Search results for: Nonlinear Algebraic Equations

Authors: M. A. Koroma, C. Zhan, A. F. Kamara, A. B. Sesay

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In this work we adopt a combination of Laplace transform and the decomposition method to find numerical solutions of a system of multi-pantograph equations. The procedure leads to a rapid convergence of the series to the exact solution after computing a few terms. The effectiveness of the method is demonstrated in some examples by obtaining the exact solution and in others by computing the absolute error which decreases as the number of terms of the series increases.

Keywords: Laplace decomposition, pantograph equations, exact solution, numerical solution, approximate solution.

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Authors: Nhon Do, Hien Nguyen

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Nowadays there are many methods for representing knowledge such as semantic network, neural network, and conceptual graphs. Nonetheless, these methods are not sufficiently efficient when applied to perform and deduce on knowledge domains about supporting in general education such as algebra, analysis or plane geometry. This leads to the introduction of computational network which is a useful tool for representation knowledge base, especially for computational knowledge, especially knowledge domain about general education. However, when dealing with a practical problem, we often do not immediately find a new solution, but we search related problems which have been solved before and then proposing an appropriate solution for the problem. Besides that, when finding related problems, we have to determine whether the result of them can be used to solve the practical problem or not. In this paper, the extension model of computational network has been presented. In this model, Sample Problems, which are related problems, will be used like the experience of human about practical problem, simulate the way of human thinking, and give the good solution for the practical problem faster and more effectively. This extension model is applied to construct an automatic system for solving algebraic problems in middle school.

Keywords: educational software, artificial intelligence, knowledge base system, knowledge representation.

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Authors: Ahmed Badawi

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This paper proposes a method for speckle reduction in medical ultrasound imaging while preserving the edges with the added advantages of adaptive noise filtering and speed. A nonlinear image diffusion method that incorporates local image parameter, namely, scatterer density in addition to gradient, to weight the nonlinear diffusion process, is proposed. The method was tested for the isotropic case with a contrast detail phantom and varieties of clinical ultrasound images, and then compared to linear and some other diffusion enhancement methods. Different diffusion parameters were tested and tuned to best reduce speckle noise and preserve edges. The method showed superior performance measured both quantitatively and qualitatively when incorporating scatterer density into the diffusivity function. The proposed filter can be used as a preprocessing step for ultrasound image enhancement before applying automatic segmentation, automatic volumetric calculations, or 3D ultrasound volume rendering.

Keywords: Ultrasound imaging, Nonlinear isotropic diffusion, Speckle noise, Scattering.

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

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This paper investigates the problem of designing a robust state-feedback controller for a class of uncertain Markovian jump nonlinear systems that guarantees the L2-gain from an exogenous input to a regulated output is less than or equal to a prescribed value. First, we approximate this class of uncertain Markovian jump nonlinear systems by a class of uncertain Takagi-Sugeno fuzzy models with Markovian jumps. Then, based on an LMI approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear systems to have an H performance are derived. An illustrative example is used to illustrate the effectiveness of the proposed design techniques.

Keywords: Robust H, Fuzzy Control, Markovian Jump Systems, LMI.

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Authors: Sarun Phibanchon, Michael A. Allen

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A variational method is used to obtain the growth rate of a transverse long-wavelength perturbation applied to the soliton solution of a nonlinear Schr¨odinger equation with a three-half order potential. We demonstrate numerically that this unstable perturbed soliton will eventually transform into a cylindrical soliton.

Keywords: Soliton, instability, variational method, spectral method.

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Authors: Ghasem Abbasnejad, Soheil Zarkandi, Misagh Imani

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In this article the homotopy continuation method (HCM) to solve the forward kinematic problem of the 3-PRS parallel manipulator is used. Since there are many difficulties in solving the system of nonlinear equations in kinematics of manipulators, the numerical solutions like Newton-Raphson are inevitably used. When dealing with any numerical solution, there are two troublesome problems. One is that good initial guesses are not easy to detect and another is related to whether the used method will converge to useful solutions. Results of this paper reveal that the homotopy continuation method can alleviate the drawbacks of traditional numerical techniques.

Keywords: Forward kinematics, Homotopy continuationmethod, Parallel manipulators, Rotation matrix

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Authors: Hidetoshi Konno, Akio Suzuki

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The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-dependent transition rate is given. Then, the exact solution of the mean field equation for the nonlinear Langevin equation is also given. It is demonstrated that transient population dynamics is successfully identified by the generalized Logistic equation with fractional higher order nonlinear term. It is also demonstrated the necessity of introducing time-dependent transition rate in the master equation approach to incorporate the effect of nonlinearity.

Keywords: Transient population dynamics, Phase singularity, Birth-death process, Non-stationary Master equation, nonlinear Langevin equation, generalized Logistic equation.

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Authors: Deepak Kumar, Vivek Kumar, V. P. Singh

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This paper describes a steady state model of a multiple effect evaporator system for simulation and control purposes. The model includes overall as well as component mass balance equations, energy balance equations and heat transfer rate equations for area calculations for all the effects. Each effect in the process is represented by a number of variables which are related by the energy and material balance equations for the feed, product and vapor flow for backward, mixed and split feed. For simulation 'fsolve' solver in MATLAB source code is used. The optimality of three sequences i.e. backward, mixed and splitting feed is studied by varying the various input parameters.

Keywords: MATLAB "fsolve" solver, multiple effectevaporators, black liquor, feeding sequences.

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Authors: Alia Alghosoun, Michael Herty, Mohammed Seaid

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We present a new class of numerical techniques to solve shallow water flows over dry areas including run-up. Many recent investigations on wave run-up in coastal areas are based on the well-known shallow water equations. Numerical simulations have also performed to understand the effects of several factors on tsunami wave impact and run-up in the presence of coastal areas. In all these simulations the shallow water equations are solved in entire domain including dry areas and special treatments are used for numerical solution of singularities at these dry regions. In the present study we propose a new method to deal with these difficulties by reformulating the shallow water equations into a new system to be solved only in the wetted domain. The system is obtained by a change in the coordinates leading to a set of equations in a moving domain for which the wet/dry interface is the reconstructed using the wave speed. To solve the new system we present a finite volume method of Lax-Friedrich type along with a modified method of characteristics. The method is well-balanced and accurately resolves dam-break problems over dry areas.

Keywords: Run-up waves, Shallow water equations, finite volume method, wet/dry interface, dam-break problem.

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Authors: H. Bensouilah, H. Boucherit, M. Lahmar

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A theoretical investigation on the effects of both steady-state and dynamic deformations of the foils on the dynamic performance characteristics of a self-acting air foil journal bearing operating under small harmonic vibrations is proposed. To take into account the dynamic deformations of foils, the perturbation method is used for determining the gas-film stiffness and damping coefficients for given values of excitation frequency, compressibility number, and compliance factor of the bump foil. The nonlinear stationary Reynolds’ equation is solved by means of the Galerkins’ finite element formulation while the finite differences method are used to solve the first order complex dynamic equations resulting from the perturbation of the nonlinear transient compressible Reynolds’ equation. The stiffness of a bump is uniformly distributed throughout the bearing surface (generation I bearing). It was found that the dynamic properties of the compliant finite length journal bearing are significantly affected by the compliance of foils especially whenthe dynamic deformation of foils is considered in addition to the static one by applying the principle of superposition.

Keywords: Elasto-aerodynamic lubrication, Air foil bearing, Steady-state deformation, Dynamic deformation, Stiffness and damping coefficients, Perturbation method, Fluid-structure interaction, Galerk infinite element method, Finite difference method.

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Authors: Dezhi Liu Guiyuan Yang Wei Zhang

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Strict stability can present the rate of decay of the solution, so more and more investigators are beginning to study the topic and some results have been obtained. However, there are few results about strict stability of stochastic differential equations. In this paper, using Lyapunov functions and Razumikhin technique, we have gotten some criteria for the strict stability of impulsive stochastic functional differential equations with markovian switching.

Keywords: Impulsive; Stochastic functional differential equation; Strict stability; Razumikhin technique.

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Authors: Hyun-Woo Cho

Abstract:

The fault detection and diagnosis of complicated production processes is one of essential tasks needed to run the process safely with good final product quality. Unexpected events occurred in the process may have a serious impact on the process. In this work, triangular representation of process measurement data obtained in an on-line basis is evaluated using simulation process. The effect of using linear and nonlinear reduced spaces is also tested. Their diagnosis performance was demonstrated using multivariate fault data. It has shown that the nonlinear technique based diagnosis method produced more reliable results and outperforms linear method. The use of appropriate reduced space yielded better diagnosis performance. The presented diagnosis framework is different from existing ones in that it attempts to extract the fault pattern in the reduced space, not in the original process variable space. The use of reduced model space helps to mitigate the sensitivity of the fault pattern to noise.

Keywords: Real-time Fault diagnosis, triangular representation of patterns in reduced spaces, Nonlinear kernel technique, multivariate statistical modeling.

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

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Three-dimensional simulation of harmonic up generation in free electron laser amplifier operating simultaneously with a cold and relativistic electron beam is presented in steady-state regime where the slippage of the electromagnetic wave with respect to the electron beam is ignored. By using slowly varying envelope approximation and applying the source-dependent expansion to wave equations, electromagnetic fields are represented in terms of the Hermit Gaussian modes which are well suited for the planar wiggler configuration. The electron dynamics is described by the fully threedimensional Lorentz force equation in presence of the realistic planar magnetostatic wiggler and electromagnetic fields. A set of coupled nonlinear first-order differential equations is derived and solved numerically. The fundamental and third harmonic radiation of the beam is considered. In addition to uniform beam, prebunched electron beam has also been studied. For this effect of sinusoidal distribution of entry times for the electron beam on the evolution of radiation is compared with uniform distribution. It is shown that prebunching reduces the saturation length substantially. For efficiency enhancement the wiggler is set to decrease linearly when the radiation of the third harmonic saturates. The optimum starting point of tapering and the slope of radiation in the amplitude of wiggler are found by successive run of the code.

Keywords: Free electron laser, Prebunching, Undulator, Wiggler.

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Authors: Diego Garijo

Abstract:

A numerical approach for solving constant-coefficient differential equations whose solutions exhibit boundary layer structure is built by inserting Bernstein Partition of Unity into Galerkin variational weak form. Due to the reproduction capability of Bernstein basis, such implementation shows excellent accuracy at boundaries and is able to capture sharp gradients of the field variable by p-refinement using regular distributions of equi-spaced evaluation points. The approximation is subjected to convergence experimentation and a procedure to assemble the discrete equations without a background integration mesh is proposed.

Keywords: Bernstein polynomials, Galerkin, differential equation, boundary layer.

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Authors: Yang Liu, Hong Li, Siriguleng He, Wei Gao, Zhichao Fang

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In this paper, the C1-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes.

Keywords: Nonlinear fourth-order hyperbolic equation, Lyapunov functional, existence, uniqueness and regularity, conforming finite element method, optimal error estimates.

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Authors: P.-W. Tsai, C.-Y. Chen, C.-W. Chen

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In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

Keywords: Adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm.

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Authors: Sara Barati, Karim Ivaz

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In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.

Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.

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Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei

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As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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Authors: Ahmad Forouzantabar, Babak Gholami, Mohammad Azadi

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An adaptive neural network controller for autonomous underwater vehicles (AUVs) is presented in this paper. The AUV model is highly nonlinear because of many factors, such as hydrodynamic drag, damping, and lift forces, Coriolis and centripetal forces, gravity and buoyancy forces, as well as forces from thruster. In this regards, a nonlinear neural network is used to approximate the nonlinear uncertainties of AUV dynamics, thus overcoming some limitations of conventional controllers and ensure good performance. The uniform ultimate boundedness of AUV tracking errors and the stability of the proposed control system are guaranteed based on Lyapunov theory. Numerical simulation studies for motion control of an AUV are performed to demonstrate the effectiveness of the proposed controller.

Keywords: Autonomous Underwater Vehicle (AUV), Neural Network Controller, Composite Adaptation.

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Authors: A. Majid Bahari, Kourosh Hejazi

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Different variants for buoyancy-affected terms in k-ε turbulence model have been utilized to predict the flow parameters more accurately, and investigate applicability of alternative k-ε turbulence buoyant closures in numerical simulation of a horizontal gravity current. The additional non-isotropic turbulent stress due to buoyancy has been considered in production term, based on Algebraic Stress Model (ASM). In order to account for turbulent scalar fluxes, general gradient diffusion hypothesis has been used along with Boussinesq gradient diffusion hypothesis with a variable turbulent Schmidt number and additional empirical constant c3ε.To simulate buoyant flow domain a 2D vertical numerical model (WISE, Width Integrated Stratified Environments), based on Reynolds- Averaged Navier-Stokes (RANS) equations, has been deployed and the model has been further developed for different k-ε turbulence closures. Results are compared against measured laboratory values of a saline gravity current to explore the efficient turbulence model.

Keywords: Buoyant flows, Buoyant k-ε turbulence model, saline gravity current.

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Authors: M. Saeedi, R. Wuchner, K.-U. Bletzinger

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In order to study the aerodynamic performance of a semi-flexible membrane wing, Fluid-Structure Interaction simulations have been performed. The fluid problem has been modeled using two different approaches which are the vortex panel method and the numerical solution of the Navier-Stokes equations. Nonlinear analysis of the structural problem is performed using the Finite Element Method. Comparison between the two fluid solvers has been made. Aerodynamic performance of the wing is discussed regarding its lift and drag coefficients and they are compared with those of the equivalent rigid wing.

Keywords: CFD, FSI, Membrane wing, Vortex panel method.

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Authors: Rangoli Goyal, Rama Bhargava

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The triple diffusive boundary layer flow of nanofluid under the action of constant magnetic field over a non-linear stretching sheet has been investigated numerically. The model includes the effect of Brownian motion, thermophoresis, and cross-diffusion; slip mechanisms which are primarily responsible for the enhancement of the convective features of nanofluid. The governing partial differential equations are transformed into a system of ordinary differential equations (by using group theory transformations) and solved numerically by using variational finite element method. The effects of various controlling parameters, such as the magnetic influence number, thermophoresis parameter, Brownian motion parameter, modified Dufour parameter, and Dufour solutal Lewis number, on the fluid flow as well as on heat and mass transfer coefficients (both of solute and nanofluid) are presented graphically and discussed quantitatively. The present study has industrial applications in aerodynamic extrusion of plastic sheets, coating and suspensions, melt spinning, hot rolling, wire drawing, glass-fibre production, and manufacture of polymer and rubber sheets, where the quality of the desired product depends on the stretching rate as well as external field including magnetic effects.

Keywords: FEM, Thermophoresis, Diffusiophoresis, Brownian motion.

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Authors: Khaled S. Ragab

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This paper deals with behavior and capacity of punching shear force for flat slabs produced from steel fiber reinforced self compacting concrete (SFRSCC) by application nonlinear finite element method. Nonlinear finite element analysis on nine slab specimens was achieved by using ANSYS software. A general description of the finite element method, theoretical modeling of concrete and reinforcement are presented. The nonlinear finite element analysis program ANSYS is utilized owing to its capabilities to predict either the response of reinforced concrete slabs in the post elastic range or the ultimate strength of a flat slabs produced from steel fiber reinforced self compacting concrete (SFRSCC). In order to verify the analytical model used in this research using test results of the experimental data, the finite element analysis were performed then a parametric study of the effect ratio of flexural reinforcement, ratio of the upper reinforcement, and volume fraction of steel fibers were investigated. A comparison between the experimental results and those predicted by the existing models are presented. Results and conclusions may be useful for designers, have been raised, and represented.

Keywords: Nonlinear FEM, Punching shear behavior, Flat slabs and Steel fiber reinforced self compacting concrete (SFRSCC).

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Authors: I. Zamani, M. H. Zarif

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In this paper a method for designing of nonlinear controller for a fuzzy model of Double Inverted Pendulum is proposed. This system can be considered as a fuzzy large-scale system that includes offset terms and disturbance in each subsystem. Offset terms are deterministic and disturbances are satisfied a matching condition that is mentioned in the paper. Based on Lyapunov theorem, a nonlinear controller is designed for this fuzzy system (as a model reference base) which is simple in computation and guarantees stability. This idea can be used for other fuzzy large- scale systems that include more subsystems Finally, the results are shown.

Keywords: Controller, Fuzzy Double Inverted Pendulums, Fuzzy Large-Scale Systems, Lyapunov Stability.

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Authors: H. Bouadi, M. Tadjine

Abstract:

In this paper; we are interested in dynamic modelling of quadrotor while taking into account the high-order nonholonomic constraints as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new state-space representation and new control scheme. We present after the development and the synthesis of a stabilizing control laws design based on sliding mode in order to perform best tracking results. It ensures locally asymptotic stability and desired tracking trajectories. Nonlinear observer is then synthesized in order to estimate the unmeasured states and the effects of the external disturbances such as wind and noise. Finally simulation results are also provided in order to illustrate the performances of the proposed controllers.

Keywords: Dynamic modelling, nonholonomic constraints, sliding mode, nonlinear observer.

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Authors: Caigen Zhou, Haibo Jiang

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The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive singular perturbed systems with time-varying delay is investigated by employing Lyapunov functions. The nonlinear delay system is built based on the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for global exponential stability of the closed-loop system are derived in terms of linear matrix inequalities (LMIs), which can be easily solved by LMI technique. Some simulations illustrate the effectiveness of the proposed method.

Keywords: T–S fuzzy model, singular perturbed systems, time-varying delay, robust control.

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Authors: Miroslav Byrtus

Abstract:

Large rotating systems, especially gear drives and gearboxes, occur as parts of many mechanical devices transmitting the torque with relatively small loss of power. With the increased demand for high speed machinery, mathematical modeling and dynamic analysis of gear drives gained importance. Mathematical description of such mechanical systems is a complex task evolving for several decades. In gear drive dynamic models, which include flexible shafts, bearings and gearing and use the finite elements, nonlinear effects due to gear mesh and bearings are usually ignored, for such models have large number of degrees of freedom (DOF) and it is computationally expensive to analyze nonlinear systems with large number of DOF. Therefore, these models are not suitable for simulation of nonlinear behavior with amplitude jumps in frequency response. The contribution uses a methodology of nonlinear large rotating system modeling which is based on degrees of freedom (DOF) number reduction using modal synthesis method (MSM). The MSM enables significant DOF number reduction while keeping the nonlinear behavior of the system in a specific frequency range. Further, the MSM with DOF number reduction is suitable for including detail models of nonlinear couplings (mainly gear and bearing couplings) into the complete gear drive models. Since each subsystem is modeled separately using different FEM systems, it is advantageous to parameterize models of subsystems and to use the parameterization for optimization of chosen design parameters. Final complex model of gear drive is assembled in MATLAB and MATLAB tools are used for dynamical analysis of the nonlinear system. The contribution is further focused on developing of a methodology for investigation of behavior of the system by Nonlinear Normal Modes with combination of the MSM using numerical continuation method. The proposed methodology will be tested using a two-stage gearbox including its housing.

Keywords: Vibro-impact system, rotating system, gear drive, modal synthesis method, numerical continuation method, periodic solution.

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Authors: Abdu Masanawa Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations of the form y′′ = f(x,y), a < = x < = b with associated initial or boundary conditions. The continuaous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different three discrete schemes, each of order (4,4,4)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on linear and non-linear ordinary differential equations whose solutions are oscillatory or nearly periodic in nature, and the results obtained compared favourably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: E.Darzi

Abstract:

In this study, a reformer model simulation to use refinery (Farashband refinery, Iran) waste natural gas. In the petroleum and allied sectors where natural gas is being encountered (in form of associated gas) without prior preparation for its positive use, its combustion (which takes place in flares, an equipment through which they are being disposed) has become a great problem because of its associated environmental problems in form of gaseous emission. The proposed model is used to product syngas from waste natural gas. A detailed steady model described by a set of ordinary differential and algebraic equations was developed to predict the behavior of the overall process. The proposed steady reactor model was validated against process data of a reformer synthesis plant recorded and a good agreement was achieved. H2/CO ratio has important effect on Fischer- Tropsch synthesis reactor product and we try to achieve this parameter with best designing reformer reactor. We study different kind of reformer reactors and then select auto thermal reforming process of natural gas in a fixed bed reformer that adjustment H2/CO ratio with CO2 and H2O injection. Finally a strategy was proposed for prevention of extra natural gas to atmosphere.

Keywords: Fischer-Tropsch, injection, reformer, syngas, waste natural gas.

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Authors: Hassan Manouzi

Abstract:

We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: Least squares, Wick product, SPDEs, finite element, Wiener chaos expansion, gradient method.

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