Search results for: Nonlinear ODE

Authors: Swarniv Chandra, Basudev Ghosh

Abstract:

Nonlinear solitary structures of electron plasma waves have been investigated by using nonlinear quantum fluid equations for electrons with an arbitrary temperature. It is shown that the electron degeneracy parameter has significant effects on the linear and nonlinear properties of electron plasma waves. Depending on its value both compressive and rarefactive solitons can be excited in the model plasma under consideration.

Keywords: Electron Plasma Waves, Finite Temperature Model, Modulational Instability, Quantum Plasma, Solitary structure

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Authors: Rafat Alshorman, Safwan Al-Shara', I. Obeidat

Abstract:

Most real world systems express themselves formally as a set of nonlinear algebraic equations. As applications grow, the size and complexity of these equations also increase. In this work, we highlight the key concepts in using the homotopy analysis method as a methodology used to construct efficient iteration formulas for nonlinear equations solving. The proposed method is experimentally characterized according to a set of determined parameters which affect the systems. The experimental results show the potential and limitations of the new method and imply directions for future work.

Keywords: Nonlinear Algebraic Equations, Iterative Methods, Homotopy Analysis Method.

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Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid.

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Authors: Ruediger Schmidt, Thang Duy Vu

Abstract:

Two geometrically nonlinear plate theories, based either on first- or third-order transverse shear deformation theory are used for finite element modeling and simulation of the transient response of smart structures incorporating piezoelectric layers. In particular the time histories of nonlinear vibrations and sensor voltage output of a thin beam with a piezoelectric patch bonded to the surface due to an applied step force are studied.

Keywords: Nonlinear vibrations, piezoelectric patches, sensor voltage output, smart structures.

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Authors: Alireza Rezaei, Fatemeh Baharifard, Kourosh Parand

Abstract:

In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.

Keywords: Quasilinearization method, Barycentric lagrange interpolation, nonlinear ODE, fin problem, heat transfer.

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Authors: Chikara Egami, Kazuhiro Kuwahara

Abstract:

Polarization-interferometric nonlinear confocal microscopy is proposed for measuring a nano-sized particle with optical anisotropy. The anisotropy in the particle was spectroscopically imaged through a three-dimensional distribution of third-order nonlinear dielectric polarization photoinduced.

Keywords: nanoparticle, optical storage, microscope

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Authors: Rakesh Kumar, A. K. Ghosh

Abstract:

The paper presents the modeling of nonlinear longitudinal aerodynamics using flight data of Hansa-3 aircraft at high angles of attack near stall. The Kirchhoff-s quasi-steady stall model has been used to incorporate nonlinear aerodynamic effects in the aerodynamic model used to estimate the parameters, thereby, making the aerodynamic model nonlinear. The Maximum Likelihood method has been applied to the flight data (at high angles of attack) for the estimation of parameters (aerodynamic and stall characteristics) using the nonlinear aerodynamic model. To improve the accuracy level of the estimates, an approach of fixing the strong parameters has also been presented.

Keywords: Maximum Likelihood, nonlinear, parameters, stall.

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Authors: A. R. Tavakolpour-Saleh, A. R. Setoodeh, E. Ansari

Abstract:

This paper presents modeling and control of a highly nonlinear system including, non-interacting two spherical tanks using iterative learning control (ILC). Consequently, the objective of the paper is to control the liquid levels in the nonlinear tanks. First, a proportional-integral-derivative (PID) controller is applied to the plant model as a suitable benchmark for comparison. Then, dynamic responses of the control system corresponding to different step inputs are investigated. It is found that the conventional PID control is not able to fulfill the design criteria such as desired time constant. Consequently, an iterative learning controller is proposed to accurately control the coupled nonlinear tanks system. The simulation results clearly demonstrate the superiority of the presented ILC approach over the conventional PID controller to cope with the nonlinearities presented in the dynamic system.

Keywords: Iterative learning control, spherical tanks, nonlinear system.

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Authors: J. B. Seo, K. J. Kim, S. W. Nam

Abstract:

In this paper, a nonlinear acoustic echo cancellation (AEC) system is proposed, whereby 3rd order Volterra filtering is utilized along with a variable step-size Gauss-Seidel pseudo affine projection (VSSGS-PAP) algorithm. In particular, the proposed nonlinear AEC system is developed by considering a double-talk situation with near-end signal variation. Simulation results demonstrate that the proposed approach yields better nonlinear AEC performance than conventional approaches.

Keywords: Acoustic echo cancellation (AEC), Volterra filtering, variable step-size, GS-PAP.

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Authors: Mohamed M. El-Gendy, Ibrahim A. El-Arabi, Rafik W. Abdel-Missih, Omar A. Kandil

Abstract:

In the present research, a finite element model is presented to study the geometrical and material nonlinear behavior of reinforced concrete plane frames considering soil-structure interaction. The nonlinear behaviors of concrete and reinforcing steel are considered both in compression and tension up to failure. The model takes account also for the number, diameter, and distribution of rebar along every cross section. Soil behavior is taken into consideration using four different models; namely: linear-, nonlinear Winkler's model, and linear-, nonlinear continuum model. A computer program (NARC) is specially developed in order to perform the analysis. The results achieved by the present model show good agreement with both theoretical and experimental published literature. The nonlinear behavior of a rectangular frame resting on soft soil up to failure using the proposed model is introduced for demonstration.

Keywords: Nonlinear analysis, Geometric nonlinearity, Material nonlinearity, Reinforced concrete, Finite element method, Soilstructure interaction, Winkler's soil model, Continuum soil model

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Authors: M. A. Ghorbani, M. Pasbani Khiavi, F. Rezaie Moghaddam

Abstract:

In the analysis of structures, the nonlinear effects due to large displacement, large rotation and materially-nonlinear are very important and must be considered for the reliable analysis. The non-linear fmite element analysis has potential as usable and reliable means for analyzing of civil structures with the availability of computer technology. In this research the large displacements and materially nonlinear behavior of shear wall is presented with developing of fmite element code using the standard Galerkin weighted residual formulation. Two-dimensional plane stress model was carried out to present the shear wall response. Total Lagangian formulation, which is computationally more effective, is used in the formulation of stiffness matrices and the Newton-Raphson method is applied for the solution of nonlinear transient equations. The details of the program formulation are highlighted and the results of the analyses are presented, along with a comparison of the response of the structure with Ansys software results. The presented model in this paper can be developed for nonlinear analysis of civil engineering structures with different material behavior and complicated geometry.

Keywords: Finite element, large displacements, materially nonlinear, shear wall.

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Authors: Nicolò Vaiana, Giorgio Serino

Abstract:

The nonlinear time history analysis of seismically base-isolated structures can require a significant computational effort when the behavior of each seismic isolator is predicted by adopting the widely used differential equation Bouc-Wen model. In this paper, a nonlinear exponential model, able to simulate the response of seismic isolation bearings within a relatively large displacements range, is described and adopted in order to reduce the numerical computations and speed up the nonlinear dynamic analysis. Compared to the Bouc-Wen model, the proposed one does not require the numerical solution of a nonlinear differential equation for each time step of the analysis. The seismic response of a 3d base-isolated structure with a lead rubber bearing system subjected to harmonic earthquake excitation is simulated by modeling each isolator using the proposed analytical model. The comparison of the numerical results and computational time with those obtained by modeling the lead rubber bearings using the Bouc-Wen model demonstrates the good accuracy of the proposed model and its capability to reduce significantly the computational effort of the analysis.

Keywords: Base isolation, computational efficiency, nonlinear exponential model, nonlinear time history analysis.

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Authors: Shun-Chang Chang

Abstract:

In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.

Keywords: bifurcation, Poincare map, Lyapunov exponent, chaotic motion.

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Authors: B.P. Bezruchko, D.A. Smirnov

Abstract:

Quantitative characterization of nonlinear directional couplings between stochastic oscillators from data is considered. We suggest coupling characteristics readily interpreted from a physical viewpoint and their estimators. An expression for a statistical significance level is derived analytically that allows reliable coupling detection from a relatively short time series. Performance of the technique is demonstrated in numerical experiments.

Keywords: Nonlinear time series analysis, directional couplings, coupled oscillators.

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Authors: B. Baigzadeh, V.Nazarzehi, H.Khaloozadeh

Abstract:

The two cart inverted pendulum system is a good bench mark for testing the performance of system dynamics and control engineering principles. Devasia introduced this system to study the asymptotic tracking problem for nonlinear systems. In this paper the problem of asymptotic tracking of the two-cart with an inverted-pendulum system to a sinusoidal reference inputs via introducing a novel method for solving finite-horizon nonlinear optimal control problems is presented. In this method, an iterative method applied to state dependent Riccati equation (SDRE) to obtain a reliable algorithm. The superiority of this technique has been shown by simulation and comparison with the nonlinear approach.

Keywords: Nonlinear optimal control, State dependent Riccatiequation, Asymptotic tracking, inverted pendulum

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Authors: Win Ko Ko, A. N. Temnov

Abstract:

The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations.

Keywords: Hydrodynamic coefficients, instability region, nonlinear oscillations, resonance frequency, two-layered liquid.

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Authors: S. Kahvecioglu, A. Karamancioglu, A. Yazici

Abstract:

In this paper, a nonlinear model predictive swing-up and stabilizing sliding controller is proposed for an inverted pendulum-cart system. In the swing up phase, the nonlinear model predictive control is formulated as a nonlinear programming problem with energy based objective function. By solving this problem at each sampling instant, a sequence of control inputs that optimize the nonlinear objective function subject to various constraints over a finite horizon are obtained. Then, this control drives the pendulum to a predefined neighborhood of the upper equilibrium point, at where sliding mode based model predictive control is used to stabilize the systems with the specified constraints. It is shown by the simulations that, due to the way of formulating the problem, short horizon lengths are sufficient for attaining the swing up goal.

Keywords: Inverted pendulum, model predictive control, swingup, stabilization.

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Authors: Shan-Jen Cheng, Te-Jen Chang, Kuang-Hsiung Tan, Shou-Ling Kuo

Abstract:

Polymer Electrolyte Membrane Fuel Cell (PEMFC) is such a time-vary nonlinear dynamic system. The traditional linear modeling approach is hard to estimate structure correctly of PEMFC system. From this reason, this paper presents a nonlinear modeling of the PEMFC using Neural Network Auto-regressive model with eXogenous inputs (NNARX) approach. The multilayer perception (MLP) network is applied to evaluate the structure of the NNARX model of PEMFC. The validity and accuracy of NNARX model are tested by one step ahead relating output voltage to input current from measured experimental of PEMFC. The results show that the obtained nonlinear NNARX model can efficiently approximate the dynamic mode of the PEMFC and model output and system measured output consistently.

Keywords: PEMFC, neural network, nonlinear identification, NNARX.

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Authors: jianhua Hou, Changqing Yang, and Beibo Qin

Abstract:

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function  approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

Keywords: Hybrid functions, Fredholm integral equation, Blockpulse, Chebyshev polynomials, product operational matrix.

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Authors: Somkiat Lerkvaranyu, Yoshikazu Miyanaga

Abstract:

In this paper, a new technique of signal detection has been proposed for detecting the orthogonal frequency-division multiplexing (OFDM) signal in the presence of nonlinear distortion.There are several advantages of OFDM communications system.However, one of the existing problems is remain considered as the nonlinear distortion generated by high-power-amplifier at the transmitter end due to the large dynamic range of an OFDM signal. The proposed method is the maximum likelihood detection with the symbol estimation. When the training data are available, the neural network has been used to learn the characteristic of received signal and to estimate the new positions of the transmitted symbol which are provided to the maximum likelihood detector. Resulting in the system performance, the nonlinear distortions of a traveling wave tube amplifier with OFDM signal are considered in this paper.Simulation results of the bit-error-rate performance are obtained with 16-QAM OFDM systems.

Keywords: OFDM, TWTA, nonlinear distortion, detection.

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Authors: M.V Rajesh, Archana R, A Unnikrishnan, R Gopikakumari, Jeevamma Jacob

Abstract:

The System Identification problem looks for a suitably parameterized model, representing a given process. The parameters of the model are adjusted to optimize a performance function based on error between the given process output and identified process output. The linear system identification field is well established with many classical approaches whereas most of those methods cannot be applied for nonlinear systems. The problem becomes tougher if the system is completely unknown with only the output time series is available. It has been reported that the capability of Artificial Neural Network to approximate all linear and nonlinear input-output maps makes it predominantly suitable for the identification of nonlinear systems, where only the output time series is available. [1][2][4][5]. The work reported here is an attempt to implement few of the well known algorithms in the context of modeling of nonlinear systems, and to make a performance comparison to establish the relative merits and demerits.

Keywords: Multilayer neural networks, Radial Basis Functions, Clustering algorithm, Back Propagation training, Extended Kalmanfiltering, Mean Square Error, Nonlinear Modeling, Cramer RaoLower Bound.

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Authors: Meng Hu, Lili Wang

Abstract:

In this paper, applying He-s energy balance method to determine frequency formulation relations of nonlinear oscillators with discontinuous term or fractional potential. By calculation and computer simulations, compared with the exact solutions show that the results obtained are of high accuracy.

Keywords: He's energy balance method, periodic solution, nonlinear oscillator, discontinuous, fractional potential.

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Authors: Tian Baoguang, Liang Chunyan, Chen Nan

Abstract:

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_i are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_i<0 is proposed.

Keywords: Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion

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Authors: Hamza Nejib, Okba Taouali

Abstract:

This paper presents two of the most knowing kernel adaptive filtering (KAF) approaches, the kernel least mean squares and the kernel recursive least squares, in order to predict a new output of nonlinear signal processing. Both of these methods implement a nonlinear transfer function using kernel methods in a particular space named reproducing kernel Hilbert space (RKHS) where the model is a linear combination of kernel functions applied to transform the observed data from the input space to a high dimensional feature space of vectors, this idea known as the kernel trick. Then KAF is the developing filters in RKHS. We use two nonlinear signal processing problems, Mackey Glass chaotic time series prediction and nonlinear channel equalization to figure the performance of the approaches presented and finally to result which of them is the adapted one.

Keywords: KLMS, online prediction, KAF, signal processing, RKHS, Kernel methods, KRLS, KLMS.

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Authors: A. R. Tavakolpour-Saleh, H. Jokar

Abstract:

Liquid level control of conical tank system is known to be a great challenge in many industries such as food processing, hydrometallurgical industries and wastewater treatment plant due to its highly nonlinear characteristics. In this research, an adaptive fuzzy PID control scheme is applied to the problem of liquid level control in a nonlinear tank process. A conical tank process is first modeled and primarily simulated. A PID controller is then applied to the plant model as a suitable benchmark for comparison and the dynamic responses of the control system to different step inputs were investigated. It is found that the conventional PID controller is not able to fulfill the controller design criteria such as desired time constant due to highly nonlinear characteristics of the plant model. Consequently, a nonlinear control strategy based on gain-scheduling adaptive control incorporating a fuzzy logic observer is proposed to accurately control the nonlinear tank system. The simulation results clearly demonstrated the superiority of the proposed adaptive fuzzy control method over the conventional PID controller.

Keywords: Adaptive control, fuzzy logic, conical tank, PID controller.

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Authors: Şaban Çetin, Özgür Demir

Abstract:

In this study, Fuzzy PID Control scheme is designed for an active suspension system. The main goal of an active suspension system for using in a vehicle model is reducing body deflections and handling high comfort for a passenger car. The present system was modelled as a two-degree-of-freedom (2-DOF) nonlinear vehicle model.

Keywords: Active suspension system, Fuzzy PID controller, a nonlinear quarter car model.

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Authors: Cai-Wan Chang-Jian

Abstract:

This study presents a systematic analysis of the dynamic behaviors of a gear-bearing system with porous squeeze film damper (PSFD) under nonlinear suspension, nonlinear oil-film force and nonlinear gear meshing force effect. It can be found that the system exhibits very rich forms of sub-harmonic and even the chaotic vibrations. The bifurcation diagrams also reveal that greater values of permeability may not only improve non-periodic motions effectively, but also suppress dynamic amplitudes of the system. Therefore, porous effect plays an important role to improve dynamic stability of gear-bearing systems or other mechanical systems. The results presented in this study provide some useful insights into the design and development of a gear-bearing system for rotating machinery that operates in highly rotational speed and highly nonlinear regimes.

Keywords: Gear, PSFD, bifurcation, chaos.

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Authors: Mai S. Mabrouk, Nahed H. Solouma, Abou-Bakr M. Youssef, Yasser M. Kadah

Abstract:

Many digital signal processing, techniques have been used to automatically distinguish protein coding regions (exons) from non-coding regions (introns) in DNA sequences. In this work, we have characterized these sequences according to their nonlinear dynamical features such as moment invariants, correlation dimension, and largest Lyapunov exponent estimates. We have applied our model to a number of real sequences encoded into a time series using EIIP sequence indicators. In order to discriminate between coding and non coding DNA regions, the phase space trajectory was first reconstructed for coding and non-coding regions. Nonlinear dynamical features are extracted from those regions and used to investigate a difference between them. Our results indicate that the nonlinear dynamical characteristics have yielded significant differences between coding (CR) and non-coding regions (NCR) in DNA sequences. Finally, the classifier is tested on real genes where coding and non-coding regions are well known.

Keywords: Gene prediction, nonlinear dynamics, correlation dimension, Lyapunov exponent.

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Authors: Meng Hu, Lili Wang

Abstract:

In this paper, He-s amplitude frequency formulation is used to obtain a periodic solution for a nonlinear oscillator with fractional potential. By calculation and computer simulations, compared with the exact solution shows that the result obtained is of high accuracy.

Keywords: He's amplitude frequency formulation, Periodic solution, Nonlinear oscillator, Fractional potential.

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Authors: Youguo Wang, Lenan Wu

Abstract:

Stochastic resonance (SR) is a phenomenon whereby the signal transmission or signal processing through certain nonlinear systems can be improved by adding noise. This paper discusses SR in nonlinear signal detection by a simple test statistic, which can be computed from multiple noisy data in a binary decision problem based on a maximum a posteriori probability criterion. The performance of detection is assessed by the probability of detection error Per . When the input signal is subthreshold signal, we establish that benefit from noise can be gained for different noises and confirm further that the subthreshold SR exists in nonlinear signal detection. The efficacy of SR is significantly improved and the minimum of Per can dramatically approach to zero as the sample number increases. These results show the robustness of SR in signal detection and extend the applicability of SR in signal processing.

Keywords: Probability of detection error, signal detection, stochastic resonance.

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