157 research outputs found

    Solution of Dual Fuzzy Equations Using a New Iterative Method

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    In this paper, a new hybrid scheme based on learning algorithm of fuzzy neural network (FNN) is offered in order to extract the approximate solution of fully fuzzy dual polynomials (FFDPs). Our FNN in this paper is a five-layer feed-back FNN with the identity activation function. The input-output relation of each unit is defined by the extension principle of Zadeh. The output from this neural network, which is also a fuzzy number, is numerically compared with the target output. The comparison of the feed-back FNN method with the feed-forward FNN method shows that the less error is observed in the feed-back FNN method. An example based on applications are given to illustrate the concepts, which are discussed in this paper

    Numerical Approximate Methods for Solving Linear and Nonlinear Integral Equations

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    Integral equation has been one of the essential tools for various area of applied mathematics. In this work, we employed different numerical methods for solving both linear and nonlinear Fredholm integral equations. A goal is to categorize the selected methods and assess their accuracy and efficiency. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study on numerical methods for solving integral equations. Integral equations can be viewed as equations which are results of transformation of points in a given vector spaces of integrable functions by the use of certain specific integral operators to points in the same space. If, in particular, one is concerned with function spaces spanned by polynomials for which the kernel of the corresponding transforming integral operator is separable being comprised of polynomial functions only, then several approximate methods of solution of integral equations can be developed. This work, specially, deals with the development of different wavelet methods for solving integral and intgro-differential equations. Wavelets theory is a relatively new and emerging area in mathematical research. It has been applied in a wide range of engineering disciplines; particularly, wavelets are very successfully used in signal analysis for waveform representations and segmentations, time frequency analysis, and fast algorithms for easy implementation. Wavelets permit the accurate representation of a variety of functions and operators. Moreover, wavelets establish a connection with fast numerical algorithms. Wavelets can be separated into two distinct types, orthogonal and semi-orthogonal. The preliminary concept of integral equations and wavelets are first presented in Chapter 1. Classification of integral equations, construction of wavelets and multi-resolution analysis (MRA) have been briefly discussed and provided in this chapter. In Chapter 2, different wavelet methods are constructed and function approximation by these methods with convergence analysis have been presented. In Chapter 3, linear semi-orthogonal compactly supported B-spline wavelets together with their dual wavelets have been applied to approximate the solutions of Fredholm integral equations (both linear and nonlinear) of the second kind and their systems. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. Convergence analysis of B-spline method has been discussed in this chapter. Again, in Chapter 4, system of nonlinear Fredholm integral equations have been solved by using hybrid Legendre Block-Pulse functions and xiii Bernstein collocation method. In Chapter 5, two practical problems arising from chemical phenomenon, have been modeled as Fredholm- Hammerstein integral equations and solved numerically by different numerical techniques. First, COSMO-RS model has been solved by Bernstein collocation method, Haar wavelet method and Sinc collocation method. Second, Hammerstein integral equation arising from chemical reactor theory has been solved by B-spline wavelet method. Comparison of results have been demonstrated through illustrative examples. In Chapter 6, Legendre wavelet method and Bernoulli wavelet method have been developed to solve system of integro-differential equations. Legendre wavelets along with their operational matrices are developed to approximate the solutions of system of nonlinear Volterra integro-differential equations. Also, nonlinear Volterra weakly singular integro-differential equations system has been solved by Bernoulli wavelet method. The properties of these wavelets are used to reduce the system of integral equations to a system of algebraic equations which can be solved numerically by Newton's method. Rigorous convergence analysis has been done for these wavelet methods. Illustrative examples have been included to demonstrate the validity and applicability of the proposed techniques. In Chapter 7, we have solved the second order Lane-Emden type singular differential equation. First, the second order differential equation is transformed into integro-differential equation and then solved by Legendre multi-wavelet method and Chebyshev wavelet method. Convergence of these wavelet methods have been discussed in this chapter. In Chapter 8, we have developed a efficient collocation technique called Legendre spectral collocation method to solve the Fredholm integro-differential-difference equations with variable coefficients and system of two nonlinear integro-differential equations which arise in biological model. The proposed method is based on the Gauss-Legendre points with the basis functions of Lagrange polynomials. The present method reduces this model to a system of nonlinear algebraic equations and again this algebraic system has been solved numerically by Newton's method. The study of fuzzy integral equations and fuzzy differential equations is an emerging area of research for many authors. In Chapter 9, we have proposed some numerical techniques for solving fuzzy integral equations and fuzzy integro-differential equations. Fundamentals of fuzzy calculus have been discussed in this chapter. Nonlinear fuzzy Hammerstein integral equation has been solved by Bernstein polynomials and Legendre wavelets, and then compared with homotopy analysis method. We have solved nonlinear fuzzy Hammerstein Volterra integral equations with constant delay by Bernoulli wavelet method and then compared with B-spline wavelet method. Finally, fuzzy integro-differential equation has been solved by Legendre wavelet method and compared with homotopy analysis method. In fuzzy case, we have applied two-dimensional numerical methods which are discussed in chapter 2. Convergence analysis and error estimate have been also provided for Bernoulli wavelet method. xiv The study of fractional calculus, fractional differential equations and fractional integral equations has a great importance in the field of science and engineering. Most of the physical phenomenon can be best modeled by using fractional calculus. Applications of fractional differential equations and fractional integral equations create a wide area of research for many researchers. This motivates to work on fractional integral equations, which results in the form of Chapter 10. First, the preliminary definitions and theorems of fractional calculus have been presented in this chapter. The nonlinear fractional mixed Volterra-Fredholm integro-differential equations along with mixed boundary conditions have been solved by Legendre wavelet method. A numerical scheme has been developed by using Petrov-Galerkin method where the trial and test functions are Legendre wavelets basis functions. Also, this method has been applied to solve fractional Volterra integro-differential equations. Uniqueness and existence of the problem have been discussed and the error estimate of the proposed method has been presented in this work. Sinc Galerkin method is developed to approximate the solution of fractional Volterra-Fredholm integro-differential equations with weakly singular kernels. The proposed method is based on the Sinc function approximation. Uniqueness and existence of the problem have been discussed and the error analysis of the proposed method have been presented in this chapte

    Postprocesamiento CAM-ROBOTICA orientado al prototipado y mecanizado en células robotizadas complejas

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    The main interest of this thesis consists of the study and implementation of postprocessors to adapt the toolpath generated by a Computer Aided Manufacturing (CAM) system to a complex robotic workcell of eight joints, devoted to the rapid prototyping of 3D CAD-defined products. It consists of a 6R industrial manipulator mounted on a linear track and synchronized with a rotary table. To accomplish this main objective, previous work is required. Each task carried out entails a methodology, objective and partial results that complement each other, namely: - It is described the architecture of the workcell in depth, at both displacement and joint-rate levels, for both direct and inverse resolutions. The conditioning of the Jacobian matrix is described as kinetostatic performance index to evaluate the vicinity to singular postures. These ones are analysed from a geometric point of view. - Prior to any machining, the additional external joints require a calibration done in situ, usually in an industrial environment. A novel Non-contact Planar Constraint Calibration method is developed to estimate the external joints configuration parameters by means of a laser displacement sensor. - A first control is originally done by means of a fuzzy inference engine at the displacement level, which is integrated within the postprocessor of the CAM software. - Several Redundancy Resolution Schemes (RRS) at the joint-rate level are compared for the configuration of the postprocessor, dealing not only with the additional joints (intrinsic redundancy) but also with the redundancy due to the symmetry on the milling tool (functional redundancy). - The use of these schemes is optimized by adjusting two performance criterion vectors related to both singularity avoidance and maintenance of a preferred reference posture, as secondary tasks to be done during the path tracking. Two innovative fuzzy inference engines actively adjust the weight of each joint in these tasks.Andrés De La Esperanza, FJ. (2011). Postprocesamiento CAM-ROBOTICA orientado al prototipado y mecanizado en células robotizadas complejas [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/10627Palanci

    Fuzzy Logic

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    Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems

    Power system contingency ranking using Newton Raphson load flow method and its prediction using soft computing techniques

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    The most important requirement and need of proper operation of power system is maintenance of the system security. Power system security assessment helps in monitoring and in giving up to date analysis regarding currents, bus voltages, power flows, status of circuit breaker, etc. This system assessment has been done in offline mode in which the system conditions are determined using ac power flows. The use of AC power flows is it gives information of power flows in terms of MW and MVAR , line over loadings and voltage limit violation with accurate values. Contingency selection or contingency screening is a process in which probable and potential critical contingencies are identified for which it requires consideration of each line or generator outage. . Contingency ranking is a procedure of contingency analysis in which contingencies are arranged in descending order, sorted out by the severity of contingency. Overall severity index (OPI) is calculated for determining the ranking of contingency. Overall performance index is the summation of two performance index , one of the performance index determines line overloading and other performance index determines bus voltage drop limit violation and are known as active power performance index and voltage performance index respectively. Here in this proposed work the contingency ranking has been done with IEEE 5 bus and 14 bus system. But the system parameters are dynamic in nature, keeps on changing and may affect the system parameters that are why there is need of soft computing techniques for the prediction purpose. Fuzzy logic approach has also been used. Two model of Artificial Neural Network namely, Multi Layer Feed Forward Neural Network (MFNN) and Radial Basis Function Network (RBFNN) have been considered. With these soft computing techniques the prediction method helps in obtaining the OPI with greater accuracy

    Numerical Simulation

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    Nowadays mathematical modeling and numerical simulations play an important role in life and natural science. Numerous researchers are working in developing different methods and techniques to help understand the behavior of very complex systems, from the brain activity with real importance in medicine to the turbulent flows with important applications in physics and engineering. This book presents an overview of some models, methods, and numerical computations that are useful for the applied research scientists and mathematicians, fluid tech engineers, and postgraduate students

    ACADEMIC HANDBOOK (UNDERGRADUATE) COLLEGE OF ENGINEERING (CoE)

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    New Advancements in Pure and Applied Mathematics via Fractals and Fractional Calculus

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    This reprint focuses on exploring new developments in both pure and applied mathematics as a result of fractional behaviour. It covers the range of ongoing activities in the context of fractional calculus by offering alternate viewpoints, workable solutions, new derivatives, and methods to solve real-world problems. It is impossible to deny that fractional behaviour exists in nature. Any phenomenon that has a pulse, rhythm, or pattern appears to be a fractal. The 17 papers that were published and are part of this volume provide credence to that claim. A variety of topics illustrate the use of fractional calculus in a range of disciplines and offer sufficient coverage to pique every reader's attention

    A Hybrid intelligent system for diagnosing and solving financial problems

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    Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnologico. Programa de Pós-Graduação em Engenharia de Produção2012-10-16T09:55:39

    The Third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization

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    The third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization was held on 24-26 Sept. 1990. Sessions were on the following topics: dynamics and controls; multilevel optimization; sensitivity analysis; aerodynamic design software systems; optimization theory; analysis and design; shape optimization; vehicle components; structural optimization; aeroelasticity; artificial intelligence; multidisciplinary optimization; and composites
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