Showing papers in "Mathematical Problems in Engineering in 2010"

Some Applications of Fractional Calculus in Engineering

Abstract: Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.

Fractional Order Calculus: Basic Concepts and Engineering Applications

Abstract: The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.

Assessment of Landslide Susceptibility by Decision Trees in the Metropolitan Area of Istanbul, Turkey

Abstract: The main purpose of the present study is to investigate the possible application of decision tree in landslide susceptibility assessment. The study area having a surface area of 174.8 km2 locates at the northern coast of the Sea of Marmara and western part of Istanbul metropolitan area. When applying data mining and extracting decision tree, geological formations, altitude, slope, plan curvature, profile curvature, heat load and stream power index parameters are taken into consideration as landslide conditioning factors. Using the predicted values, the landslide susceptibility map of the study area is produced. The AUC value of the produced landslide susceptibility map has been obtained as 89.6%. According to the results of the AUC evaluation, the produced map has exhibited a good enough performance.

Fractal Time Series—A Tutorial Review

Abstract: Fractal time series substantially differs from conventional one in its statistic properties. For instance, it may have a heavy-tailed probability distribution function (PDF), a slowly decayed autocorrelation function (ACF), and a power spectrum function (PSD) of type. It may have the statistical dependence, either long-range dependence (LRD) or short-range dependence (SRD), and global or local self-similarity. This article will give a tutorial review about those concepts. Note that a conventional time series can be regarded as the solution to a differential equation of integer order with the excitation of white noise in mathematics. In engineering, such as mechanical engineering or electronics engineering, engineers may usually consider it as the output or response of a differential system or filter of integer order under the excitation of white noise. In this paper, a fractal time series is taken as the solution to a differential equation of fractional order or a response of a fractional system or a fractional filter driven with a white noise in the domain of stochastic processes.

Improved Continuous Models for Discrete Media

Abstract: The paper focuses on continuous models derived from a discrete microstructure Various continualization procedures that take into account the nonlocal interaction between variables of the discrete media are analysed

Fractals and Hidden Symmetries in DNA

Abstract: This paper deals with the digital complex representation of a DNA sequence and the analysis of existing correlations by wavelets. The symbolic DNA sequence is mapped into a nonlinear time series. By studying this time series the existence of fractal shapes and symmetries will be shown. At first step, the indicator matrix enables us to recognize some typical patterns of nucleotide distribution. The DNA sequence, of the influenza virus A (H1N1), is investigated by using the complex representation, together with the corresponding walks on DNA; in particular, it is shown that DNA walks are fractals. Finally, by using the wavelet analysis, the existence of symmetries is proven.

Applications of an Extended (′/)-Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics

Abstract: We construct the traveling wave solutions of the (1+1)-dimensional modified Benjamin-Bona-Mahony equation, the (2+1)-dimensional typical breaking soliton equation, the (1+1)-dimensional classical Boussinesq equations, and the (2+1)-dimensional Broer-Kaup-Kuperschmidt equations by using an extended ( 𝐺  / 𝐺 ) -expansion method, where G satisfies the second-order linear ordinary differential equation. By using this method, new exact solutions involving parameters, expressed by three types of functions which are hyperbolic, trigonometric and rational function solutions, are obtained. When the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions.

Chaotic Time Series Analysis

Abstract: Chaotic dynamical systems are ubiquitous in nature and most of them does not have an explicit dynamical equation and can be only understood through the available time series. We here briefly review the basic concepts of time series and its analytic tools, such as dimension, Lyapunov exponent, Hilbert transform, and attractor reconstruction. Then we discuss its applications in a few fields such as the construction of differential equations, identification of synchronization and coupling direction, coherence resonance, and traffic data analysis in Internet.

The Effects of Thermal Radiation, Hall Currents, Soret, and Dufour on MHD Flow by Mixed Convection over a Vertical Surface in Porous Media

Abstract: The study sought to investigate the influence of a magnetic field on heat and mass transfer by mixed convection from vertical surfaces in the presence of Hall, radiation, Soret (thermal-diffusion), and Dufour (diffusion-thermo) effects. The similarity solutions were obtained using suitable transformations. The similarity ordinary differential equations were then solved by MATLAB routine bvp4c. The numerical results for some special cases were compared with the exact solution and those obtained by Elgazery (2009) and were found to be in good agreement. A parametric study illustrating the influence of the magnetic strength, Hall current, Dufour, and Soret, Eckert number, thermal radiation, and permeability parameter on the velocity, temperature, and concentration was investigated.

Chebyshev Wavelet Method for Numerical Solution of Fredholm Integral Equations of the First Kind

Abstract: A computational method for solving Fredholm integral equations of the first kind is presented. The method utilizes Chebyshev wavelets constructed on the unit interval as basis in Galerkin method and reduces solving the integral equation to solving a system of algebraic equations. The properties of Chebyshev wavelets are used to make the wavelet coefficient matrices sparse which eventually leads to the sparsity of the coefficients matrix of obtained system. Finally, numerical examples are presented to show the validity and efficiency of the technique.

Using Differential Transform Method and Padé Approximant for Solving MHD Flow in a Laminar Liquid Film from a Horizontal Stretching Surface

Abstract: The purpose of this study is to approximate the stream function and temperature distribution of the MHD flow in a laminar liquid film from a horizontal stretching surface. In this paper DTM-Pade method was used which is a combination of differential transform method (DTM) and Pade approximant. The DTM solutions are only valid for small values of independent variables. Comparison between the solutions obtained by the DTM and the DTM-Pade with numerical solution (fourth-order Runge–Kutta) revealed that the DTM-Pade method is an excellent method for solving MHD boundary-layer equations.

Modeling and Fuzzy PDC Control and Its Application to an Oscillatory TLP Structure

Abstract: An analytical solution is derived to describe the wave-induced flow field and surge motion of a deformable platform structure controlled with fuzzy controllers in an oceanic environment. In the controller design procedure, a parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic controller by blending all local state feedback controllers. The Lyapunov method is used to carry out stability analysis of a real system structure. The corresponding boundary value problems are then incorporated into scattering and radiation problems. These are analytically solved, based on the separation of variables, to obtain a series of solutions showing the harmonic incident wave motion and surge motion. The dependence of the wave-induced flow field and its resonant frequency on wave characteristics and structural properties including platform width, thickness and mass can thus be drawn with a parametric approach. The wave-induced displacement of the surge motion is determined from these mathematical models. The vibration of the floating structure and mechanical motion caused by the wave force are also discussed analytically based on fuzzy logic theory and the mathematical framework to find the decay in amplitude of the surge motion in the tension leg platform (TLP) system. The expected effects of the damping in amplitude of the surge motion due to the control force on the structural response are obvious.

Furuta's Pendulum: A Conservative Nonlinear Model for Theory and Practise

Abstract: Furuta's pendulum has been an excellent benchmark for the automatic control community in the last years, providing, among others, a better understanding of model-based Nonlinear Control Techniques. Since most of these techniques are based on invariants and/or integrals of motion then, the dynamic model plays an important role. This paper describes, in detail, the successful dynamical model developed for the available laboratory pendulum. The success relies on a basic dynamical model derived from Classical Mechanics which has been augmented to compensate the non-conservative torques. Thus, the quasi-conservative “practical” model developed allows to design all the controllers as if the system was strictly conservative. A survey of all the nonlinear controllers designed and experimentally tested on the available laboratory pendulum is also reported.

Application of the Cole-Hopf Transformation for Finding Exact Solutions to Several Forms of the Seventh-Order KdV Equation

Abstract: We use a generalized Cole-Hopf transformation to obtain a condition that allows us to find exact solutions for several forms of the general seventh-order KdV equation (KdV7). A remarkable fact is that this condition is satisfied by three well-known particular cases of the KdV7. We also show some solutions in these cases. In the particular case of the seventh-order Kaup-Kupershmidt KdV equation we obtain other solutions by some ansatzes different from the Cole-Hopf transformation.

Modeling of Ship Roll Dynamics and Its Coupling with Heave and Pitch

Abstract: In order to study the dynamic behavior of ships navigating in severe environmental conditions it is imperative to develop their governing equations of motion taking into account the inherent nonlinearity of large-amplitude ship motion The purpose of this paper is to present the coupled nonlinear equations of motion in heave, roll, and pitch based on physical grounds The ingredients of the formulation are comprised of three main components These are the inertia forces and moments, restoring forces and moments, and damping forces and moments with an emphasis to the roll damping moment In the formulation of the restoring forces and moments, the influence of large-amplitude ship motions will be considered together with ocean wave loads The special cases of coupled roll-pitch and purely roll equations of motion are obtained from the general formulation The paper includes an assessment of roll stochastic stability and probabilistic approaches used to estimate the probability of capsizing and parameter identification

A Survey of Some Recent Results on Nonlinear Fault Tolerant Control

Abstract: Fault tolerant control (FTC) is the branch of control theory, dealing with the control of systems that become faulty during their operating life. Following the systems classification, as linear and nonlinear models, FTC can be classified in two different groups, linear FTC (LFTC) dealing with linear models, and the one of interest to us in this paper, nonlinear FTC (NFTC), which deals with nonlinear models. We present in this paper a survey of some of the results obtained in these last years on NFTC.

Designing a Reverse Logistics Network for End-of-Life Vehicles Recovery

Abstract: The environmental factors are receiving increasing attention in different life cycle stages of products. When a product reaches its End-Of-Life (EOL) stage, the management of its recovery process is affected by the environmental and also economical factors. Selecting efficient methods for the collection and recovery of EOL products has become an important issue. The European Union Directive 2000/53/EC extends the responsibility of the vehicle manufacturers to the postconsumer stage of the vehicle. In order to fulfill the requirements of this Directive and also efficient management of the whole recovery process, the conceptual framework of a reverse logistics network is presented. The distribution of new vehicles in an area and also collecting the End-of-Life Vehicles (ELVs) and their recovery are considered jointly. It is assumed that the new vehicles distributors are also responsible for collecting the ELVs. Then a mathematical model is developed which minimizes the costs of setting up the network and also the relevant transportation costs. Because of the complexity of the model, a solution methodology based on the genetic algorithm is designed which enables achieving good quality solutions in a reasonable algorithm run time.

Chaos Control of a Fractional-Order Financial System

Abstract: Fractional-order financial system introduced by W.-C. Chen (2008) displays chaotic motions at order less than 3. In this paper we have extended the nonlinear feedback control in ODE systems to fractional-order systems, in order to eliminate the chaotic behavior. The results are proved analytically by applying the Lyapunov linearization method and stability condition for fractional system. Moreover numerical simulations are shown to verify the effectiveness of the proposed control scheme.

A Novel Numerical Technique for Two-Dimensional Laminar Flow between Two Moving Porous Walls

Abstract: We investigate the steady two-dimensional flow of a viscous incompressible fluid in a rectangular domain that is bounded by two permeable surfaces. The governing fourth-order nonlinear differential equation is solved by applying the spectral-homotopy analysis method and a novel successive linearisation method. Semianalytical results are obtained and the convergence rate of the solution series was compared with numerical approximations and with earlier results where the homotopy analysis and homotopy perturbation methods were used. We show that both the spectral-homotopy analysis method and successive linearisation method are computationally efficient and accurate in finding solutions of nonlinear boundary value problems.

A Comparative Study of Redundant Constraints Identification Methods in Linear Programming Problems

Abstract: The objective function and the constraints can be formulated as linear functions of independent variables in most of the real-world optimization problems. Linear Programming (LP) is the process of optimizing a linear function subject to a finite number of linear equality and inequality constraints. Solving linear programming problems efficiently has always been a fascinating pursuit for computer scientists and mathematicians. The computational complexity of any linear programming problem depends on the number of constraints and variables of the LP problem. Quite often large-scale LP problems may contain many constraints which are redundant or cause infeasibility on account of inefficient formulation or some errors in data input. The presence of redundant constraints does not alter the optimal solutions(s). Nevertheless, they may consume extra computational effort. Many researchers have proposed different approaches for identifying the redundant constraints in linear programming problems. This paper compares five of such methods and discusses the efficiency of each method by solving various size LP problems and netlib problems. The algorithms of each method are coded by using a computer programming language C. The computational results are presented and analyzed in this paper.

Analytical Solution for Different Profiles of Fin with Temperature-Dependent Thermal Conductivity

Abstract: Three different profiles of the straight fin that has a temperature-dependent thermal conductivity are investigated by differential transformation methodDTMand compared with numerical solution. Fin profiles are rectangular, convex, and exponential. For validation of the DTM, the heat equation is solved numerically by the fourth-order Runge-Kutta method. The temperature distribution, fin efficiency, and fin heat transfer rate are presented for three fin profiles and a range of values of heat transfer parameters. DTM results indicate that series converge rapidly with high accuracy. The efficiency and base temperature of the exponential profile are higher than the rectangular and the convex profiles. The results indicate that the numerical data and analytical method are in agreement with each other.

Some New Iterative Methods for Nonlinear Equations

Abstract: We suggest and analyze some new iterative methods for solving the nonlinear equations using the decomposition technique coupled with the system of equations. We prove that new methods have convergence of fourth order. Several numerical examples are given to illustrate the efficiency and performance of the new methods. Comparison with other similar methods is given.

Application of Homotopy Analysis Method to the Unsteady Squeezing Flow of a Second-Grade Fluid between Circular Plates

Abstract: We investigated an axisymmetric unsteady two-dimensional flow of nonconducting, incompress- ible second grade fluid between two circular plates. The similarity transformation is applied to reduce governing partial differential equationPDEto a nonlinear ordinary differential equation � ODEin dimensionless form. The resulting nonlinear boundary value problem is solved using homotopy analysis method and numerical method. The effects of appropriate dimensionless parameters on the velocity profiles are studied. The total resistance to the upper plate has been calculated.

Shannon Wavelets for the Solution of Integrodifferential Equations

Abstract: Shannon wavelets are used to define a method for the solution of integrodifferential equations. This method is based on (1) the Galerking method, (2) the Shannon wavelet representation, (3) the decorrelation of the generalized Shannon sampling theorem, and (4) the definition of connection coefficients. The Shannon sampling theorem is considered in a more general approach suitable for analysing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction of functions. Shannon wavelets are -functions and their any order derivatives can be analytically defined by some kind of a finite hypergeometric series (connection coefficients).

Advances in Structural Control in Civil Engineering in China

Abstract: In the recent years, much attention has been paid to the research and development of structural control techniques with particular emphasis on alleviation of wind and seismic responses of buildings and bridges in China. Structural control in civil engineering has been developed from the concept into a workable technology and applied into practical engineering structures. The aim of this paper is to review a state of the art of researches and applications of structural control in civil engineering in China. It includes the passive control, active control, hybrid controland semiactive control. Finally, the possible future directions of structural control in civil engineering in China are presented.

A Comparative Analysis of Recent Identification Approaches for Discrete-Event Systems

Abstract: Analogous to the identification of continuous dynamical systems, identification of discrete-event systems (DESs) consists of determining the mathematical model that describes the behaviour of a given ill-known or eventually unknown system from the observation of the evolution of its inputs and outputs. First, the paper overviews identification approaches of DES found in the literature, and then it provides a comparative analysis of three recent and innovative contributions.

Stability Analysis of Interconnected Fuzzy Systems Using the Fuzzy Lyapunov Method

Abstract: The fuzzy Lyapunov method is investigated for use with a class of interconnected fuzzy systems. The interconnected fuzzy systems consist of interconnected fuzzy subsystems, and the stability analysis is based on Lyapunov functions. Based on traditional Lyapunov stability theory, we further propose a fuzzy Lyapunov method for the stability analysis of interconnected fuzzy systems. The fuzzy Lyapunov function is defined in fuzzy blending quadratic Lyapunov functions. Some stability conditions are derived through the use of fuzzy Lyapunov functions to ensure that the interconnected fuzzy systems are asymptotically stable. Common solutions can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. Finally, simulations are performed in order to verify the effectiveness of the proposed stability conditions in this paper.

Nonlinear Time Series: Computations and Applications 2012

Abstract: 1 School of Information Science & Technology, East China Normal University, Shanghai 200241, China 2 Department of Mathematics, University of Rome “La Sapienza”, Piazzale Aldo Moro 2, 00185 Rome, Italy 3 Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy 4 Faculty of Engineering, Multimedia University, 63100 Cyberjaya, Selanger, Malaysia 5 College of Computer Science, Chongqing University, Chongqing 400044, China 6 Department of Electrical, Computer, Software, & Systems Engineering, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114, USA

On the Predictability of Long-Range Dependent Series

Abstract: This paper points out that the predictability analysis of conventional time series may in general be invalid for long-range dependent (LRD) series since the conventional mean-square error (MSE) may generally not exist for predicting LRD series. To make the MSE of LRD series prediction exist, we introduce a generalized MSE. With that, the proof of the predictability of LRD series is presented in Hilbert space.

Robust State-Derivative Feedback LMI-Based Designs for Linear Descriptor Systems

Abstract: Techniques for stabilization of linear descriptor systems by state-derivative feedback are proposed. The methods are based on Linear Matrix Inequalities (LMIs) and assume that the plant is a controllable system with poles different from zero. They can include design constraints such as: decay rate, bounds on output peak and bounds on the state-derivative feedback matrix , and can be applied in a class of uncertain systems subject to structural failures. These designs consider a broader class of plants than the related results available in the literature. The LMI can be efficiently solved using convex programming techniques. Numerical examples illustrate the efficiency of the proposed methods.