Search results for: Gaussian linearization

Authors: R. J. Chang

Abstract:

A cyclostationary Gaussian linearization method is formulated for investigating the time average response of nonlinear system under sinusoidal signal and white noise excitation. The quantitative measure of cyclostationary mean, variance, spectrum of mean amplitude, and mean power spectral density of noise are analyzed. The qualitative response behavior of stochastic jump and bifurcation are investigated. The validity of the present approach in predicting the quantitative and qualitative statistical responses is supported by utilizing Monte Carlo simulations. The present analysis without imposing restrictive analytical conditions can be directly derived by solving non-linear algebraic equations. The analytical solution gives reliable quantitative and qualitative prediction of mean and noise response for the Duffing system subjected to both sinusoidal signal and white noise excitation.

Keywords: Cyclostationary, Duffing system, Gaussian linearization, sinusoidal signal and white noise.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, nonlinear observer, formal linearization, Chebyshev interpolation.

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Authors: A. R. Nemati, M. Haddad Zarif, M. M. Fateh

Abstract:

This paper presents an adaptive feedback linearization approach to derive helicopter. Ideal feedback linearization is defined for the cases when the system model is known. Adaptive feedback linearization is employed to get asymptotically exact cancellation for the inherent uncertainty in the knowledge of the given parameters of system. The control algorithm is implemented using the feedback linearization technique and adaptive method. The controller parameters are unknown where an adaptive control law aims to drive them towards their ideal values for providing perfect model matching between the reference model and the closed-loop plant model. The converged parameters of controller would then provide good estimates for the unknown plant parameters.

Keywords: Adaptive control, helicopter, feedback linearization, nonlinear control.

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Authors: Martin Steinberger, Martin Horn

Abstract:

In this article, a high vacuum system for the evaporation of organic semiconductors is introduced and a mathematical model is given. Based on the exact input output linearization a deposition rate controller is designed and tested with different evaporation materials.

Keywords: Effusion cell, organic semiconductors, deposition rate, exact linearization.

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Authors: Chien-Chun Kung, Feng-Lung Chiang, Kuei-Yi Chen

Abstract:

In this paper, we will implement three-dimensional pursuit guidance law with feedback linearization control method and study the effects of parameters. First, we introduce guidance laws and equations of motion of a missile. Pursuit guidance law is our highlight. We apply feedback linearization control method to obtain the accelerations to implement pursuit guidance law. The solution makes warhead direction follow with line-of-sight. Final, the simulation results show that the exact solution derived in this paper is correct and some factors e.g. control gain, time delay, are important to implement pursuit guidance law.

Keywords: Pursuit guidance law, feedback linearization.

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Authors: E. Shahsavari, R. Ghasemi, A. Akramizadeh

Abstract:

This paper presents a new method to design nonlinear feedback linearization controller for PEMFCs (Polymer Electrolyte Membrane Fuel Cells). A nonlinear controller is designed based on nonlinear model to prolong the stack life of PEMFCs. Since it is known that large deviations between hydrogen and oxygen partial pressures can cause severe membrane damage in the fuel cell, feedback linearization is applied to the PEMFC system so that the deviation can be kept as small as possible during disturbances or load variations. To obtain an accurate feedback linearization controller, tuning the linear parameters are always important. So in proposed study NSGA (Non-Dominated Sorting Genetic Algorithm)-II method was used to tune the designed controller in aim to decrease the controller tracking error. The simulation result showed that the proposed method tuned the controller efficiently.

Keywords: Feedback Linearization controller, NSGA, Optimal Control, PEMFC.

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Authors: Omid Heydarnia, Akbar Allahverdizadeh, Behnam Dadashzadeh, M. R. Sayyed Noorani

Abstract:

Underactuated biped robots control is one of the interesting topics in robotics. The main difficulties are its highly nonlinear dynamics, open-loop instability, and discrete event at the end of the gait. One of the methods to control underactuated systems is the partial feedback linearization, but it is not robust against uncertainties and disturbances that restrict its performance to control biped walking and running. In this paper, fuzzy partial feedback linearization is presented to overcome its drawback. Numerical simulations verify the effectiveness of the proposed method to generate stable and robust biped walking and running gaits.

Keywords: Underactuated system, biped robot, fuzzy control, partial feedback linearization.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

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: Gabriel I. Loaiza O., Carlos A. Cadavid M., Juan C. Arango P.

Abstract:

It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ = −1/2 , as does the family of usual Gaussian distributions. In the present paper, firstly we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ1, θ2; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the Inverse q−Gaussian distribution family (q < 3), as the family obtained by replacing the usual exponential function by the Tsallis q−exponential function in the expression for the Inverse Gaussian distribution, and observe that it supports two possible geometries, the Fisher and the q−Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q−Fisher geometry of the Inverse q−Gaussian distribution family, similar to the ones obtained in the case of the Inverse Gaussian distribution family.

Keywords: Base of Changes, Information Geometry, Inverse Gaussian distribution, Inverse q-Gaussian distribution, Statistical Manifolds.

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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: Nyah C. Temaneh, F. A. Phiri, E. Ruhunga

Abstract:

Most of the well known methods for generating Gaussian variables require at least one standard uniform distributed value, for each Gaussian variable generated. The length of the random number generator therefore, limits the number of independent Gaussian distributed variables that can be generated meanwhile the statistical solution of complex systems requires a large number of random numbers for their statistical analysis. We propose an alternative simple method of generating almost infinite number of Gaussian distributed variables using a limited number of standard uniform distributed random numbers.

Keywords: Gaussian variable, statistical analysis, simulation ofCommunication Network, Random numbers.

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Authors: A. Keshavarz

Abstract:

A physical model for guiding the wave in photorefractive media is studied. Propagation of cos-Gaussian beam as the special cases of sinusoidal-Gaussian beams in photorefractive crystal is simulated numerically by the Crank-Nicolson method in one dimension. Results show that the beam profile deforms as the energy transfers from the center to the tails under propagation. This simulation approach is of significant interest for application in optical telecommunication. The results are presented graphically and discussed.

Keywords: Beam propagation, cos-Gaussian beam, Numerical simulation, Photorefractive crystal.

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Authors: Tomohiro Hachino, Hitoshi Takata, Seiji Fukushima, Yasutaka Igarashi

Abstract:

This paper presents a Gaussian process model-based short-term electric load forecasting. The Gaussian process model is a nonparametric model and the output of the model has Gaussian distribution with mean and variance. The multiple Gaussian process models as every hour ahead predictors are used to forecast future electric load demands up to 24 hours ahead in accordance with the direct forecasting approach. The separable least-squares approach that combines the linear least-squares method and genetic algorithm is applied to train these Gaussian process models. Simulation results are shown to demonstrate the effectiveness of the proposed electric load forecasting.

Keywords: Direct method, electric load forecasting, Gaussian process model, genetic algorithm, separable least-squares method.

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Authors: A. Izadbakhsh, M. M. Fateh, M. A. Sadrnia

Abstract:

A multivariable discontinuous feedback linearization approach is proposed to position control of an electrically driven fast robot manipulator. A desired performance is achieved by selecting a useful controller and suitable sampling rate and considering saturation for actuators. There is a high flexibility to apply the proposed control approach on different electrically driven manipulators. The control approach can guarantee the stability and satisfactory tracking performance. A PUMA 560 robot driven by geared permanent magnet dc motors is simulated. The simulation results show a desired performance for control system under technical specifications.

Keywords: Fast robot, feedback linearization, multivariabledigital control, PUMA560.

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Authors: Keunhong Chae, Seokho Yoon

Abstract:

In this paper, frequency offset (FO) estimation schemes robust to the non-Gaussian noise environments are proposed for orthogonal frequency division multiplexing (OFDM) systems. First, a maximum-likelihood (ML) estimation scheme in non-Gaussian noise environments is proposed, and then, the complexity of the ML estimation scheme is reduced by employing a reduced set of candidate values. In numerical results, it is demonstrated that the proposed schemes provide a significant performance improvement over the conventional estimation scheme in non-Gaussian noise environments while maintaining the performance similar to the estimation performance in Gaussian noise environments.

Keywords: Frequency offset estimation, maximum-likelihood, non-Gaussian noise environment, OFDM, training symbol.

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Authors: Hu Haibo, Zhao Hong

Abstract:

Gaussian mixture background model is widely used in moving target detection of the image sequences. However, traditional Gaussian mixture background model usually considers the time continuity of the pixels, and establishes background through statistical distribution of pixels without taking into account the pixels- spatial similarity, which will cause noise, imperfection and other problems. This paper proposes a new Gaussian mixture modeling approach, which combines the color and gradient of the spatial information, and integrates the spatial information of the pixel sequences to establish Gaussian mixture background. The experimental results show that the movement background can be extracted accurately and efficiently, and the algorithm is more robust, and can work in real time in tracking applications.

Keywords: Gaussian mixture model, real-time tracking, sequence image, gradient.

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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: M. B. Meenavathi, K. Rajesh

Abstract:

In this paper, we propose a new class of Volterra series based filters for image enhancement and restoration. Generally the linear filters reduce the noise and cause blurring at the edges. Some nonlinear filters based on median operator or rank operator deal with only impulse noise and fail to cancel the most common Gaussian distributed noise. A class of second order Volterra filters is proposed to optimize the trade-off between noise removal and edge preservation. In this paper, we consider both the Gaussian and mixed Gaussian-impulse noise to test the robustness of the filter. Image enhancement and restoration results using the proposed Volterra filter are found to be superior to those obtained with standard linear and nonlinear filters.

Keywords: Gaussian noise, Image enhancement, Imagerestoration, Linear filters, Nonlinear filters, Volterra series.

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Authors: Cuneyt Yucelbas, Seral Ozsen, Sule Yucelbas, Gulay Tezel

Abstract:

Due to the fact that there exist only a small number of complex systems in artificial immune system (AIS) that work out nonlinear problems, nonlinear AIS approaches, among the well-known solution techniques, need to be developed. Gaussian function is usually used as similarity estimation in classification problems and pattern recognition. In this study, diagnosis of breast cancer, the second type of the most widespread cancer in women, was performed with different distance calculation functions that euclidean, gaussian and gaussian-euclidean hybrid function in the clonal selection model of classical AIS on Wisconsin Breast Cancer Dataset (WBCD), which was taken from the University of California, Irvine Machine-Learning Repository. We used 3-fold cross validation method to train and test the dataset. According to the results, the maximum test classification accuracy was reported as 97.35% by using of gaussian-euclidean hybrid function for fold-3. Also, mean of test classification accuracies for all of functions were obtained as 94.78%, 94.45% and 95.31% with use of euclidean, gaussian and gaussian-euclidean, respectively. With these results, gaussian-euclidean hybrid function seems to be a potential distance calculation method, and it may be considered as an alternative distance calculation method for hard nonlinear classification problems.

Keywords: Artificial Immune System, Breast Cancer Diagnosis, Euclidean Function, Gaussian Function.

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Authors: Roozbeh Molavi, Davood A. Khaburi

Abstract:

The permanent magnet synchronous motor (PMSM) is very useful in many applications. Vector control of PMSM is popular kind of its control. In this paper, at first an optimal vector control for PMSM is designed and then results are compared with conventional vector control. Then, it is assumed that the measurements are noisy and linear quadratic Gaussian (LQG) methodology is used to filter the noises. The results of noisy optimal vector control and filtered optimal vector control are compared to each other. Nonlinearity of PMSM and existence of inverter in its control circuit caused that the system is nonlinear and time-variant. With deriving average model, the system is changed to nonlinear time-invariant and then the nonlinear system is converted to linear system by linearization of model around average values. This model is used to optimize vector control then two optimal vector controls are compared to each other. Simulation results show that the performance and robustness to noise of the control system has been highly improved.

Keywords: Kalman filter, Linear quadratic Gaussian (LQG), Linear quadratic regulator (LQR), Permanent-Magnet synchronousmotor (PMSM).

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Authors: Hany Osman, M. F. Baki

Abstract:

We address the balancing problem of transfer lines in this paper to find the optimal line balancing that minimizes the nonproductive time. We focus on the tool change time and face orientation change time both of which influence the makespane. We consider machine capacity limitations and technological constraints associated with the manufacturing process of auto cylinder heads. The problem is represented by a mixed integer programming model that aims at distributing the design features to workstations and sequencing the machining processes at a minimum non-productive time. The proposed model is solved by an algorithm established using linearization schemes and Benders- decomposition approach. The experiments show the efficiency of the algorithm in reaching the exact solution of small and medium problem instances at reasonable time.

Keywords: Transfer line balancing, Benders' decomposition, Linearization.

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Authors: Shu-Xin Miao

Abstract:

In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples.

Keywords: Guassian quadrature rules, fuzzy number, fuzzy integral, fuzzy solution.

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Authors: R. K. Saxena, Ravi Saxena

Abstract:

In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

Keywords: Fox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

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Authors: Fabrice Poirion, Benedicte Puig

Abstract:

Mathematical justifications are given for a simulation technique of multivariate nonGaussian random processes and fields based on Rosenblatt-s transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrelation function.

Keywords: Simulation, nonGaussian, random field, multivariate, stochastic process.

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Authors: Hacene Benkhoula, Mohamed Badreddine Benabdella, Hamid Bouzeboudja, Abderrahmane Asraoui

Abstract:

The wind is a random variable difficult to master, for this, we developed a mathematical and statistical methods enable to modeling and forecast wind power. Gaussian Processes (GP) is one of the most widely used families of stochastic processes for modeling dependent data observed over time, or space or time and space. GP is an underlying process formed by unrecognized operator’s uses to solve a problem. The purpose of this paper is to present how to forecast wind power by using the GP. The Gaussian process method for forecasting are presented. To validate the presented approach, a simulation under the MATLAB environment has been given.

Keywords: Forecasting, Gaussian process, modeling, wind power.

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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: Adnan Al-Smadi

Abstract:

One of the primary uses of higher order statistics in signal processing has been for detecting and estimation of non- Gaussian signals in Gaussian noise of unknown covariance. This is motivated by the ability of higher order statistics to suppress additive Gaussian noise. In this paper, several methods to test for non- Gaussianity of a given process are presented. These methods include histogram plot, kurtosis test, and hypothesis testing using cumulants and bispectrum of the available sequence. The hypothesis testing is performed by constructing a statistic to test whether the bispectrum of the given signal is non-zero. A zero bispectrum is not a proof of Gaussianity. Hence, other tests such as the kurtosis test should be employed. Examples are given to demonstrate the performance of the presented methods.

Keywords: Non-Gaussian, bispectrum, kurtosis, hypothesistesting, histogram.

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Authors: Keunhong Chae, Seokho Yoon

Abstract:

This paper proposes frequency offset (FO) estimation schemes robust to the non-Gaussian noise for orthogonal frequency division multiplexing (OFDM) systems. A maximum-likelihood (ML) scheme and a low-complexity estimation scheme are proposed by applying the probability density function of the cyclic prefix of OFDM symbols to the ML criterion. From simulation results, it is confirmed that the proposed schemes offer a significant FO estimation performance improvement over the conventional estimation scheme in non-Gaussian noise environments.

Keywords: Frequency offset, cyclic prefix, maximum-likelihood, non-Gaussian noise, OFDM.

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Authors: Bhawna Tandon, Shiv Narayan, Jagdish Kumar

Abstract:

This study proposes the transformation of nonlinear Magnetic Levitation System into linear one, via state and feedback transformations using explicit algorithm. This algorithm allows computing explicitly the linearizing state coordinates and feedback for any nonlinear control system, which is feedback linearizable, without solving the Partial Differential Equations. The algorithm is performed using a maximum of N-1 steps where N being the dimension of the system.

Keywords: Explicit Algorithm, Feedback Linearization, Nonlinear control, Magnetic Levitation System.

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Authors: S. Beyou, B. Grondin-Perez, M. Benne, C. Damour, J.-P. Chabriat

Abstract:

The industrial process of the sugar cane crystallization produces a residual that still contains a lot of soluble sucrose and the objective of the factory is to improve its extraction. Therefore, there are substantial losses justifying the search for the optimization of the process. Crystallization process studied on the industrial site is based on the “three massecuites process". The third step of this process constitutes the final stage of exhaustion of the sucrose dissolved in the mother liquor. During the process of the third step of crystallization (Ccrystallization), the phase that is studied and whose control is to be improved, is the growing phase (crystal growth phase). The study of this process on the industrial site is a problem in its own. A control scheme is proposed to improve the standard PID control law used in the factory. An auto-tuning PID controller based on instantaneous linearization of a neural network is then proposed.

Keywords: Auto-tuning, PID, Instantaneous linearization, Neural network, Non linear process, C-crystallisation.

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