Search results for: Fractional order calculus

Authors: D. H. Kim, Y. H. Kim, T. Kim

Abstract:

A new method identifies coupled fluid-structure system with a reduced set of state variables is presented. Assuming that the structural model is known a priori either from an analysis or a test and using linear transformations between structural and aeroelastic states, it is possible to deduce aerodynamic information from sampled time histories of the aeroelastic system. More specifically given a finite set of structural modes the method extracts generalized aerodynamic force matrix corresponding to these mode shapes. Once the aerodynamic forces are known, an aeroelastic reduced-order model can be constructed in discrete-time, state-space format by coupling the structural model and the aerodynamic system. The resulting reduced-order model is suitable for constant Mach, varying density analysis.

Keywords: ROM (Reduced-Order Model), aero elasticity, AGARD 445.6 wing.

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Authors: S. Panda, J. S. Yadav, N. P. Patidar, C. Ardil

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Recently, genetic algorithms (GA) and particle swarm optimization (PSO) technique have attracted considerable attention among various modern heuristic optimization techniques. The GA has been popular in academia and the industry mainly because of its intuitiveness, ease of implementation, and the ability to effectively solve highly non-linear, mixed integer optimization problems that are typical of complex engineering systems. PSO technique is a relatively recent heuristic search method whose mechanics are inspired by the swarming or collaborative behavior of biological populations. In this paper both PSO and GA optimization are employed for finding stable reduced order models of single-input- single-output large-scale linear systems. Both the techniques guarantee stability of reduced order model if the original high order model is stable. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example from literature and the results are compared with recently published conventional model reduction technique.

Keywords: Genetic Algorithm, Particle Swarm Optimization, Order Reduction, Stability, Transfer Function, Integral Squared Error.

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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: Benshi Zhu

Abstract:

In this paper, the existence of multiple positive solutions for a class of third-order three-point discrete boundary value problem is studied by applying algebraic topology method.

Keywords: Positive solutions, Discrete boundary value problem, Third-order, Three-point, Algebraic topology

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Authors: Li Feng

Abstract:

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated.With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. At last, we give an system which could bifurcate 10 limit circles.

Keywords: Three-order nilpotent critical point, center-focus problem, bifurcation of limit cycles, Quasi-Lyapunov constant.

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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: López-Gutiérrez R.M., Rodríguez-Orozco E., Cruz-Hernández C., Inzunza-González E., Posadas-Castillo C., García-Guerrero E.E., Cardoza-Avendaño L.

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In this paper, we use Generalized Hamiltonian systems approach to synchronize a modified sixth-order Chua's circuit, which generates hyperchaotic dynamics. Synchronization is obtained between the master and slave dynamics with the slave being given by an observer. We apply this approach to transmit private information (analog and binary), while the encoding remains potentially secure.

Keywords: Hyperchaos synchronization, sixth-order Chua's circuit, observers, simulation, secure communication.

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Authors: Ling Zhang, Feng Liu

Abstract:

A matrix is called a ray pattern matrix if its entries are either 0 or a ray in complex plane which originates from 0. A ray pattern A of order n is called spectrally arbitrary if the complex matrices in the ray pattern class of A give rise to all possible nth degree complex polynomial. Otherwise, it is said to be spectrally non-arbitrary ray pattern. We call that a spectrally arbitrary ray pattern A of order n is minimally spectrally arbitrary if any nonzero entry of A is replaced, then A is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.

Keywords: Spectrally arbitrary, Nilpotent matrix, Ray patterns, sign patterns.

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Authors: G. Parmar, S. Mukherjee, R. Prasad

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The authors present an algorithm for order reduction of linear time invariant dynamic systems using the combined advantages of the eigen spectrum analysis and the error minimization by particle swarm optimization technique. Pole centroid and system stiffness of both original and reduced order systems remain same in this method to determine the poles, whereas zeros are synthesized by minimizing the integral square error in between the transient responses of original and reduced order models using particle swarm optimization technique, pertaining to a unit step input. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. The algorithm is illustrated with the help of two numerical examples and the results are compared with the other existing techniques.

Keywords: Eigen spectrum, Integral square error, Orderreduction, Particle swarm optimization, Stability.

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Authors: Ramaswamy Palaniappan

Abstract:

In this paper, a second order autoregressive (AR) model is proposed to discriminate alcoholics using single trial gamma band Visual Evoked Potential (VEP) signals using 3 different classifiers: Simplified Fuzzy ARTMAP (SFA) neural network (NN), Multilayer-perceptron-backpropagation (MLP-BP) NN and Linear Discriminant (LD). Electroencephalogram (EEG) signals were recorded from alcoholic and control subjects during the presentation of visuals from Snodgrass and Vanderwart picture set. Single trial VEP signals were extracted from EEG signals using Elliptic filtering in the gamma band spectral range. A second order AR model was used as gamma band VEP exhibits pseudo-periodic behaviour and second order AR is optimal to represent this behaviour. This circumvents the requirement of having to use some criteria to choose the correct order. The averaged discrimination errors of 2.6%, 2.8% and 11.9% were given by LD, MLP-BP and SFA classifiers. The high LD discrimination results show the validity of the proposed method to discriminate between alcoholic subjects.

Keywords: Linear Discriminant, Neural Network, VisualEvoked Potential.

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Authors: Osama Yusuf Ababneh

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For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

Keywords: Third-order convergence, non-linear equations, root finding, iterative method.

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Authors: R. Fatehi, M.A. Fayazbakhsh, M.T. Manzari

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Discretization of spatial derivatives is an important issue in meshfree methods especially when the derivative terms contain non-linear coefficients. In this paper, various methods used for discretization of second-order spatial derivatives are investigated in the context of Smoothed Particle Hydrodynamics. Three popular forms (i.e. "double summation", "second-order kernel derivation", and "difference scheme") are studied using one-dimensional unsteady heat conduction equation. To assess these schemes, transient response to a step function initial condition is considered. Due to parabolic nature of the heat equation, one can expect smooth and monotone solutions. It is shown, however in this paper, that regardless of the type of kernel function used and the size of smoothing radius, the double summation discretization form leads to non-physical oscillations which persist in the solution. Also, results show that when a second-order kernel derivative is used, a high-order kernel function shall be employed in such a way that the distance of inflection point from origin in the kernel function be less than the nearest particle distance. Otherwise, solutions may exhibit oscillations near discontinuities unlike the "difference scheme" which unconditionally produces monotone results.

Keywords: Heat conduction, Meshfree methods, Smoothed ParticleHydrodynamics (SPH), Second-order derivatives.

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Authors: Malathi Balakrishnan, Gananathan M. Nadarajah, Saraswathy Vellasamy, Evelyn Gnanam William George

Abstract:

The purpose of the study is to explore how the fun game-learning approach enhances teacher trainers’ higher order thinking skills. Two-day fun filled fun game learning-approach was introduced to teacher trainers as a Continuous Professional Development Program (CPD). 26 teacher trainers participated in this Transformation of Teaching and Learning Fun Way Program, organized by Institute of Teacher Education Malaysia. Qualitative research technique was adopted as the researchers observed the participants’ higher order thinking skills developed during the program. Data were collected from observational checklist; interview transcriptions of four participants and participants’ reflection notes. All the data were later analyzed with NVivo data analysis process. The finding of this study presented five main themes, which are critical thinking, hands on activities, creating, application and use of technology. The studies showed that the teacher trainers’ higher order thinking skills were enhanced after the two-day CPD program. Therefore, Institute of Teacher Education will have more success using the fun way game-learning approach to develop higher order thinking skills among its teacher trainers who can implement these skills to their trainee teachers in future. This study also added knowledge to Constructivism learning theory, which will further highlight the prominence of the fun way learning approach to enhance higher order thinking skills.

Keywords: Constructivism, game-learning approach, higher order thinking skill, teacher trainer.

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Authors: Bhaba Priyo Das, Neville Watson, Yonghe Liu

Abstract:

In recent years Operational Transconductance Amplifier based high frequency integrated circuits, filters and systems have been widely investigated. The usefulness of OTAs over conventional OP-Amps in the design of both first order and second order active filters are well documented. This paper discusses some of the tunability issues using the Matlab/Simulink® software which are previously unreported for any commercial OTA. Using the simulation results two first order voltage controlled all pass filters with phase tuning capability are proposed.

Keywords: All pass filter, Operational Transconductance Amplifier, Simulation.

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Authors: Adnan Al-Smadi, Mahmoud Smadi

Abstract:

This paper presents an algorithm for reconstructing phase and magnitude responses of the impulse response when only the output data are available. The system is driven by a zero-mean independent identically distributed (i.i.d) non-Gaussian sequence that is not observed. The additive noise is assumed to be Gaussian. This is an important and essential problem in many practical applications of various science and engineering areas such as biomedical, seismic, and speech processing signals. The method is based on evaluating the bicepstrum of the third-order statistics of the observed output data. Simulations results are presented that demonstrate the performance of this method.

Keywords: Cepstrum, bicepstrum, third order statistics

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Authors: Souhir Ben Amor, Heni Boubaker, Lotfi Belkacem

Abstract:

This aims of this paper is to forecast the electricity spot prices. First, we focus on modeling the conditional mean of the series so we adopt a generalized fractional -factor Gegenbauer process (k-factor GARMA). Secondly, the residual from the -factor GARMA model has used as a proxy for the conditional variance; these residuals were predicted using two different approaches. In the first approach, a local linear wavelet neural network model (LLWNN) has developed to predict the conditional variance using the Back Propagation learning algorithms. In the second approach, the Gegenbauer generalized autoregressive conditional heteroscedasticity process (G-GARCH) has adopted, and the parameters of the k-factor GARMA-G-GARCH model has estimated using the wavelet methodology based on the discrete wavelet packet transform (DWPT) approach. The empirical results have shown that the k-factor GARMA-G-GARCH model outperform the hybrid k-factor GARMA-LLWNN model, and find it is more appropriate for forecasts.

Keywords: k-factor, GARMA, LLWNN, G-GARCH, electricity price, forecasting.

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Authors: Md. Armin Islam, Les Dallin, Mark Boland, W. J. Zhang

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This paper reports a study on the optimal magnetic design of a compact quadrupole electromagnet for the Canadian Light Source (CLS 2.0). The nature of the design is to determine a quadrupole with low relative higher order harmonics and better field quality. The design problem was formulated as an optimization model, in which the objective function is the higher order harmonics (multipole errors) and the variable to be optimized is the material distribution on the pole. The higher order harmonics arose in the quadrupole due to truncating the ideal hyperbola at a certain point to make the pole. In this project, the arisen harmonics have been optimized both transversely and longitudinally by adjusting material on the poles in a controlled way. For optimization, finite element analysis (FEA) has been conducted. A better higher order harmonics amplitudes and field quality have been achieved through the optimization. On the basis of the optimized magnetic design, electrical and cooling calculation has been performed for the magnet.

Keywords: Drift, electrical, and cooling calculation, integrated field, higher order harmonics (multipole errors), magnetic field gradient, quadrupole.

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Authors: Shengfeng Li, Rujing Wang

Abstract:

In this paper, we present two new one-step iterative methods based on Thiele-s continued fraction for solving nonlinear equations. By applying the truncated Thiele-s continued fraction twice, the iterative methods are obtained respectively. Analysis of convergence shows that the new methods are fourth-order convergent. Numerical tests verifying the theory are given and based on the methods, two new one-step iterations are developed.

Keywords: Iterative method, Fixed-point iteration, Thiele's continued fraction, Order of convergence.

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Authors: Zhenying Hong, Guangwei Yuan, Xuedong Fu, Shulin Yang

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In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spherical neutron transport equation by discrete ordinates method. The numerical results show that second-order time evolution scheme associated exponential method has some good properties. The time differential curve about neutron current is more smooth than that of exponential method and diamond difference and modified time discrete scheme.

Keywords: Exponential method, diamond difference, modified time discrete scheme, second-order time evolution scheme.

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Authors: Revaz Gvelesiani

Abstract:

The intrinsic contradictions of entrepreneurship development and self-development strategies complicate the task of reaching compliance between the state economic policy and the company entrepreneurship policy: on the one hand, there is a contradiction between the social and the competitive order within economic order policy and on the other hand, the contradiction exists between entrepreneurship strategy and entrepreneurship culture within entrepreneurship policy.

Keywords: Economic Order Policy, Entrepreneurship, Development Contradictions, Self-Development Contradictions.

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

Keywords: Stochastic integrals, single–server queue model, catastrophes, busy period.

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Authors: Yanling Zhu

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In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained.

Keywords: Neutral functional differential equation, higher order, periodic solution, coincidence degree theory.

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Authors: S. Bourennane, A. Bendjama

Abstract:

This paper deals with the localization of the wideband sources. We develop a new approach for estimating the wide band sources parameters. This method is based on the high order statistics of the recorded data in order to eliminate the Gaussian components from the signals received on the various hydrophones.In fact the noise of sea bottom is regarded as being Gaussian. Thanks to the coherent signal subspace algorithm based on the cumulant matrix of the received data instead of the cross-spectral matrix the wideband correlated sources are perfectly located in the very noisy environment. We demonstrate the performance of the proposed algorithm on the real data recorded during an underwater acoustics experiments.

Keywords: Higher-order statistics, high resolution array processing techniques, localization of acoustics sources, wide band sources.

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Authors: J.S.C. Prentice

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The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe the propagation of local errors in this method, and show that the global order of RK5GL3 is expected to be six, one better than the underlying Runge- Kutta method.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, order, local error, global error.

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Authors: S. N. Deepa, G. Sugumaran

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This paper proposes a new version of the Particle Swarm Optimization (PSO) namely, Modified PSO (MPSO) for model order formulation of Single Input Single Output (SISO) linear time invariant continuous systems. In the General PSO, the movement of a particle is governed by three behaviors namely inertia, cognitive and social. The cognitive behavior helps the particle to remember its previous visited best position. In Modified PSO technique split the cognitive behavior into two sections like previous visited best position and also previous visited worst position. This modification helps the particle to search the target very effectively. MPSO approach is proposed to formulate the higher order model. The method based on the minimization of error between the transient responses of original higher order model and the reduced order model pertaining to the unit step input. The results obtained are compared with the earlier techniques utilized, to validate its ease of computation. The proposed method is illustrated through numerical example from literature.

Keywords: Continuous System, Model Order Formulation, Modified Particle Swarm Optimization, Single Input Single Output, Transfer Function Approach

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Authors: Pham Luu Trung Duong, Moonyong Lee

Abstract:

To increase precision and reliability of automatic control systems, we have to take into account of random factors affecting the control system. Thus, operational matrix technique is used for statistical analysis of first order plus time delay system with uniform random parameter. Examples with deterministic and stochastic disturbance are considered to demonstrate the validity of the method. Comparison with Monte Carlo method is made to show the computational effectiveness of the method.

Keywords: First order plus dead-time, Operational matrix, Statistical analysis, Walsh function.

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Authors: P. W. C. Prasad, A. Assi, M. Raseen, A. Harb

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The goal of this work is to describe a new algorithm for finding the optimal variable order, number of nodes for any order and other ROBDD parameters, based on a tabular method. The tabular method makes use of a pre-built backend database table that stores the ROBDD size for selected combinations of min-terms. The user uses the backend table and the proposed algorithm to find the necessary ROBDD parameters, such as best variable order, number of nodes etc. Experimental results on benchmarks are given for this technique.

Keywords: Tabular Method, Binary Decision Diagram, BDD Manipulation, Boolean Function.

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Authors: Roza Dastres, Mohsen Soori

Abstract:

Networks are vulnerable devices due to their basic feature of facilitating remote access and data communication. The information in the networks needs to be kept secured and safe in order to provide an effective communication and sharing device in the web of data. Due to challenges and threats of the data in networks, the network security is one of the most important considerations in information technology infrastructures. As a result, the security measures are considered in the network in order to decrease the probability of accessing the secured data by the hackers. The purpose of network security is to protect the network and its components from unauthorized access and abuse in order to provide a safe and secured communication device for the users. In the present research work a review in recent development of network threats and security measures is presented and future research works are also suggested. Different attacks to the networks and security measured against them are discussed in order to increase security in the web of data. So, new ideas in the network security systems can be presented by analyzing the published papers in order to move forward the research field.

Keywords: Network threats, network security, security measures, firewalls.

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Authors: P. Ramana , K. Alice Mary, M. Surya Kalavathi, M. Phani Kumar

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This paper discusses two observers, which are used for the estimation of parameters of PMSM. Former one, reduced order observer, which is used to estimate the inaccessible parameters of PMSM. Later one, full order observer, which is used to estimate all the parameters of PMSM even though some of the parameters are directly available for measurement, so as to meet with the insensitivity to the parameter variation. However, the state space model contains some nonlinear terms i.e. the product of different state variables. The asymptotic state observer, which approximately reconstructs the state vector for linear systems without uncertainties, was presented by Luenberger. In this work, a modified form of such an observer is used by including a non-linear term involving the speed. So, both the observers are designed in the framework of nonlinear control; their stability and rate of convergence is discussed.

Keywords: Permanent magnet synchronous motor, Mathematicalmodelling, Rotor reference frame, parameter estimation, Luenbergerobserver, reduced order observer, full order observer

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Authors: Luis A. Morales Rosales, Saul E. Pomares Hernandez, Gustavo Rodriguez Gomez

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Synchronous cooperative systems (SCS) bring together users that are geographically distributed and connected through a network to carry out a task. Examples of SCS include Tele- Immersion and Tele-Conferences. In SCS, the coordination is the core of the system, and it has been defined as the act of managing interdependencies between activities performed to achieve a goal. Some of the main problems that SCS present deal with the management of constraints between simultaneous activities and the execution ordering of these activities. In order to resolve these problems, orderings based on Lamport-s happened-before relation have been used, namely, causal, Δ-causal, and causal-total orderings. They mainly differ in the degree of asynchronous execution allowed. One of the most important orderings is the causal order, which establishes that the events must be seen in the cause-effect order as they occur in the system. In this paper we show that for certain SCS (e.g. videoconferences, tele-immersion) where some degradation of the system is allowed, ensuring the causal order is still rigid, which can render negative affects to the system. In this paper, we illustrate how a more relaxed ordering, which we call Fuzzy Causal Order (FCO), is useful for such kind of systems by allowing a more asynchronous execution than the causal order. The benefit of the FCO is illustrated by applying it to a particular scenario of intermedia synchronization of an audio-conference system.

Keywords: Event ordering, fuzzy causal ordering, happenedbefore relation and cooperative systems.

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