Search results for: Non-Linear Dimension Reduction

Authors: A. Bahmanikashkouli, O.R. Bahadori Nezhad

Abstract:

In this article, the phenomenon of nonlinear consolidation in saturated and homogeneous clay layer is studied. Considering time-varied drainage model, the excess pore water pressure in the layer depth is calculated. The Generalized Differential Quadrature (GDQ) method is used for the modeling and numerical analysis. For the purpose of analysis, first the domain of independent variables (i.e., time and clay layer depth) is discretized by the Chebyshev-Gauss-Lobatto series and then the nonlinear system of equations obtained from the GDQ method is solved by means of the Newton-Raphson approach. The obtained results indicate that the Generalized Differential Quadrature method, in addition to being simple to apply, enjoys a very high accuracy in the calculation of excess pore water pressure.

Keywords: Generalized Differential Quadrature method, Nonlinear consolidation, Nonlinear system of equations, Time-varied drainage

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Authors: A. El Ougli, I. Lagrat, I. Boumhidi

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In this paper we propose a robust adaptive fuzzy controller for a class of nonlinear system with unknown dynamic. The method is based on type-2 fuzzy logic system to approximate unknown non-linear function. The design of the on-line adaptive scheme of the proposed controller is based on Lyapunov technique. Simulation results are given to illustrate the effectiveness of the proposed approach.

Keywords: Fuzzy set type-2, Adaptive fuzzy control, Nonlinear system.

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Authors: I. Khabbazi, R. Ghasemi

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This paper presents a combination of both robust nonlinear controller and nonlinear controller for a class of nonlinear 4Y Octorotor UAV using Back-stepping and sliding mode controller. The robustness against internal and external disturbance and decoupling control are the merits of the proposed paper. The proposed controller decouples the Octorotor dynamical system. The controller is then applied to a 4Y Octortor UAV and its feature will be shown.

Keywords: Backstepping, Decoupling, Octorotor UAV, sliding mode.

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Authors: Gülnihal Meral

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In this study, the density dependent nonlinear reactiondiffusion equation, which arises in the insect dispersal models, is solved using the combined application of differential quadrature method(DQM) and implicit Euler method. The polynomial based DQM is used to discretize the spatial derivatives of the problem. The resulting time-dependent nonlinear system of ordinary differential equations(ODE-s) is solved by using implicit Euler method. The computations are carried out for a Cauchy problem defined by a onedimensional density dependent nonlinear reaction-diffusion equation which has an exact solution. The DQM solution is found to be in a very good agreement with the exact solution in terms of maximum absolute error. The DQM solution exhibits superior accuracy at large time levels tending to steady-state. Furthermore, using an implicit method in the solution procedure leads to stable solutions and larger time steps could be used.

Keywords: Density Dependent Nonlinear Reaction-Diffusion Equation, Differential Quadrature Method, Implicit Euler Method.

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Authors: Magdy G. Asaad

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The objective of this paper is to use the Pfaffian technique to construct different classes of exact Pfaffian solutions and N-soliton solutions to some of the generalized integrable nonlinear partial differential equations in (3+1) dimensions. In this paper, I will show that the Pfaffian solutions to the nonlinear PDEs are nothing but Pfaffian identities. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.

Keywords: Bilinear operator, G-BKP equation, Integrable nonlinear PDEs, Jimbo-Miwa equation, Ma-Fan equation, N-soliton solutions, Pfaffian solutions.

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Authors: Yiqin Lin, Wenbo Li

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Dimensionality reduction and feature extraction are of crucial importance for achieving high efficiency in manipulating the high dimensional data. Two-dimensional discriminant locality preserving projection (2D-DLPP) and two-dimensional discriminant supervised LPP (2D-DSLPP) are two effective two-dimensional projection methods for dimensionality reduction and feature extraction of face image matrices. Since 2D-DLPP and 2D-DSLPP preserve the local structure information of the original data and exploit the discriminant information, they usually have good recognition performance. However, 2D-DLPP and 2D-DSLPP only employ single-sided projection, and thus the generated low dimensional data matrices have still many features. In this paper, by combining the discriminant supervised LPP with the bidirectional projection, we propose the bidirectional discriminant supervised LPP (BDSLPP). The left and right projection matrices for BDSLPP can be computed iteratively. Experimental results show that the proposed BDSLPP achieves higher recognition accuracy than 2D-DLPP, 2D-DSLPP, and bidirectional discriminant LPP (BDLPP).

Keywords: Face recognition, dimension reduction, locality preserving projection, discriminant information, bidirectional projection.

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Authors: Sachin Bhalekar, Varsha Daftardar-Gejji

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In the present paper, we present a modification of the New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari [J. Math. Anal. Appl. 2006;316:753–763] and use it for solving systems of nonlinear functional equations. This modification yields a series with faster convergence. Illustrative examples are presented to demonstrate the method.

Keywords: Caputo fractional derivative, System of nonlinear functional equations, Revised new iterative method.

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Authors: Gholamreza Hojjati, Kourosh Parand

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In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane- Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.

Keywords: Lane-Emden type equations, nonlinear ODE, stiff problems, multistep methods, astrophysics.

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Authors: Toshinori Nawata

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In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input using weighted gradient optimization automatic choosing functions. Constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: Augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Leila Motamed-Jahromi, Mohsen Hatami, Alireza Keshavarz

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This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As₂S₃ chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

Keywords: Nonlinear optics, propagation equation, plasmonic waveguide.

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Authors: M.O. Makhmalbaf, M. GhanooniBagha, M.A. Tutunchian, M. Zabihi Samani

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In this paper first, Two buildings have been modeled and then analyzed using nonlinear static analysis method under two different conditions in Nonlinear SAP 2000 software. In the first condition the interaction of soil adjacent to the walls of basement are ignored while in the second case this interaction have been modeled using Gap elements of nonlinear SAP2000 software. Finally, comparing the results of two models, the effects of soil-structure on period, target point displacement, internal forces, shape deformations and base shears have been studied. According to the results, this interaction has always increased the base shear of buildings, decreased the period of structure and target point displacement, and often decreased the internal forces and displacements.

Keywords: Seismic Rehabilitation, Soil-Structure Interaction, Short Structure, Nonlinear Static Analysis.

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Authors: Sanjay Singh, M Sathish Kumar, H. S Mruthyunjaya

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Multicarrier transmission system such as Orthogonal Frequency Division Multiplexing (OFDM) is a promising technique for high bit rate transmission in wireless communication system. OFDM is a spectrally efficient modulation technique that can achieve high speed data transmission over multipath fading channels without the need for powerful equalization techniques. However the price paid for this high spectral efficiency and less intensive equalization is low power efficiency. OFDM signals are very sensitive to nonlinear effects due to the high Peak-to-Average Power Ratio (PAPR), which leads to the power inefficiency in the RF section of the transmitter. This paper investigates the effect of PAPR reduction on the performance parameter of multicarrier communication system. Performance parameters considered are power consumption of Power Amplifier (PA) and Digital-to-Analog Converter (DAC), power amplifier efficiency, SNR of DAC and BER performance of the system. From our analysis it is found that irrespective of PAPR reduction technique being employed, the power consumption of PA and DAC reduces and power amplifier efficiency increases due to reduction in PAPR. Moreover, it has been shown that for a given BER performance the requirement of Input-Backoff (IBO) reduces with reduction in PAPR.

Keywords: BER, Crest Factor (CF), Digital-to-Analog Converter(DAC), Input-Backoff (IBO), Orthogonal Frequency Division Multiplexing(OFDM), Peak-to-Average Power Ratio (PAPR), PowerAmplifier efficiency, SNR

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Authors: Toshinori Nawata, Hitoshi Takata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input. Constant terms which arise from section wise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics.Parameters included in the control are suboptimally selectedby extremizing a combination of Hamiltonian and Lyapunov functions with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: Augmented Automatic Choosing Control, NonlinearControl, Genetic Algorithm, Hamiltonian, Lyapunovfunction

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Authors: Saeed Rahjoo, Babak H. Mamaqani

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Concentric bracing systems have been in practice for many years because of their effectiveness in reducing seismic response. Depending on concept, seismic design codes provide various response modification factors (R), which itself consists of different terms, for different types of lateral load bearing systems but configuration of these systems are often ignored in the proposed values. This study aims at considering the effect of different x-bracing diagonal configuration on values of ductility dependent term in R computation. 51 models were created and nonlinear push over analysis has been performed. The main variables of this study were the suitable location of X–bracing diagonal configurations, which establishes better nonlinear behavior in concentric braced steel frames. Results show that some x-bracing diagonal configurations improve the seismic performance of CBF significantly and explicit consideration of lateral load bearing systems seems necessary.

Keywords: Bracing configuration, concentrically braced frame (CBF), Push over analyses, Response reduction factor.

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová

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The article presents two mathematical models of the interaction between a rotating shaft and an incompressible fluid. The mathematical model includes both the journal bearings and the axially traversed hydrodynamic sealing gaps of hydraulic machines. A method is shown for the identification of additional effects of the fluid acting on the rotor of the machine, both for a linear and a nonlinear model. The interaction is expressed by matrices of mass, stiffness and damping.

Keywords: CFD modeling, hydrodynamic gap, matrices of mass, stiffness and damping, nonlinear mathematical model.

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Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun

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In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

Keywords: Grey relational degree, multiple linear regression, membership function, nonlinear programming.

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Authors: W. J. Strydom, K. Puren

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Place-making is viewed here as an empowering process in which people represent, improve and maintain their spatial (natural or built) environment. With the above-mentioned in mind, place-making is multi-dimensional and include a spatial dimension (including visual properties or the end product/plan), a procedural dimension during which (negotiation/discussion of ideas with all relevant stakeholders in terms of end product/plan) and a psychological dimension (inclusion of intrinsic values and meanings related to a place in the end product/plan). These three represent dimensions of place-making. The purpose of this paper is to explore these dimensions of place-making in a case study of a local community in Ikageng, Potchefstroom, North-West Province, South Africa. This case study represents an inclusive process that strives to empower a local community (forcefully relocated due to Apartheid legislation in South Africa). This case study focussed on the inclusion of participants in the decision-making process regarding their daily environment. By means of focus group discussions and a collaborative design workshop, data is generated and ultimately creates a linkage with the theoretical dimensions of place-making. This paper contributes to the field of spatial planning due to the exploration of the dimensions of place-making and the relevancy of this process on spatial planning (especially in a South African setting).

Keywords: Case study, place-making, spatial planning, spatial dimension, procedural dimension, psychological dimension.

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Authors: Hadi Farhadian, Homayoon Katibeh

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Groundwater inflow to the tunnels is one of the most important problems in tunneling operation. The objective of this study is the investigation of model dimension effects on tunnel inflow assessment in discontinuous rock masses using numerical modeling. In the numerical simulation, the model dimension has an important role in prediction of water inflow rate. When the model dimension is very small, due to low distance to the tunnel border, the model boundary conditions affect the estimated amount of groundwater flow into the tunnel and results show a very high inflow to tunnel. Hence, in this study, the two-dimensional universal distinct element code (UDEC) used and the impact of different model parameters, such as tunnel radius, joint spacing, horizontal and vertical model domain extent has been evaluated. Results show that the model domain extent is a function of the most significant parameters, which are tunnel radius and joint spacing.

Keywords: Water inflow, Tunnel, Discontinues rock, Numerical simulation.

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Authors: Mussa Mahmoudi

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For Seismic design, it is important to estimate, maximum lateral displacement (inelastic displacement) of the structures due to sever earthquakes for several reasons. Seismic design provisions estimate the maximum roof and storey drifts occurring in major earthquakes by amplifying the drifts of the structures obtained by elastic analysis subjected to seismic design load, with a coefficient named “displacement amplification factor" which is greater than one. Here, this coefficient depends on various parameters, such as ductility and overstrength factors. The present research aims to evaluate the value of the displacement amplification factor in seismic design codes and then tries to propose a value to estimate the maximum lateral structural displacement from sever earthquakes, without using non-linear analysis. In seismic codes, since the displacement amplification is related to “force reduction factor" hence; this aspect has been accepted in the current study. Meanwhile, two methodologies are applied to evaluate the value of displacement amplification factor and its relation with the force reduction factor. In the first methodology, which is applied for all structures, the ratio of displacement amplification and force reduction factors is determined directly. Whereas, in the second methodology that is applicable just for R/C moment resisting frame, the ratio is obtained by calculating both factors, separately. The acquired results of these methodologies are alike and estimate the ratio of two factors from 1 to 1.2. The results indicate that the ratio of the displacement amplification factor and the force reduction factor differs to those proposed by seismic provisions such as NEHRP, IBC and Iranian seismic code (standard no. 2800).

Keywords: Displacement amplification factor, Ductility factor, Force reduction factor, Maximum lateral displacement.

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Authors: Lianglin Xiong, Xiuyong Ding, Shouming Zhong

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In this paper, the problem of asymptotical stability of neutral systems with nonlinear perturbations is investigated. Based on a class of novel augment Lyapunov functionals which contain freeweighting matrices, some new delay-dependent asymptotical stability criteria are formulated in terms of linear matrix inequalities (LMIs) by using new inequality analysis technique. Numerical examples are given to demonstrate the derived condition are much less conservative than those given in the literature.

Keywords: Asymptotical stability, neutral system, nonlinear perturbation, delay-dependent, linear matrix inequality (LMI).

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Authors: Kholod M. Abu-Alnaja

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In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.

Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential Equations

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Authors: Mahmoud R. Shaghaghian

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Genetic Algorithms (GAs) are direct searching methods which require little information from design space. This characteristic beside robustness of these algorithms makes them to be very popular in recent decades. On the other hand, while this method is employed, there is no guarantee to achieve optimum results. This obliged designer to run such algorithms more than one time to achieve more reliable results. There are many attempts to modify the algorithms to make them more efficient. In this paper, by application of fractal dimension (particularly, Box Counting Method), the complexity of design space are established for determination of mutation and crossover probabilities (Pm and Pc). This methodology is followed by a numerical example for more clarification. It is concluded that this modification will improve efficiency of GAs and make them to bring about more reliable results especially for design space with higher fractal dimensions.

Keywords: Genetic Algorithm, Fractal Dimension, BoxCounting Method, Weierstrass-Mandelbrot function.

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Authors: Michael Todinov, Eberechi Weli

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The paper suggests for the first time the use of dynamic programming techniques for optimal risk reduction in the railway industry. It is shown that by using the concept ‘amount of removed risk by a risk reduction option’, the problem related to optimal allocation of a fixed budget to achieve a maximum risk reduction in the railway industry can be reduced to an optimisation problem from dynamic programming. For n risk reduction options and size of the available risk reduction budget B (expressed as integer number), the worst-case running time of the proposed algorithm is O (n x (B+1)), which makes the proposed method a very efficient tool for solving the optimal risk reduction problem in the railway industry. 

Keywords: Optimisation, railway risk reduction, budget constraints, dynamic programming.

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Authors: B. Siva Kumar Reddy, B. Lakshmi

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This paper addresses the reduction of peak to average power ratio (PAPR) for the OFDM in Mobile-WiMAX physical layer (PHY) standard. In the process, the best achievable PAPR of 0 dB is found for the OFDM spectrum using phase modulation technique which avoids the nonlinear distortion. The performance of the WiMAX PHY standard is handled by the software defined radio (SDR) prototype in which GNU Radio and USRP N210 employed as software and hardware platforms respectively. It is also found that BER performance is shown for different coding and different modulation schemes. To empathize wireless propagation in specific environments, a sliding correlator wireless channel sounding system is designed by using SDR testbed.

Keywords: BER, Channel sounding, GNU Radio, OFDM/OFDMA, USRP N210.

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Authors: Akbar H. Borzabadi, Omid S. Fard

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In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Keywords: Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming

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Authors: Ali Reza Mehrabian, Caro Lucas

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In this paper a new control strategy based on Brain Emotional Learning (BEL) model has been introduced. A modified BEL model has been proposed to increase the degree of freedom, controlling capability, reliability and robustness, which can be implemented in real engineering systems. The performance of the proposed BEL controller has been illustrated by applying it on different nonlinear uncertain systems, showing very good adaptability and robustness, while maintaining stability.

Keywords: Learning control systems, emotional decision making, nonlinear systems, adaptive control.

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Authors: Nemat Abazari, Reza Abazari

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In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.

Keywords: Nonlinear multi-pantograph equation, delay differential equation, differential transformation method, proportional delay conditions, closed form solution.

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Authors: Weifeng Pan

Abstract:

Complex networks have been intensively studied across many fields, especially in Internet technology, biological engineering, and nonlinear science. Software is built up out of many interacting components at various levels of granularity, such as functions, classes, and packages, representing another important class of complex networks. It can also be studied using complex network theory. Over the last decade, many papers on the interdisciplinary research between software engineering and complex networks have been published. It provides a different dimension to our understanding of software and also is very useful for the design and development of software systems. This paper will explore how to use the complex network theory to analyze software structure, and briefly review the main advances in corresponding aspects.

Keywords: Metrics, measurement, complex networks, software.

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Authors: Tomohiro Hachino, Hitoshi Takata, Shigeru Nakayama, Ichiro Iimura, Seiji Fukushima, Yasutaka Igarashi

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This paper presents a nonparametric identification of continuous-time nonlinear systems by using a Gaussian process (GP) model. The GP prior model is trained by artificial bee colony algorithm. The nonlinear function of the objective system is estimated as the predictive mean function of the GP, and the confidence measure of the estimated nonlinear function is given by the predictive covariance of the GP. The proposed identification method is applied to modeling of a simplified electric power system. Simulation results are shown to demonstrate the effectiveness of the proposed method.

Keywords: Artificial bee colony algorithm, Gaussian process model, identification, nonlinear system, electric power system.

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Authors: Shishen Xie

Abstract:

In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations

Keywords: variation iteration method, decomposition method, nonlinear integro-differential equations

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