Search results for: Nonlinear Models.

Authors: Thevaneyan K. David, John P. Forth

Abstract:

Integral Abutment Bridges (IAB) are defined as simple or multiple span bridges in which the bridge deck is cast monolithically with the abutment walls. This kind of bridges are becoming very popular due to different aspects such as good response under seismic loading, low initial costs, elimination of bearings, and less maintenance. However the main issue related to the analysis of this type of structures is dealing with soil-structure interaction of the abutment walls and the supporting piles. Various soil constitutive models have been used in studies of soil-structure interaction in this kind of structures by researchers. This paper is an effort to review the implementation of various finite elements model which explicitly incorporates the nonlinear soil and linear structural response considering various soil constitutive models and finite element mesh.

Keywords: Constitutive Models, FEM, Integral AbutmentBridges, Soil-structure Interactions

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Authors: R. Ghasemi, M. R. Rahimi Khoygani

Abstract:

This paper proposes the designing direct adaptive neural controller to apply for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) neural adaptive controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are importance of this paper. The simulation results show the promising performance of the proposed controller.

Keywords: Adaptive Neural Controller, Nonlinear Dynamical, Neural Network, RBF, Driven Pendulum, Position Control.

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Authors: A. Reyes-Salazar, M. D. Llanes-Tizoc, E. Bojorquez, F. Valenzuela-Beltran, J. Bojorquez, J. R. Gaxiola-Camacho, A. Haldar

Abstract:

Seismic analysis of steel buildings is usually based on the use of the concentrated mass (ML) matrix and the Rayleigh damping matrix (C). Similarly, the initial stiffness matrix (KO) and the first two modes associated to lateral vibrations are commonly used to develop the matrix C. The evaluation of the accuracy of these practices for the particular case of steel buildings with moment-resisting steel frames constitutes the main objective of this research. For this, the nonlinear seismic responses of three models of steel frames, representing low-, medium- and high-rise steel buildings, are considered. Results indicate that if the ML matrix is used, shears and bending moments in columns are underestimated by up to 30% and 65%, respectively, when compared to the corresponding results obtained with the consistent mass matrix (MC). It is also shown that if KO is used in C instead the tangent stiffness matrix (Kt), axial loads in columns are underestimated by up to 80%. It is concluded that the consistent mass matrix should be used in the structural modelling of moment resisting steel frames and the tangent stiffness matrix should be used to develop the Rayleigh damping matrix.

Keywords: Moment-resisting steel frames, consistent and concentrated mass matrices, nonlinear seismic response, Rayleigh damping.

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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

Abstract:

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

Abstract:

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: George D. Hatzigeorgiou, Nikos G. Pnevmatikos

Abstract:

This study examines the inelastic behavior of adjacent planar reinforced concrete (R.C.) frames subjected to strong ground motions. The investigation focuses on the effects of vertical ground motion on the seismic pounding. The examined structures are modeled and analyzed by RUAUMOKO dynamic nonlinear analysis program using reliable hysteretic models for both structural members and contact elements. It is found that the vertical ground motion mildly affects the seismic response of adjacent buildings subjected to structural pounding and, for this reason, it can be ignored from the displacement and interstorey drifts assessment. However, the structural damage is moderately affected by the vertical component of earthquakes.

Keywords: Nonlinear seismic behavior, reinforced concrete structures, structural pounding, vertical ground motions.

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Authors: Magdy G. Asaad

Abstract:

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: Sachin Bhalekar, Varsha Daftardar-Gejji

Abstract:

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: Ana Clara Santos, Maria Manuela Portela, Bettina Schaefli

Abstract:

This work assesses the performance of an analytical model framework to generate daily flow duration curves, FDCs, based on climatic characteristics of the catchments and on their streamflow recession coefficients. According to the analytical model framework, precipitation is considered to be a stochastic process, modeled as a marked Poisson process, and recession is considered to be deterministic, with parameters that can be computed based on different models. The analytical model framework was tested for three case studies with different hydrological regimes located in Switzerland: pluvial, snow-dominated and glacier. For that purpose, five time intervals were analyzed (the four meteorological seasons and the civil year) and two developments of the model were tested: one considering a linear recession model and the other adopting a nonlinear recession model. Those developments were combined with recession coefficients obtained from two different approaches: forward and inverse estimation. The performance of the analytical framework when considering forward parameter estimation is poor in comparison with the inverse estimation for both, linear and nonlinear models. For the pluvial catchment, the inverse estimation shows exceptional good results, especially for the nonlinear model, clearing suggesting that the model has the ability to describe FDCs. For the snow-dominated and glacier catchments the seasonal results are better than the annual ones suggesting that the model can describe streamflows in those conditions and that future efforts should focus on improving and combining seasonal curves instead of considering single annual ones.

Keywords: Analytical streamflow distribution, stochastic process, linear and non-linear recession, hydrological modelling, daily discharges.

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Authors: Gholamreza Hojjati, Kourosh Parand

Abstract:

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: Osama A. Marzouk

Abstract:

We propose a reduced-ordermodel for the instantaneous hydrodynamic force on a cylinder. The model consists of a system of two ordinary differential equations (ODEs), which can be integrated in time to yield very accurate histories of the resultant force and its direction. In contrast to several existing models, the proposed model considers the actual (total) hydrodynamic force rather than its perpendicular or parallel projection (the lift and drag), and captures the complete force rather than the oscillatory part only. We study and provide descriptions of the relationship between the model parameters, evaluated utilizing results from numerical simulations, and the Reynolds number so that the model can be used at any arbitrary value within the considered range of 100 to 500 to provide accurate representation of the force without the need to perform timeconsuming simulations and solving the partial differential equations (PDEs) governing the flow field.

Keywords: reduced-order model, wake oscillator, nonlinear, ODEsystem

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Authors: Toshinori Nawata

Abstract:

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

Abstract:

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: Mohammed Farag, Mina Attari, S. Andrew Gadsden, Saeid R. Habibi

Abstract:

Battery state of charge (SOC) estimation is an important parameter as it measures the total amount of electrical energy stored at a current time. The SOC percentage acts as a fuel gauge if it is compared with a conventional vehicle. Estimating the SOC is, therefore, essential for monitoring the amount of useful life remaining in the battery system. This paper looks at the implementation of three nonlinear estimation strategies for Li-Ion battery SOC estimation. One of the most common behavioral battery models is the one state hysteresis (OSH) model. The extended Kalman filter (EKF), the smooth variable structure filter (SVSF), and the time-varying smoothing boundary layer SVSF are applied on this model, and the results are compared.

Keywords: State of charge estimation, battery modeling, one-state hysteresis, filtering and estimation.

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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: 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: Jin Zhang, Wing Lon Ng

Abstract:

In recent years, copulas have become very popular in financial research and actuarial science as they are more flexible in modelling the co-movements and relationships of risk factors as compared to the conventional linear correlation coefficient by Pearson. However, a precise estimation of the copula parameters is vital in order to correctly capture the (possibly nonlinear) dependence structure and joint tail events. In this study, we employ two optimization heuristics, namely Differential Evolution and Threshold Accepting to tackle the parameter estimation of multivariate t distribution models in the EML approach. Since the evolutionary optimizer does not rely on gradient search, the EML approach can be applied to estimation of more complicated copula models such as high-dimensional copulas. Our experimental study shows that the proposed method provides more robust and more accurate estimates as compared to the IFM approach.

Keywords: Copula Models, Student t Copula, Parameter Inference, Differential Evolution, Threshold Accepting.

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Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun

Abstract:

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: Lianglin Xiong, Xiuyong Ding, Shouming Zhong

Abstract:

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

Abstract:

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: Akbar H. Borzabadi, Omid S. Fard

Abstract:

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

Abstract:

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

Abstract:

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

Abstract:

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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Authors: N. Kaewpraek, W. Assawinchaichote

Abstract:

This paper considers an H_∞ TS fuzzy state-derivative feedback controller for a class of nonlinear dynamical systems. A Takagi-Sugeno (TS) fuzzy model is used to approximate a class of nonlinear dynamical systems. Then, based on a linear matrix inequality (LMI) approach, we design an H_∞ TS fuzzy state-derivative feedback control law which guarantees L₂-gain of the mapping from the exogenous input noise to the regulated output to be less or equal to a prescribed value. We derive a sufficient condition such that the system with the fuzzy controller is asymptotically stable and H_∞ performance is satisfied. Finally, we provide and simulate a numerical example is provided to illustrate the stability and the effectiveness of the proposed controller.

Keywords: H∞ fuzzy control, LMI, Takagi-Sugano (TS) fuzzy model, nonlinear dynamic systems, state-derivative feedback.

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Authors: A. N. K. Nasir, M. A. Ahmad, R. M. T. Raja Ismail

Abstract:

The research on two-wheels balancing robot has gained momentum due to their functionality and reliability when completing certain tasks. This paper presents investigations into the performance comparison of Linear Quadratic Regulator (LQR) and PID-PID controllers for a highly nonlinear 2–wheels balancing robot. The mathematical model of 2-wheels balancing robot that is highly nonlinear is derived. The final model is then represented in statespace form and the system suffers from mismatched condition. Two system responses namely the robot position and robot angular position are obtained. The performances of the LQR and PID-PID controllers are examined in terms of input tracking and disturbances rejection capability. Simulation results of the responses of the nonlinear 2–wheels balancing robot are presented in time domain. A comparative assessment of both control schemes to the system performance is presented and discussed.

Keywords: PID, LQR, Two-wheels balancing robot.

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Authors: Dong Sang Yoo

Abstract:

We consider nonlinear uncertain systems such that a  priori information of the uncertainties is not available. For such  systems, we assume that the upper bound of the uncertainties is  represented as a Fredholm integral equation of the first kind and we  propose an adaptation law that is capable of estimating the upper  bound and design a continuous robust control which renders nonlinear  uncertain systems ultimately bounded.

 

Keywords: Adaptive Control, Estimation, Fredholm Integral, Uncertain System.

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Authors: N. N. Omehe

Abstract:

CdSiP2 and CdsiAs2 are nonlinear optical materials for near and mid-infrared applications. Density functional theory has been applied to study the structure, band gap, and optical properties of these materials. The pseudopotential method was used in the form of projector augmented wave (PAW) and norm-conserving, the band structure calculations yielded a band gap of 1.55 eV and 0.88 eV for CdSiP2 and CdsiAs2 respectively. The values of ε1(ω)  from the doelectric function calculations are 15 and 14.9 CdSiP2 and CdsiAs2 respectively.

Keywords: Band structure, chalcopyrite, near-infrared materials, mid-infrared materials, nonlinear material, optical properties.

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