Search results for: switching function

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: Panpan Xu, Shulin Sui

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The crossover probability and mutation probability are the two important factors in genetic algorithm. The adaptive genetic algorithm can improve the convergence performance of genetic algorithm, in which the crossover probability and mutation probability are adaptively designed with the changes of fitness value. We apply adaptive genetic algorithm into a function optimization problem. The numerical experiment represents that adaptive genetic algorithm improves the convergence speed and avoids local convergence.

Keywords: Genetic algorithm, Adaptive genetic algorithm, Function optimization.

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Authors: Tsunwai Gary Yip

Abstract:

Phase locked loops in 10 Gb/s and faster data links are low phase noise devices. Characterization of their phase jitter transfer functions is difficult because the intrinsic noise of the PLLs is comparable to the phase noise of the reference clock signal. The problem is solved by using a linear model to account for the intrinsic noise. This study also introduces a novel technique for measuring the transfer function. It involves the use of the reference clock as a source of wideband excitation, in contrast to the commonly used sinusoidal excitations at discrete frequencies. The data reported here include the intrinsic noise of a PLL for 10 Gb/s links and the jitter transfer function of a PLL for 12.8 Gb/s links. The measured transfer function suggests that the PLL responded like a second order linear system to a low noise reference clock.

Keywords: Intrinsic phase noise, jitter in data link, PLL jitter transfer function, high speed clocking in electronic circuit

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Authors: M.M. Namazi, S.M. Saghaiannejad, A. Rashidi

Abstract:

In this paper by using the port-controlled Hamiltonian (PCH) systems theory, a full-order nonlinear controlled model is first developed. Then a nonlinear passivity-based robust adaptive control (PBRAC) of switched reluctance motor in the presence of external disturbances for the purpose of torque ripple reduction and characteristic improvement is presented. The proposed controller design is separated into the inner loop and the outer loop controller. In the inner loop, passivity-based control is employed by using energy shaping techniques to produce the proper switching function. The outer loop control is employed by robust adaptive controller to determine the appropriate Torque command. It can also overcome the inherent nonlinear characteristics of the system and make the whole system robust to uncertainties and bounded disturbances. A 4KW 8/6 SRM with experimental characteristics that takes magnetic saturation into account is modeled, simulation results show that the proposed scheme has good performance and practical application prospects.

Keywords: Switched Reluctance Motor, Port HamiltonianSystem, Passivity-Based Control, Torque Ripple Minimization

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Authors: Bing Yu , Xingshi He

Abstract:

In this paper, Differential Evolution (DE) algorithm, a new promising evolutionary algorithm, is proposed to train Radial Basis Function (RBF) network related to automatic configuration of network architecture. Classification tasks on data sets: Iris, Wine, New-thyroid, and Glass are conducted to measure the performance of neural networks. Compared with a standard RBF training algorithm in Matlab neural network toolbox, DE achieves more rational architecture for RBF networks. The resulting networks hence obtain strong generalization abilities.

Keywords: differential evolution, neural network, Rbf function

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Authors: Ehsan Hassankhan, Davood A. Khaburi

Abstract:

Direct Torque Control is a control technique in AC drive systems to obtain high performance torque control. The conventional DTC drive contains a pair of hysteresis comparators. DTC drives utilizing hysteresis comparators suffer from high torque ripple and variable switching frequency. The most common solution to those problems is to use the space vector depends on the reference torque and flux. In this Paper The space vector modulation technique (SVPWM) is applied to 2 level inverter control in the proposed DTC-based induction motor drive system, thereby dramatically reducing the torque ripple. Then the controller based on space vector modulation is designed to be applied in the control of Induction Motor (IM) with a three-level Inverter. This type of Inverter has several advantages over the standard two-level VSI, such as a greater number of levels in the output voltage waveforms, Lower dV/dt, less harmonic distortion in voltage and current waveforms and lower switching frequencies. This paper proposes a general SVPWM algorithm for three-level based on standard two-level SVPWM. The proposed scheme is described clearly and simulation results are reported to demonstrate its effectiveness. The entire control scheme is implemented with Matlab/Simulink.

Keywords: Direct torque control, space vector Pulsewidthmodulation(SVPWM), neutral point clamped(NPC), two-levelinverter.

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Authors: Yoichi Hikino, Mutsuto Kawahara

Abstract:

The purpose of this study is to derive optimal shapes of a body located in viscous flows by the finite element method using the acoustic velocity and the four-step explicit scheme. The formulation is based on an optimal control theory in which a performance function of the fluid force is introduced. The performance function should be minimized satisfying the state equation. This problem can be transformed into the minimization problem without constraint conditions by using the adjoint equation with adjoint variables corresponding to the state equation. The performance function is defined by the drag and lift forces acting on the body. The weighted gradient method is applied as a minimization technique, the Galerkin finite element method is used as a spatial discretization and the four-step explicit scheme is used as a temporal discretization to solve the state equation and the adjoint equation. As the interpolation, the orthogonal basis bubble function for velocity and the linear function for pressure are employed. In case that the orthogonal basis bubble function is used, the mass matrix can be diagonalized without any artificial centralization. The shape optimization is performed by the presented method.

Keywords: Shape Optimization, Optimal Control Theory, Finite Element Method, Weighted Gradient Method, Fluid Force, Orthogonal Basis Bubble Function, Four-step Explicit Scheme, Acoustic Velocity.

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Authors: U.K. Saha, L.K. Arora

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The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist between the Riemann-Liouville fractional calculus and multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration with multiindex Mittag-Leffler function.

Keywords: Multiindex Mittag-Leffler function, Multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration, Riemann-Liouville fractional integrals and derivatives.

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Authors: Byung-Joo Oh

Abstract:

This paper describes a method to improve the robustness of a face recognition system based on the combination of two compensating classifiers. The face images are preprocessed by the appearance-based statistical approaches such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). LDA features of the face image are taken as the input of the Radial Basis Function Network (RBFN). The proposed approach has been tested on the ORL database. The experimental results show that the LDA+RBFN algorithm has achieved a recognition rate of 93.5%

Keywords: Face recognition, linear discriminant analysis, radial basis function network.

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Authors: M. Govindarajan, R. M.Chandrasekaran

Abstract:

Text data mining is a process of exploratory data analysis. Classification maps data into predefined groups or classes. It is often referred to as supervised learning because the classes are determined before examining the data. This paper describes proposed radial basis function Classifier that performs comparative crossvalidation for existing radial basis function Classifier. The feasibility and the benefits of the proposed approach are demonstrated by means of data mining problem: direct Marketing. Direct marketing has become an important application field of data mining. Comparative Cross-validation involves estimation of accuracy by either stratified k-fold cross-validation or equivalent repeated random subsampling. While the proposed method may have high bias; its performance (accuracy estimation in our case) may be poor due to high variance. Thus the accuracy with proposed radial basis function Classifier was less than with the existing radial basis function Classifier. However there is smaller the improvement in runtime and larger improvement in precision and recall. In the proposed method Classification accuracy and prediction accuracy are determined where the prediction accuracy is comparatively high.

Keywords: Text Data Mining, Comparative Cross-validation, Radial Basis Function, runtime, accuracy.

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Authors: Satyendra Nath Mandal, J. Pal Choudhury, Dilip De, S. R. Bhadra Chaudhuri

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The selection for plantation of a particular type of mustard plant depending on its productivity (pod yield) at the stage of maturity. The growth of mustard plant dependent on some parameters of that plant, these are shoot length, number of leaves, number of roots and roots length etc. As the plant is growing, some leaves may be fall down and some new leaves may come, so it can not gives the idea to develop the relationship with the seeds weight at mature stage of that plant. It is not possible to find the number of roots and root length of mustard plant at growing stage that will be harmful of this plant as roots goes deeper to deeper inside the land. Only the value of shoot length which increases in course of time can be measured at different time instances. Weather parameters are maximum and minimum humidity, rain fall, maximum and minimum temperature may effect the growth of the plant. The parameters of pollution, water, soil, distance and crop management may be dominant factors of growth of plant and its productivity. Considering all parameters, the growth of the plant is very uncertain, fuzzy environment can be considered for the prediction of shoot length at maturity of the plant. Fuzzification plays a greater role for fuzzification of data, which is based on certain membership functions. Here an effort has been made to fuzzify the original data based on gaussian function, triangular function, s-function, Trapezoidal and L –function. After that all fuzzified data are defuzzified to get normal form. Finally the error analysis (calculation of forecasting error and average error) indicates the membership function appropriate for fuzzification of data and use to predict the shoot length at maturity. The result is also verified using residual (Absolute Residual, Maximum of Absolute Residual, Mean Absolute Residual, Mean of Mean Absolute Residual, Median of Absolute Residual and Standard Deviation) analysis.

Keywords: Fuzzification, defuzzification, gaussian function, triangular function, trapezoidal function, s-function, , membership function, residual analysis.

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Authors: Abed Sami Qawasme, Sameer Khader

Abstract:

This paper describes the effects of photovoltaic voltage changes on Multi-level inverter (MLI) due to solar irradiation variations, and methods to overcome these changes. The irradiation variation affects the generated voltage, which in turn varies the switching angles required to turn-on the inverter power switches in order to obtain minimum harmonic content in the output voltage profile. Genetic Algorithm (GA) is used to solve harmonics elimination equations of eleven level inverters with equal and non-equal dc sources. After that artificial neural network (ANN) algorithm is proposed to generate appropriate set of switching angles for MLI at any level of input dc sources voltage causing minimization of the total harmonic distortion (THD) to an acceptable limit. MATLAB/Simulink platform is used as a simulation tool and Fast Fourier Transform (FFT) analyses are carried out for output voltage profile to verify the reliability and accuracy of the applied technique for controlling the MLI harmonic distortion. According to the simulation results, the obtained THD for equal dc source is 9.38%, while for variable or unequal dc sources it varies between 10.26% and 12.93% as the input dc voltage varies between 4.47V nd 11.43V respectively. The proposed ANN algorithm provides satisfied simulation results that match with results obtained by alternative algorithms.

Keywords: Multi level inverter, genetic algorithm, artificial neural network, total harmonic distortion.

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Authors: Marwen Kermani, Anis Sakly, Faouzi M'sahli

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In this paper, we aim to investigate a new stability analysis for discrete-time switched linear systems based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. This stability conditions issued from vector norms correspond to a vector Lyapunov function. In fact, the switched system to be controlled will be represented in the Companion form. A comparison system relative to a regular vector norm is used in order to get the simple arrow form of the state matrix that yields to a suitable use of Borne-Gentina criterion for the establishment of sufficient conditions for global asymptotic stability. This proposed approach could be a constructive solution to the state and static output feedback stabilization problems.

Keywords: Discrete-time switched linear systems, Global asymptotic stability, Vector norms, Borne-Gentina criterion, Arrow form state matrix, Arbitrary switching, State feedback controller, Static output feedback controller.

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Authors: S. Choodoung, U. Smutkupt

Abstract:

This study systemizes processes and methods in wooden furniture design that contains uniqueness in function and aesthetics. The study was done by research and analysis for designer-s consideration factors that affect function and production. Therefore, the study result indicates that such factors are design process (planning for design, product specifications, concept design, product architecture, industrial design, production), design evaluation as well as wooden furniture design dependent factors i.e. art (art style; furniture history, form), functionality (the strength and durability, area place, using), material (appropriate to function, wood mechanical properties), joints, cost, safety, and social responsibility. Specifically, all aforementioned factors affect good design. Resulting from direct experience gained through user-s usage, the designer must design the wooden furniture systemically and effectively. As a result, this study selected dinning armchair as a case study with all involving factors and all design process stated in this study.

Keywords: Furniture Design, Function Design, Aesthetic, Wooden Furniture.

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Authors: C. C. Liang

Abstract:

MSN used to be the most popular application for communicating among social networks, but Facebook chat is now the most popular. Facebook and MSN have similar characteristics, including usefulness, ease-of-use, and a similar function, which is the exchanging of information with friends. Facebook outperforms MSN in both of these areas. However, the adoption of Facebook and abandonment of MSN have occurred for other reasons. Functions can be improved, but users’ willingness to use does not just depend on functionality. Flow status has been established to be crucial to users’ adoption of cyber applications and to affects users’ adoption of software applications. If users experience flow in using software application, they will enjoy using it frequently, and even change their preferred application from an old to this new one. However, no investigation has examined choice behavior related to switching from Facebook to MSN based on a consideration of flow experiences and functions. This investigation discusses the flow experiences and functions of social-networking applications. Flow experience is found to affect perceived ease of use and perceived usefulness; perceived ease of use influences information ex-change with friends, and perceived usefulness; information exchange influences perceived usefulness, but information exchange has no effect on flow experience.

Keywords: Consumer behavior, social media, technology acceptance model.

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Authors: Hazem J. Smadi

Abstract:

FMEA has been used for several years and proved its efficiency for system’s risk analysis due to failures. Risk priority number found in FMEA is used to rank failure modes that may occur in a system. There are some guidelines in the literature to assign the values of FMEA components known as Severity, Occurrence and Detection. This paper propose a method to assign the value for occurrence in more realistic manner representing the state of the system under study rather than depending totally on the experience of the analyst. This method uses the hazard function of a system to determine the value of occurrence depending on the behavior of the hazard being constant, increasing or decreasing.

Keywords: FMEA, Hazard Function, Risk Priority Number.

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Authors: S. H. Yahaya, J. M. Ali, T.A. Abdullah

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The exploration of this paper will focus on the Cshaped transition curve. This curve is designed by using the concept of circle to circle where one circle lies inside other. The degree of smoothness employed is curvature continuity. The function used in designing the C-curve is Bézier-like cubic function. This function has a low degree, flexible for the interactive design of curves and surfaces and has a shape parameter. The shape parameter is used to control the C-shape curve. Once the C-shaped curve design is completed, this curve will be applied to design spur gear tooth. After the tooth design procedure is finished, the design will be analyzed by using Finite Element Analysis (FEA). This analysis is used to find out the applicability of the tooth design and the gear material that chosen. In this research, Cast Iron 4.5 % Carbon, ASTM A-48 is selected as a gear material.

Keywords: Bézier-like cubic function, Curvature continuity, Cshapedtransition curve, Spur gear tooth.

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Authors: Zeitoun D. G., Thierry Dana-Picard

Abstract:

The study of a real function of two real variables can be supported by visualization using a Computer Algebra System (CAS). One type of constraints of the system is due to the algorithms implemented, yielding continuous approximations of the given function by interpolation. This often masks discontinuities of the function and can provide strange plots, not compatible with the mathematics. In recent years, point based geometry has gained increasing attention as an alternative surface representation, both for efficient rendering and for flexible geometry processing of complex surfaces. In this paper we present different artifacts created by mesh surfaces near discontinuities and propose a point based method that controls and reduces these artifacts. A least squares penalty method for an automatic generation of the mesh that controls the behavior of the chosen function is presented. The special feature of this method is the ability to improve the accuracy of the surface visualization near a set of interior points where the function may be discontinuous. The present method is formulated as a minimax problem and the non uniform mesh is generated using an iterative algorithm. Results show that for large poorly conditioned matrices, the new algorithm gives more accurate results than the classical preconditioned conjugate algorithm.

Keywords: Function singularities, mesh generation, point allocation, visualization, collocation least squares method, Augmented Lagrangian method, Uzawa's Algorithm, Preconditioned Conjugate Gradien

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Authors: Myung-Gon Yoon, Jung-Ho Moon, Tae Kwon Ha

Abstract:

This paper studies a robust stabilization problem of a single agent in a multi-agent consensus system composed of identical agents, when the network topology of the system is completely unknown. It is shown that the transfer function of an agent in a consensus system can be described as a multiplicative perturbation of the isolated agent transfer function in frequency domain. From an existing robust stabilization result, we present sufficient conditions for a robust stabilization of an agent against unknown network topology.

Keywords: Multi-agent System, Robust Stabilization, Transfer Function.

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

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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: Mohammad Reza Ghasemi, Amin Ghorbani

Abstract:

The main goal of the present work is to decrease the computational burden for optimum design of steel frames with frequency constraints using a new type of neural networks called Wavelet Neural Network. It is contested to train a suitable neural network for frequency approximation work as the analysis program. The combination of wavelet theory and Neural Networks (NN) has lead to the development of wavelet neural networks. Wavelet neural networks are feed-forward networks using wavelet as activation function. Wavelets are mathematical functions within suitable inner parameters, which help them to approximate arbitrary functions. WNN was used to predict the frequency of the structures. In WNN a RAtional function with Second order Poles (RASP) wavelet was used as a transfer function. It is shown that the convergence speed was faster than other neural networks. Also comparisons of WNN with the embedded Artificial Neural Network (ANN) and with approximate techniques and also with analytical solutions are available in the literature.

Keywords: Weight Minimization, Frequency Constraints, Steel Frames, ANN, WNN, RASP Function.

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Authors: Arkady Bolotin

Abstract:

One-way functions are functions that are easy to compute but hard to invert. Their existence is an open conjecture; it would imply the existence of intractable problems (i.e. NP-problems which are not in the P complexity class). If true, the existence of one-way functions would have an impact on the theoretical framework of physics, in particularly, quantum mechanics. Such aspect of one-way functions has never been shown before. In the present work, we put forward the following. We can calculate the microscopic state (say, the particle spin in the z direction) of a macroscopic system (a measuring apparatus registering the particle z-spin) by the system macroscopic state (the apparatus output); let us call this association the function F. The question is: can we compute the function F in the inverse direction? In other words, can we compute the macroscopic state of the system through its microscopic state (the preimage F -1)? In the paper, we assume that the function F is a one-way function. The assumption implies that at the macroscopic level the Schrödinger equation becomes unfeasible to compute. This unfeasibility plays a role of limit of the validity of the linear Schrödinger equation.

Keywords: One-way functions, P versus NP problem, quantummeasurements.

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Authors: A. Abedian, M. H. Ghiasi, B. Dehghan-Manshadi

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A stiffened laminated composite panel (1 m length × 0.5m width) was optimized for minimum weight and deflection under several constraints using genetic algorithm. Here, a significant study on the performance of a penalty function with two kinds of static and dynamic penalty factors was conducted. The results have shown that linear dynamic penalty factors are more effective than the static ones. Also, a specially combined linear-exponential function has shown to perform more effective than the previously mentioned penalty functions. This was then resulted in the less sensitivity of the GA to the amount of penalty factor.

Keywords: Genetic algorithms, penalty function, stiffenedcomposite panel, finite element method.

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Authors: Ephraim Gower, Thato Tsalaile, Monageng Kgwadi, Malcolm Hawksford.

Abstract:

In this paper, the statistical properties of filtered or convolved signals are considered by deriving the resulting density functions as well as the exact mean and variance expressions given a prior knowledge about the statistics of the individual signals in the filtering or convolution process. It is shown that the density function after linear convolution is a mixture density, where the number of density components is equal to the number of observations of the shortest signal. For circular convolution, the observed samples are characterized by a single density function, which is a sum of products.

Keywords: Circular Convolution, linear Convolution, mixture density function.

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Authors: Omid Mirmotahari, Yngvar Berg, Ahmad Habibizad Navin

Abstract:

Reversible logic is becoming more and more prominent as the technology sets higher demands on heat, power, scaling and stability. Reversible gates are able at any time to "undo" the current step or function. Multiple-valued logic has the advantage of transporting and evaluating higher bits each clock cycle than binary. Moreover, we demonstrate in this paper, combining these disciplines we can construct powerful multiple-valued reversible logic structures. In this paper a reversible block implemented by pseudo floatinggate can perform AD-function and a DA-function as its reverse application.

Keywords: Reversible logic, bi-directional, Pseudo floating-gate(PFG), multiple-valued logic (MVL).

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Authors: Nora Taghavi, Ali Sadr

Abstract:

System identification is the process of creating models of dynamic process from input- output signals. The aim of system identification can be identified as “ to find a model with adjustable parameters and then to adjust them so that the predicted output matches the measured output". This paper presents a method of modeling and simulating with system identification to achieve the maximum fitness for transformation function. First by using optimized KLM equivalent circuit for PVDF piezoelectric transducer and assuming different inputs including: sinuside, step and sum of sinusides, get the outputs, then by using system identification toolbox in MATLAB, we estimate the transformation function from inputs and outputs resulted in last program. Then compare the fitness of transformation function resulted from using ARX,OE(Output- Error) and BJ(Box-Jenkins) models in system identification toolbox and primary transformation function form KLM equivalent circuit.

Keywords: PVDF modeling, ARX, BJ(Box-Jenkins), OE(Output-Error), System Identification.

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Authors: Bhanu Gupta

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In this paper, the criteria of Ψ-eventual stability have been established for generalized impulsive differential systems of multiple dependent variables. The sufficient conditions have been obtained using piecewise continuous Lyapunov function. An example is given to support our theoretical result.

Keywords: impulsive differential equations, Lyapunov function, eventual stability

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Authors: R.N.Pise, S.A.Kulkarni, R.V.Pawar

Abstract:

MultiProtocol Label Switching (MPLS) is an emerging technology that aims to address many of the existing issues associated with packet forwarding in today-s Internetworking environment. It provides a method of forwarding packets at a high rate of speed by combining the speed and performance of Layer 2 with the scalability and IP intelligence of Layer 3. In a traditional IP (Internet Protocol) routing network, a router analyzes the destination IP address contained in the packet header. The router independently determines the next hop for the packet using the destination IP address and the interior gateway protocol. This process is repeated at each hop to deliver the packet to its final destination. In contrast, in the MPLS forwarding paradigm routers on the edge of the network (label edge routers) attach labels to packets based on the forwarding Equivalence class (FEC). Packets are then forwarded through the MPLS domain, based on their associated FECs , through swapping the labels by routers in the core of the network called label switch routers. The act of simply swapping the label instead of referencing the IP header of the packet in the routing table at each hop provides a more efficient manner of forwarding packets, which in turn allows the opportunity for traffic to be forwarded at tremendous speeds and to have granular control over the path taken by a packet. This paper deals with the process of MPLS forwarding mechanism, implementation of MPLS datapath , and test results showing the performance comparison of MPLS and IP routing. The discussion will focus primarily on MPLS IP packet networks – by far the most common application of MPLS today.

Keywords: Forwarding equivalence class, incoming label map, label, next hop label forwarding entry.

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Authors: Guangpu Chen

Abstract:

When the failure function is monotone, some monotonic reliability methods are used to gratefully simplify and facilitate the reliability computations. However, these methods often work in a transformed iso-probabilistic space. To this end, a monotonic simulator or transformation is needed in order that the transformed failure function is still monotone. This note proves at first that the output distribution of failure function is invariant under the transformation. And then it presents some conditions under which the transformed function is still monotone in the newly obtained space. These concern the copulas and the dependence concepts. In many engineering applications, the Gaussian copulas are often used to approximate the real word copulas while the available information on the random variables is limited to the set of marginal distributions and the covariances. So this note catches an importance on the conditional monotonicity of the often used transformation from an independent random vector into a dependent random vector with Gaussian copulas.

Keywords: Monotonic, Rosenblatt, Nataf transformation, dependence concepts, completely positive matrices, Gaussiancopulas

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Authors: Edward Aris D. Fajardo, Hamdi Muhyuddin D. Barra

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This study employs the use of the fourth order Numerov scheme to determine the eigenstates and eigenvalues of particles, electrons in particular, in single and double delta function potentials. For the single delta potential, it is found that the eigenstates could only be attained by using specific potential depths. The depth of the delta potential well has a value that varies depending on the delta strength. These depths are used for each well on the double delta function potential and the eigenvalues are determined. There are two bound states found in the computation, one with a symmetric eigenstate and another one which is antisymmetric.

Keywords: Double Delta Potential, Eigenstates, Eigenvalue, Numerov Method, Single Delta Potential

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