Search results for: nonlinear calculation

Authors: R. Z. R. R. Rosdin, N. M. Ali, S. W. Harun, H. Arof

Abstract:

We have experimentally demonstrated bright-dark pulses in a nonlinear polarization rotation (NPR) based mode-locked Erbium-doped fiber laser (EDFL) with a long cavity configuration. Bright–dark pulses could be achieved when the laser works in the passively mode-locking regime and the net group velocity dispersion is quite anomalous. The EDFL starts to generate a bright pulse train with degenerated dark pulse at the mode-locking threshold pump power of 35.09 mW by manipulating the polarization states of the laser oscillation modes using a polarization controller (PC). A split bright–dark pulse is generated when further increasing the pump power up to 37.95 mW. Stable bright pulses with no obvious evidence of a dark pulse can also be generated when further adjusting PC and increasing the pump power up to 52.19 mW. At higher pump power of 54.96 mW, a new form of bright-dark pulse emission was successfully identified with the repetition rate of 29 kHz. The bright and dark pulses have a duration of 795.5 ns and 640 ns, respectively.

Keywords: Erbium-doped fiber laser, Nonlinear polarization rotation, bright-dark pulse.

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Authors: Gilberto Gonzalez-A, Dunia Nuñez-P

Abstract:

Bond graph models of an electrical transformer including the nonlinear saturation are presented. The transformer using electrical and magnetic circuits are modelled. These models determine the relation between self and mutual inductances, and the leakage and magnetizing inductances of power transformers with two windings using the properties of a bond graph. The equivalence between electrical and magnetic variables is given. The modelling and analysis using this methodology to three phase power transformers can be extended.

Keywords: Bond graph, electrical transformer, magnetic circuits, nonlinear saturation.

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Authors: Imad Chaddad, Andrei A. Kolyshkin

Abstract:

Linear and weakly nonlinear analysis of shallow wake flows is presented in the present paper. The evolution of the most unstable linear mode is described by the complex Ginzburg-Landau equation (CGLE). The coefficients of the CGLE are calculated numerically from the solution of the corresponding linear stability problem for a one-parametric family of shallow wake flows. It is shown that the coefficients of the CGLE are not so sensitive to the variation of the base flow profile.

Keywords: Ginzburg-Landau equation, shallow wake flow, weakly nonlinear theory.

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Authors: Praloy Kumar Biswas, Prof. Dipanwita Roy Chowdhury

Abstract:

Grobner basis calculation forms a key part of computational commutative algebra and many other areas. One important ramification of the theory of Grobner basis provides a means to solve a system of non-linear equations. This is why it has become very important in the areas where the solution of non-linear equations is needed, for instance in algebraic cryptanalysis and coding theory. This paper explores on a parallel-distributed implementation for Grobner basis calculation over GF(2). For doing so Buchberger algorithm is used. OpenMP and MPI-C language constructs have been used to implement the scheme. Some relevant results have been furnished to compare the performances between the standalone and hybrid (parallel-distributed) implementation.

Keywords: Grobner basis, Buchberger Algorithm, Distributed- Parallel Computation, OpenMP, MPI.

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Authors: Rabah Diabi

Abstract:

As known, the guard wires of overhead high voltage are usually grounded through the grounding systems of support and of the terminal stations. They do affect the zero sequence impedance value of the line, Z0, which is generally, calculated assuming that the wires guard are at ground potential. In this way it is not considered the effect of the resistances of earth of supports and stations. In this work is formed a formula for the calculation of Z0 which takes account of said resistances. Is also proposed a method of calculating the impedance zero sequence overhead lines in which, in various sections or spans, the guard wires are connected to the supports, or isolated from them, or are absent. Parametric analysis is given for lines 220 kV and 400 kV, which shows the extent of the errors made with traditional methods of calculation.

Keywords: Overhead line, power system, zero sequence, wire guard, grounding.

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Authors: M. Zahedian, B. Maraghechi, M. H. Rouhani

Abstract:

A nonlinear model of two-beam free-electron laser (FEL) in the absence of slippage is presented. The two beams are assumed to be cold with different energies and the fundamental resonance of the higher energy beam is at the third harmonic of lower energy beam. By using Maxwell-s equations and full Lorentz force equations of motion for the electron beams, coupled differential equations are derived and solved numerically by the fourth order Runge–Kutta method. In this method a considerable growth of third harmonic electromagnetic field in the XUV and X-ray regions is predicted.

Keywords: Free-electron laser, Higher energy beam, Lowerenergy beam, Two-beam

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Authors: M. Meenasaranya, S. Saravanan

Abstract:

Conditions corresponding to the unconditional stability of convection in a mechanically anisotropic fluid saturated porous medium of infinite horizontal extent are determined. The medium is heated from below and its bounding surfaces are subjected to temperature modulation which consists of a steady part and a time periodic oscillating part. The Brinkman model is employed in the momentum equation with the Bousinessq approximation. The stability region is found for arbitrary values of modulational frequency and amplitude using the energy method. Higher order numerical computations are carried out to find critical boundaries and subcritical instability regions more accurately.

Keywords: Convection, porous medium, anisotropy, temperature modulation, nonlinear stability.

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Authors: M. Harir, A. Bendiabdellah, A. Chaouch, N. Benouzza

Abstract:

This paper deals with the modelling and simulation of the squirrel cage induction motor by taking into account all space harmonic components as well as the introduction of the bars skew in the calculation of the linear evolution of the magnetomotive force (MMF) between the slots extremities. The model used is based on multiple coupled circuits and the modified winding function approach (MWFA). The effect of skewing is included in the calculation of motors inductances with an axial asymmetry in the rotor. The simulation results in both time and spectral domains show the effectiveness and merits of the model and the error that may be caused if the skew of the bars are neglected.

Keywords: Modelling, MWFA, Skew effect, Squirrel cage induction motor, Spectral domain.

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Authors: Farhad Asadi, S. Hossein Sadati

Abstract:

This paper presents a prediction performance of feedforward Multilayer Perceptron (MLP) and Echo State Networks (ESN) trained with extended Kalman filter. Feedforward neural networks and ESN are powerful neural networks which can track and predict nonlinear signals. However, their tracking performance depends on the specific signals or data sets, having the risk of instability accompanied by large error. In this study we explore this process by applying different network size and leaking rate for prediction of nonlinear or chaotic signals in MLP neural networks. Major problems of ESN training such as the problem of initialization of the network and improvement in the prediction performance are tackled. The influence of coefficient of activation function in the hidden layer and other key parameters are investigated by simulation results. Extended Kalman filter is employed in order to improve the sequential and regulation learning rate of the feedforward neural networks. This training approach has vital features in the training of the network when signals have chaotic or non-stationary sequential pattern. Minimization of the variance in each step of the computation and hence smoothing of tracking were obtained by examining the results, indicating satisfactory tracking characteristics for certain conditions. In addition, simulation results confirmed satisfactory performance of both of the two neural networks with modified parameterization in tracking of the nonlinear signals.

Keywords: Feedforward neural networks, nonlinear signal prediction, echo state neural networks approach, leaking rates, capacity of neural networks.

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Authors: Arshia Azam, J. Amarnath, Ch. D. V. Paradesi Rao

Abstract:

The advantage of solving the complex nonlinear problems by utilizing fuzzy logic methodologies is that the experience or expert-s knowledge described as a fuzzy rule base can be directly embedded into the systems for dealing with the problems. The current limitation of appropriate and automated designing of fuzzy controllers are focused in this paper. The structure discovery and parameter adjustment of the Branched T-S fuzzy model is addressed by a hybrid technique of type constrained sparse tree algorithms. The simulation result for different system model is evaluated and the identification error is observed to be minimum.

Keywords: Fuzzy logic, branch T-S fuzzy model, tree modeling, complex nonlinear system.

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Authors: Phang Chang, Phang Piau

Abstract:

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In numerical analysis, wavelets also serve as a Galerkin basis to solve partial differential equations. Haar transform or Haar wavelet transform has been used as a simplest and earliest example for orthonormal wavelet transform. Since its popularity in wavelet analysis, there are several definitions and various generalizations or algorithms for calculating Haar transform. Fast Haar transform, FHT, is one of the algorithms which can reduce the tedious calculation works in Haar transform. In this paper, we present a modified fast and exact algorithm for FHT, namely Modified Fast Haar Transform, MFHT. The algorithm or procedure proposed allows certain calculation in the process decomposition be ignored without affecting the results.

Keywords: Fast Haar Transform, Haar transform, Wavelet analysis.

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Authors: A. Reyes-Salazar, M. D. Llanes-Tizoc, E. Bojorquez, F. Valenzuela-Beltran, J. Bojorquez, J. R. Gaxiola-Camacho, A. Haldar

Abstract:

Seismic analysis of steel buildings is usually based on the use of the concentrated mass (ML) matrix and the Rayleigh damping matrix (C). Similarly, the initial stiffness matrix (KO) and the first two modes associated to lateral vibrations are commonly used to develop the matrix C. The evaluation of the accuracy of these practices for the particular case of steel buildings with moment-resisting steel frames constitutes the main objective of this research. For this, the nonlinear seismic responses of three models of steel frames, representing low-, medium- and high-rise steel buildings, are considered. Results indicate that if the ML matrix is used, shears and bending moments in columns are underestimated by up to 30% and 65%, respectively, when compared to the corresponding results obtained with the consistent mass matrix (MC). It is also shown that if KO is used in C instead the tangent stiffness matrix (Kt), axial loads in columns are underestimated by up to 80%. It is concluded that the consistent mass matrix should be used in the structural modelling of moment resisting steel frames and the tangent stiffness matrix should be used to develop the Rayleigh damping matrix.

Keywords: Moment-resisting steel frames, consistent and concentrated mass matrices, nonlinear seismic response, Rayleigh damping.

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Authors: M. Palizvan, M. H. Sadr, M. T. Abadi

Abstract:

The representative volume element (RVE) plays a central role in the mechanics of random heterogeneous materials with a view to predicting their effective properties. In this paper, a computational homogenization methodology, developed to determine effective linear elastic properties of composite materials, is extended to predict the effective nonlinear elastoplastic response of long fiber reinforced composite. Finite element simulations of volumes of different sizes and fiber volume fractures are performed for calculation of the overall response RVE. The dependencies of the overall stress-strain curves on the number of fibers inside the RVE are studied in the 2D cases. Volume averaged stress-strain responses are generated from RVEs and compared with the finite element calculations available in the literature at moderate and high fiber volume fractions. For these materials, the existence of an RVE is demonstrated for the sizes of RVE corresponding to 10–100 times the diameter of the fibers. In addition, the response of small size RVE is found anisotropic, whereas the average of all large ones leads to recover the isotropic material properties.

Keywords: Homogenization, periodic boundary condition, elastoplastic properties, RVE.

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Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

By means of the idea of three-wave method, we obtain some analytic solutions for high nonlinear form of Benjamin-Bona- Mahony-Burgers (shortly BBMB) equations in its bilinear form.

Keywords: Benjamin-Bona-Mahony-Burgers equations, Hirota's bilinear form, three-wave method.

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Authors: S. Burgalat, L. Teilhac, A. Brand, E. Chastel, M. Jumeline

Abstract:

The paper presents actual benefits and drawbacks of a multidirectional autonomous hovercraft conceived with limited resources and designed for indoor exploration. Recent developments in the field have led to the apparition of very powerful automotive systems capable of very high calculation and exploration in complex unknown environments. They usually propose very complex algorithms, high precision/cost sensors and sometimes have heavy calculation consumption with complex data fusion. These systems are usually powerful but have a certain price, and the benefits may not be worth the cost, especially considering their hardware limitations and their power consumption. The present approach is to build a compromise between cost, power consumption and results preciseness.

Keywords: Hovercraft, Indoor Exploration, Autonomous, Multidirectional, Wireless Control.

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Authors: C. C. Wang, N. S. Pai, H. T. Yau, T. T. Liao, M. J. Jang, C. W. Lee, W. M. Hong

Abstract:

Horizontal platform system (HPS) is popularly applied in offshore and earthquake technology, but it is difficult and time-consuming for regulation. In order to understand the nonlinear dynamic behavior of HPS and reduce the cost when using it, this paper employs differential transformation method to study the bifurcation behavior of HPS. The numerical results reveal a complex dynamic behavior comprising periodic, sub-harmonic, and chaotic responses. Furthermore, the results reveal the changes which take place in the dynamic behavior of the HPS as the external torque is increased. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of horizontal platform system.

Keywords: horizontal platform system, differentialtransformation method, chaotic.

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Authors: Mustafa Resa Becan

Abstract:

Sliding mode control with a fuzzy boundary layer is presented to hydraulic position control problem in this paper. A nonlinear hydraulic servomechanism which has an asymmetric cylinder is modeled and simulated first, then the proposed control scheme is applied to this model versus the conventional sliding mode control. Simulation results proved that the chattering free position control is achieved by tuning the fuzzy scaling factors properly.

Keywords: Hydraulic servomechanism, position control, sliding mode control, chattering, fuzzy boundary layer.

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Authors: Martin Cermak, Stanislav Sysala

Abstract:

In this paper we present the efficient parallel implementation of elastoplastic problems based on the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. This approach allow us to use parallel solution and compute this nonlinear problem on the supercomputers and decrease the solution time and compute problems with millions of DOFs. In our approach we consider an associated elastoplastic model with the von Mises plastic criterion and the combination of linear isotropic-kinematic hardening law. This model is discretized by the implicit Euler method in time and by the finite element method in space. We consider the system of nonlinear equations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel by the above mentioned TFETI. The implementation of this problem is realized in our in-house MatSol packages developed in MatLab.

Keywords: Isotropic-kinematic hardening, TFETI, domain decomposition, parallel solution.

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Authors: M.M. Namazi, S.M. Saghaiannejad, A. Rashidi

Abstract:

In this paper by using the port-controlled Hamiltonian (PCH) systems theory, a full-order nonlinear controlled model is first developed. Then a nonlinear passivity-based robust adaptive control (PBRAC) of switched reluctance motor in the presence of external disturbances for the purpose of torque ripple reduction and characteristic improvement is presented. The proposed controller design is separated into the inner loop and the outer loop controller. In the inner loop, passivity-based control is employed by using energy shaping techniques to produce the proper switching function. The outer loop control is employed by robust adaptive controller to determine the appropriate Torque command. It can also overcome the inherent nonlinear characteristics of the system and make the whole system robust to uncertainties and bounded disturbances. A 4KW 8/6 SRM with experimental characteristics that takes magnetic saturation into account is modeled, simulation results show that the proposed scheme has good performance and practical application prospects.

Keywords: Switched Reluctance Motor, Port HamiltonianSystem, Passivity-Based Control, Torque Ripple Minimization

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Authors: Lianglin Xiong, Shouming Zhong, Mao Ye

Abstract:

This paper addresses the stabilization issues for a class of uncertain switched neutral systems with nonlinear perturbations. Based on new classes of piecewise Lyapunov functionals, the stability assumption on all the main operators or the convex combination of coefficient matrices is avoid, and a new switching rule is introduced to stabilize the neutral systems. The switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. Finally, three simulation examples are given to demonstrate the significant improvements over the existing results.

Keywords: Switched neutral system, piecewise Lyapunov functional, nonlinear perturbation, Lyapunov-Metzler linear matrix inequality.

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Authors: Ruxandra Barbulescu, Daniel Ioan, Gabriela Ciuprina

Abstract:

The saltatory conduction is the way the action potential is transmitted along a myelinated axon. The potential diffuses along the myelinated compartments and it is regenerated in the Ranvier nodes due to the ion channels allowing the flow across the membrane. For an efficient simulation of populations of neurons, it is important to use reduced order models both for myelinated compartments and for Ranvier nodes and to have control over their accuracy and inner parameters. The paper presents a reduced order model of this neural system which allows an efficient simulation method for the saltatory conduction in myelinated axons. This model is obtained by concatenating reduced order linear models of 1D myelinated compartments and nonlinear 0D models of Ranvier nodes. The models for the myelinated compartments are selected from a series of spatially distributed models developed and hierarchized according to their modeling errors. The extracted model described by a nonlinear PDE of hyperbolic type is able to reproduce the saltatory conduction with acceptable accuracy and takes into account the finite propagation speed of potential. Finally, this model is again reduced in order to make it suitable for the inclusion in large-scale neural circuits.

Keywords: Saltatory conduction, action potential, myelinated compartments, nonlinear, Ranvier nodes, reduced order models, POD.

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Authors: D. Liu, D. M. Donskoy

Abstract:

The vibroacoustic modulation method is based on the modulation effect of high-frequency ultrasonic wave (carrier) by low-frequency vibration in the presence of various defects, primarily contact-type such as cracks, delamination, etc. The presence and severity of the defect are measured by the ratio of the spectral sidebands and the carrier in the spectrum of the modulated signal. This approach, however, does not differentiate between amplitude and frequency modulations, AM and FM, respectfully. This paper is an attempt to explain the generation mechanisms of FM and its correlation with the flaw properties. Here we proposed two possible mechanisms leading to FM modulation based on nonlinear local defect resonance and dynamic acoustoelastic models.

Keywords: Non-destructive testing, nonlinear acoustics, structural health monitoring, acoustoelasticity, local defect resonance.

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Authors: G. Akgun, I. Algul, H. Kurtaran

Abstract:

In this paper geometrically nonlinear static behavior of laminated composite hollow super-elliptic beams is investigated using generalized differential quadrature method. Super-elliptic beam can have both oval and elliptic cross-sections by adjusting parameters in super-ellipse formulation (also known as Lamé curves). Equilibrium equations of super-elliptic beam are obtained using the virtual work principle. Geometric nonlinearity is taken into account using von-Kármán nonlinear strain-displacement relations. Spatial derivatives in strains are expressed with the generalized differential quadrature method. Transverse shear effect is considered through the first-order shear deformation theory. Static equilibrium equations are solved using Newton-Raphson method. Several composite super-elliptic beam problems are solved with the proposed method. Effects of layer orientations of composite material, boundary conditions, ovality and ellipticity on bending behavior are investigated.

Keywords: Generalized differential quadrature, geometric nonlinearity, laminated composite, super-elliptic cross-section.

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Authors: Fengxia Zheng, Chuanyun Gu

Abstract:

By using a fixed point theorem of a sum operator, the existence and uniqueness of positive solution for a class of boundary value problem of nonlinear fractional differential equation is studied. An iterative scheme is constructed to approximate it. Finally, an example is given to illustrate the main result.

Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator.

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Authors: H. Masaeli, R. Ziaei, F. Khoshnoudian

Abstract:

Shock response analysis of the soil–structure systems induced by near–fault pulses is investigated. Vibration transmissibility of the soil–structure systems is evaluated by shock response spectra (SRS). Medium–to–high rise buildings with different aspect ratios located on different soil types as well as different foundations with respect to vertical load bearing safety factors are studied. Two types of mathematical near–fault pulses, i.e. forward directivity and fling step, with different pulse periods as well as pulse amplitudes are selected as incident ground shock. Linear versus nonlinear soil–structure interaction (SSI) condition are considered alternatively and the corresponding results are compared. The results show that nonlinear SSI is likely to amplify the acceleration responses when subjected to long–period incident pulses with normalized period exceeding a threshold. It is also shown that this threshold correlates with soil type, so that increased shear–wave velocity of the underlying soil makes the threshold period decrease.

Keywords: Nonlinear soil–structure interaction, shock response spectrum, near–fault ground shock, rocking isolation.

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Authors: Da-Xue Chen, Guang-Hui Liu

Abstract:

In this paper, we establish several oscillation criteria for the nonlinear second-order damped delay dynamic equation r(t)|xΔ(t)|β-1xΔ(t)Δ + p(t)|xΔσ(t)|β-1xΔσ(t) + q(t)f(x(τ (t))) = 0 on an arbitrary time scale T, where β > 0 is a constant. Our results generalize and improve some known results in which β > 0 is a quotient of odd positive integers. Some examples are given to illustrate our main results.

Keywords: Oscillation, damped delay dynamic equation, time scale.

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Authors: Meng Hu, Lili Wang

Abstract:

This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form:  Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.

Keywords: Fractional differential equation, Integral boundary condition, Schauder fixed point theorem, Banach contraction principle.

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Authors: Junji Kaneko, Shigeyuki Haruyama, Ken Kaminishi, Tadayuki Kyoutani, Siti Ruhana Omar, Oke Oktavianty

Abstract:

This study is used as a definition method to the value and function in manufacturing sector. In concurrence of discussion about present condition of modeling method, until now definition of 1D-CAE is ambiguity and not conceptual. Across all the physic fields, those methods are defined with the formulation of differential algebraic equation which only applied time derivation and simulation. At the same time, we propose semi-acausal modeling concept and differential algebraic equation method as a newly modeling method which the efficiency has been verified through the comparison of numerical analysis result between the semi-acausal modeling calculation and FEM theory calculation.

Keywords: System Model, Physical Models, Empirical Models, Conservation Law, Differential Algebraic Equation, Object-Oriented.

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Authors: Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian

Abstract:

Hammerstein–Wiener model is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output and could be used to model various processes. This paper contains an optimization approach method for analysing the problem of Hammerstein–Wiener systems identification. The method relies on reformulate the identification problem; solve it as constraint quadratic problem and analysing its solutions. During the formulation of the problem, effects of adding noise to both input and output signals of nonlinear blocks and disturbance to linear block, in the emerged equations are discussed. Additionally, the possible parametric form of matrix operations to reduce the equation size is presented. To analyse the possible solutions to the mentioned system of equations, a method to reduce the difference between the number of equations and number of unknown variables by formulate and importing existing knowledge about nonlinear functions is presented. Obtained equations are applied to an instance H–W system to validate the results and illustrate the proposed method.

Keywords: Identification, Hammerstein-Wiener, optimization, quantization.

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Authors: B. Selma, S. Chouraqui

Abstract:

Nonlinear system identification is becoming an important tool which can be used to improve control performance. This paper describes the application of adaptive neuro-fuzzy inference system (ANFIS) model for controlling a car. The vehicle must follow a predefined path by supervised learning. Backpropagation gradient descent method was performed to train the ANFIS system. The performance of the ANFIS model was evaluated in terms of training performance and classification accuracies and the results confirmed that the proposed ANFIS model has potential in controlling the non linear system.

Keywords: Adaptive neuro-fuzzy inference system (ANFIS), Fuzzy logic, neural network, nonlinear system, control

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