Search results for: Linear co-positive Lyapunov functions

Authors: E. Menga, S. Hernandez

Abstract:

Finite Element Models (FEMs) are widely used in order to study and predict the dynamic properties of structures and usually, the prediction can be obtained with much more accuracy in the case of a single component than in the case of assemblies. Especially for structural dynamics studies, in the low and middle frequency range, most complex FEMs can be seen as assemblies made by linear components joined together at interfaces. From a modelling and computational point of view, these types of joints can be seen as localized sources of stiffness and damping and can be modelled as lumped spring/damper elements, most of time, characterized by nonlinear constitutive laws. On the other side, most of FE programs are able to run nonlinear analysis in time-domain. They treat the whole structure as nonlinear, even if there is one nonlinear degree of freedom (DOF) out of thousands of linear ones, making the analysis unnecessarily expensive from a computational point of view. In this work, a methodology in order to obtain the nonlinear frequency response of structures, whose nonlinearities can be considered as localized sources, is presented. The work extends the well-known Structural Dynamic Modification Method (SDMM) to a nonlinear set of modifications, and allows getting the Nonlinear Frequency Response Functions (NLFRFs), through an ‘updating’ process of the Linear Frequency Response Functions (LFRFs). A brief summary of the analytical concepts is given, starting from the linear formulation and understanding what the implications of the nonlinear one, are. The response of the system is formulated in both: time and frequency domain. First the Modal Database is extracted and the linear response is calculated. Secondly the nonlinear response is obtained thru the NL SDMM, by updating the underlying linear behavior of the system. The methodology, implemented in MATLAB, has been successfully applied to estimate the nonlinear frequency response of two systems. The first one is a two DOFs spring-mass-damper system, and the second example takes into account a full aircraft FE Model. In spite of the different levels of complexity, both examples show the reliability and effectiveness of the method. The results highlight a feasible and robust procedure, which allows a quick estimation of the effect of localized nonlinearities on the dynamic behavior. The method is particularly powerful when most of the FE Model can be considered as acting linearly and the nonlinear behavior is restricted to few degrees of freedom. The procedure is very attractive from a computational point of view because the FEM needs to be run just once, which allows faster nonlinear sensitivity analysis and easier implementation of optimization procedures for the calibration of nonlinear models.

Keywords: Frequency response, nonlinear dynamics, structural dynamic modification, softening effect, rubber.

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Authors: Dursun Aydın, Bilgin Senel

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In this paper, the sum of squares in linear regression is reduced to sum of squares in semi-parametric regression. We indicated that different sums of squares in the linear regression are similar to various deviance statements in semi-parametric regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the semi-parametric regression model. Then, it is made an application in order to support the theory of the linear regression and semi-parametric regression. In this way, study is supported with a simulated data example.

Keywords: Semi-parametric regression, Penalized LeastSquares, Residuals, Deviance, Smoothing Spline.

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Authors: Mohammed A. Abutheraa, David Lester

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We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.

Keywords: Approximation Theory, Chebyshev Polynomial, Computable Functions, Computable Real Arithmetic, Integration, Numerical Analysis.

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Authors: Nisha Budhwar, Sunita Daniel

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In this paper, we analyse the stability of the SEIR model of malaria with infective immigrants which was recently formulated by the authors. The model consists of an SEIR model for the human population and SI Model for the mosquitoes. Susceptible humans become infected after they are bitten by infectious mosquitoes and move on to the Exposed, Infected and Recovered classes respectively. The susceptible mosquito becomes infected after biting an infected person and remains infected till death. We calculate the reproduction number R0 using the next generation method and then discuss about the stability of the equilibrium points. We use the Lyapunov function to show the global stability of the equilibrium points.

Keywords: Susceptible, exposed, infective, recovered, infective immigrants, reproduction number, Lyapunov function, equilibrium points, global stability.

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Authors: Fituri H Belgassem, Abdulbasit Nigrat, Seddeeq Ghrari

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In this paper, the construction of fast algorithms for the computation of Periodic Walsh Piecewise-Linear PWL transform and the Periodic Haar Piecewise-Linear PHL transform will be presented. Algorithms for the computation of the inverse transforms are also proposed. The matrix equation of the PWL and PHL transforms are introduced. Comparison of the computational requirements for the periodic piecewise-linear transforms and other orthogonal transforms shows that the periodic piecewise-linear transforms require less number of operations than some orthogonal transforms such as the Fourier, Walsh and the Discrete Cosine transforms.

Keywords: Piece wise linear transforms, Fast transforms, Fast algorithms.

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Authors: Chia-Hung Lin, Mei-Sung Kang, Cong-Hui Huang, Chao-Lin Kuo

Abstract:

This paper proposes fractal patterns for power quality (PQ) detection using color relational analysis (CRA) based classifier. Iterated function system (IFS) uses the non-linear interpolation in the map and uses similarity maps to construct various fractal patterns of power quality disturbances, including harmonics, voltage sag, voltage swell, voltage sag involving harmonics, voltage swell involving harmonics, and voltage interruption. The non-linear interpolation functions (NIFs) with fractal dimension (FD) make fractal patterns more distinguishing between normal and abnormal voltage signals. The classifier based on CRA discriminates the disturbance events in a power system. Compared with the wavelet neural networks, the test results will show accurate discrimination, good robustness, and faster processing time for detecting disturbing events.

Keywords: Power Quality (PQ), Color Relational Analysis(CRA), Iterated Function System (IFS), Non-linear InterpolationFunction (NIF), Fractal Dimension (FD).

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Authors: Seiichi Gohshi, Hiroyuki Sekiguchi, Yoshiyasu Shimizu, Takeshi Ikenaga

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Super resolution (SR) technologies are now being applied to video to improve resolution. Some TV sets are now equipped with SR functions. However, it is not known if super resolution image reconstruction (SRR) for TV really works or not. Super resolution with non-linear signal processing (SRNL) has recently been proposed. SRR and SRNL are the only methods for processing video signals in real time. The results from subjective assessments of SSR and SRNL are described in this paper. SRR video was produced in simulations with quarter precision motion vectors and 100 iterations. These are ideal conditions for SRR. We found that the image quality of SRNL is better than that of SRR even though SRR was processed under ideal conditions.

Keywords: Super Resolution Image Reconstruction, Super Resolution with Non-Linear Signal Processing, Subjective Assessment, Image Quality

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, Semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions

Keywords: Integro-differential equations, Quartic B-spline wavelet, Operational matrices.

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Authors: Mehdi Tatari

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Finding the interpolation function of a given set of nodes is an important problem in scientific computing. In this work a kind of localization is introduced using the radial basis functions which finds a sufficiently smooth solution without consuming large amount of time and computer memory. Some examples will be presented to show the efficiency of the new method.

Keywords: Radial basis functions, local interpolation method, closed form solution.

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Authors: G. C. Mahata, A. Goswami

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This paper deals with infinite time horizon fuzzy Economic Order Quantity (EOQ) models for deteriorating items with  stock dependent demand rate and nonlinear holding costs by taking deterioration rate θ0 as a triangular fuzzy number  (θ0 −δ 1, θ0, θ0 +δ 2), where 1 2 0 0 <δ ,δ <θ are fixed real numbers. The traditional parameters such as unit cost and ordering  cost have been kept constant but holding cost is considered to vary. Two possibilities of variations in the holding cost function namely, a non-linear function of the length of time for which the item is held in stock and a non-linear function of the amount of on-hand inventory have been used in the models. The approximate optimal solution for the fuzzy cost functions in both these cases have been obtained and the effect of non-linearity in holding costs is studied with the help of a numerical example.

Keywords: Inventory Model, Deterioration, Holding Cost, Fuzzy Total Cost, Extension Principle.

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Authors: Yuichi Masukake, Yoshihisa Ishida

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In this paper, we proposed a method to design a model-following adaptive controller for linear/nonlinear plants. Radial basis function neural networks (RBF-NNs), which are known for their stable learning capability and fast training, are used to identify linear/nonlinear plants. Simulation results show that the proposed method is effective in controlling both linear and nonlinear plants with disturbance in the plant input.

Keywords: Linear/nonlinear plants, neural networks, radial basisfunction networks.

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Authors: C. Selvaraj, K. R. Karthikeyan

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We obtain several interesting subordination results for a class of analytic functions defined by using a generalized integral operator.

Keywords: Analytic functions, Hadamard product, Subordinating factor sequence

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Authors: Qasim M. Kriri

Abstract:

Few Saudi Arabia production companies face financial profit issues until this moment. This work presents a linear integer programming model that solves a production problem of a Saudi Food Company in Saudi Arabia. An optimal solution to the above-mentioned problem is a Linear Programming solution. In this regard, the main purpose of this project is to maximize profit. Linear Programming Technique has been used to derive the maximum profit from production of natural juice at Saudi Food Co. The operations of production of the company were formulated and optimal results are found out by using Lindo Software that employed Sensitivity Analysis and Parametric linear programming in order develop Linear Programming. In addition, the parameter values are increased, then the values of the objective function will be increased.

Keywords: Parameter linear programming, objective function, sensitivity analysis, optimize profit.

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Authors: Kenichiro Hida, Shin-Ichi Kuribayashi

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In a conventional network, most network devices, such as routers, are dedicated devices that do not have much variation in capacity. In recent years, a new concept of network functions virtualisation (NFV) has come into use. The intention is to implement a variety of network functions with software on general-purpose servers and this allows the network operator to select their capacities and locations without any constraints. This paper focuses on the allocation of NFV-based routing functions which are one of critical network functions, and presents the virtual routing function allocation algorithm that minimizes the total power consumption. In addition, this study presents the useful allocation policy of virtual routing functions, based on an evaluation with a ladder-shaped network model. This policy takes the ratio of the power consumption of a routing function to that of a circuit and traffic distribution between areas into consideration. Furthermore, the present paper shows that there are cases where the use of NFV-based routing functions makes it possible to reduce the total power consumption dramatically, in comparison to a conventional network, in which it is not economically viable to distribute small-capacity routing functions.

Keywords: Virtual routing function, NFV, resource allocation, minimum power consumption.

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Authors: Michela Lecca, Stefano Messelodi

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A new automatic system for the recognition and re¬construction of resealed and/or rotated partially occluded objects is presented. The objects to be recognized are described by 2D views and each view is occluded by several half-planes. The whole object views and their visible parts (linear cuts) are then stored in a database. To establish if a region R of an input image represents an object possibly occluded, the system generates a set of linear cuts of R and compare them with the elements in the database. Each linear cut of R is associated to the most similar database linear cut. R is recognized as an instance of the object 0 if the majority of the linear cuts of R are associated to a linear cut of views of 0. In the case of recognition, the system reconstructs the occluded part of R and determines the scale factor and the orientation in the image plane of the recognized object view. The system has been tested on two different datasets of objects, showing good performance both in terms of recognition and reconstruction accuracy.

Keywords: Occluded Object Recognition, Shape Reconstruction, Automatic Self-Adaptive Systems, Linear Cut.

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Authors: Sun Lim, Il-Kyun Jung

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This paper describes a newly designed decentralized nonlinear control strategy to control a robot manipulator. Based on the concept of the nonlinear state feedback theory and decentralized concept is developed to improve the drawbacks in previous works concerned with complicate intelligent control and low cost effective sensor. The control methodology is derived in the sense of Lyapunov theorem so that the stability of the control system is guaranteed. The decentralized algorithm does not require other joint angle and velocity information. Individual Joint controller is implemented using a digital processor with nearly actuator to make it possible to achieve good dynamics and modular. Computer simulation result has been conducted to validate the effectiveness of the proposed control scheme under the occurrence of possible uncertainties and different reference trajectories. The merit of the proposed control system is indicated in comparison with a classical control system.

Keywords: Robot manipulator control, nonlinear controller, Lyapunov based stability, Interconnection compensation.

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Authors: Maslina Darus, Khalifa Al-Shaqsi

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In this paper, a generalized derivatives operator n λ,βf introduced by the authors will be discussed. Some subordination and superordination results involving this operator for certain normalized analytic functions in the open unit disk will be investigated. Our results extend corresponding previously known results.

Keywords: Analytic functions, Univalent functions, Derivative operator, Differential subordination, Differential superordination.

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

Abstract:

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

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

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Authors: Kazuo Komatsu, Hitoshi Takata

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In this paper we consider a nonlinear control design for nonlinear systems by using two-stage formal linearization and twotype LQ controls. The ordinary LQ control is designed on almost linear region around the steady state point. On the other region, another control is derived as follows. This derivation is based on coordinate transformation twice with respect to linearization functions which are defined by polynomials. The linearized systems can be made up by using Taylor expansion considered up to the higher order. To the resulting formal linear system, the LQ control theory is applied to obtain another LQ control. Finally these two-type LQ controls are smoothly united to form a single nonlinear control. Numerical experiments indicate that this control show remarkable performances for a nonlinear system.

Keywords: Formal Linearization, LQ Control, Nonlinear Control, Taylor Expansion, Zero Function.

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Authors: Richard L. Summers

Abstract:

The advanced computational analysis of biological systems is becoming increasingly dependent upon an understanding of the information-theoretic structure of the materials, energy and interactive processes that comprise those systems. The stability and survival of these living systems is fundamentally contingent upon their ability to acquire and process the meaning of information concerning the physical state of its biological continuum (biocontinuum). The drive for adaptive system reconciliation of a divergence from steady state within this biocontinuum can be described by an information metric-based formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of Kullback-Leibler information minimization driven by survival replicator dynamics. If the mathematical expression of this process is the Lagrangian integrand for any change within the biocontinuum then it can also be considered as an action functional for the living system. In the direct method of Lyapunov, such a summarizing mathematical formulation of global system behavior based on the driving forces of energy currents and constraints within the system can serve as a platform for the analysis of stability. As the system evolves in time in response to biocontinuum perturbations, the summarizing function then conveys information about its overall stability. This stability information portends survival and therefore has absolute existential meaning for the living system. The first derivative of the Lyapunov energy information function will have a negative trajectory toward a system steady state if the driving force is dissipating. By contrast, system instability leading to system dissolution will have a positive trajectory. The direction and magnitude of the vector for the trajectory then serves as a quantifiable signature of the meaning associated with the living system’s stability information, homeostasis and survival potential.

Keywords: Semiotic meaning, Shannon information, Lyapunov, living systems.

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Authors: Mojtaba Hakimi-Moghaddam

Abstract:

Positive real and strictly positive real transfer functions are important concepts in the control theory. In this paper, the results of researches in these areas are summarized. Definitions together with their graphical interpretations are mentioned. The equivalent conditions in the frequency domain and state space representations are reviewed. Their equivalent electrical networks are explained. Also, a comprehensive discussion about a difference between behavior of real part of positive real and strictly positive real transfer functions in high frequencies is presented. Furthermore, several illustrative examples are given.

Keywords: Real rational transfer functions, positive realness property, strictly positive realness property, equivalent conditions.

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Authors: Guangbin Wang, Ning Zhang, Fuping Tan

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In this paper, we present parallel alternating two-stage methods for solving linear system Ax = b, where A is a monotone matrix or an H-matrix. And we give some convergence results of these methods for nonsingular linear system.

Keywords: Parallel, alternating two-stage, convergence, linear system.

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Authors: Mengzhuo Luo, Shouming Zhong

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This paper investigates the problem of exponential stability for a class of uncertain discrete-time stochastic neural network with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional, combining the stochastic stability theory, the free-weighting matrix method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Compared with some previous results, the new conditions obtain in this paper are less conservative. Finally, two numerical examples are exploited to show the usefulness of the results derived.

Keywords: Delay-dependent stability, Neural networks, Time varying delay, Linear matrix inequality (LMI).

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Authors: Siham G. Farag

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The main objective of this paper is to provide a new methodology for road safety assessment in Oman through the development of suitable accident prediction models. GLM technique with Poisson or NBR using SAS package was carried out to develop these models. The paper utilized the accidents data of 31 un-signalized T-intersections during three years. Five goodness-of-fit measures were used to assess the overall quality of the developed models. Two types of models were developed separately; the flow-based models including only traffic exposure functions, and the full models containing both exposure functions and other significant geometry and traffic variables. The results show that, traffic exposure functions produced much better fit to the accident data. The most effective geometric variables were major-road mean speed, minor-road 85th percentile speed, major-road lane width, distance to the nearest junction, and right-turn curb radius. The developed models can be used for intersection treatment or upgrading and specify the appropriate design parameters of T-intersections. Finally, the models presented in this thesis reflect the intersection conditions in Oman and could represent the typical conditions in several countries in the middle east area, especially gulf countries.

Keywords: Accidents Prediction Models (APMs), Generalized Linear Model (GLM), T-intersections, Oman.

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Authors: Dursun M., Koc F., Ozbay H.

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In this study, a double-sided linear switched reluctance motor (LSRM) drive was investigated as an alternative actuator for vertical linear transportation applications such as a linear elevator door, hospital and subway doors which move linearly and where accurate position control and rapid response is requested. A prototype sliding elevator door that is focused on a home elevator with LSRMs is designed. The motor has 6/4 poles, 3 phases, 8A, 24V, 250 W and 250 N pull forces. Air gap between rotor and translator poles of the designed motor and phase coil-s ideal inductance profile are obtained in compliance with the geometric dimensions. Operation and switching sections as motor and generator has been determined from the inductance profile.

Keywords: Linear switched reluctance motor, sliding door, elevator door, linear motor design.

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Authors: A. K. Al-Othman

Abstract:

This study presents a new approach based on Tanaka's fuzzy linear regression (FLP) algorithm to solve well-known power system economic load dispatch problem (ELD). Tanaka's fuzzy linear regression (FLP) formulation will be employed to compute the optimal solution of optimization problem after linearization. The unknowns are expressed as fuzzy numbers with a triangular membership function that has middle and spread value reflected on the unknowns. The proposed fuzzy model is formulated as a linear optimization problem, where the objective is to minimize the sum of the spread of the unknowns, subject to double inequality constraints. Linear programming technique is employed to obtain the middle and the symmetric spread for every unknown (power generation level). Simulation results of the proposed approach will be compared with those reported in literature.

Keywords: Economic Dispatch, Fuzzy Linear Regression (FLP)and Optimization.

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Authors: Hsuan-Ku Liu

Abstract:

A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.

Keywords: Fully fuzzy linear equations, iterative method, homotopy perturbation method, approximate solutions.

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Authors: Zixin Liu, Huawei Yang, Fangwei Chen

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This paper studies the mean square exponential synchronization problem of a class of stochastic neutral type chaotic neural networks with mixed delay. On the Basis of Lyapunov stability theory, some sufficient conditions ensuring the mean square exponential synchronization of two identical chaotic neural networks are obtained by using stochastic analysis and inequality technique. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. The feedback controller used in this paper is more general than those used in previous literatures. One simulation example is presented to demonstrate the effectiveness of the derived results.

Keywords: Exponential synchronization, stochastic analysis, chaotic neural networks, neutral type system.

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Authors: K. S. Subari, C. H. Shadle, A. Barney, R. I. Damper

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The acoustic and articulatory properties of fricative speech sounds are being studied using magnetic resonance imaging (MRI) and acoustic recordings from a single subject. Area functions were derived from a complete set of axial and coronal MR slices using two different methods: the Mermelstein technique and the Blum transform. Area functions derived from the two techniques were shown to differ significantly in some cases. Such differences will lead to different acoustic predictions and it is important to know which is the more accurate. The vocal tract acoustic transfer function (VTTF) was derived from these area functions for each fricative and compared with measured speech signals for the same fricative and same subject. The VTTFs for /f/ in two vowel contexts and the corresponding acoustic spectra are derived here; the Blum transform appears to show a better match between prediction and measurement than the Mermelstein technique.

Keywords: Area functions, fricatives, vocal tract transferfunction, MRI, speech.

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Authors: Abdolamir Nekoubin

Abstract:

One of Effective parameters on the performance of linear induction motors is number of poles which must be selected and optimized to increase power efficiency and motor performance significantly. In this paper a double-sided linear induction motor with different poles number by using MAXWELL3D software is designed and with finite element method is analyzed electromagnetically. Then for dynamic simulation, linear motor by using MATLAB software is simulated. The results show that by adding poles number, system time response is increased and motor after more time reaches to steady state. Also propulsion force of motor is increased.

Keywords: Linear motor, poles number, finite element method.

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