problems by providing a programming system to ease the user-system interface. A simple set of rules is used to select an optimization technique or to switch from one technique to another in an attempt to detect, diagnose, and solve some potential problems. Numerical examples involving finite element based optimal design of space trusses and rotor bearing systems are used to illustrate the applicability of the proposed methodology.
Application of new novel energy balance method to strongly nonlinear oscillator systems
Directory of Open Access Journals (Sweden)
Md. Abdur Razzak
2015-01-01
Full Text Available In this paper, a new novel energy balance method based on the harmonic balance method is proposed to obtain higher-order approximations of strongly nonlinear problems arising in engineering. Especially, second-order approximation is considered in this paper. Results found in this paper are compared with the exact result and other existing results. The results show that the proposed method gives better result for both small and large amplitudes of oscillation than other existing results. The method is illustrated by examples. It has been shown that the proposed method is very effective, convenient and quite accurate to nonlinear engineering problems.
Exact solutions of some nonlinear partial differential equations using functional variable method
Indian Academy of Sciences (India)
A Nazarzadeh; M Eslami; M Mirzazadeh
2013-08-01
The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm Kadomtsev–Petviashvili equation and the higher-order nonlinear Schrödinger equation. By using this useful method, we found some exact solutions of the above-mentioned equations. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. It is shown that the proposed method is effective and general.
Nonlinear system identification NARMAX methods in the time, frequency, and spatio-temporal domains
Billings, Stephen A
2013-01-01
Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) modelThe orthogonal least squares algorithm that allows models to be built term by
The (′/)-expansion method for a discrete nonlinear Schrödinger equation
Indian Academy of Sciences (India)
Sheng Zhang; Ling Dong; Jin-Mei Ba; Ying-Na Sun
2010-02-01
An improved algorithm is devised for using the (′/)-expansion method to solve nonlinear differential-difference equations. With the aid of symbolic computation, we choose a discrete nonlinear Schrödinger equation to illustrate the validity and advantages of the improved algorithm. As a result, hyperbolic function solutions, trigonometric function solutions and rational solutions with parameters are obtained, from which some special solutions including the known solitary wave solution are derived by setting the parameters as appropriate values. It is shown that the improved algorithm is effective and can be used for many other nonlinear differential-difference equations in mathematical physics.
Control design for the nonlinear benchmark problem via the output regulation method
Institute of Scientific and Technical Information of China (English)
Jie HUANG; Guoqiang HU
2004-01-01
The problem of designing a feedback controller to achieve asymptotic disturbance rejection / attenuation while maintaining good transient response in the RTAC system is known as a benchmark nonlinear control problem, which has been an intensive research subject since 1995. In this paper, we will further investigate the solvability of the robust disturbance rejection problem of the RTAC system by the measurement output feedback control based on the robust output regulation method. We have obtained a design by overcoming two major obstacles: find a closed-form solution of the regulator equations; and devise a nonlinear internal model to account for non-polynomial nonlinearities.
Application of nonlinear systems in nanomechanics and nanofluids analytical methods and applications
Ganji, Davood Domairry
2015-01-01
With Application of Nonlinear Systems in Nanomechanics and Nanofluids the reader gains a deep and practice-oriented understanding of nonlinear systems within areas of nanotechnology application as well as the necessary knowledge enabling the handling of such systems. The book helps readers understand relevant methods and techniques for solving nonlinear problems, and is an invaluable reference for researchers, professionals and PhD students interested in research areas and industries where nanofluidics and dynamic nano-mechanical systems are studied or applied. The book is useful in areas suc
GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Yin-nian He; Yan-ren Hou; Li-quan Mei
2001-01-01
A global finite element nonlinear Galerkin method for the penalized Navier-Stokes equations is presented. This method is based on two finite element spaces XH and Xh,defined respectively on one coarse grid with grid size H and one fine grid with grid size h ＜＜ H. Comparison is also made with the finite element Galerkin method. If we choose H = O(ε-1/4h1/2), ε＞ 0 being the penalty parameter, then two methods are of the same order of approximation. However, the global finite element nonlinear Galerkin method is much cheaper than the standard finite element Galerkin method. In fact, in the finite element Galerkin method the nonlinearity is treated on the fine grid finite element space Xh and while in the global finite element nonlinear Galerkin method the similar nonlinearity is treated on the coarse grid finite element space XH and only the linearity needs to be treated on the fine grid increment finite element space Wh. Finally, we provide numerical test which shows above results stated.
Application of nonlinear ultrasonic method for monitoring of stress state in concrete
Energy Technology Data Exchange (ETDEWEB)
Kim, Gyu Jin; Kwak, Hyo Gyoung [Dept. of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Park, Sun Jong [Dept. of Structural System and Site Safety Evaluation, Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of)
2016-04-15
As the lifespan of concrete structures increases, their load carrying capacity decreases owing to cyclic loads and long-term effects such as creep and shrinkage. For these reasons, there is a necessity for stress state monitoring of concrete members. Particularly, it is necessary to evaluate the concrete structures for behavioral changes by using a technique that can overcome the measuring limitations of usual ultrasonic nondestructive evaluation methods. This paper proposes the use of a nonlinear ultrasonic method, namely, nonlinear resonant ultrasonic spectroscopy (NRUS) for the measurement of nonlinearity parameters for stress monitoring. An experiment compared the use of NRUS method and a linear ultrasonic method, namely, ultrasonic pulse velocity (UPV) to study the effects of continuously increasing loads and cyclic loads on the nonlinearity parameter. Both NRUS and UPV methods found a similar direct relationship between load level and that parameter. The NRUS method showed a higher sensitivity to micro-structural changes of concrete than UPV method. Thus, the experiment confirms the possibility of using the nonlinear ultrasonic method for stress state monitoring of concrete members.
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2016-07-01
Full Text Available In this paper, we improve the extended trial equation method to construct the exact solutions for nonlinear coupled system of partial differential equations in mathematical physics. We use the extended trial equation method to find some different types of exact solutions such as the Jacobi elliptic function solutions, soliton solutions, trigonometric function solutions and rational, exact solutions to the nonlinear coupled Schrodinger Boussinesq equations when the balance number is a positive integer. The performance of this method is reliable, effective and powerful for solving more complicated nonlinear partial differential equations in mathematical physics. The balance number of this method is not constant as we have in other methods. This method allows us to construct many new types of exact solutions. By using the Maple software package we show that all obtained solutions satisfy the original partial differential equations.
Acceleration of the AFEN method by two-node nonlinear iteration
Energy Technology Data Exchange (ETDEWEB)
Moon, Kap Suk; Cho, Nam Zin; Noh, Jae Man; Hong, Ser Gi [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)
1998-12-31
A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AFEN method and the computing time is significantly reduced in comparison with the original AFEN method. 7 refs., 1 fig., 1 tab. (Author)
Directory of Open Access Journals (Sweden)
Kohei Arai
2013-01-01
Full Text Available Method for image prediction with nonlinear control lines which are derived from extracted feature points from the previously acquired imagery data based on Kriging method and morphing method is proposed. Through comparisons between the proposed method and the conventional linear interpolation and widely used Cubic Spline interpolation methods, it is found that the proposed method is superior to the conventional methods in terms of prediction accuracy.
Nonlinear Spline Kernel-based Partial Least Squares Regression Method and Its Application
Institute of Scientific and Technical Information of China (English)
JIA Jin-ming; WEN Xiang-jun
2008-01-01
Inspired by the traditional Wold's nonlinear PLS algorithm comprises of NIPALS approach and a spline inner function model,a novel nonlinear partial least squares algorithm based on spline kernel(named SK-PLS)is proposed for nonlinear modeling in the presence of multicollinearity.Based on the iuner-product kernel spanned by the spline basis functions with infinite numher of nodes,this method firstly maps the input data into a high dimensional feature space,and then calculates a linear PLS model with reformed NIPALS procedure in the feature space and gives a unified framework of traditional PLS"kernel"algorithms in consequence.The linear PLS in the feature space corresponds to a nonlinear PLS in the original input (primal)space.The good approximating property of spline kernel function enhances the generalization ability of the novel model,and two numerical experiments are given to illustrate the feasibility of the proposed method.
Institute of Scientific and Technical Information of China (English)
Pan Jun-Ting; Gong Lun-Xun
2008-01-01
Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation,and by converting it into a new expansion form,this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations.Being concise and straightforward,themethod is applied to modified Benjamin-Bona-Mahony (mBBM) model,and some new exact solutions to the system are obtained.The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations.
Directory of Open Access Journals (Sweden)
Wang Pidong
2016-01-01
Full Text Available Blind source separation is a hot topic in signal processing. Most existing works focus on dealing with linear combined signals, while in practice we always encounter with nonlinear mixed signals. To address the problem of nonlinear source separation, in this paper we propose a novel algorithm using radial basis function neutral network, optimized by multi-universe parallel quantum genetic algorithm. Experiments show the efficiency of the proposed method.
A One-parameter Filled Function Method for Nonlinear Integer Programming
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
This paper gives a new definition of the filled function for nonlinear integer programming problem. A filled function satisfying our definition is presented. This function contains only one parameter. The properties of the proposed filled function and the method using this filled function to solve nonlinear integer programming problem are also discussed. Numerical results indicate the efficiency and reliability of the proposed filled function algorithm.
Singular perturbation methods for nonlinear dynamic systems with time delays
Energy Technology Data Exchange (ETDEWEB)
Hu, H.Y. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)], E-mail: hhyae@nuaa.edu.cn; Wang, Z.H. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)
2009-04-15
This review article surveys the recent advances in the dynamics and control of time-delay systems, with emphasis on the singular perturbation methods, such as the method of multiple scales, the method of averaging, and two newly developed methods, the energy analysis and the pseudo-oscillator analysis. Some examples are given to demonstrate the advantages of the methods. The comparisons with other methods show that these methods lead to easier computations and higher accurate prediction on the local dynamics of time-delay systems near a Hopf bifurcation.
A stabilised nodal spectral element method for fully nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, C.; Bigoni, Daniele
2016-01-01
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although...... the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions...
He-Laplace Method for Linear and Nonlinear Partial Differential Equations
Directory of Open Access Journals (Sweden)
Hradyesh Kumar Mishra
2012-01-01
Full Text Available A new treatment for homotopy perturbation method is introduced. The new treatment is called He-Laplace method which is the coupling of the Laplace transform and the homotopy perturbation method using He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The method is implemented on linear and nonlinear partial differential equations. It is found that the proposed scheme provides the solution without any discretization or restrictive assumptions and avoids the round-off errors.
Directory of Open Access Journals (Sweden)
Banan Maayah
2014-01-01
Full Text Available A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillator’s models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of convergence for the series solution. The numerical results demonstrate the validity and the applicability of the new technique. A very good agreement was found between the results obtained using the presented algorithm and the Runge-Kutta method, which shows that the multistep reproducing kernel Hilbert space method is very efficient and convenient for solving nonlinear oscillator’s models.
Solution of (3+1-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method
Directory of Open Access Journals (Sweden)
Hassan A. Zedan
2012-01-01
Full Text Available Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions.
Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems
Directory of Open Access Journals (Sweden)
Daniel Olvera
2014-01-01
Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.
Energy Technology Data Exchange (ETDEWEB)
Ravi Kanth, A.S.V. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)], E-mail: asvravikanth@yahoo.com; Aruna, K. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)
2008-11-17
In this Letter, we propose a reliable algorithm to develop exact and approximate solutions for the linear and non-linear systems of partial differential equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.
Nonlinear viscosity derived by means of Grad's moment method
Eu, Byung Chan
2002-03-01
In this paper we examine the stress tensor component evolution equations recently derived by Uribe and Garcia-Colin [Phys. Rev. E 60, 4052 (1999)] for unidirectional flow at uniform temperature under the assumption/approximation of vanishing transversal velocity gradients. By removing this assumption/approximation we derive the stress tensor evolution equation from the Boltzmann equation within the framework of the Grad moment expansion for the case of uniform temperature (the same condition as theirs). Specializing the evolution equation to the case of steady unidirectional flow in a square channel, we obtain a set of steady state evolution equations for the components of the stress tensor. Because the transversal velocity gradients are not assumed to vanish in this paper in contrast to their paper, the present result is more general than theirs. Its special case corresponding to the one-dimensional flow considered by Uribe and Garcia-Colin is at variance with theirs because of a missing term in their stress evolution equation for the xy component. The nonlinear viscosity formulas are also different. A general remark is given with regard to the relation of dimensionalities of hydrodynamic equations and the kinetic equation underlying the former. They are not necessarily the same.
Nonlinear mode decomposition: A noise-robust, adaptive decomposition method
Iatsenko, Dmytro; McClintock, Peter V. E.; Stefanovska, Aneta
2015-09-01
The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool—nonlinear mode decomposition (NMD)—which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques—which, together with the adaptive choice of their parameters, make it extremely noise robust—and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.
Nonlinear mode decomposition: a noise-robust, adaptive decomposition method.
Iatsenko, Dmytro; McClintock, Peter V E; Stefanovska, Aneta
2015-09-01
The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool-nonlinear mode decomposition (NMD)-which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques-which, together with the adaptive choice of their parameters, make it extremely noise robust-and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.
A new method for observing the running states of a single-variable nonlinear system.
Meng, Yu; Chen, Hong; Chen, Cheng
2015-03-01
In order to timely grasp a single variable nonlinear system running states, a new method called Scatter Point method is put forward in this paper. It can be used to observe or monitor the running states of a single variable nonlinear system in real-time. In this paper, the definition of the method is given at first, and then its working principle is expounded theoretically, after this, some physical experiments based on Chua's nonlinear system are conducted. At the same time, many scatter point graphs are measured by a general analog oscilloscope. The motion, number, and distribution of these scatter points shown on the oscilloscope screen can directly reflect the current states of the tested system. The experimental results further confirm that the method is effective and practical, in which the system running states are not easily lost. In addition, this method is not only suitable for single variable systems but also for multivariable systems.
Demi, L; van Dongen, K W A; Verweij, M D
2011-03-01
Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented full-wave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, three-dimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation.
A time stepping method in analysis of nonlinear structural dynamics
Directory of Open Access Journals (Sweden)
Gholampour A. A.
2011-12-01
Full Text Available In this paper a new method is proposed for the direct time integration method for structural dynamics problems. The proposed method assumes second order variations of the acceleration at each time step. Therefore more terms in the Taylor series expansion were used compared to other methods. Because of the increase in order of variations of acceleration, this method has higher accuracy than classical methods. The displacement function is a polynomial with five constants and they are calculated using: two equations for initial conditions (from the end of previous time step, two equations for satisfying the equilibrium at both ends of the time step, and one equation for the weighted residual integration. Proposed method has higher stability and order of accuracy than the other methods.
On Newton-Like Methods for Solving Nonlinear Equations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we present a family of general Newton-like methods with a parametric function for finding a zero of a univariate function, permitting f′(x)=0 in some points. The case of multiple roots is not treated. The methods are proved to be quadratically convergent provided the weak condition. Thus the methods remove the severe condition f′(x)≠0. Based on the general form of the Newton-like methods, a family of new iterative methods with a variable parameter are developed.
Stability analysis of nonlinear systems by multiple time scaling. [using perturbation methods
Morino, L.
1974-01-01
The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary was obtained by using the multiple-time-scaling asymptotic-expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order epsilon to the 3rd power (where epsilon is the order of amplitude of the unknown) are included in the solution. The solution indicates that there is always a limit cycle which is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Comparisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.
Akbarzade, M.; Langari, J.
2011-02-01
In this paper a new approach combining the features of the homotopy concept with variational approach is proposed to find accurate analytical solutions for nonlinear oscillators with and without a fractional power restoring force. Since the first-order approximation leads to very accurate results, comparisons with other results are presented to show the effectiveness of this method. The validity of the method is independent of whether or not there exist small or large parameters in the considered nonlinear equations; the obtained results prove the validity and efficiency of the method, which can be easily extended to other strongly nonlinear problems. At the end we compare our procedure with the optimal homotopy perturbation method.
Image quality assessment method based on nonlinear feature extraction in kernel space
Institute of Scientific and Technical Information of China (English)
Yong DING‡; Nan LI; Yang ZHAO; Kai HUANG
2016-01-01
To match human perception, extracting perceptual features effectively plays an important role in image quality assessment. In contrast to most existing methods that use linear transformations or models to represent images, we employ a complex mathematical expression of high dimensionality to reveal the statistical characteristics of the images. Furthermore, by introducing kernel methods to transform the linear problem into a nonlinear one, a full-reference image quality assessment method is proposed based on high-dimensional nonlinear feature extraction. Experiments on the LIVE, TID2008, and CSIQ databases demonstrate that nonlinear features offer competitive performance for image inherent quality representation and the proposed method achieves a promising performance that is consistent with human subjective evaluation.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-09-22
An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities.
Method of Green’s function of nonlinear vibration of corrugated shallow shells
Institute of Scientific and Technical Information of China (English)
2008-01-01
Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution, the nonlinear free vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated. The nonlinear partial differential equations of shallow shell were re-duced to the nonlinear integral-differential equations by using the method of Green’s function. To solve the integral-differential equations, the expansion method was used to obtain Green’s function. Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green’s function as a series of characteristic function. Therefore, the integral-differential equations be-came nonlinear ordinary differential equations with regard to time. The ampli-tude-frequency relation, with respect to the natural frequency of the lowest order and the amplitude-frequency response under harmonic force, were obtained by considering single mode vibration. As a numerical example, nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied. The obtained solutions are available for reference to the design of corrugated shells.
Method of Green's function of nonlinear vibration of corrugated shallow shells
Institute of Scientific and Technical Information of China (English)
YUAN Hong
2008-01-01
Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution,the nonlinear free vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated.The nonlinear partial differential equations of shallow shell were re-duced to the nonlinear integral-differential equations by using the method of Green's function.To solve the integral-differential equations,the expansion method was used to obtain Green's function.Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green's function as a series of characteristic function.Therefore,the integral-differential equations be-came nonlinear ordinary differential equations with regard to time.The ampli-tude-frequency relation,with respect to the natural frequency of the lowest order and the amplitude-frequency response under harmonic force,were obtained by considering single mode vibration.As a numerical example,nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied.The obtained solutions are available for reference to the design of corrugated shells.
Institute of Scientific and Technical Information of China (English)
DUAN Wan-suo; MU Mu
2005-01-01
Linear singular vector and linear singular value can only describe the evolution of sufficiently small perturbations during the period in which the tangent linear model is valid.With this in mind, the applications of nonlinear optimization methods to the atmospheric and oceanic sciences are introduced, which include nonlinear singular vector (NSV) and nonlinear singular value (NSVA), conditional nonlinear optimal perturbation (CNOP), and their applications to the studies of predictability in numerical weather and climate prediction.The results suggest that the nonlinear characteristics of the motions of atmosphere and oceans can be explored by NSV and CNOP. Also attentions are paid to the introduction of the classification of predictability problems, which are related to the maximum predictable time,the maximum prediction error, and the maximum allowing error of initial value and the parameters. All the information has the background of application to the evaluation of products of numerical weather and climate prediction. Furthermore the nonlinear optimization methods of the sensitivity analysis with numerical model are also introduced, which can give a quantitative assessment whether a numerical model is able to simulate the observations and find the initial field that yield the optimal simulation. Finally, the difficulties in the lack of ripe algorithms are also discussed, which leave future work to both computational mathematics and scientists in geophysics.
Sparse Nonlinear Electromagnetic Imaging Accelerated With Projected Steepest Descent Algorithm
Desmal, Abdulla
2017-04-03
An efficient electromagnetic inversion scheme for imaging sparse 3-D domains is proposed. The scheme achieves its efficiency and accuracy by integrating two concepts. First, the nonlinear optimization problem is constrained using L₀ or L₁-norm of the solution as the penalty term to alleviate the ill-posedness of the inverse problem. The resulting Tikhonov minimization problem is solved using nonlinear Landweber iterations (NLW). Second, the efficiency of the NLW is significantly increased using a steepest descent algorithm. The algorithm uses a projection operator to enforce the sparsity constraint by thresholding the solution at every iteration. Thresholding level and iteration step are selected carefully to increase the efficiency without sacrificing the convergence of the algorithm. Numerical results demonstrate the efficiency and accuracy of the proposed imaging scheme in reconstructing sparse 3-D dielectric profiles.
Institute of Scientific and Technical Information of China (English)
WANG Mei-Jiao; WANG Qi
2006-01-01
In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons & Fractals 25 (2005) 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions' soliton-like solutions and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.
Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics
Wu, Shen R
2012-01-01
A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit FiniteElement Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in master
A new variable coefficient algebraic method and non-traveling wave solutions of nonlinear equations
Institute of Scientific and Technical Information of China (English)
Lu Bin; Zhang Hong-Qing
2008-01-01
In this paper,a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics,which is direct and more powerful than projective Riccati equation method.In order to illustrate the validity and the advantages of the method,(2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained.This algorithm can also be applied to other nonlinear differential equations.
Application of nonlinear optimization method to sensitivity analysis of numerical model
Institute of Scientific and Technical Information of China (English)
XU Hui; MU Mu; LUO Dehai
2004-01-01
A nonlinear optimization method is applied to sensitivity analysis of a numerical model. Theoretical analysis and numerical experiments indicate that this method can give not only a quantitative assessment whether the numerical model is able to simulate the observations or not, but also the initial field that yields the optimal simulation. In particular, when the simulation results are apparently satisfactory, and sometimes both model error and initial error are considerably large, the nonlinear optimization method, under some conditions, can identify the error that plays a dominant role.
Directory of Open Access Journals (Sweden)
H. M. Abdelhafez
2016-03-01
Full Text Available The modified differential transform method (MDTM, Laplace transform and Padé approximants are used to investigate a semi-analytic form of solutions of nonlinear oscillators in a large time domain. Forced Duffing and forced van der Pol oscillators under damping effect are studied to investigate semi-analytic forms of solutions. Moreover, solutions of the suggested nonlinear oscillators are obtained using the fourth-order Runge-Kutta numerical solution method. A comparison of the result by the numerical Runge-Kutta fourth-order accuracy method is compared with the result by the MDTM and plotted in a long time domain.
A new method of thermal network modeling - A nonlinear programming approach
Adachi, M.; Miyaoka, S.; Muramatsu, A.; Funabashi, M.; Nakajima, T.
A new method for correcting thermal network model coefficients is described. This method sharply reduces discrepancies obtained by the nonlinear programming approach in the conductance coefficients and radiation coefficients for determining the heat balance of a spacecraft. The method consists of an experimental design and a nonlinear parameter identification. An experimental design for obtaining useful data for the thermal network model correction is discussed. A simulation study has shown that the standard deviation of the estimated temperature and estimation error of the parameters are reduced by 50 percent and 70 percent respectively.
A weak condition for secant method to solve systems of nonlinear equations
Institute of Scientific and Technical Information of China (English)
LIANG Ke-wei; HAN Dan-fu; ZHANG Hong; ZHU Cheng-yan
2009-01-01
In this paper, a new weak condition for the convergence of secant method to solve the systems of nonlinear equations is proposed. A convergence ball with the center x0 is replaced by that with X1, the first approximation generated by the secant method with the initial data x-1 and x0. Under the bounded conditions of the divided difference, a convergence theorem is obtained and two examples to illustrate the weakness of convergence conditions are provided.Moreover, the secant method is applied to a system of nonlinear equations to demonstrate the viability and effectiveness of the results in the paper.
Simple equation method for nonlinear partial differential equations and its applications
Directory of Open Access Journals (Sweden)
Taher A. Nofal
2016-04-01
Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.
An iterative regularization method for nonlinear problems based on Bregman projections
Maaß, Peter; Strehlow, Robin
2016-11-01
In this paper, we present an iterative method for the regularization of ill-posed, nonlinear problems. The approach is based on the Bregman projection onto stripes the width of which is controlled by both the noise level and the structure of the operator. In our investigations, we follow (Lorenz et al 2014 SIAM J. Imaging Sci. 7 1237-62) and extend the respective method to the setting of nonlinear operators. Furthermore, we present a proof for the regularizing properties of the method.
A NOTE ON THE NONLINEAR CONJUGATE GRADIENT METHOD
Institute of Scientific and Technical Information of China (English)
Yu-hong Dai; Ya-xiang Yuan
2002-01-01
The conjugate gradient method for unconstrained optimization problems varies with a scalar. In this note, a general condition concerning the scalar is given, which ensures the global convergence of the method in the case of strong Wolfe line searches. It is also discussed how to use the result to obtain the convergence of the famous Fletcher-Reeves, and Polak-Ribiere-Polyak conjugate gradient methods. That the condition cannot be relaxed in some sense is mentioned.
Multi-Symplectic Splitting Method for Two-Dimensional Nonlinear Schriidinger Equation
Institute of Scientific and Technical Information of China (English)
陈亚铭; 朱华君; 宋松和
2011-01-01
Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.
Three-Step Iterative Methods with Sixth-Order Convergence for Solving Nonlinear Equations
Directory of Open Access Journals (Sweden)
Behzad GHANBARI
2012-09-01
Full Text Available In this paper, we develop new families of sixth-order methods for solving simple zeros of non-linear equations. These methods are constructed such that the convergence is of order six. Each member of the families requires two evaluations of the given function and two of its derivative per iteration. These methods have more advantages than Newton’s method and other methods with the same convergence order, as shown in the illustration examples.
A nonlinearity compensation method for a matrix converter drive
DEFF Research Database (Denmark)
Lee, Kyo-Beum; Blaabjerg, Frede
2005-01-01
converter model using the direction of current. The proposed method does not need any additional hardware or complicated software and it is easy to realize by applying the algorithm to the conventional vector control. The proposed compensation method is applied for high-performance induction motor drives...
Kamalian, Morteza; Prilepsky, Jaroslaw E; Le, Son Thai; Turitsyn, Sergei K
2016-08-08
In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.
Tiffany, Sherwood H.; Adams, William M., Jr.
1988-01-01
The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.
Shi, Zhong-Ke; Wu, Fang-Xiang
2013-06-01
A common assumption is that the model structure is known for modelling high performance aircraft. In practice, this is not the case. Actually, structure identification plays the most important role in the processing of nonlinear system modelling. The integration of mode structure identification and parameter estimation is an efficient method to construct the model for high performance aircraft, which is nonlinear and also contains uncertainties. This article presents an efficient method for identifying nonlinear model structure and estimating parameters for high-performance aircraft model, which contains uncertainties. The parameters associated with nonlinear terms are considered one after the other if they should be included in the nonlinear model until a stopping criterion is met, which is based on Akaike's information criterion. A numerically efficient U-D factorisation is presented to avoid complex computation of high-order matrices. The proposed method is applied to flight test data of a high-performance aircraft. The results demonstrate that the proposed method could obtain the good aircraft model with a reasonably good fidelity based on the comparison with flight test data.
Institute of Scientific and Technical Information of China (English)
QIN Xinqiang; MA Yichen; GONG Chunqiong
2004-01-01
A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.
Nonlinear system identification with global and local soft computing methods
Energy Technology Data Exchange (ETDEWEB)
Runkler, T.A. [Siemens AG, Muenchen (Germany). Zentralabt. Technik Information und Kommunikation
2000-10-01
An important step in the design of control systems is system identification. Data driven system identification finds functional models for the system's input output behavior. Regression methods are simple and effective, but may cause overshoots for complicated characteristics. Neural network approaches such as the multilayer perceptron yield very accurate models, but are black box approaches which leads to problems in system and stability analysis. In contrast to these global modeling methods crisp and fuzzy rule bases represent local models that can be extracted from data by clustering methods. Depending on the type and number of models different degrees of model accuracy can be achieved. (orig.)
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In this paper, we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method, many explicit and exact general solutions with arbitrary functions for some nonlinear partial differential equations, which contain solitary wave solutions, trigonometric function solutions, and rational solutions, are obtained.
A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations
Institute of Scientific and Technical Information of China (English)
Zhang Zhi-Yong; Yong Xue-Lin; Chen Yu-Fu
2009-01-01
A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.
Institute of Scientific and Technical Information of China (English)
CHEN Jiang; HE Hong-Sheng; YANG Kong-Qing
2005-01-01
A generalized F-expansion method is introduced and applied to (3+ 1)-dimensional Kadomstev-Petviashvili(KP) equation. As a result, some new Jacobi elliptic function solutions of the equation are found, from which the trigonometric function solutions and the solitary wave solutions can be obtained. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.
Indian Academy of Sciences (India)
Wenjun Liu; Kewang Chen
2013-09-01
In this paper, we implemented the functional variable method and the modified Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled KdV system. This method is extremely simple but effective for handling nonlinear time-fractional differential equations.
A Smooth Newton Method for Nonlinear Programming Problems with Inequality Constraints
Directory of Open Access Journals (Sweden)
Vasile Moraru
2012-02-01
Full Text Available The paper presents a reformulation of the Karush-Kuhn-Tucker (KKT system associated nonlinear programming problem into an equivalent system of smooth equations. Classical Newton method is applied to solve the system of equations. The superlinear convergence of the primal sequence, generated by proposed method, is proved. The preliminary numerical results with a problems test set are presented.
Asymptotic Analysis to Two Nonlinear Equations in Fluid Mechanics by Homotopy Renormalisation Method
Guan, Jiang; Kai, Yue
2016-09-01
By the homotopy renormalisation method, the global approximate solutions to Falkner-Skan equation and Von Kármá's problem of a rotating disk in an infinite viscous fluid are obtained. The homotopy renormalisation method is simple and powerful for finding global approximate solutions to nonlinear perturbed differential equations arising in mathematical physics.
Variational space–time (dis)continuous Galerkin method for nonlinear free surface water waves
Gagarina, E.; Ambati, V.R.; Vegt, van der J.J.W.; Bokhove, O.
2014-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation. This method also handles waves generated by a wave maker. Its formulation stems from Miles’ variational principle for water waves together with a finite element
Variational space-time (dis)continuous Galerkin method for nonlinear free surface waves
Gagarina, E.; Vegt, van der J.J.W.; Ambati, V.R.; Bokhove, O.
2013-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a space-time finite element discretization that is cont
Energy Technology Data Exchange (ETDEWEB)
Zhang Huiqun [College of Mathematical Science, Qingdao University, Qingdao, Shandong 266071 (China)], E-mail: hellozhq@yahoo.com.cn
2009-02-15
By using some exact solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the NLS equation, a new Hamiltonian amplitude equation, the coupled Schrodinger-KdV equations and the Hirota-Maccari equations. New exact complex solutions are obtained.
Directory of Open Access Journals (Sweden)
Abaker. A. Hassaballa.
2015-10-01
Full Text Available - In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical, and engineering problems linear and nonlinear. This paper applies the homotopy perturbation method (HPM to find exact solution of partial differential equation with the Dirichlet and Neumann boundary conditions.
Numerical Analysis of Strongly Nonlinear Oscillation Systems using He's Max-Min Method
DEFF Research Database (Denmark)
Babazadeh, H; Domairry, G; Barari, Amin;
2011-01-01
Nonlinear functions are crucial points and terms in engineering problems. Actual and physical problems can be solved by solving and processing such functions. Thus, most scientists and engineers focus on solving these equations. This paper presents a novel method called the max-min method...
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation an
Indian Academy of Sciences (India)
Yusuf Gurefe; Abdullah Sonmezoglu; Emine Misirli
2011-12-01
In this paper some exact solutions including soliton solutions for the KdV equation with dual power law nonlinearity and the (, ) equation with generalized evolution are obtained using the trial equation method. Also a more general trial equation method is proposed.
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation
Application of a new method of nonlinear dynamical system identification to biochemical problems.
Karnaukhov, A V; Karnaukhova, E V
2003-03-01
The system identification method for a variety of nonlinear dynamic models is elaborated. The problem of identification of an original nonlinear model presented as a system of ordinary differential equations in the Cauchy explicit form with a polynomial right part reduces to the solution of the system of linear equations for the constants of the dynamical model. In other words, to construct an integral model of the complex system (phenomenon), it is enough to collect some data array characterizing the time-course of dynamical parameters of the system. Collection of such a data array has always been a problem. However difficulties emerging are, as a rule, not principal and may be overcome almost without exception. The potentialities of the method under discussion are demonstrated by the example of the test problem of multiparametric nonlinear oscillator identification. The identification method proposed may be applied to the study of different biological systems and in particular the enzyme kinetics of complex biochemical reactions.
Directory of Open Access Journals (Sweden)
Fukang Yin
2013-01-01
Full Text Available This paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs. The approximate solutions of PDEs are calculated in the form of a series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The main advantage of the new method is that it can avoid solving the nonlinear algebraic system and symbolic computation. Furthermore, the developed vector-matrix form makes it computationally efficient. The results show that the proposed method is very effective and easy to implement.
Hein, Matthias
2010-01-01
Many problems in machine learning and statistics can be formulated as (generalized) eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding critical points of a quadratic function subject to quadratic constraints. In this paper we show that a certain class of constrained optimization problems with nonquadratic objective and constraints can be understood as nonlinear eigenproblems. We derive a generalization of the inverse power method which is guaranteed to converge to a nonlinear eigenvector. We apply the inverse power method to 1-spectral clustering and sparse PCA which can naturally be formulated as nonlinear eigenproblems. In both applications we achieve state-of-the-art results in terms of solution quality and runtime. Moving beyond the standard eigenproblem should be useful also in many other applications and our inverse power method can be easily adapted to new problems.
Stability for a class of nonlinear time-delay systems via Hamiltonian functional method
Institute of Scientific and Technical Information of China (English)
YANG RenMing; WANG YuZhen
2012-01-01
This paper investigates the stability of a class of nonlinear time-delay systems via Hamiltonian functional method,and proposes a number of new results on generalized Hamiltonian realization (GHR) and stability analysis for this class of systems.Firstly,the concept of GHR of general nonlinear time-delay systems is proposed,and several new GHR methods are given.Then,based on the new GHR methods obtained,the stability of time-delay systems is investigated,and several delay-dependent sufficient conditions in term of matrix inequalities are derived for the stability analysis by constructing suitable Lyapunov-Krasovskii (L-K) functionals.Finally,an illustrative example shows that the results obtained in this paper have less conservatism,and work very well in the stability analysis of some nonlinear time-delay Hamiltonian systems.
Directory of Open Access Journals (Sweden)
Mahsa Khoeiniha
2012-01-01
Full Text Available This paper investigated study of dynamics of nonlinear electrical circuit by means of modern nonlinear techniques and the control of a class of chaotic system by using backstepping method based on Lyapunov function. The behavior of such nonlinear system when they are under the influence of external sinusoidal disturbances with unknown amplitudes has been considered. The objective is to analyze the performance of this system at different amplitudes of disturbances. We illustrate the proposed approach for controlling duffing oscillator problem to stabilize this system at the equilibrium point. Also Genetic Algorithm method (GA for computing the parameters of controller has been used. GA can be successfully applied to achieve a better controller. Simulation results have shown the effectiveness of the proposed method.
The Optical Nonlinearity of Au and Ag Nanoparticle Prepared by the Γ-Radiation Method
Directory of Open Access Journals (Sweden)
Esmaeil Shahriari
2010-01-01
Full Text Available Problem statement: The third order nonlinear optical properties of metal nanoparticles have been of interest in physical chemistry, medical diagnostics and optical devices. Gold colloidal nanoparticles are responsible for the brilliant reds seen in stained glass windows and silver particles are typically yellow. The purpose of the study was to determine the nonlinear refraction and absorption coefficient of the Au and Ag nanoparticles in PVP solution. Approach: The samples were prepared by Γ-radiation method and the nonlinear optical properties of the composites were investigated using a single beam Z-scan technique with a beam power of 40 mW and operated at wavelength of 532 nm. The measurements were carried out for both Open and closed aperture Z-scan arrangements. Results: For both Au/PVP and Ag/PVP samples the results exhibited reverse saturable absorption. The closed aperture Z-scan of the nano-fluid samples revealed self-defocusing effect while the open aperture Z-scan of the samples show a reversible saturable absorption. Conclusion: The Z-scan measurement showed that silver and gold nano-fluid prepared by gamma radiation exhibited large thermal nonlinear refractive index n2 as -8.78×10-7 and -2.478×10-6 cm2/W, respectively. We have also investigated nonlinear absorption of these samples and we found a large value of nonlinear absorption for Ag nanoparticle and a weak absorption for Au nanoparticle. In conclusion, the experimental result shows a good nonlinear refractive index at low laser power in which encouraging for possible applications in nonlinear optical devices.
Directory of Open Access Journals (Sweden)
Uswah Qasim
2016-03-01
Full Text Available A homotopy method is presented for the construction of frozen Jacobian iterative methods. The frozen Jacobian iterative methods are attractive because the inversion of the Jacobian is performed in terms of LUfactorization only once, for a single instance of the iterative method. We embedded parameters in the iterative methods with the help of the homotopy method: the values of the parameters are determined in such a way that a better convergence rate is achieved. The proposed homotopy technique is general and has the ability to construct different families of iterative methods, for solving weakly nonlinear systems of equations. Further iterative methods are also proposed for solving general systems of nonlinear equations.
Yelve, Nitesh P; Mitra, Mira; Mujumdar, P M; Ramadas, C
2016-08-01
A new hybrid method based upon nonlinear Lamb wave response in time and frequency domains is introduced to locate a delamination in composite laminates. In Lamb wave based nonlinear method, the presence of damage is shown by the appearance of higher harmonics in the Lamb wave response. The proposed method not only uses this spectral information but also the corresponding temporal response data, for locating the delamination. Thus, the method is termed as a hybrid method. The paper includes formulation of the method and its application to locate a Barely Visible Impact Damage (BVID) induced delamination in a Carbon Fiber Reinforced Polymer (CFRP) laminate. The method gives the damage location fairly well. It is a baseline free method, as it does not need data from the pristine specimen.
Measurement of heart rate variability by methods based on nonlinear dynamics.
Huikuri, Heikki V; Mäkikallio, Timo H; Perkiömäki, Juha
2003-01-01
Heart rate (HR) variability has been conventionally analyzed with time and frequency domain methods, which measure the overall magnitude of R-R interval fluctuations around its mean value or the magnitude of fluctuations in some predetermined frequencies. Analysis of HR dynamics by methods based on chaos theory and nonlinear system theory has gained recent interest. This interest is based on observations suggesting that the mechanisms involved in cardiovascular regulation likely interact with each other in a nonlinear way. Furthermore, recent observational studies suggest that some indexes describing nonlinear HR dynamics, such as fractal scaling exponents, may provide more powerful prognostic information than the traditional HR variability indexes. In particular, short-term fractal scaling exponent measured by detrended fluctuation analysis method has been shown to predict fatal cardiovascular events in various populations. Approximate entropy, a nonlinear index of HR dynamics, which describes the complexity of R-R interval behavior, has provided information on the vulnerability to atrial fibrillation. There are many other nonlinear indexes, eg, Lyapunov exponent and correlation dimensions, which also give information on the characteristics of HR dynamics, but their clinical utility is not well established. Although concepts of chaos theory, fractal mathematics, and complexity measures of HR behavior in relation to cardiovascular physiology or various cardiovascular events are still far away from clinical medicine, they are a fruitful area for future research to expand our knowledge concerning the behavior of cardiovascular oscillations in normal healthy conditions as well as in disease states.
Li, Xingfeng; Coyle, Damien; Maguire, Liam; McGinnity, Thomas M; Benali, Habib
2011-07-01
In this paper a model selection algorithm for a nonlinear system identification method is proposed to study functional magnetic resonance imaging (fMRI) effective connectivity. Unlike most other methods, this method does not need a pre-defined structure/model for effective connectivity analysis. Instead, it relies on selecting significant nonlinear or linear covariates for the differential equations to describe the mapping relationship between brain output (fMRI response) and input (experiment design). These covariates, as well as their coefficients, are estimated based on a least angle regression (LARS) method. In the implementation of the LARS method, Akaike's information criterion corrected (AICc) algorithm and the leave-one-out (LOO) cross-validation method were employed and compared for model selection. Simulation comparison between the dynamic causal model (DCM), nonlinear identification method, and model selection method for modelling the single-input-single-output (SISO) and multiple-input multiple-output (MIMO) systems were conducted. Results show that the LARS model selection method is faster than DCM and achieves a compact and economic nonlinear model simultaneously. To verify the efficacy of the proposed approach, an analysis of the dorsal and ventral visual pathway networks was carried out based on three real datasets. The results show that LARS can be used for model selection in an fMRI effective connectivity study with phase-encoded, standard block, and random block designs. It is also shown that the LOO cross-validation method for nonlinear model selection has less residual sum squares than the AICc algorithm for the study.
A mixed Newton-Tikhonov method for nonlinear ill-posed problems
Institute of Scientific and Technical Information of China (English)
Chuan-gang KANG; Guo-qiang HE
2009-01-01
Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems,which have attracted extensive attention.However,computational cost of Newton type methods is high because practical problems are complicated.We propose a mixed Newton-Tikhonov method,i.e.,one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method.Convergence and stability of this method are proved under some conditions.Numerical experiments show that the proposed method has obvious advantages over the classical Newton method in terms of computational costs.
Recursive prediction error methods for online estimation in nonlinear state-space models
Directory of Open Access Journals (Sweden)
Dag Ljungquist
1994-04-01
Full Text Available Several recursive algorithms for online, combined state and parameter estimation in nonlinear state-space models are discussed in this paper. Well-known algorithms such as the extended Kalman filter and alternative formulations of the recursive prediction error method are included, as well as a new method based on a line-search strategy. A comparison of the algorithms illustrates that they are very similar although the differences can be important for the online tracking capabilities and robustness. Simulation experiments on a simple nonlinear process show that the performance under certain conditions can be improved by including a line-search strategy.
Extension of the homotopy pertubation method for solving nonlinear differential-difference equations
Energy Technology Data Exchange (ETDEWEB)
Mousa, Mohamed Medhat [Benha Univ. (Egypt). Benha High Inst. of Technology; Al-Farabi Kazakh National Univ., Almaty (Kazakhstan); Kaltayev, Aidarkan [Al-Farabi Kazakh National Univ., Almaty (Kazakhstan); Bulut, Hasan [Firat Univ., Elazig (Turkey). Dept. of Mathematics
2010-12-15
In this paper, we have extended the homotopy perturbation method (HPM) to find approximate analytical solutions for some nonlinear differential-difference equations (NDDEs). The discretized modified Korteweg-de Vries (mKdV) lattice equation and the discretized nonlinear Schroedinger equation are taken as examples to demonstrate the validity and the great potential of the HPM in solving such NDDEs. Comparisons are made between the results of the presented method and exact solutions. The obtained results reveal that the HPM is a very effective and convenient tool for solving such kind of equations. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Hagstrom, T. [Univ. of New Mexico, Albuquerque, NM (United States); Radhakrishnan, K. [Sverdrup Technology, Brook Park, OH (United States)
1994-12-31
The authors report on some iterative methods which they have tested for use in combustion simulations. In particular, they have developed a code to solve zero Mach number reacting flow equations with complex reaction and diffusion physics. These equations have the form of a nonlinear parabolic system coupled with constraints. In semi-discrete form, one obtains DAE`s of index two or three depending on the number of spatial dimensions. The authors have implemented a fourth order (fully implicit) BDF method in time, coupled with a suite of fourth order explicit and implicit spatial difference approximations. Most codes they know of for simulating reacting flows use a splitting strategy to march in time. This results in a sequence of nonlinear systems to solve, each of which has a simpler structure than the one they are faced with. The rapid and robust solution of the coupled system is the essential requirement for the success of their approach. They have implemented and analyzed nonlinear generalizations of conjugate gradient-like methods for nonsymmetric systems, including CGS and the quasi-Newton based method of Eirola and Nevanlinna. They develop a general framework for the nonlinearization of linear methods in terms of the acceleration of fixed-point iterations, where the latter is assumed to include the {open_quote}preconditioning{open_quote}. Their preconditioning is a single step of a split method, using lower order spatial difference approximations as well as simplified (Fickian) approximations of the diffusion physics.
An assessment of a semi analytical AG method for solving nonlinear oscillators
Directory of Open Access Journals (Sweden)
Hadi Mirgolbabaee
2016-02-01
Based on the comparison between AGM and numerical methods, AGM can be successfully applied for a broad range of nonlinear equations. One of the important reasons of selecting AGM for solving differential equations in miscellaneous fields not only in vibrations but also in different fields of sciences for instance fluid mechanics, solid mechanics, chemical engineering, etc. The main benefit of this method in comparison with the other approaches are as follows: normally according to the order of differential equations, we need boundary conditions so in the case of the number of boundary conditions is less than the order of the differential equation, AGM can create additional new boundary conditions in regard to the own differential equation and its derivatives. Results illustrate that method is efficient and has enough accuracy in comparison with other semi analytical and numerical methods because of the simplicity of this method. Moreover results demonstrate that AGM could be applicable through other methods in nonlinear problems with high nonlinearity. Furthermore convergence problems for solving nonlinear equations by using AGM appear small.
Nonlinear simulation of arch dam cracking with mixed finite element method
Directory of Open Access Journals (Sweden)
Ren Hao
2008-06-01
Full Text Available This paper proposes a new, simple and efficient method for nonlinear simulation of arch dam cracking from the construction period to the operation period, which takes into account the arch dam construction process and temperature loads. In the calculation mesh, the contact surface of pair nodes is located at places on the arch dam where cracking is possible. A new effective iterative method, the mixed finite element method for friction-contact problems, is improved and used for nonlinear simulation of the cracking process. The forces acting on the structure are divided into two parts: external forces and contact forces. The displacement of the structure is chosen as the basic variable and the nodal contact force in the possible contact region of the local coordinate system is chosen as the iterative variable, so that the nonlinear iterative process is only limited within the possible contact surface and is much more economical. This method was used to simulate the cracking process of the Shuanghe Arch Dam in Southwest China. In order to prove the validity and accuracy of this method and to study the effect of thermal stress on arch dam cracking, three schemes were designed for calculation. Numerical results agree with actual measured data, proving that it is feasible to use this method to simulate the entire process of nonlinear arch dam cracking.
A conservative Fourier pseudo-spectral method for the nonlinear Schrödinger equation
Gong, Yuezheng; Wang, Qi; Wang, Yushun; Cai, Jiaxiang
2017-01-01
A Fourier pseudo-spectral method that conserves mass and energy is developed for a two-dimensional nonlinear Schrödinger equation. By establishing the equivalence between the semi-norm in the Fourier pseudo-spectral method and that in the finite difference method, we are able to extend the result in Ref. [56] to prove that the optimal rate of convergence of the new method is in the order of O (N-r +τ2) in the discrete L2 norm without any restrictions on the grid ratio, where N is the number of modes used in the spectral method and τ is the time step size. A fast solver is then applied to the discrete nonlinear equation system to speed up the numerical computation for the high order method. Numerical examples are presented to show the efficiency and accuracy of the new method.
A LQP BASED INTERIOR PREDICTION-CORRECTION METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS
Institute of Scientific and Technical Information of China (English)
Bing-sheng He; Li-zhi Liao; Xiao-ming Yuan
2006-01-01
To solve nonlinear complementarity problems (NCP), at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the LogarithmicQuadratic Proximal (LQP) method solves a system of nonlinear equations (LQP system). This paper presents a practical LQP method-based prediction-correction method for NCP.The predictor is obtained via solving the LQP system approximately under significantly relaxed restriction, and the new iterate (the corrector) is computed directly by an explicit formula derived from the original LQP method. The implementations are very easy to be carried out. Global convergence of the method is proved under the same mild assumptions as the original LQP method. Finally, numerical results for traffic equilibrium problems are provided to verify that the method is effective for some practical problems.
Adaptive discontinuous Galerkin methods for non-linear reactive flows
Uzunca, Murat
2016-01-01
The focus of this monograph is the development of space-time adaptive methods to solve the convection/reaction dominated non-stationary semi-linear advection diffusion reaction (ADR) equations with internal/boundary layers in an accurate and efficient way. After introducing the ADR equations and discontinuous Galerkin discretization, robust residual-based a posteriori error estimators in space and time are derived. The elliptic reconstruction technique is then utilized to derive the a posteriori error bounds for the fully discrete system and to obtain optimal orders of convergence. As coupled surface and subsurface flow over large space and time scales is described by (ADR) equation the methods described in this book are of high importance in many areas of Geosciences including oil and gas recovery, groundwater contamination and sustainable use of groundwater resources, storing greenhouse gases or radioactive waste in the subsurface.
Nonlinear Least Squares Methods for Joint DOA and Pitch Estimation
DEFF Research Database (Denmark)
Jensen, Jesper Rindom; Christensen, Mads Græsbøll; Jensen, Søren Holdt
2013-01-01
In this paper, we consider the problem of joint direction-of-arrival (DOA) and fundamental frequency estimation. Joint estimation enables robust estimation of these parameters in multi-source scenarios where separate estimators may fail. First, we derive the exact and asymptotic Cram\\'{e}r-Rao...... estimation. Moreover, simulations on real-life data indicate that the NLS and aNLS methods are applicable even when reverberation is present and the noise is not white Gaussian....
Material nonlinear analysis via mixed-iterative finite element method
Sutjahjo, Edhi; Chamis, Christos C.
1992-01-01
The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.
Controlling Beam Halo-chaos Using a Special Nonlinear Method
Institute of Scientific and Technical Information of China (English)
2002-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry,medicine, and national defense. Some general engineering methods for chaos control have been developedin recent years, but they generally are unsuccessful for beam halo-chaos suppression due to manytechnical constraints. Beam halo-chaos is essentially a spatotemporal chaotic motion within a high power
Easy-to-implement method to target nonlinear systems
Baptista, Murilo S.; Caldas, Iberê L.
1998-03-01
In this work we present a method to rapidly direct a chaotic system, to an aimed state or target, through a sequence of control perturbations, with few different amplitudes chosen according to the allowed control-parameter changes. We applied this procedure to the one-dimensional Logistic map, to the two-dimensional Hénon map, and to the Double Scroll circuit described by a three-dimensional system of differential equations. Furthermore, for the Logistic map, we show numerically that the resulting trajectory (from the starting point to the target) goes along a stable manifold of the target. Moreover, using the Hénon map, we create and stabilize unstable periodic orbits, and also verify the procedure robustness in the presence of noise. We apply our method to the Double Scroll circuit, without using any low-dimensional mapping to represent its dynamics, an improvement with respect to previous targeting methods only applied for experimental systems that are mapping-modeled.
Nonlinear preprocessing method for detecting peaks from gas chromatograms
Directory of Open Access Journals (Sweden)
Min Hyeyoung
2009-11-01
Full Text Available Abstract Background The problem of locating valid peaks from data corrupted by noise frequently arises while analyzing experimental data. In various biological and chemical data analysis tasks, peak detection thus constitutes a critical preprocessing step that greatly affects downstream analysis and eventual quality of experiments. Many existing techniques require the users to adjust parameters by trial and error, which is error-prone, time-consuming and often leads to incorrect analysis results. Worse, conventional approaches tend to report an excessive number of false alarms by finding fictitious peaks generated by mere noise. Results We have designed a novel peak detection method that can significantly reduce parameter sensitivity, yet providing excellent peak detection performance and negligible false alarm rates from gas chromatographic data. The key feature of our new algorithm is the successive use of peak enhancement algorithms that are deliberately designed for a gradual improvement of peak detection quality. We tested our approach with real gas chromatograms as well as intentionally contaminated spectra that contain Gaussian or speckle-type noise. Conclusion Our results demonstrate that the proposed method can achieve near perfect peak detection performance while maintaining very small false alarm probabilities in case of gas chromatograms. Given the fact that biological signals appear in the form of peaks in various experimental data and that the propose method can easily be extended to such data, our approach will be a useful and robust tool that can help researchers highlight valid signals in their noisy measurements.
Zhang, Songchuan; Xia, Youshen
2016-12-28
Much research has been devoted to complex-variable optimization problems due to their engineering applications. However, the complex-valued optimization method for solving complex-variable optimization problems is still an active research area. This paper proposes two efficient complex-valued optimization methods for solving constrained nonlinear optimization problems of real functions in complex variables, respectively. One solves the complex-valued nonlinear programming problem with linear equality constraints. Another solves the complex-valued nonlinear programming problem with both linear equality constraints and an ℓ₁-norm constraint. Theoretically, we prove the global convergence of the proposed two complex-valued optimization algorithms under mild conditions. The proposed two algorithms can solve the complex-valued optimization problem completely in the complex domain and significantly extend existing complex-valued optimization algorithms. Numerical results further show that the proposed two algorithms have a faster speed than several conventional real-valued optimization algorithms.
Analysis of search-extension method for finding multiple solutions of nonlinear problem
Institute of Scientific and Technical Information of China (English)
2008-01-01
For numerical computations of multiple solutions of the nonlinear elliptic problemΔu+ f（u）=0 inΩ, u=0 onΓ, a search-extension method （SEM） was proposed and systematically studied by the authors. This paper shall complete its theoretical analysis. It is assumed that the nonlinearity is non-convex and its solution is isolated, under some conditions the corresponding linearized problem has a unique solution. By use of the compactness of the solution family and the contradiction argument, in general conditions, the high order regularity of the solution u∈H1+α,α>0 is proved. Assume that some initial value searched by suitably many eigenbases is already fallen into the neighborhood of the isolated solution, then the optimal error estimates of its nonlinear finite element approximation are shown by the duality argument and continuation method.
An efficient and accurate method for calculating nonlinear diffraction beam fields
Energy Technology Data Exchange (ETDEWEB)
Jeong, Hyun Jo; Cho, Sung Jong; Nam, Ki Woong; Lee, Jang Hyun [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan (Korea, Republic of)
2016-04-15
This study develops an efficient and accurate method for calculating nonlinear diffraction beam fields propagating in fluids or solids. The Westervelt equation and quasilinear theory, from which the integral solutions for the fundamental and second harmonics can be obtained, are first considered. A computationally efficient method is then developed using a multi-Gaussian beam (MGB) model that easily separates the diffraction effects from the plane wave solution. The MGB models provide accurate beam fields when compared with the integral solutions for a number of transmitter-receiver geometries. These models can also serve as fast, powerful modeling tools for many nonlinear acoustics applications, especially in making diffraction corrections for the nonlinearity parameter determination, because of their computational efficiency and accuracy.
NONLINEAR FILTER METHOD OF GPS DYNAMIC POSITIONING BASED ON BANCROFT ALGORITHM
Institute of Scientific and Technical Information of China (English)
ZHANGQin; TAOBen-zao; ZHAOChao-ying; WANGLi
2005-01-01
Because of the ignored items after linearization, the extended Kalman filter (EKF) becomes a form of suboptimal gradient descent algorithm. The emanative tendency exists in GPS solution when the filter equations are ill-posed. The deviation in the estimation cannot be avoided. Furthermore, the true solution may be lost in pseudorange positioning because the linearized pseudorange equations are partial solutions. To solve the above problems in GPS dynamic positioning by using EKF, a closed-form Kalman filter method called the two-stage algorithm is presented for the nonlinear algebraic solution of GPS dynamic positioning based on the global nonlinear least squares closed algorithm--Bancroft numerical algorithm of American. The method separates the spatial parts from temporal parts during processing the GPS filter problems, and solves the nonlinear GPS dynamic positioning, thus getting stable and reliable dynamic positioning solutions.
Energy Technology Data Exchange (ETDEWEB)
Etchepareborda, Andres [Department of Nuclear Engineering, Argentine National Atomic Energy Commission, Centro Atomico Bariloche, Av. E. Bustillo 9500, Bariloche 8400 (Argentina)]. E-mail: etche@cab.cnea.gov.ar; Lolich, Jose [INVAP S.E., Moreno 1089, Bariloche 8400 (Argentina)
2007-02-15
A constrained, output feedback nonlinear receding horizon control (NRHC) method is applied to design a research reactor power controller. The method uses a nonlinear plant model subject to state, control and terminal set constraints; a nonlinear cost function; and a high gain observer. The controller regulates reactor power from 1% to 100% of full power; considers known disturbances, such as reactivity insertions and changes in core inlet flow and temperature; and includes upper limits constraints on neutron flux, neutron flux rate, core outlet temperature and core inlet-outlet temperature difference. Simulation results show an excellent performance for power regulation and known disturbances rejection: all process variables are kept within the admissible limits avoiding the actuation of the safety systems.
Directory of Open Access Journals (Sweden)
Aijia Ouyang
2015-01-01
Full Text Available Nonlinear Muskingum models are important tools in hydrological forecasting. In this paper, we have come up with a class of new discretization schemes including a parameter θ to approximate the nonlinear Muskingum model based on general trapezoid formulas. The accuracy of these schemes is second order, if θ≠1/3, but interestingly when θ=1/3, the accuracy of the presented scheme gets improved to third order. Then, the present schemes are transformed into an unconstrained optimization problem which can be solved by a hybrid invasive weed optimization (HIWO algorithm. Finally, a numerical example is provided to illustrate the effectiveness of the present methods. The numerical results substantiate the fact that the presented methods have better precision in estimating the parameters of nonlinear Muskingum models.
DEFF Research Database (Denmark)
Ibsen, Lars Bo; Barari, Amin; Kimiaeifar, Amin
2010-01-01
/approximate analytical solution to strong nonlinear oscillators. Furthermore, it is shown that a large class of linear or nonlinear differential equations can be solved without the tangible restriction of sensitivity to the degree of the nonlinear term, adding that the method is quite convenient due to reduction in size...
New implicit method for analysis of problems in nonlinear structural dynamics
Directory of Open Access Journals (Sweden)
Gholampour A. A.
2011-06-01
Full Text Available In this paper a new method is proposed for direct time integration of nonlinear structural dynamics problems. In the proposed method the order of time integration scheme is higher than the conventional Newmark’s family of methods. This method assumes second order variation of the acceleration at each time step. Two variable parameters are used to increase the stability and accuracy of the method. The result obtained from this new higher order method is compared with two implicit methods; namely the Wilson-θ and the Newmark’s average acceleration methods.
Application of the G'/G Expansion Method in Ultrashort Pulses in Nonlinear Optical Fibers
Directory of Open Access Journals (Sweden)
Jiang Xing-Fang
2013-01-01
Full Text Available With the increasing input power in optical fibers, the dispersion problem is becoming a severe restriction on wavelength division multiplexing (WDM. With the aid of solitons, in which the shape and speed can remain constant during propagation, it is expected that the transmission of nonlinear ultrashort pulses in optical fibers can effectively control the dispersion. The propagation of a nonlinear ultrashort laser pulse in an optical fiber, which fits the high-order nonlinear Schrödinger equation (NLSE, has been solved using the G'/G expansion method. Group velocity dispersion, self-phase modulation, the fourth-order dispersion, and the fifth-order nonlinearity of the high-order NLSE were taken into consideration. A series of solutions has been obtained such as the solitary wave solutions of kink, inverse kink, the tangent trigonometric function, and the cotangent trigonometric function. The results have shown that the G'/G expansion method is an effective way to obtain the exact solutions for the high-order NLSE, and it provides a theoretical basis for the transmission of ultrashort pulses in nonlinear optical fibers.
Sequential Monte Carlo methods for nonlinear discrete-time filtering
Bruno, Marcelo GS
2013-01-01
In these notes, we introduce particle filtering as a recursive importance sampling method that approximates the minimum-mean-square-error (MMSE) estimate of a sequence of hidden state vectors in scenarios where the joint probability distribution of the states and the observations is non-Gaussian and, therefore, closed-form analytical expressions for the MMSE estimate are generally unavailable.We begin the notes with a review of Bayesian approaches to static (i.e., time-invariant) parameter estimation. In the sequel, we describe the solution to the problem of sequential state estimation in line
A VARIATIONAL EXPECTATION-MAXIMIZATION METHOD FOR THE INVERSE BLACK BODY RADIATION PROBLEM
Institute of Scientific and Technical Information of China (English)
Jiantao Cheng; Tie Zhou
2008-01-01
The inverse black body radiation problem, which is to reconstruct the area tempera-ture distribution from the measurement of power spectrum distribution, is a well-known ill-posed problem. In this paper, a variational expectation-maximization (EM) method is developed and its convergence is studied. Numerical experiments demonstrate that the variational EM method is more efficient and accurate than the traditional methods, in-cluding the Tikhonov regularization method, the Landweber method and the conjugate gradient method.
Nonlinear dimensionality reduction methods for synthetic biology biobricks' visualization.
Yang, Jiaoyun; Wang, Haipeng; Ding, Huitong; An, Ning; Alterovitz, Gil
2017-01-19
Visualizing data by dimensionality reduction is an important strategy in Bioinformatics, which could help to discover hidden data properties and detect data quality issues, e.g. data noise, inappropriately labeled data, etc. As crowdsourcing-based synthetic biology databases face similar data quality issues, we propose to visualize biobricks to tackle them. However, existing dimensionality reduction methods could not be directly applied on biobricks datasets. Hereby, we use normalized edit distance to enhance dimensionality reduction methods, including Isomap and Laplacian Eigenmaps. By extracting biobricks from synthetic biology database Registry of Standard Biological Parts, six combinations of various types of biobricks are tested. The visualization graphs illustrate discriminated biobricks and inappropriately labeled biobricks. Clustering algorithm K-means is adopted to quantify the reduction results. The average clustering accuracy for Isomap and Laplacian Eigenmaps are 0.857 and 0.844, respectively. Besides, Laplacian Eigenmaps is 5 times faster than Isomap, and its visualization graph is more concentrated to discriminate biobricks. By combining normalized edit distance with Isomap and Laplacian Eigenmaps, synthetic biology biobircks are successfully visualized in two dimensional space. Various types of biobricks could be discriminated and inappropriately labeled biobricks could be determined, which could help to assess crowdsourcing-based synthetic biology databases' quality, and make biobricks selection.
Hu, Zhan; Zheng, Gangtie
2016-08-01
A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.
Institute of Scientific and Technical Information of China (English)
R.Mokhtari; A.Samadi Toodar; N.G.Chegini
2011-01-01
@@ We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schr(o)dinger equations.The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method.The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly.Some comparisons with the methods applied in the literature are carried out.%We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrodinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out.
Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.
1989-01-01
In response to the tremendous growth in the development of advanced materials, such as fiber-reinforced plastic (FRP) composite materials, a new numerical method is developed to analyze and predict the time-dependent properties of these materials. Basic concepts in viscoelasticity, laminated composites, and previous viscoelastic numerical methods are presented. A stable numerical method, called the nonlinear differential equation method (NDEM), is developed to calculate the in-plane stresses and strains over any time period for a general laminate constructed from nonlinear viscoelastic orthotropic plies. The method is implemented in an in-plane stress analysis computer program, called VCAP, to demonstrate its usefulness and to verify its accuracy. A number of actual experimental test results performed on Kevlar/epoxy composite laminates are compared to predictions calculated from the numerical method.
A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems
Directory of Open Access Journals (Sweden)
S. S. Motsa
2013-01-01
Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.
A Theoretical Method for Characterizing Nonlinear Effects in Paul Traps with Added Octopole Field.
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Chen, Suming; Nie, Zongxiu
2015-08-01
In comparison with numerical methods, theoretical characterizations of ion motion in the nonlinear Paul traps always suffer from low accuracy and little applicability. To overcome the difficulties, the theoretical harmonic balance (HB) method was developed, and was validated by the numerical fourth-order Runge-Kutta (4th RK) method. Using the HB method, analytical ion trajectory and ion motion frequency in the superimposed octopole field, ε, were obtained by solving the nonlinear Mathieu equation (NME). The obtained accuracy of the HB method was comparable with that of the 4th RK method at the Mathieu parameter, q = 0.6, and the applicable q values could be extended to the entire first stability region with satisfactory accuracy. Two sorts of nonlinear effects of ion motion were studied, including ion frequency shift, Δβ, and ion amplitude variation, Δ(C(2n)/C0) (n ≠ 0). New phenomena regarding Δβ were observed, although extensive studies have been performed based on the pseudo-potential well (PW) model. For instance, the |Δβ| at ε = 0.1 and ε = -0.1 were found to be different, but they were the same in the PW model. This is the first time the nonlinear effects regarding Δ(C(2n)/C0) (n ≠ 0) are studied, and the associated study has been a challenge for both theoretical and numerical methods. The nonlinear effects of Δ(C(2n)/C0) (n ≠ 0) and Δβ were found to share some similarities at q < 0.6: both of them were proportional to ε, and the square of the initial ion displacement, z(0)(2).
Institute of Scientific and Technical Information of China (English)
Rui QI; Cheng-jian ZHANG; Yu-jie ZHANG
2012-01-01
This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of (k,l)-algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid.The finitedimensional and infinite-dimensional dissipativity results of (k,l)-algebraically stable Runge-Kutta methods are obtained.
Directory of Open Access Journals (Sweden)
Behzad Ghanbari
2014-01-01
Full Text Available We aim to study the convergence of the homotopy analysis method (HAM in short for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.
Kutev, N.; Kolkovska, N.; Dimova, M.
2013-10-01
The Cauchy problem to the generalized Boussinesq equation with Bernoulli type nonlinearities is studied. Global solvability of the solutions with sub-critical initial energy is proved by means of different techniques - nonstandard potential well method and method of the conservation low of the energy. In the framework of the nonstandard potential well method a new critical energy constant is introduced and estimated. The performed numerical experiments support the theoretical results.
Evaluation of a physically based quasi-linear and a conceptually based nonlinear Muskingum methods
Perumal, Muthiah; Tayfur, Gokmen; Rao, C. Madhusudana; Gurarslan, Gurhan
2017-03-01
Two variants of the Muskingum flood routing method formulated for accounting nonlinearity of the channel routing process are investigated in this study. These variant methods are: (1) The three-parameter conceptual Nonlinear Muskingum (NLM) method advocated by Gillin 1978, and (2) The Variable Parameter McCarthy-Muskingum (VPMM) method recently proposed by Perumal and Price in 2013. The VPMM method does not require rigorous calibration and validation procedures as required in the case of NLM method due to established relationships of its parameters with flow and channel characteristics based on hydrodynamic principles. The parameters of the conceptual nonlinear storage equation used in the NLM method were calibrated using the Artificial Intelligence Application (AIA) techniques, such as the Genetic Algorithm (GA), the Differential Evolution (DE), the Particle Swarm Optimization (PSO) and the Harmony Search (HS). The calibration was carried out on a given set of hypothetical flood events obtained by routing a given inflow hydrograph in a set of 40 km length prismatic channel reaches using the Saint-Venant (SV) equations. The validation of the calibrated NLM method was investigated using a different set of hypothetical flood hydrographs obtained in the same set of channel reaches used for calibration studies. Both the sets of solutions obtained in the calibration and validation cases using the NLM method were compared with the corresponding solutions of the VPMM method based on some pertinent evaluation measures. The results of the study reveal that the physically based VPMM method is capable of accounting for nonlinear characteristics of flood wave movement better than the conceptually based NLM method which requires the use of tedious calibration and validation procedures.
On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations
Directory of Open Access Journals (Sweden)
H. Montazeri
2012-01-01
Full Text Available We consider a system of nonlinear equations F(x=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.
C-L METHOD AND ITS APPLICATION TO ENGINEERING NONLINEAR DYNAMICAL PROBLEMS
Institute of Scientific and Technical Information of China (English)
陈予恕; 丁千
2001-01-01
The C-L method was generalized from Liapunov-Schmidt reduction method,combined with theory of singularities, for study of non-autonomous dynamical systems to obtain the typical bifurcating response curves in the system parameter spaces. This method has been used , as an example, to analyze the engineering nonlinear dynamical problems by obtaining the bifurcation programs and response curves which are useful in developing tech niques of control to subharmonic instability of large rotating machinery.
Institute of Scientific and Technical Information of China (English)
Dongyang Shi; Haihong Wang; Yuepeng Du
2009-01-01
An anisotropic nonconforming finite element method is presented for a class of nonlinear Sobolev equations. The optimal error estimates and supercloseness are obtained for both semi-discrete and fully-discrete approximate schemes, which are the same as the traditional finite element methods. In addition, the global superconvergence is derived through the postprocessing technique. Numerical experiments are included to illustrate the feasibility of the proposed method.
Institute of Scientific and Technical Information of China (English)
FU Jing-Li; FU Hao
2008-01-01
We deai with the generalization of the field method to weakly non-linear mechanico-electricai coupling systems.The field co-ordinates and field momenta approaches are combined with the method of multiple time scales in order to obtain the amplitudes and phase of oscillations in the frst approximation. An example in mechanico-electrical coupling systems is given to illustrate this method.
A New UKF Based Fault Detection Method in Non-linear Systems
Institute of Scientific and Technical Information of China (English)
GE Zhe-xue; YANG Yong-min; HU Zheng
2006-01-01
To detect the bias fault in stochastic non-linear dynamic systems, a new Unscented Kalman Filtering(UKF) based real-time recursion detection method is brought forward with the consideration of the flaws of traditional Extended Kalman Filtering(EKF). It uses the UKF as the residual generation method and the Weighted-Sum Squared Residual (WSSR) as the fault detection strategy. The simulation results are provided which demonstrate better effectiveness and a higher detection ratio of the developed methods.
Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method
Energy Technology Data Exchange (ETDEWEB)
Jerome L.V. Lewandowski
2005-01-25
A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details.
Stupishin, L.; Nikitin, K.; Kolesnikov, A.
2017-05-01
A methodology for shell stability research and determining buckling load, based on the mixed finite element method are proposed. Axisymmetric geometrically nonlinear shallow shells made of orthotropic material are considered. The results of numerical research of stability by changing the shape of shells, ratio of elastic modulus of the material and parameters of the support contour are presented.
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.
A Kernel Time Structure Independent Component Analysis Method for Nonlinear Process Monitoring☆
Institute of Scientific and Technical Information of China (English)
Lianfang Cai; Xuemin Tian; Ni Zhang
2014-01-01
Kernel independent component analysis (KICA) is a newly emerging nonlinear process monitoring method, which can extract mutually independent latent variables cal ed independent components (ICs) from process var-iables. However, when more than one IC have Gaussian distribution, it cannot extract the IC feature effectively and thus its monitoring performance will be degraded drastical y. To solve such a problem, a kernel time struc-ture independent component analysis (KTSICA) method is proposed for monitoring nonlinear process in this paper. The original process data are mapped into a feature space nonlinearly and then the whitened data are calculated in the feature space by the kernel trick. Subsequently, a time structure independent component analysis algorithm, which has no requirement for the distribution of ICs, is proposed to extract the IC feature. Finally, two monitoring statistics are built to detect process faults. When some fault is detected, a nonlinear fault identification method is developed to identify fault variables based on sensitivity analysis. The proposed monitoring method is applied in the Tennessee Eastman benchmark process. Applications demonstrate the superiority of KTSICA over KICA.
An Assessment of Linear Versus Non-linear Multigrid Methods for Unstructured Mesh Solvers
2001-05-01
problems is investigated. The first case consists of a transient radiation-diffusion problem for which an exact linearization is available, while the...to the Jacobian of a second-order accurate discretization. When an exact linearization is employed, the linear and non-linear multigrid methods
Adaptive Wavelet Methods for Linear and Nonlinear Least-Squares Problems
Stevenson, R.
2014-01-01
The adaptive wavelet Galerkin method for solving linear, elliptic operator equations introduced by Cohen et al. (Math Comp 70:27-75, 2001) is extended to nonlinear equations and is shown to converge with optimal rates without coarsening. Moreover, when an appropriate scheme is available for the appr
Regularization method with two parameters for nonlinear ill-posed problems
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper is devoted to the regularization of a class of nonlinear ill-posed problems in Banach spaces. The operators involved are multi-valued and the data are assumed to be known approximately. Under the assumption that the original problem is solvable, a strongly convergent approximation procedure is designed by means of the Tikhonov regularization method with two pa- rameters.
Approximation for Transient of Nonlinear Circuits Using RHPM and BPES Methods
Directory of Open Access Journals (Sweden)
H. Vazquez-Leal
2013-01-01
Full Text Available The microelectronics area constantly demands better and improved circuit simulation tools. Therefore, in this paper, rational homotopy perturbation method and Boubaker Polynomials Expansion Scheme are applied to a differential equation from a nonlinear circuit. Comparing the results obtained by both techniques revealed that they are effective and convenient.
Van Dijk, N.P.
2012-01-01
This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself.
Travelling wave solutions to nonlinear physical models by means of the ﬁrst integral method
Indian Academy of Sciences (India)
İsmail Aslan Aslan
2011-04-01
This paper presents the ﬁrst integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established ﬁrst integrals, exact solutions are successfully constructed for the equations considered.
Bonito, Andrea
2013-10-03
We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL condition. © 2013 American Mathematical Society.
THE FINITE ELEMENT METHODS FOR A CLASS OF NONLINEAR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Error estimates are established for the finite dement methods to solve a class of second or der nonlinear parabolic equations. Optimal rates of convergence in L2-and H1-norms are derived. Meanwhile,the schenes are second order correct in time.
Indian Academy of Sciences (India)
Ranjit Kumar
2012-09-01
Travelling and solitary wave solutions of certain coupled nonlinear diffusion-reaction equations have been constructed using the auxiliary equation method. These equations arise in a variety of contexts not only in biological, chemical and physical sciences but also in ecological and social sciences.
Indian Academy of Sciences (India)
Ranjit Kumar; R S Kaushal; Awadhesh Prasad
2010-10-01
An auto-Bäcklund transformation derived in the homogeneous balance method is employed to obtain several new exact solutions of certain kinds of nonlinear diffusion-reaction (D-R) equations. These equations arise in a variety of problems in physical, chemical, biological, social and ecological sciences.
Solving Nonlinear Differential Algebraic Equations by an Implicit Lie-Group Method
Directory of Open Access Journals (Sweden)
Chein-Shan Liu
2013-01-01
Full Text Available We derive an implicit Lie-group algorithm together with the Newton iterative scheme to solve nonlinear differential algebraic equations. Four numerical examples are given to evaluate the efficiency and accuracy of the new method when comparing the computational results with the closed-form solutions.
THE EFFECT OF NUMERICAL INTEGRATION IN FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
N＇guimbi; Germain
2001-01-01
Abstract. The effect of numerical integration in finite element methods applied to a class of nonlinear parabolic equations is considered and some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered in the presence of numerical integration are given. Optimal Lz and H1 estimates for the error and its time derivative are established.
The Superconvergence of Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
Institute of Scientific and Technical Information of China (English)
YanpingCHEN; YunqingHUANG
1998-01-01
Imprioved L2-error estimates are computed for mixed finte element methods for second order nonlinear hyperbolic equations.Superconvergence results,L∞ in time and discrete L2 in space,are derived for both the solution and gradients on the rectangular domain.Results are given for the continuous-time case.
Institute of Scientific and Technical Information of China (English)
Yao-lin Jiang
2003-01-01
In this paper we presented a convergence condition of parallel dynamic iteration methods for a nonlinear system of differential-algebraic equations with a periodic constraint.The convergence criterion is decided by the spectral expression of a linear operator derivedfrom system partitions. Numerical experiments given here confirm the theoretical work ofthe paper.
ESTIMATE ACCURACY OF NONLINEAR COEFFICIENTS OF SQUEEZEFILM DAMPER USING STATE VARIABLE FILTER METHOD
Institute of Scientific and Technical Information of China (English)
1998-01-01
The estimate model for a nonlinear system of squeeze-film damper (SFD) is described.The method of state variable filter (SVF) is used to estimate the coefficients of SFD.The factors which are critical to the estimate accuracy are discussed.
A numerical-perturbation method for the nonlinear analysis of structural vibrations
Nayfeh, A. H.; Mook, D. T.; Lobitz, D. W.
1974-01-01
A numerical-perturbation method is proposed for the determination of the nonlinear forced response of structural elements. Purely analytical techniques are capable of determining the response of structural elements having simple geometries and simple variations in thickness and properties, but they are not applicable to elements with complicated structure and boundaries. Numerical techniques are effective in determining the linear response of complicated structures, but they are not optimal for determining the nonlinear response of even simple elements when modal interactions take place due to the complicated nature of the response. Therefore, the optimum is a combined numerical and perturbation technique. The present technique is applied to beams with varying cross sections.
Computation of Nonlinear Backscattering Using a High-Order Numerical Method
Fibich, G.; Ilan, B.; Tsynkov, S.
2001-01-01
The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.
Prospects and limitations of mathematical methods for decision making in nonlinear complex systems
DEFF Research Database (Denmark)
Starke, Jens; Berkemer, Rainer
2007-01-01
This report discusses the art of scientific modeling in general. Different modeling approaches and their investigation are outlined. The final issue is to elaborate on the preconditions for utilizing mathematical models for decision making. We are very much indebted to the participants...... of the workshop Decision making and uncertainty in nonlinear complex systems for their valuable input on topics like uncertainty, nonlinearity, and complex systems in general. Scientists with different research backgrounds from various fields discussed several aspects of mathematical methods for decision making...... and strategic planning....
Generalized Kudryashov method for solving some (3+1-dimensional nonlinear evolution equations
Directory of Open Access Journals (Sweden)
Md. Shafiqul Islam
2015-06-01
Full Text Available In this work, we have applied the generalized Kudryashov methods to obtain the exact travelling wave solutions for the (3+1-dimensional Jimbo-Miwa (JM equation, the (3+1-dimensional Kadomtsev-Petviashvili (KP equation and the (3+1-dimensional Zakharov-Kuznetsov (ZK. The attained solutions show distinct physical configurations. The constraints that will guarantee the existence of specific solutions will be investigated. These solutions may be useful and desirable for enlightening specific nonlinear physical phenomena in genuinely nonlinear dynamical systems.
DEFF Research Database (Denmark)
Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian
2014-01-01
differences and differences between the solution found by each optimisation method. One of the investigated approaches utilises LP (linear programming) for optimisation, one uses LP with binary operation constraints, while the third approach uses NLP (non-linear programming). The LP model is used...... of selected units by 23%, while for a non-linear approach the increase can be higher than 39%. The results indicate a higher coherence between the two latter approaches, and that the MLP (mixed integer programming) optimisation is most appropriate from a viewpoint of accuracy and runtime. © 2014 Elsevier Ltd...
Prospects and limitations of mathematical methods for decision making in nonlinear complex systems
DEFF Research Database (Denmark)
Starke, Jens; Berkemer, Rainer
2007-01-01
of the workshop Decision making and uncertainty in nonlinear complex systems for their valuable input on topics like uncertainty, nonlinearity, and complex systems in general. Scientists with different research backgrounds from various fields discussed several aspects of mathematical methods for decision making......This report discusses the art of scientific modeling in general. Different modeling approaches and their investigation are outlined. The final issue is to elaborate on the preconditions for utilizing mathematical models for decision making. We are very much indebted to the participants...
Soliton solution for nonlinear partial differential equations by cosine-function method
Energy Technology Data Exchange (ETDEWEB)
Ali, A.H.A. [Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom (Egypt); Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish), Suez Canal University, AL-Arish 45111 (Egypt)], E-mail: asoliman_99@yahoo.com; Raslan, K.R. [Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo (Egypt)
2007-08-20
In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations.
Directory of Open Access Journals (Sweden)
Suxiang He
2014-01-01
Full Text Available An implementable nonlinear Lagrange algorithm for stochastic minimax problems is presented based on sample average approximation method in this paper, in which the second step minimizes a nonlinear Lagrange function with sample average approximation functions of original functions and the sample average approximation of the Lagrange multiplier is adopted. Under a set of mild assumptions, it is proven that the sequences of solution and multiplier obtained by the proposed algorithm converge to the Kuhn-Tucker pair of the original problem with probability one as the sample size increases. At last, the numerical experiments for five test examples are performed and the numerical results indicate that the algorithm is promising.
On approximation of nonlinear boundary integral equations for the combined method
Energy Technology Data Exchange (ETDEWEB)
Gregus, M.; Khoromsky, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.
1989-09-22
The nonlinear boundary integral equations that arise in research of nonlinear magnetostatic problems are investigated in combined formulation on an unbounded domain. Approximations of the derived operator equations are studied based on the Galerkin method. The investigated boundary operators are strongly monotone, Lipschitz-continuous, potential and have a symmetrical Gateaux derivative. The error estimates of the Galerkin's approximation in Sobolev spaces of fractional powers are obtained using the above-mentioned properties of the operators, too. The problem has been studied on surfaces in two and three-dimensional spaces. We answer also some questions on convergence connected with the discretized systems of equations. 21 refs.
The Modified Adomian Decomposition Method for Nonlinear Fractional Boundary Value Problems
Institute of Scientific and Technical Information of China (English)
WANG Jie
2012-01-01
We use the modified Adomian decomposition method(ADM) for solving the nonlinear fractional boundary value problem Dα0+u(x)=f(x,u(x)), 0＜x＜1, 3＜α≤4u(0) =α0, u″(0) =α2 (1)u(1) =β0, u″(1) =β2where Dα0+u is Caputo fractional derivative and α0,α2,β0,β2 is not zero at all,and f:[0,1] x R → R is continuous.The calculated numerical results show reliability and efficiency of the algorithm given.The numerical procedure is tested on linear and nonlinear problems.
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Energy Technology Data Exchange (ETDEWEB)
Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
Homotopy deform method for reproducing kernel space for nonlinear boundary value problems
Indian Academy of Sciences (India)
MIN-QIANG XU; YING-ZHEN LIN
2016-10-01
In this paper, the combination of homotopy deform method (HDM) and simplified reproducing kernel method (SRKM) is introduced for solving the boundary value problems (BVPs) of nonlinear differential equations. The solution methodology is based on Adomian decomposition and reproducing kernel method (RKM). By the HDM, the nonlinear equations can be converted into a series of linear BVPs. After that, the simplified reproducing kernel method, which not only facilitates the reproducing kernel but also avoids the time-consuming Schmidt orthogonalization process, is proposed to solve linear equations. Some numerical test problems including ordinary differential equations and partial differential equations are analysed to illustrate the procedure and confirm the performance of the proposed method. The results faithfully reveal that our algorithm is considerably accurate and effective as expected.
Sharma, Dinkar; Singh, Prince; Chauhan, Shubha
2016-01-01
In this paper, a combined form of the Laplace transform method with the homotopy perturbation method (HPTM) is applied to solve nonlinear systems of partial differential equations viz. the system of third order KdV Equations and the systems of coupled Burgers' equations in one- and two- dimensions. The nonlinear terms can be easily handled by the use of He's polynomials. The results shows that the HPTM is very efficient, simple and avoids the round-off errors. Four test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM) which shows that this method is a suitable method for solving systems of partial differential equations.
A Haar wavelet collocation method for coupled nonlinear Schrödinger-KdV equations
Oruç, Ömer; Esen, Alaattin; Bulut, Fatih
2016-04-01
In this paper, to obtain accurate numerical solutions of coupled nonlinear Schrödinger-Korteweg-de Vries (KdV) equations a Haar wavelet collocation method is proposed. An explicit time stepping scheme is used for discretization of time derivatives and nonlinear terms that appeared in the equations are linearized by a linearization technique and space derivatives are discretized by Haar wavelets. In order to test the accuracy and reliability of the proposed method L2, L∞ error norms and conserved quantities are used. Also obtained results are compared with previous ones obtained by finite element method, Crank-Nicolson method and radial basis function meshless methods. Error analysis of Haar wavelets is also given.
An Object Detection Method Using Wavelet Optical Flow and Hybrid Linear-Nonlinear Classifier
Directory of Open Access Journals (Sweden)
Pengcheng Han
2013-01-01
Full Text Available We propose a new computational intelligence method using wavelet optical flow and hybrid linear-nonlinear classifier for object detection. With the existing optical flow methods, it is difficult to accurately estimate moving objects with diverse speeds. We propose a wavelet-based optical flow method, which uses wavelet decomposition in optical flow motion estimation. The algorithm can accurately detect moving objects with variable speeds in a scene. In addition, we use the hybrid linear-nonlinear classifier (HLNLC to classify moving objects and static background. HLNLC transforms a nonoptimal scalar variable into its likelihood ratio and uses a scalar quantity as the decision variable. This approach is appropriate for the classification of optical flow feature vectors with unequal variance matrices. The experimental results confirm that our proposed object detection method has an improved accuracy and computation efficiency over other state-of-the-art methods.
Institute of Scientific and Technical Information of China (English)
SUN LiYing; WANG YuZhen
2009-01-01
This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonlan function method.Firstly,based on the Hamiltonian realization of the nonlinear descriptor systems and a suitable output feedback,two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by a nonsingular transformation,and a sufficient condition for two closed-loop systems to be impulse-free is given.The two systems are then combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique,based on which a simultaneous stabilization controller and a robust simultaneous stabilization controller are designed for the two systems.Secondly,the case of more than two nonlinear descriptor systems is investigated,and two new results are proposed for the simultaneous stabilization and robust simultaneous stabilization,respectively.Finally,an illustrative example is studied by using the results proposed in this paper,and simulations show that the simultaneous stabilization controllers obtained in this paper work very well.
Methods for Fault Diagnosability Analysis of a Class of Affine Nonlinear Systems
Directory of Open Access Journals (Sweden)
Xiafu Peng
2015-01-01
Full Text Available The fault diagnosability analysis for a given model, before developing a diagnosis algorithm, can be used to answer questions like “can the fault fi be detected by observed states?” and “can it separate fault fi from fault fj by observed states?” If not, we should redesign the sensor placement. This paper deals with the problem of the evaluation of detectability and separability for the diagnosability analysis of affine nonlinear system. First, we used differential geometry theory to analyze the nonlinear system and proposed new detectability criterion and separability criterion. Second, the related matrix between the faults and outputs of the system and the fault separable matrix are designed for quantitative fault diagnosability calculation and fault separability calculation, respectively. Finally, we illustrate our approach to exemplify how to analyze diagnosability by a certain nonlinear system example, and the experiment results indicate the effectiveness of the fault evaluation methods.
Directory of Open Access Journals (Sweden)
Shaolong Chen
2016-01-01
Full Text Available Parameter estimation is an important problem in nonlinear system modeling and control. Through constructing an appropriate fitness function, parameter estimation of system could be converted to a multidimensional parameter optimization problem. As a novel swarm intelligence algorithm, chicken swarm optimization (CSO has attracted much attention owing to its good global convergence and robustness. In this paper, a method based on improved boundary chicken swarm optimization (IBCSO is proposed for parameter estimation of nonlinear systems, demonstrated and tested by Lorenz system and a coupling motor system. Furthermore, we have analyzed the influence of time series on the estimation accuracy. Computer simulation results show it is feasible and with desirable performance for parameter estimation of nonlinear systems.
Extending lock-in methods: term isolation detection of nonlinear signals.
Jarvis, Thomas W
2016-08-01
We show that components of a nonlinear signal can be measured using phase-sensitive detection at unconventional demodulation frequencies, allowing us to isolate individual terms from the signal. To demonstrate this technique, autocorrelation measurements of an ultrafast pulsed laser were performed using two-photon absorption. In this example, the isolation of individual autocorrelation terms may provide internal consistency checks to improve the precision and accuracy of pulse characterization. More generally, this scheme can be extended to a range of nonlinear measurements. As a demonstration, we analyze a three-photon autocorrelation model, showing that many nonlinear signals can be studied with this method. We anticipate that term isolation detection will find application in a broad range of experiments, such as multidimensional Fourier transform spectroscopy or coherent anti-Stokes Raman spectroscopy.
A new Liu-Storey type nonlinear conjugate gradient method for unconstrained optimization problems
Zhang, Li
2009-03-01
Although the Liu-Storey (LS) nonlinear conjugate gradient method has a similar structure as the well-known Polak-Ribière-Polyak (PRP) and Hestenes-Stiefel (HS) methods, research about this method is very rare. In this paper, based on the memoryless BFGS quasi-Newton method, we propose a new LS type method, which converges globally for general functions with the Grippo-Lucidi line search. Moreover, we modify this new LS method such that the modified scheme is globally convergent for nonconvex minimization if the strong Wolfe line search is used. Numerical results are also reported.
A Derivative-Free Method of Eighth-Order For Finding Simple Root of Nonlinear Equations
Directory of Open Access Journals (Sweden)
Neha Choubey
2015-06-01
Full Text Available In this paper we have constructed an optimal eighth-order method with four function evaluations to solve the non-linear equations. The proposed method is a three-step method in which no derivative is required. Our scheme is optimal in the sense of Kung and Traub. Moreover, some test functions have been also included to confirm the superiority of the proposed method. At the end, we have presented the basins of attraction of some existing methods along with our proposed method to illustrate their performances.
Motulsky, Harvey J; Brown, Ronald E
2006-03-09
Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. This assumption leads to the familiar goal of regression: to minimize the sum of the squares of the vertical or Y-value distances between the points and the curve. Outliers can dominate the sum-of-the-squares calculation, and lead to misleading results. However, we know of no practical method for routinely identifying outliers when fitting curves with nonlinear regression. We describe a new method for identifying outliers when fitting data with nonlinear regression. We first fit the data using a robust form of nonlinear regression, based on the assumption that scatter follows a Lorentzian distribution. We devised a new adaptive method that gradually becomes more robust as the method proceeds. To define outliers, we adapted the false discovery rate approach to handling multiple comparisons. We then remove the outliers, and analyze the data using ordinary least-squares regression. Because the method combines robust regression and outlier removal, we call it the ROUT method. When analyzing simulated data, where all scatter is Gaussian, our method detects (falsely) one or more outlier in only about 1-3% of experiments. When analyzing data contaminated with one or several outliers, the ROUT method performs well at outlier identification, with an average False Discovery Rate less than 1%. Our method, which combines a new method of robust nonlinear regression with a new method of outlier identification, identifies outliers from nonlinear curve fits with reasonable power and few false positives.
Directory of Open Access Journals (Sweden)
Motulsky Harvey J
2006-03-01
Full Text Available Abstract Background Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. This assumption leads to the familiar goal of regression: to minimize the sum of the squares of the vertical or Y-value distances between the points and the curve. Outliers can dominate the sum-of-the-squares calculation, and lead to misleading results. However, we know of no practical method for routinely identifying outliers when fitting curves with nonlinear regression. Results We describe a new method for identifying outliers when fitting data with nonlinear regression. We first fit the data using a robust form of nonlinear regression, based on the assumption that scatter follows a Lorentzian distribution. We devised a new adaptive method that gradually becomes more robust as the method proceeds. To define outliers, we adapted the false discovery rate approach to handling multiple comparisons. We then remove the outliers, and analyze the data using ordinary least-squares regression. Because the method combines robust regression and outlier removal, we call it the ROUT method. When analyzing simulated data, where all scatter is Gaussian, our method detects (falsely one or more outlier in only about 1–3% of experiments. When analyzing data contaminated with one or several outliers, the ROUT method performs well at outlier identification, with an average False Discovery Rate less than 1%. Conclusion Our method, which combines a new method of robust nonlinear regression with a new method of outlier identification, identifies outliers from nonlinear curve fits with reasonable power and few false positives.
Numerical method of studying nonlinear interactions between long waves and multiple short waves
Institute of Scientific and Technical Information of China (English)
Xie Tao; Kuang Hai-Lan; William Perrie; Zou Guang-Hui; Nan Cheng-Feng; He Chao; Shen Tao; Chen Wei
2009-01-01
Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically,the solution is less tractable in more general cases involving multiple short waves.In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water.Specifically,this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves.Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train.From simulation results,we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train(expressed as wave train 2)leads to the energy focusing of the other short wave train(expressed as wave train 31.This mechanism Occurs on wave components with a narrow frequency bandwidth,whose frequencies are near that of wave train 3.
The heritability of the functional connectome is robust to common nonlinear registration methods
Hafzalla, George W.; Prasad, Gautam; Baboyan, Vatche G.; Faskowitz, Joshua; Jahanshad, Neda; McMahon, Katie L.; de Zubicaray, Greig I.; Wright, Margaret J.; Braskie, Meredith N.; Thompson, Paul M.
2016-03-01
Nonlinear registration algorithms are routinely used in brain imaging, to align data for inter-subject and group comparisons, and for voxelwise statistical analyses. To understand how the choice of registration method affects maps of functional brain connectivity in a sample of 611 twins, we evaluated three popular nonlinear registration methods: Advanced Normalization Tools (ANTs), Automatic Registration Toolbox (ART), and FMRIB's Nonlinear Image Registration Tool (FNIRT). Using both structural and functional MRI, we used each of the three methods to align the MNI152 brain template, and 80 regions of interest (ROIs), to each subject's T1-weighted (T1w) anatomical image. We then transformed each subject's ROIs onto the associated resting state functional MRI (rs-fMRI) scans and computed a connectivity network or functional connectome for each subject. Given the different degrees of genetic similarity between pairs of monozygotic (MZ) and same-sex dizygotic (DZ) twins, we used structural equation modeling to estimate the additive genetic influences on the elements of the function networks, or their heritability. The functional connectome and derived statistics were relatively robust to nonlinear registration effects.
An improved numerical method for nonlinear terms of spectral model and its applications
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
At present, the spectral model is one of the most widely applied numerical models in the research of numerical prediction and climatic variation. To improve the precision and efficiency of spectral method can greatly contribute to the development of numerical prediction. As the core part of spectral method, the calculating method of nonlinear terms always concentrates on numerical solution of atmospheric dynamical processes in the spectral space. However, there was little study in this field in the late thirty years. According to the principle of nonlinear term calculation with the dimensionality degradation and latitudinal perfect spectral method, we designed a new nonlinear term calculating method and made it compatible well with the common numerical algorithms of the spectral model used internationally. With an own-designed spectral dynamical framework suiting for the numerical application in common uses, theoretical analyses and numerical experiments have also been deeply conducted to compare our new method with the widely-used transform method in an attempt to advance the development of numerical algorithms of spectral model.
A nonlinear equivalent circuit method for analysis of passive intermodulation of mesh reflectors
Directory of Open Access Journals (Sweden)
Jiang Jie
2014-08-01
Full Text Available Passive intermodulation (PIM has gradually become a serious electromagnetic interference due to the development of high-power and high-sensitivity RF/microwave communication systems, especially large deployable mesh reflector antennas. This paper proposes a field-circuit coupling method to analyze the PIM level of mesh reflectors. With the existence of many metal–metal (MM contacts in mesh reflectors, the contact nonlinearity becomes the main reason for PIM generation. To analyze these potential PIM sources, an equivalent circuit model including nonlinear components is constructed to model a single MM contact so that the transient current through the MM contact point induced by incident electromagnetic waves can be calculated. Taking the electric current as a new electromagnetic wave source, the far-field scattering can be obtained by the use of electromagnetic numerical methods or the communication link method. Finally, a comparison between simulation and experimental results is illustrated to verify the validity of the proposed method.
Nonlinear Differential Geometry Method and Its Application in Induction Motor Decoupling Control
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Linyuan Fan
2016-05-01
Full Text Available An alternating current induction motor is a nonlinear, multi-variable, and strong-coupled system that is difficult to control. To address this problem, a novel control strategy based on nonlinear differential geometry theory was proposed. First, a five-order affine mathematical model for an alternating current induction motor was provided. Then, the feedback linearization method was used to realize decoupling and full linearization of the system model. Moreover, a general and simplified control law was adopted to facilitate practical applications. Finally, a controller was designed using the pole assignment method. Simulation results show that the proposed method can decouple the system model into two independent subsystems, and that the closed-loop system exhibits good dynamic and static performances. The proposed decoupling control method is useful to reduce the system complexity of an induction motor and to improve its control performance, thereby providing a new and feasible dynamic decoupling control for an alternating current induction motor.
Liu, Qian; OuYang, Liangfei; Liang, Heng; Li, Nan; Geng, Xindu
2012-06-01
A novel thermodynamic state recursion (TSR) method, which is based on nonequilibrium thermodynamic path described by the Lagrangian-Eulerian representation, is presented to simulate the whole chromatographic process of frontal analysis using the spatial distribution of solute bands in time series like as a series of images. TSR differs from the current numerical methods using the partial differential equations in Eulerian representation. The novel method is used to simulate the nonideal, nonlinear hydrophobic interaction chromatography (HIC) processes of lysozyme and myoglobin under the discrete complex boundary conditions. The results show that the simulated breakthrough curves agree well with the experimental ones. The apparent diffusion coefficient and the Langmuir isotherm parameters of the two proteins in HIC are obtained by the state recursion inverse method. Due to its the time domain and Markov characteristics, TSR is applicable to the design and online control of the nonlinear multicolumn chromatographic systems.
Hieber, Simone E.; Koumoutsakos, Petros
2008-11-01
We present a novel Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue. Linear solids are represented by the Lagrangian formulation of the stress-strain relationship that is extended to nonlinear solids by using the Lagrangian evolution of the deformation gradient described in a moving framework. The present method introduces a level set description, along with the particles, to capture the body deformations and to enforce the boundary conditions. Furthermore, the accuracy of the method in cases of large deformations is ensured by implementing a particle remeshing procedure. The method is validated in several benchmark problems, in two and three dimensions and the results compare well with the results of respective finite elements simulations. In simulations of large solid deformation under plane strain compression, the finite element solver exhibits spurious structures that are not present in the Lagrangian particle simulations. The particle simulations are compared with experimental results in an aspiration test of liver tissue.
An analysis of the stress formula for energy-momentum methods in nonlinear elastodynamics
Romero, Ignacio
2012-11-01
The energy-momentum method, a space-time discretization strategy for elastic problems in nonlinear solid, structural, and multibody mechanics relies critically on a discrete derivative operation that defines an approximation of the internal forces that guarantees the discrete conservation of energy and momenta. In the case of nonlinear elastodynamics, the formulation for general hyperelastic materials is due to Simo and Gonzalez, dating back to the mid-nineties. In this work we show that there are actually infinite second order energy-momentum methods for elastodynamics, all of them deriving from a modified midpoint integrator by an appropriate redefinition of the stress tensor at equilibrium. Such stress tensors can be interpreted as the solutions to local convex projections, whose precise definitions lead to different methods. The mathematical requirements of such projections are identified. Based on this geometrical interpretation several conserving methods are examined.
A multiple-scale power series method for solving nonlinear ordinary differential equations
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Chein-Shan Liu
2016-02-01
Full Text Available The power series solution is a cheap and effective method to solve nonlinear problems, like the Duffing-van der Pol oscillator, the Volterra population model and the nonlinear boundary value problems. A novel power series method by considering the multiple scales $R_k$ in the power term $(t/R_k^k$ is developed, which are derived explicitly to reduce the ill-conditioned behavior in the data interpolation. In the method a huge value times a tiny value is avoided, such that we can decrease the numerical instability and which is the main reason to cause the failure of the conventional power series method. The multiple scales derived from an integral can be used in the power series expansion, which provide very accurate numerical solutions of the problems considered in this paper.
A Stabilised Nodal Spectral Element Method for Fully Nonlinear Water Waves
Engsig-Karup, Allan Peter; Bigoni, Daniele
2015-01-01
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al (1998) \\cite{CaiEtAl1998}, although the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global $L^2$ projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively removes any aliasing driven instabilities while retaining the high-order accuracy of the numerical...
Nonlinear nonuniform torsional vibrations of bars by the boundary element method
Sapountzakis, E. J.; Tsipiras, V. J.
2010-05-01
In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross-section taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement-small strain theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post-buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an "average" axial displacement of the cross-section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the analog equation method, a BEM based method, leading to a system of nonlinear differential-algebraic equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental mode shape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the direct iteration technique (DIT), with a geometrically linear fundamental mode shape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand.
Application of Exp-function method for nonlinear evolution equations with variable coefficients
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A.; Madkour, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Faculty of Education for Girls, Physics Department, King Kahlid University, Bisha, Kingdom Saudi Arabia (Saudi Arabia)], E-mail: m_abdou_eg@yahoo.com
2007-09-10
In this Letter, the Exp-function method with the aid of symbolic computational system Maple is used to obtain generalized solitary solutions and periodic solutions of a generalized Zakharov-Kuznetsov equation with variable coefficients. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving other nonlinear evolution equations arising in mathematical physics.
On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation
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Hameed Husam Hameed
2015-01-01
Full Text Available We develop the Newton-Kantorovich method to solve the system of 2×2 nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.
The (G'/G)-expansion method for the nonlinear time fractional differential equations
Unsal, Omer; Guner, Ozkan; Bekir, Ahmet; Cevikel, Adem C.
2017-01-01
In this paper, we obtain exact solutions of two time fractional differential equations using Jumarie's modified Riemann-Liouville derivative which is encountered in mathematical physics and applied mathematics; namely (3 + 1)-dimensional time fractional KdV-ZK equation and time fractional ADR equation by using fractional complex transform and (G/'G )-expansion method. It is shown that the considered transform and method are very useful in solving nonlinear fractional differential equations.
A New Variable-Coefficient Riccati Subequation Method for Solving Nonlinear Lattice Equations
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Fanwei Meng
2013-01-01
Full Text Available We propose a new variable-coefficient Riccati subequation method to establish new exact solutions for nonlinear differential-difference equations. For illustrating the validity of this method, we apply it to the discrete (2 + 1-dimensional Toda lattice equation. As a result, some new and generalized traveling wave solutions including hyperbolic function solutions, trigonometric function solutions, and rational function solutions are obtained.
Variational space-time (dis)continuous Galerkin method for nonlinear free surface waves
Gagarina, E; Vegt, van der, N.F.A.; Ambati, V.R.; Bokhove, O.
2013-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a space-time finite element discretization that is continuous in space and discontinuous in time. The key features of this formulation are: (i) a discrete variational approach that gives rise to conservation of discrete energy and phase space and prese...
Energy Technology Data Exchange (ETDEWEB)
Zhang, Sheng [Department of Mathematics, Bohai University, Jinzhou 121000 (China)]. E-mail: zhshaeng@yahoo.com.cn; Xia, Tiecheng [Department of Mathematics, Bohai University, Jinzhou 121000 (China); Department of Mathematics, Shanghai University, Shanghai 200444 (China)
2007-04-09
In this Letter, a generalized new auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose the combined KdV-mKdV equation and the (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equations to illustrate the validity and advantages of the method. As a result, many new and more general exact solutions are obtained.
A new mapping method and its applications to nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Zeng Xin [Department of Mathematics, Zhengzhou University, Zhengzhou 450052 (China)], E-mail: zeng79723@163.com; Yong Xuelin [Department of Mathematics and Physics, North China Electric Power University, Beijing 102206 (China)
2008-10-27
In this Letter, a new mapping method is proposed for constructing more exact solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose the (2+1)-dimensional Konopelchenko-Dubrovsky equation and the (2+1)-dimensional KdV equations to illustrate the validity and advantages of the method. As a result, many new and more general exact solutions are obtained.
Direct adaptive control for nonlinear uncertain system based on control Lyapunov function method
Institute of Scientific and Technical Information of China (English)
Chen Yimei; Han Zhengzhi; Tang Houjun
2006-01-01
The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapunov function method, a direct adaptive controller is designed to complete the global adaptive stability of the uncertain system. At the same time, the controller is also verified to possess the optimality. Example and simulations are provided to illustrate the effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Z. Pashazadeh Atabakan
2013-01-01
Full Text Available Spectral homotopy analysis method (SHAM as a modification of homotopy analysis method (HAM is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.
Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations
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Huiping Cao
2014-01-01
Full Text Available Schubert’s method is an extension of Broyden’s method for solving sparse nonlinear equations, which can preserve the zero-nonzero structure defined by the sparse Jacobian matrix and can retain many good properties of Broyden’s method. In particular, Schubert’s method has been proved to be locally and q-superlinearly convergent. In this paper, we globalize Schubert’s method by using a nonmonotone line search. Under appropriate conditions, we show that the proposed algorithm converges globally and superlinearly. Some preliminary numerical experiments are presented, which demonstrate that our algorithm is effective for large-scale problems.
The exact solutions of nonlinear problems by Homotopy Analysis Method (HAM
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Hafiz Abdul Wahab
2016-06-01
Full Text Available The present paper presents the comparison of analytical techniques. We establish the existence of the phenomena of the noise terms in the perturbation series solution and find the exact solution of the nonlinear problems. If the noise terms exist, the Homotopy Analysis method gives the same series solution as in Adomian Decomposition Method as well as homotopy Perturbation Method (Wahab et al, 2015 and we get the exact solution using the initial guess in Homotopy Analysis Method using the results obtained by Adomian Decomposition Method.
Institute of Scientific and Technical Information of China (English)
FAN En-Gui
2001-01-01
Two new applications of homogeneous balance (HB) method are presented.It is shown that HB methodcan be extended to search for the Backlund transformations and similarity reductions of nonlinear partial differentialequations.The close relations among the HB method,Weiss-Tabor-Carnevale method and Clarkson-Kruskal directreduction method are also found.KdV-MKdV equation is considered as an illustrative example,and its one kind of Backlund transformation,three kinds of similarity reductions and several kinds of travelling wave solutions are obtained by using extended HB method.
A New Method to Solve Numeric Solution of Nonlinear Dynamic System
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Min Hu
2016-01-01
Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.
Energy Technology Data Exchange (ETDEWEB)
Wang, Hailing [Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong); Chung, Kwok-wai, E-mail: makchung@cityu.edu.hk [Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong)
2012-02-27
The analytical solutions of nonlinear oscillators obtained from most perturbation or approximate methods usually have poor accuracy near homoclinic/heteroclinic (HH) orbits. In this Letter, we propose a nonlinear time transformation method to overcome such difficulty. In particular, we apply such method with Padé approximation to find analytical solutions of a generalized Duffing-harmonic oscillator having a rational form for the potential energy. For some parametric ranges, HH orbits exist in such an oscillator. For analytical approximation of periodic solution obtained from the present method, it is shown that the relative error of period with respect to the exact period tends to zero when the amplitude of periodic solution tends to either zero or infinity. The relative error is still very small even near to HH orbits. Furthermore, analytical approximate of HH orbits can also be obtained. From the illustrative examples, the phase portraits are in excellent agreement with the exact HH orbits. The results from the present method are compared with the exact solutions and that from the cubication method. -- Highlights: ► A nonlinear transformation is proposed for a generalized Duffing-harmonic oscillator. ► The relative error of period with respect to the exact one is always very small. ► Approximate solution of homoclinic/heteroclinic orbits can be obtained. ► Phase portraits are in excellent agreement even at homoclinic/heteroclinic orbits.
Torres Cedillo, Sergio G.; Bonello, Philip
2016-01-01
The high pressure (HP) rotor in an aero-engine assembly cannot be accessed under operational conditions because of the restricted space for instrumentation and high temperatures. This motivates the development of a non-invasive inverse problem approach for unbalance identification and balancing, requiring prior knowledge of the structure. Most such methods in the literature necessitate linear bearing models, making them unsuitable for aero-engine applications which use nonlinear squeeze-film damper (SFD) bearings. A previously proposed inverse method for nonlinear rotating systems was highly limited in its application (e.g. assumed circular centered SFD orbits). The methodology proposed in this paper overcomes such limitations. It uses the Receptance Harmonic Balance Method (RHBM) to generate the backward operator using measurements of the vibration at the engine casing, provided there is at least one linear connection between rotor and casing, apart from the nonlinear connections. A least-squares solution yields the equivalent unbalance distribution in prescribed planes of the rotor, which is consequently used to balance it. The method is validated on distinct rotordynamic systems using simulated casing vibration readings. The method is shown to provide effective balancing under hitherto unconsidered practical conditions. The repeatability of the method, as well as its robustness to noise, model uncertainty and balancing errors, are satisfactorily demonstrated and the limitations of the process discussed.
K-Profiles: A Nonlinear Clustering Method for Pattern Detection in High Dimensional Data
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Kai Wang
2015-01-01
Full Text Available With modern technologies such as microarray, deep sequencing, and liquid chromatography-mass spectrometry (LC-MS, it is possible to measure the expression levels of thousands of genes/proteins simultaneously to unravel important biological processes. A very first step towards elucidating hidden patterns and understanding the massive data is the application of clustering techniques. Nonlinear relations, which were mostly unutilized in contrast to linear correlations, are prevalent in high-throughput data. In many cases, nonlinear relations can model the biological relationship more precisely and reflect critical patterns in the biological systems. Using the general dependency measure, Distance Based on Conditional Ordered List (DCOL that we introduced before, we designed the nonlinear K-profiles clustering method, which can be seen as the nonlinear counterpart of the K-means clustering algorithm. The method has a built-in statistical testing procedure that ensures genes not belonging to any cluster do not impact the estimation of cluster profiles. Results from extensive simulation studies showed that K-profiles clustering not only outperformed traditional linear K-means algorithm, but also presented significantly better performance over our previous General Dependency Hierarchical Clustering (GDHC algorithm. We further analyzed a gene expression dataset, on which K-profile clustering generated biologically meaningful results.
Jaksic, V; Mandic, D P; Ryan, K; Basu, B; Pakrashi, V
2016-01-01
Although vibration monitoring is a popular method to monitor and assess dynamic structures, quantification of linearity or nonlinearity of the dynamic responses remains a challenging problem. We investigate the delay vector variance (DVV) method in this regard in a comprehensive manner to establish the degree to which a change in signal nonlinearity can be related to system nonlinearity and how a change in system parameters affects the nonlinearity in the dynamic response of the system. A wide range of theoretical situations are considered in this regard using a single degree of freedom (SDOF) system to obtain numerical benchmarks. A number of experiments are then carried out using a physical SDOF model in the laboratory. Finally, a composite wind turbine blade is tested for different excitations and the dynamic responses are measured at a number of points to extend the investigation to continuum structures. The dynamic responses were measured using accelerometers, strain gauges and a Laser Doppler vibrometer. This comprehensive study creates a numerical and experimental benchmark for structurally dynamical systems where output-only information is typically available, especially in the context of DVV. The study also allows for comparative analysis between different systems driven by the similar input.
Mandic, D. P.; Ryan, K.; Basu, B.; Pakrashi, V.
2016-01-01
Although vibration monitoring is a popular method to monitor and assess dynamic structures, quantification of linearity or nonlinearity of the dynamic responses remains a challenging problem. We investigate the delay vector variance (DVV) method in this regard in a comprehensive manner to establish the degree to which a change in signal nonlinearity can be related to system nonlinearity and how a change in system parameters affects the nonlinearity in the dynamic response of the system. A wide range of theoretical situations are considered in this regard using a single degree of freedom (SDOF) system to obtain numerical benchmarks. A number of experiments are then carried out using a physical SDOF model in the laboratory. Finally, a composite wind turbine blade is tested for different excitations and the dynamic responses are measured at a number of points to extend the investigation to continuum structures. The dynamic responses were measured using accelerometers, strain gauges and a Laser Doppler vibrometer. This comprehensive study creates a numerical and experimental benchmark for structurally dynamical systems where output-only information is typically available, especially in the context of DVV. The study also allows for comparative analysis between different systems driven by the similar input. PMID:26909175
A quadrature based method of moments for nonlinear Fokker-Planck equations
Otten, Dustin L.; Vedula, Prakash
2011-09-01
Fokker-Planck equations which are nonlinear with respect to their probability densities and occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, fermions and bosons can be challenging to solve numerically. To address some underlying challenges, we propose the application of the direct quadrature based method of moments (DQMOM) for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations (NLFPEs). In DQMOM, probability density (or other distribution) functions are represented using a finite collection of Dirac delta functions, characterized by quadrature weights and locations (or abscissas) that are determined based on constraints due to evolution of generalized moments. Three particular examples of nonlinear Fokker-Planck equations considered in this paper include descriptions of: (i) the Shimizu-Yamada model, (ii) the Desai-Zwanzig model (both of which have been developed as models of muscular contraction) and (iii) fermions and bosons. Results based on DQMOM, for the transient and stationary solutions of the nonlinear Fokker-Planck equations, have been found to be in good agreement with other available analytical and numerical approaches. It is also shown that approximate reconstruction of the underlying probability density function from moments obtained from DQMOM can be satisfactorily achieved using a maximum entropy method.
Yang, Haijian
2016-07-26
Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.
Lajimi, Seyed Amir Mousavi
2014-01-01
The nonlinear dynamics of a microbeam-rigid body gyroscope are investigated by using a continuation method. To study the nonlinear dynamics of the system, the Lagrangian of the system is discretized and the reduced-order model is obtained. By using the continuation method, the frequency-response curves are computed and the stability of response is determined.
Energy Technology Data Exchange (ETDEWEB)
Raju, P. P.
1980-05-01
This report summarizes the results of the study program to assess the benefits of nonlinear analysis methods in Light Water Reactor (LWR) component designs. The current study reveals that despite its increased cost and other complexities, nonlinear analysis is a practical and valuable tool for the design of LWR components, especially under ASME Level D service conditions (faulted conditions) and it will greatly assist in the evaluation of ductile fracture potential of pressure boundary components. Since the nonlinear behavior is generally a local phenomenon, the design of complex components can be accomplished through substructuring isolated localized regions and evaluating them in detail using nonlinear analysis methods.
Measuring the nonlinear refractive index of graphene using the optical Kerr effect method.
Dremetsika, Evdokia; Dlubak, Bruno; Gorza, Simon-Pierre; Ciret, Charles; Martin, Marie-Blandine; Hofmann, Stephan; Seneor, Pierre; Dolfi, Daniel; Massar, Serge; Emplit, Philippe; Kockaert, Pascal
2016-07-15
By means of the ultrafast optical Kerr effect method coupled to optical heterodyne detection (OHD-OKE), we characterize the third-order nonlinear response of graphene and compare it to experimental values obtained by the Z-scan method on the same samples. From these measurements, we estimate a negative nonlinear refractive index for monolayer graphene, n2=-1.1×10-13 m2/W. This is in contradiction to previously reported values, which leads us to compare our experimental measurements obtained by the OHD-OKE and the Z-scan method with theoretical and experimental values found in the literature and to discuss the discrepancies, taking into account parameters such as doping.
Indian Academy of Sciences (India)
Junchao Chen; Biao Li
2012-03-01
In this paper, an extended multiple (′/)-expansion method is proposed to seek exact solutions of nonlinear evolution equations. The validity and advantages of the proposed method is illustrated by its applications to the Sharma–Tasso–Olver equation, the sixth-order Ramani equation, the generalized shallow water wave equation, the Caudrey–Dodd–Gibbon–Sawada–Kotera equation, the sixth-order Boussinesq equation and the Hirota–Satsuma equations. As a result, various complexiton solutions consisting of hyperbolic functions, trigonometric functions, rational functions and their mixture with parameters are obtained. When some parameters are taken as special values, the known double solitary-like wave solutions are derived from the double hyperbolic function solution. In addition, this method can also be used to deal with some high-dimensional and variable coefﬁcients’ nonlinear evolution equations.
Parallel algorithm of trigonometric collocation method in nonlinear dynamics of rotors
Directory of Open Access Journals (Sweden)
Musil T.
2007-11-01
Full Text Available A parallel algorithm of a numeric procedure based on a method of trigonometric collocation is presented for investigating an unbalance response of a rotor supported by journal bearings. After a condensation process the trigonometric collocation method results in a set of nonlinear algebraic equations which is solved by the Newton-Raphson method. The order of the set is proportional to the number of nonlinear bearing coordinates and terms of the finite Fourier series. The algorithm, realized in the MATLAB parallel computing environment (DCT/DCE, uses message passing technique for interacting among processes on nodes of a parallel computer. This technique enables portability of the source code both on parallel computers with distributed and shared memory. Tests, made on a Beowulf cluster and a symmetric multiprocessor, have revealed very good speed-up and scalability of this algorithm.
Directory of Open Access Journals (Sweden)
Ji Juan-Juan
2017-01-01
Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.
Novak, Antonin; Simon, Laurent; Lotton, Pierrick
2010-12-01
A new method of identification, based on an input synchronized exponential swept-sine signal, is used to analyze and synthesize nonlinear audio systems like overdrive pedals for guitar. Two different pedals are studied; the first one exhibiting a strong influence of the input signal level on its input/output law and the second one exhibiting a weak influence of this input signal level. The Synchronized Swept Sine method leads to a Generalized Polynomial Hammerstein model equivalent to the pedals under test. The behaviors of both pedals are illustrated through model-based resynthesized signals. Moreover, it is also shown that this method leads to a criterion allowing the classification of the nonlinear systems under test, according to the influence of the input signal levels on their input/output law.
Suppression of beam halo-chaos using nonlinear feedback discrete control method
Fang Jin Qing; Chen Guan Rong; Luo Xiao Shu; Weng Jia Qiang
2002-01-01
Based on nonlinear feedback control method, wavelet-based feedback controller as a especial nonlinear feedback function is designed for controlling beam halo-chaos in high-current accelerators of driven clean nuclear power system. PIC simulations show that suppression of beam halo-chaos are realized effectively after discrete control of wavelet-based feed-back is applied to five kinds of the initial proton beam distributions, respectively. The beam halo strength factor is quickly reduced to zero, and other statistical physical quantities of beam halo-chaos are more than doubly reduced. These performed PIC simulation results demonstrate that the developed methods are very effective for control of beam halo-chaos. Potential application of the beam halo-chaos control methods is discussed finally
Directory of Open Access Journals (Sweden)
Novak Antonin
2010-01-01
Full Text Available A new method of identification, based on an input synchronized exponential swept-sine signal, is used to analyze and synthesize nonlinear audio systems like overdrive pedals for guitar. Two different pedals are studied; the first one exhibiting a strong influence of the input signal level on its input/output law and the second one exhibiting a weak influence of this input signal level. The Synchronized Swept Sine method leads to a Generalized Polynomial Hammerstein model equivalent to the pedals under test. The behaviors of both pedals are illustrated through model-based resynthesized signals. Moreover, it is also shown that this method leads to a criterion allowing the classification of the nonlinear systems under test, according to the influence of the input signal levels on their input/output law.
Measuring the Nonlinear Refractive Index of Graphene using the Optical Kerr Effect Method
Dremetsika, Evdokia; Gorza, Simon-Pierre; Ciret, Charles; Martin, Marie-Blandine; Hofmann, Stephan; Seneor, Pierre; Dolfi, Daniel; Massar, Serge; Emplit, Philippe; Kockaert, Pascal
2016-01-01
By means of the ultrafast optical Kerr effect method coupled to optical heterodyne detection (OHD-OKE), we characterize the third order nonlinear response of graphene at telecom wavelength, and compare it to experimental values obtained by the Z-scan method on the same samples. From these measurements, we estimate a negative nonlinear refractive index for monolayer graphene, $n_2 = - 1.1\\times 10^{-13} m^2/W$. This is in contradiction to previously reported values, which leads us to compare our experimental measurements obtained by the OHD-OKE and the Z-scan method with theoretical and experimental values found in the literature, and to discuss the discrepancies, taking into account parameters such as doping.
Optimal Parameter Tuning in a Predictive Nonlinear Control Method for a Mobile Robot
Directory of Open Access Journals (Sweden)
D. Hazry
2006-01-01
Full Text Available This study contributes to a new optimal parameter tuning in a predictive nonlinear control method for stable trajectory straight line tracking with a non-holonomic mobile robot. In this method, the focus lies in finding the optimal parameter estimation and to predict the path that the mobile robot will follow for stable trajectory straight line tracking system. The stability control contains three parameters: 1 deflection parameter for the traveling direction of the mobile robot 2 deflection parameter for the distance across traveling direction of the mobile robot and 3 deflection parameter for the steering angle of the mobile robot . Two hundred and seventy three experimental were performed and the results have been analyzed and described herewith. It is found that by using a new optimal parameter tuning in a predictive nonlinear control method derived from the extension of kinematics model, the movement of the mobile robot is stabilized and adhered to the reference posture
Directory of Open Access Journals (Sweden)
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new application of the homotopy analysis method (HAM for solving evolution equations described in terms of nonlinear partial differential equations (PDEs. The new approach, termed bivariate spectral homotopy analysis method (BISHAM, is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. The applicability of the new approach has been demonstrated by application on several examples of nonlinear evolution PDEs, namely, Fisher’s, Burgers-Fisher’s, Burger-Huxley’s, and Fitzhugh-Nagumo’s equations. Comparison with known exact results from literature has been used to confirm accuracy and effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
MOHAMED KEZZAR
2015-08-01
Full Text Available In this research, an efficient technique of computation considered as a modified decomposition method was proposed and then successfully applied for solving the nonlinear problem of the two dimensional flow of an incompressible viscous fluid between nonparallel plane walls. In fact this method gives the nonlinear term Nu and the solution of the studied problem as a power series. The proposed iterative procedure gives on the one hand a computationally efficient formulation with an acceleration of convergence rate and on the other hand finds the solution without any discretization, linearization or restrictive assumptions. The comparison of our results with those of numerical treatment and other earlier works shows clearly the higher accuracy and efficiency of the used Modified Decomposition Method.
Nonlinear approximation method in Lagrangian relaxation-based algorithms for hydrothermal scheduling
Energy Technology Data Exchange (ETDEWEB)
Guan, X. [Pacific Gas and Electric, San Francisco, CA (United States); Luh, P.B.; Zhang, L. [Univ. of Connecticut, Storrs, CT (United States). Dept. of Electrical and Systems Engineering
1995-05-01
When the Lagrangian relaxation technique is used to solve hydrothermal scheduling problems, many subproblems have linear stage-wise cost functions. A well recognized difficulty is that the solutions to these subproblems may oscillate between maximum and minimum generations with slight changes of the multipliers. Furthermore, the subproblem solutions may become singular, i.e., they are un-determined when the linear coefficients become zero. This may result in large differences between subproblem solutions and the optimal primal schedule. In this paper, a nonlinear approximation method is presented which utilizes nonlinear functions, quadratic in this case, to approximate relevant linear cost functions. The analysis shows that the difficulty associated with solution oscillation is reduced, and singularity is avoided. Extensive testing based on Northeast Utilities data indicates that the method consistently generates better schedules than the standard Lagrangian relaxation method.
STUDY ON PREDICTION METHODS FOR DYNAMIC SYSTEMS OF NONLINEAR CHAOTIC TIME SERIES
Institute of Scientific and Technical Information of China (English)
马军海; 陈予恕; 辛宝贵
2004-01-01
The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions.By combining neural networks and wavelet theories,the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given.Based on wavelet networks,a new method for parameter identification was suggested,which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series.Through pre-treatment and comparison of results before and after the treatment,several useful conclusions are reached:High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.
Institute of Scientific and Technical Information of China (English)
Fan Yuxin; Xia Jian
2014-01-01
A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute tran-sient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute infla-tion is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES) method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hil-ber–Hughes–Taylor (HHT) time integration method is employed. For the fluid dynamic simula-tions, the Roe and HLLC (Harten–Lax–van Leer contact) scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS) approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.
Directory of Open Access Journals (Sweden)
Fan Yuxin
2014-12-01
Full Text Available A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute transient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute inflation is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hilber–Hughes–Taylor (HHT time integration method is employed. For the fluid dynamic simulations, the Roe and HLLC (Harten–Lax–van Leer contact scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.
Rahman, Md. Saifur; Lee, Yiu-Yin
2017-10-01
In this study, a new modified multi-level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams. Although numerous nonlinear beam or linear double-beam problems have been tackled and solved, there have been few studies of this nonlinear double-beam problem. The geometric nonlinear formulations for a double-beam model are developed. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. This heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The proposed method can generate the higher-level nonlinear solutions that are neglected by the previous modified harmonic balance method. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, and excitation magnitude on the nonlinear vibrational behaviour are examined.
Higher Order Mean Squared Error of Generalized Method of Moments Estimators for Nonlinear Models
Directory of Open Access Journals (Sweden)
Yi Hu
2014-01-01
Full Text Available Generalized method of moments (GMM has been widely applied for estimation of nonlinear models in economics and finance. Although generalized method of moments has good asymptotic properties under fairly moderate regularity conditions, its finite sample performance is not very well. In order to improve the finite sample performance of generalized method of moments estimators, this paper studies higher-order mean squared error of two-step efficient generalized method of moments estimators for nonlinear models. Specially, we consider a general nonlinear regression model with endogeneity and derive the higher-order asymptotic mean square error for two-step efficient generalized method of moments estimator for this model using iterative techniques and higher-order asymptotic theories. Our theoretical results allow the number of moments to grow with sample size, and are suitable for general moment restriction models, which contains conditional moment restriction models as special cases. The higher-order mean square error can be used to compare different estimators and to construct the selection criteria for improving estimator’s finite sample performance.
Goldsworthy, Ray L.; Greenberg, Julie E.
2004-12-01
The Speech Transmission Index (STI) is a physical metric that is well correlated with the intelligibility of speech degraded by additive noise and reverberation. The traditional STI uses modulated noise as a probe signal and is valid for assessing degradations that result from linear operations on the speech signal. Researchers have attempted to extend the STI to predict the intelligibility of nonlinearly processed speech by proposing variations that use speech as a probe signal. This work considers four previously proposed speech-based STI methods and four novel methods, studied under conditions of additive noise, reverberation, and two nonlinear operations (envelope thresholding and spectral subtraction). Analyzing intermediate metrics in the STI calculation reveals why some methods fail for nonlinear operations. Results indicate that none of the previously proposed methods is adequate for all of the conditions considered, while four proposed methods produce qualitatively reasonable results and warrant further study. The discussion considers the relevance of this work to predicting the intelligibility of cochlear-implant processed speech. .
A New Generalization of Extended Tanh-Function Method for Solving Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
ZHENG Xue-Dong; CHEN Yong; LI Biao; ZHANG Hong-Qing
2003-01-01
Making use of a new generalized ansatze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations.As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extendedtanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain othernew and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profilesolitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.
A NEW SQP-FILTER METHOD FOR SOLVING NONLINEAR PROGRAMMING PROBLEMS
Institute of Scientific and Technical Information of China (English)
Duoquan Li
2006-01-01
In [4],Fletcher and Leyffer present a new method that solves nonlinear programming problems without a penalty function by SQP-Filter algorithm. It has attracted much attention due to its good numerical results. In this paper we propose a new SQP-Filter method which can overcome Maratos effect more effectively. We give stricter acceptant criteria when the iterative points are far from the optimal points and looser ones vice-versa. About this new method,the proof of global convergence is also presented under standard assumptions. Numerical results show that our method is efficient.
Institute of Scientific and Technical Information of China (English)
Qin Ni
2001-01-01
An NGTN method was proposed for solving large-scale sparse nonlinear programming (NLP) problems. This is a hybrid method of a truncated Newton direction and a modified negative gradient direction, which is suitable for handling sparse data structure and possesses Q-quadratic convergence rate. The global convergence of this new method is proved,the convergence rate is further analysed, and the detailed implementation is discussed in this paper. Some numerical tests for solving truss optimization and large sparse problems are reported. The theoretical and numerical results show that the new method is efficient for solving large-scale sparse NLP problems.
Directory of Open Access Journals (Sweden)
C. Ünlü
2013-01-01
Full Text Available A modification of the variational iteration method (VIM for solving systems of nonlinear fractional-order differential equations is proposed. The fractional derivatives are described in the Caputo sense. The solutions of fractional differential equations (FDE obtained using the traditional variational iteration method give good approximations in the neighborhood of the initial position. The main advantage of the present method is that it can accelerate the convergence of the iterative approximate solutions relative to the approximate solutions obtained using the traditional variational iteration method. Illustrative examples are presented to show the validity of this modification.
Phase Structure of the Non-Linear σ-MODEL with Oscillator Representation Method
Mishchenko, Yuriy; Ji, Chueng-R.
2004-03-01
Non-Linear σ-model plays an important role in many areas of theoretical physics. Been initially uintended as a simple model for chiral symmetry breaking, this model exhibits such nontrivial effects as spontaneous symmetry breaking, asymptotic freedom and sometimes is considered as an effective field theory for QCD. Besides, non-linear σ-model can be related to the strong-coupling limit of O(N) ϕ4-theory, continuous limit of N-dim. system of quantum spins, fermion gas and many others and takes important place in undertanding of how symmetries are realized in quantum field theories. Because of this variety of connections, theoretical study of the critical properties of σ-model is interesting and important. Oscillator representation method is a theoretical tool for studying the phase structure of simple QFT models. It is formulated in the framework of the canonical quantization and is based on the view of the unitary non-equivalent representations as possible phases of a QFT model. Successfull application of the ORM to ϕ4 and ϕ6 theories in 1+1 and 2+1 dimensions motivates its study in more complicated models such as non-linear σ-model. In our talk we introduce ORM, establish its connections with variational approach in QFT. We then present results of ORM in non-linear σ-model and try to interprete them from the variational point of view. Finally, we point out possible directions for further research in this area.
ISS method for coordination control of nonlinear dynamical agents under directed topology.
Wang, Xiangke; Qin, Jiahu; Yu, Changbin
2014-10-01
The problems of coordination of multiagent systems with second-order locally Lipschitz continuous nonlinear dynamics under directed interaction topology are investigated in this paper. A completely nonlinear input-to-state stability (ISS)-based framework, drawing on ISS methods, with the aid of results from graph theory, matrix theory, and the ISS cyclic-small-gain theorem, is proposed for the coordination problem under directed topology, which can effectively tackle the technical challenges caused by locally Lipschitz continuous dynamics. Two coordination problems, i.e., flocking with a virtual leader and containment control, are considered. For both problems, it is assumed that only a portion of the agents can obtain the information from the leader(s). For the first problem, the proposed strategy is shown effective in driving a group of nonlinear dynamical agents reach the prespecified geometric pattern under the condition that at least one agent in each strongly connected component of the information-interconnection digraph with zero in-degree has access to the state information of the virtual leader; and the strategy proposed for the second problem can guarantee the nonlinear dynamical agents moving to the convex hull spanned by the positions of multiple leaders under the condition that for each agent there exists at least one leader that has a directed path to this agent.
The Fourier decomposition method for nonlinear and non-stationary time series analysis.
Singh, Pushpendra; Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik
2017-03-01
for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.
Teaching Numerical Methods for Non-linear Equations with GeoGebra-Based Activities
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Ana M. Martín-Caraballo
2015-08-01
Full Text Available but even in University. To be more precise, our main goal consists in putting forward the usefulness of GeoGebra as working tool so that our students manipulate several numerical (both recursive and iterative methods to solve nonlinear equations. In this sense, we show how Interactive Geometry Software makes possible to deal with these methods by means of their geometrical interpretation and to visualize their behavior and procedure. In our opinion, visualization is absolutely essential for first-year students in the University, since they must change their perception about Mathematics and start considering a completely formal and argued way to work the notions, methods and problems explained and stated. Concerning these issues, we present some applets developed using GeoGebra to explain and work with numerical methods for nonlinear equations. Moreover, we indicate how these applets are applied to our teaching. In fact, the methods selected to be dealt with this paper are those with important geometric interpretations, namely: the bisection method, the secant method, the regula-falsi (or false-position method and the tangent (or Newton-Raphson method, this last as example of fixed-point methods.
A Two-grid Method with Expanded Mixed Element for Nonlinear Reaction-diffusion Equations
Institute of Scientific and Technical Information of China (English)
Wei Liu; Hong-xing Rui; Hui Guo
2011-01-01
Expanded mixed finite element approximation of nonlinear reaction-diffusion equations is discussed. The equations considered here are used to model the hydrologic and bio-geochemical phenomena. To linearize the mixed-method equations, we use a two-grid method involving a small nonlinear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates are derived which demonstrate that the error is O(△t + hk+1 + H2k+2-d/2) (k ≥ 1), where k is the degree of the approximating space for the primary variable and d is the spatial dimension. The above estimates are useful for determining an appropriate H for the coarse grid problems.
Nonlinear tracking in a diffusion process with a Bayesian filter and the finite element method
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Thygesen, Uffe Høgsbro; Madsen, Henrik
2011-01-01
A new approach to nonlinear state estimation and object tracking from indirect observations of a continuous time process is examined. Stochastic differential equations (SDEs) are employed to model the dynamics of the unobservable state. Tracking problems in the plane subject to boundaries...... become complicated using SMC because Monte Carlo randomness is introduced. The finite element (FE) method solves the Kolmogorov equations of the SDE numerically on a triangular unstructured mesh for which boundary conditions to the state-space are simple to incorporate. The FE approach to nonlinear state...... estimation is suited for off-line data analysis because the computed smoothed state densities, maximum a posteriori parameter estimates and state sequence are deterministic conditional on the finite element mesh and the observations. The proposed method is conceptually similar to existing point...
Schroeter, Jens; Wunsch, Carl
1986-01-01
The paper studies with finite difference nonlinear circulation models the uncertainties in interesting flow properties, such as western boundary current transport, potential and kinetic energy, owing to the uncertainty in the driving surface boundary condition. The procedure is based upon nonlinear optimization methods. The same calculations permit quantitative study of the importance of new information as a function of type, region of measurement and accuracy, providing a method to study various observing strategies. Uncertainty in a model parameter, the bottom friction coefficient, is studied in conjunction with uncertain measurements. The model is free to adjust the bottom friction coefficient such that an objective function is minimized while fitting a set of data to within prescribed bounds. The relative importance of the accuracy of the knowledge about the friction coefficient with respect to various kinds of observations is then quantified, and the possible range of the friction coefficients is calculated.
Analysis of efficient preconditioned defect correction methods for nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter
2014-01-01
prediction of free-surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow......Robust computational procedures for the solution of non-hydrostatic, free surface, irrotational and inviscid free-surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable...... models. Our study is particularly relevant for fast and efficient simulation of non-breaking fully nonlinear water waves over varying bottom topography that may be limited by computational resources or requirements. To gain insight into algorithmic properties and proper choices of discretization...
A Quadratic precision generalized nonlinear global optimization migration velocity inversion method
Institute of Scientific and Technical Information of China (English)
Zhao Taiyin; Hu Guangmin; He Zhenhua; Huang Deji
2009-01-01
An important research topic for prospecting seismology is to provide a fast accurate velocity model from pre-stack depth migration. Aiming at such a problem, we propose a quadratic precision generalized nonlinear global optimization migration velocity inversion. First we discard the assumption that there is a linear relationship between residual depth and residual velocity and propose a velocity model correction equation with quadratic precision which enables the velocity model from each iteration to approach the real model as quickly as possible. Second, we use a generalized nonlinear inversion to get the global optimal velocity perturbation model to all traces. This method can expedite the convergence speed and also can decrease the probability of falling into a local minimum during inversion. The synthetic data and Marmousi data examples show that our method has a higher precision and needs only a few iterations and consequently enhances the practicability and accuracy of migration velocity analysis (MVA) in complex areas.
An operator expansion method for computing nonlinear surface waves on a ferrofluid jet
Guyenne, Philippe; Părău, Emilian I.
2016-09-01
We present a new numerical method to simulate the time evolution of axisymmetric nonlinear waves on the surface of a ferrofluid jet. It is based on the reduction of this problem to a lower-dimensional computation involving surface variables alone. To do so, we describe the associated Dirichlet-Neumann operator in terms of a Taylor series expansion where each term can be efficiently computed by a pseudo-spectral scheme using the fast Fourier transform. We show detailed numerical tests on the convergence of this operator and, to illustrate the performance of our method, we simulate the long-time propagation and pairwise collisions of axisymmetric solitary waves. Both depression and elevation waves are examined by varying the magnetic field. Comparisons with weakly nonlinear predictions are also provided.
Waveform control method for mitigating harmonics of inverter systems with nonlinear load
DEFF Research Database (Denmark)
Wang, Haoran; Zhu, Guorong; Fu, Xiaobin;
2015-01-01
DC power systems connecting to single-phase DC/AC inverters with nonlinear loads will have their DC sources being injected with AC ripple currents containing a low-frequency component at twice the output voltage frequency of the inverter and also other current harmonics. Such a current may create...... instability in the DC power system, lower its efficiency, and shorten the lifetime of the DC source. This paper presents a general waveform control method that can mitigate the injection of the low-frequency ripple current by the single-phase DC/AC inverter into the DC source. It also discusses the inhibiting...... ability of the waveform control method on other coexisting harmonics, while the DC source delivers AC power to a nonlinear load. With the application of the waveform control, the average DC output power is supplied by the DC source, while the other harmonics pulsation power can be confined to the AC side...
A method for regulating strong nonlinear vibration energy of the flexible arm
Directory of Open Access Journals (Sweden)
Yushu Bian
2015-07-01
Full Text Available For an oscillating system, large amplitude indicates strong vibration energy. In this article, modal interaction is used as a useful means to regulate strong nonlinear vibration energy of the flexible arm undergoing rigid motion. A method is put forward to migrate and dissipate vibration energy based on modal interaction. By means of multiple-scale perturbation analysis, it is proven that internal resonance can be successfully established between modes of the flexible arm and the vibration absorber. Through examples and analyses, it is verified that this control method is effective in regulating strong vibration energy and can be used to suppress strong nonlinear vibration of the flexible arm undergoing rigid motion.
Non-linear shape functions over time in the space-time finite element method
Directory of Open Access Journals (Sweden)
Kacprzyk Zbigniew
2017-01-01
Full Text Available This work presents a generalisation of the space-time finite element method proposed by Kączkowski in his seminal of 1970’s and early 1980’s works. Kączkowski used linear shape functions in time. The recurrence formula obtained by Kączkowski was conditionally stable. In this paper, non-linear shape functions in time are proposed.
Analytical Approximation Method for the Center Manifold in the Nonlinear Output Regulation Problem
Suzuki, Hidetoshi; Sakamoto, Noboru; Celikovský, Sergej
In nonlinear output regulation problems, it is necessary to solve the so-called regulator equations consisting of a partial differential equation and an algebraic equation. It is known that, for the hyperbolic zero dynamics case, solving the regulator equations is equivalent to calculating a center manifold for zero dynamics of the system. The present paper proposes a successive approximation method for obtaining center manifolds and shows its effectiveness by applying it for an inverted pendulum example.
A method for solving systems of non-linear differential equations with moving singularities
Gousheh, S S; Ghafoori-Tabrizi, K
2003-01-01
We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by establishing certain `moving' jump conditions across them. We show how a first integral of the differential equations, if available, can also be used for checking the accuracy of the numerical solution.