Search results for: nonlinear fitness functions

Authors: Manoj Singh, Mumtaz Ahmad Khan, Abdul Hakim Khan

Abstract:

The object of the present paper is to investigate several general families of bilinear and bilateral generating functions with different argument for the Gauss’ hypergeometric polynomials.

Keywords: Appell’s functions, Gauss hypergeometric functions, Heat polynomials, Kampe’ de Fe’riet function, Laguerre polynomials, Lauricella’s function, Saran’s functions.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

The objective of this study is to propose an observer design for nonlinear systems by using an augmented linear system derived by application of a formal linearization method. A given nonlinear differential equation is linearized by the formal linearization method which is based on Taylor expansion considering up to the higher order terms, and a measurement equation is transformed into an augmented linear one. To this augmented dimensional linear system, a linear estimation theory is applied and a nonlinear observer is derived. As an application of this method, an estimation problem of transient state of electric power systems is studied, and its numerical experiments indicate that this observer design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, augmented linear system, nonlinear observer, formal linearization, electric power system.

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Authors: Ping He

Abstract:

This paper addresses the problem of the partial state feedback stabilization of a class of nonlinear systems. In order to stabilization this class systems, the especial place of this paper is to reverse designing the state feedback control law from the method of judging system stability with the center manifold theory. First of all, the center manifold theory is applied to discuss the stabilization sufficient condition and design the stabilizing state control laws for a class of nonlinear. Secondly, the problem of partial stabilization for a class of plane nonlinear system is discuss using the lyapunov second method and the center manifold theory. Thirdly, we investigate specially the problem of the stabilization for a class of homogenous plane nonlinear systems, a class of nonlinear with dual-zero eigenvalues and a class of nonlinear with zero-center using the method of lyapunov function with homogenous derivative, specifically. At the end of this paper, some examples and simulation results are given show that the approach of this paper to this class of nonlinear system is effective and convenient.

Keywords: Partial stabilization, Nonlinear critical systems, Centermanifold theory, Lyapunov function, System reduction.

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Authors: Aras Adhami Mirhoseini, Mohammad J. Yazdanpanah

Abstract:

In this paper, we consider nested sliding mode control of SISO nonlinear systems, perturbed by bounded matched and unmatched uncertainties. The systems are assumed to be in strict-feedback form. A step wise procedure is introduced to obtain the controller. In each step, a continuous sliding mode controller is designed as virtual control law. Then the next step sliding surface is defined by using this virtual controller. These sliding surfaces are selected as nonlinear static functions of the system states. Finally in the last step, smooth static state feedback control law is determined such that the output reaches the desired set-point while the system is forced arbitrary close to the intersection of sliding surfaces and the states remain bounded.

Keywords: Sliding mode control, Strict-feedback form, Unmatched uncertainty, output regulation.

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Authors: Jaipong Kasemsuwan

Abstract:

A numerical solution of the initial boundary value problem of the suspended string vibrating equation with the particular nonlinear damping term based on the finite difference scheme is presented in this paper. The investigation of how the second and third power terms of the nonlinear term affect the vibration characteristic. We compare the vibration amplitude as a result of the third power nonlinear damping with the second power obtained from previous report provided that the same initial shape and initial velocities are assumed. The comparison results show that the vibration amplitude is inversely proportional to the coefficient of the damping term for the third power nonlinear damping case, while the vibration amplitude is proportional to the coefficient of the damping term in the second power nonlinear damping case.

Keywords: Finite-difference method, the nonlinear damped equation, the numerical simulation, the suspended string equation

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Authors: Boo-Sung Koh, Seung-Eock Kim

Abstract:

In this paper, a direct design using a nonlinear inelastic analysis is suggested. Also, this paper compares the load carrying capacity obtained by a nonlinear inelastic analysis with experiment results to verify the accuracy of the results. The allowable stress design results of a railroad through a plate girder bridge and the safety factor of the nonlinear inelastic analysis were compared to examine the safety performance. As a result, the load safety factor for the nonlinear inelastic analysis was twice as high as the required safety factor under the allowable stress design standard specified in the civil engineering structure design standards for urban magnetic levitation railways, which further verified the advantages of the proposed direct design method.

Keywords: Direct design, nonlinear inelastic analysis, residual stress, initial geometric imperfection.

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Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

Abstract:

The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f^-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: Analytic functions, bi-univalent functions, Hohlov operator, subordination.

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Authors: Zongqing Lu

Abstract:

It has proved that nonlinear diffusion and bilateral filtering (BF) have a closed connection. Early effort and contribution are to find a generalized representation to link them by using adaptive filtering. In this paper a new further relationship between nonlinear diffusion and bilateral filtering is explored which pays more attention to numerical calculus. We give a fresh idea that bilateral filtering can be accelerated by multigrid (MG) scheme which likes the nonlinear diffusion, and show that a bilateral filtering process with large kernel size can be approximated by a nonlinear diffusion process based on full multigrid (FMG) scheme.

Keywords: Bilateral filter, multigrid

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Authors: C. Pislaru, A. Shebani

Abstract:

This paper uses the radial basis function neural network (RBFNN) for system identification of nonlinear systems. Five nonlinear systems are used to examine the activity of RBFNN in system modeling of nonlinear systems; the five nonlinear systems are dual tank system, single tank system, DC motor system, and two academic models. The feed forward method is considered in this work for modelling the non-linear dynamic models, where the KMeans clustering algorithm used in this paper to select the centers of radial basis function network, because it is reliable, offers fast convergence and can handle large data sets. The least mean square method is used to adjust the weights to the output layer, and Euclidean distance method used to measure the width of the Gaussian function.

Keywords: System identification, Nonlinear system, Neural networks, RBF neural network.

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Authors: Zixuan Xu, Yichun Lou, Yang Song, Zihuai Lin

Abstract:

MediaPipe is an open-source machine learning computer vision framework that can be ported into a multi-platform environment, which makes it easier to use it to recognize human activity. Based on this framework, many human recognition systems have been created, but the fundamental issue is the recognition of human behavior and posture. In this paper, two methods are proposed to recognize human gestures based on MediaPipe, the first one uses the Adaptive Boosting algorithm to recognize a series of fitness gestures, and the second one uses the Fast Dynamic Time Warping algorithm to recognize 413 continuous fitness actions. These two methods are also applicable to any human posture movement recognition.

Keywords: Computer Vision, MediaPipe, Adaptive Boosting, Fast Dynamic Time Warping.

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Authors: Taher Lotfi , Parisa Bakhtiari , Katayoun Mahdiani , Mehdi Salimi

Abstract:

In this paper, verified extension of the Ostrowski method which calculates the enclosure solutions of a given nonlinear equation is introduced. Also, error analysis and convergence will be discussed. Some implemented examples with INTLAB are also included to illustrate the validity and applicability of the scheme.

Keywords: Iinterval analysis, nonlinear equations, Ostrowski method.

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Authors: A. Borji, M. Hamidi

Abstract:

A new method for color image segmentation using fuzzy logic is proposed in this paper. Our aim here is to automatically produce a fuzzy system for color classification and image segmentation with least number of rules and minimum error rate. Particle swarm optimization is a sub class of evolutionary algorithms that has been inspired from social behavior of fishes, bees, birds, etc, that live together in colonies. We use comprehensive learning particle swarm optimization (CLPSO) technique to find optimal fuzzy rules and membership functions because it discourages premature convergence. Here each particle of the swarm codes a set of fuzzy rules. During evolution, a population member tries to maximize a fitness criterion which is here high classification rate and small number of rules. Finally, particle with the highest fitness value is selected as the best set of fuzzy rules for image segmentation. Our results, using this method for soccer field image segmentation in Robocop contests shows 89% performance. Less computational load is needed when using this method compared with other methods like ANFIS, because it generates a smaller number of fuzzy rules. Large train dataset and its variety, makes the proposed method invariant to illumination noise

Keywords: Comprehensive learning Particle Swarmoptimization, fuzzy classification.

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Authors: Javad Abdalkhani

Abstract:

Convergence of power series solutions for a class of non-linear Abel type equations, including an equation that arises in nonlinear cooling of semi-infinite rods, is very slow inside their small radius of convergence. Beyond that the corresponding power series are wildly divergent. Implementation of nonlinear sequence transformation allow effortless evaluation of these power series on very large intervals..

Keywords: Nonlinear transformation, Abel Volterra Equations, Mathematica

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Authors: Jafar Biazar, Behzad Ghanbari

Abstract:

In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

Keywords: System of nonlinear equations.

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Authors: Nizami Mustafa, C. Ardil

Abstract:

In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

Keywords: Approximate solution, Fixed-point principle, Nonlinear singular integral equations, Vekua integral operator

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Authors: B. S. Raghavendra, D. Narayana Dutt

Abstract:

Many recent electrophysiological studies have revealed the importance of investigating meditation state in order to achieve an increased understanding of autonomous control of cardiovascular functions. In this paper, we characterize heart rate variability (HRV) time series acquired during meditation using nonlinear dynamical parameters. We have computed minimum embedding dimension (MED), correlation dimension (CD), largest Lyapunov exponent (LLE), and nonlinearity scores (NLS) from HRV time series of eight Chi and four Kundalini meditation practitioners. The pre-meditation state has been used as a baseline (control) state to compare the estimated parameters. The chaotic nature of HRV during both pre-meditation and meditation is confirmed by MED. The meditation state showed a significant decrease in the value of CD and increase in the value of LLE of HRV, in comparison with premeditation state, indicating a less complex and less predictable nature of HRV. In addition, it was shown that the HRV of meditation state is having highest NLS than pre-meditation state. The study indicated highly nonlinear dynamic nature of cardiac states as revealed by HRV during meditation state, rather considering it as a quiescent state.

Keywords: Correlation dimension, Embedding dimension, Heartrate variability, Largest Lyapunov exponent, Meditation, Nonlinearity score.

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Authors: Janak Raj Sharma, Rajni Sharma

Abstract:

Based on Traub-s methods for solving nonlinear equation f(x) = 0, we develop two families of third-order methods for solving system of nonlinear equations F(x) = 0. The families include well-known existing methods as special cases. The stability is corroborated by numerical results. Comparison with well-known methods shows that the present methods are robust. These higher order methods may be very useful in the numerical applications requiring high precision in their computations because these methods yield a clear reduction in number of iterations.

Keywords: Nonlinear equations and systems, Newton's method, fixed point iteration, order of convergence.

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Authors: Wataru Nakamura, Tomoaki Hashimoto, Liang-Kuang Chen

Abstract:

This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: State estimation, control systems, observer systems, unscented Kalman filter, nonlinear vehicle dynamics.

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Authors: V.P.Subramanyam Rallabandi, S.K.Sett

Abstract:

An unsupervised classification algorithm is derived by modeling observed data as a mixture of several mutually exclusive classes that are each described by linear combinations of independent non-Gaussian densities. The algorithm estimates the data density in each class by using parametric nonlinear functions that fit to the non-Gaussian structure of the data. This improves classification accuracy compared with standard Gaussian mixture models. When applied to textures, the algorithm can learn basis functions for images that capture the statistically significant structure intrinsic in the images. We apply this technique to the problem of unsupervised texture classification and segmentation.

Keywords: Gaussian Mixture Model, Independent Component Analysis, Segmentation, Unsupervised Classification.

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Authors: T. Atan, T. Ayyıldız, P. Akyol

Abstract:

The purpose of this study was to examine and compare physical fitness values of students engaged in different team sport branches Totally 60 female, and 60 male athletes, that 20 athletes in each branch which are volleyball, basketball and football participated the study as a volunteer. The mean ages of female and male athletes were 21.20 ±1.87 and 21.61 ± 1.61 respectively. Age, height, body weight, body mass index, flexibility, body fat percentage, 30m sprint, maximum oxygen consumption capacity (MaxVO2) and drop jump values were measured. As a result of measurements, significant differences were found in height, weight, MaxVO2, shuttle run speed between different sports branches in female athletes. In male athletes, height, body weight, flexibility, 30m split speed and drop jump values were found significantly different between sports branches. As a conclusion and as a literature, it can be said that structure of body has to be appropriate with the engaged sports branch. Physical fitness values that required the sports branches can be expressed clearly by increasing the number of subjects.

Keywords: Volleyball, basketball, football, athletes, physical fitness.

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Authors: M. R. Aghaebrahimi, S. H. Zahiri, M. Amiri

Abstract:

The necessity of solving multi dimensional complicated scientific problems beside the necessity of several objective functions optimization are the most motive reason of born of artificial intelligence and heuristic methods. In this paper, we introduce a new method for multiobjective optimization based on learning automata. In the proposed method, search space divides into separate hyper-cubes and each cube is considered as an action. After gathering of all objective functions with separate weights, the cumulative function is considered as the fitness function. By the application of all the cubes to the cumulative function, we calculate the amount of amplification of each action and the algorithm continues its way to find the best solutions. In this Method, a lateral memory is used to gather the significant points of each iteration of the algorithm. Finally, by considering the domination factor, pareto front is estimated. Results of several experiments show the effectiveness of this method in comparison with genetic algorithm based method.

Keywords: Function optimization, Multiobjective optimization, Learning automata.

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Authors: Ε. Giovanis

Abstract:

In this paper we propose and examine an Adaptive Neuro-Fuzzy Inference System (ANFIS) in Smoothing Transition Autoregressive (STAR) modeling. Because STAR models follow fuzzy logic approach, in the non-linear part fuzzy rules can be incorporated or other training or computational methods can be applied as the error backpropagation algorithm instead to nonlinear squares. Furthermore, additional fuzzy membership functions can be examined, beside the logistic and exponential, like the triangle, Gaussian and Generalized Bell functions among others. We examine two macroeconomic variables of US economy, the inflation rate and the 6-monthly treasury bills interest rates.

Keywords: Forecasting, Neuro-Fuzzy, Smoothing transition, Time-series

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Authors: Md. Alal Hosen

Abstract:

In this paper, a modified harmonic balance method based an analytical technique has been developed to determine higher-order approximate periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x^1/3. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. In this article, different parameters of the same nonlinear problems are found, for which the power series produces desired results even for the large oscillation. We find a modified harmonic balance method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Besides these, a suitable truncation formula is found in which the solution measures better results than existing solutions. The method is mainly illustrated by the x^1/3 force nonlinear oscillator but it is also useful for many other nonlinear problems.

Keywords: Approximate solutions, Harmonic balance method, Nonlinear oscillator, Perturbation.

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Authors: Ö. Tolga Altınöz

Abstract:

The adaptive backstepping controller for inverted pendulum is designed by using the general motion control model. Backstepping is a novel nonlinear control technique based on the Lyapunov design approach, used when higher derivatives of parameter estimation appear. For easy parameter adaptation, the mathematical model of the inverted pendulum converted into the motion control model. This conversion is performed by taking functions of unknown parameters and dynamics of the system. By using motion control model equations, inverted pendulum is simulated without any information about not only parameters but also measurable dynamics. Also these results are compare with the adaptive backstepping controller which extended with integral action that given from [1].

Keywords: Adaptive backstepping, inverted pendulum, nonlinear adaptive control.

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Authors: A. Keshavarz, Z. Roosta

Abstract:

In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: Paraxial group transformation, nonlocal nonlinear media, Cos-Gaussian beam, ABCD law.

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Authors: Swarniv Chandra, Basudev Ghosh

Abstract:

Nonlinear solitary structures of electron plasma waves have been investigated by using nonlinear quantum fluid equations for electrons with an arbitrary temperature. It is shown that the electron degeneracy parameter has significant effects on the linear and nonlinear properties of electron plasma waves. Depending on its value both compressive and rarefactive solitons can be excited in the model plasma under consideration.

Keywords: Electron Plasma Waves, Finite Temperature Model, Modulational Instability, Quantum Plasma, Solitary structure

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Authors: Hesam Mahzoon

Abstract:

By using the two existing operators, we have defined an operator, which is an extension for them. In this paper, first the operator is introduced. Then, using this operator, the subclasses of multivalent functions are defined. These subclasses of multivalent functions are utilized in order to obtain coefficient inequalities, extreme points, and integral means inequalities for functions belonging to these classes.

Keywords: Coefficient inequalities, extreme points, integral means, multivalent functions, Al-Oboudi operator, and Sãlãgean operator.

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Authors: Rafat Alshorman, Safwan Al-Shara', I. Obeidat

Abstract:

Most real world systems express themselves formally as a set of nonlinear algebraic equations. As applications grow, the size and complexity of these equations also increase. In this work, we highlight the key concepts in using the homotopy analysis method as a methodology used to construct efficient iteration formulas for nonlinear equations solving. The proposed method is experimentally characterized according to a set of determined parameters which affect the systems. The experimental results show the potential and limitations of the new method and imply directions for future work.

Keywords: Nonlinear Algebraic Equations, Iterative Methods, Homotopy Analysis Method.

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Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid.

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Authors: Ruediger Schmidt, Thang Duy Vu

Abstract:

Two geometrically nonlinear plate theories, based either on first- or third-order transverse shear deformation theory are used for finite element modeling and simulation of the transient response of smart structures incorporating piezoelectric layers. In particular the time histories of nonlinear vibrations and sensor voltage output of a thin beam with a piezoelectric patch bonded to the surface due to an applied step force are studied.

Keywords: Nonlinear vibrations, piezoelectric patches, sensor voltage output, smart structures.

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