Search results for: linear and non-linear recession

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 Octorotor UAV and its feature will be shown.

Keywords: sliding mode, backstepping, decoupling, octorotor UAV

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Authors: Lamia Bourdache, Amar Djema

Abstract:

The effect of non-Newtonian property (power law index n) on traveling waves of thin layer of power law fluid flowing over an inclined plane is investigated. For this, a simplified second-order two-equation model (SM) is used. The complete model is second-order four-equation (CM). It is derived by combining the weighted residual integral method and the lubrication theory. This is due to the fact that at the beginning of the instability waves, a very small number of waves is observed. Using a suitable set of test functions, second order terms are eliminated from the calculus so that the model is still accurate to the second order approximation. Linear, spatial, and temporal stabilities are studied. For travelling waves, a particular type of wave form that is steady in a moving frame, i.e., that travels at a constant celerity without changing its shape is studied. This type of solutions which are characterized by their celerity exists under suitable conditions, when the widening due to dispersion is balanced exactly by the narrowing effect due to the nonlinearity. Changing the parameter of celerity in some range allows exploring the entire spectrum of asymptotic behavior of these traveling waves. The (SM) model is converted into a three dimensional dynamical system. The result is that the model exhibits bifurcation scenarios such as heteroclinic, homoclinic, Hopf, and period-doubling bifurcations for different values of the power law index n. The influence of the non-Newtonian parameter on the nonlinear development of these travelling waves is discussed. It is found at the end that the qualitative characters of bifurcation scenarios are insensitive to the variation of the power law index.

Keywords: inclined plane, nonlinear stability, non-Newtonian, thin film

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

Abstract:

In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: Kanica Goel, Nilam

Abstract:

Infectious diseases are a leading cause of death worldwide and hence a great challenge for every nation. Thus, it becomes utmost essential to prevent and reduce the spread of infectious disease among humans. Mathematical models help to better understand the transmission dynamics and spread of infections. For this purpose, in the present article, we have proposed a nonlinear time-delayed SVIRS (Susceptible-Vaccinated-Infected-Recovered-Susceptible) mathematical model with nonlinear type incidence rate and nonlinear type treatment rate. Analytical study of the model shows that model exhibits two types of equilibrium points, namely, disease-free equilibrium and endemic equilibrium. Further, for the long-term behavior of the model, stability of the model is discussed with the help of basic reproduction number R₀ and we showed that disease-free equilibrium is locally asymptotically stable if the basic reproduction number R₀ is less than one and unstable if the basic reproduction number R₀ is greater than one for the time lag τ≥0. Furthermore, when basic reproduction number R₀ is one, using center manifold theory and Casillo-Chavez and Song theorem, we showed that the model undergoes transcritical bifurcation. Moreover, numerical simulations are being carried out using MATLAB 2012b to illustrate the theoretical results.

Keywords: nonlinear incidence rate, nonlinear treatment rate, stability, time delayed SVIRS epidemic model

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Authors: Mohammadsadegh Zanganehfar

Abstract:

Since the modernism, movement, and appearance of modern architecture, an aggressive desire for a general design theory in the theoretical works of architects in the form of books and essays emerges. Since Robert Venturi and Denise Scott Brown’s published complexity and contradiction in architecture in 1966, the discourse of complexity and volumetric composition has been an important and controversial issue in the discipline. Ever since various theories and essays were involved in this discourse, this paper attempt to identify chaos theory as a scientific model of complexity and its relation to architecture design theory by conducting a qualitative analysis and multidisciplinary critical approach through architecture and basic sciences resources. As a result, we identify chaotic architecture as the correlation of chaos theory and architecture as an independent nonlinear design theory with specific characteristics and properties.

Keywords: architecture complexity, chaos theory, fractals, nonlinear dynamic systems, nonlinear ontology

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Authors: B. Güney, Ç. Teke

Abstract:

In recent years, rapid and correct decision making is crucial for both people and enterprises. However, uncertainty makes decision-making difficult. Fuzzy logic is used for coping with this situation. Thus, fuzzy linear programming models are developed in order to handle uncertainty in objective function and the constraints. In this study, a problem of a factory in food industry is investigated, required data is obtained and the problem is figured out as a fuzzy linear programming model. The model is solved using Zimmerman approach which is one of the approaches for fuzzy linear programming. As a result, the solution gives the amount of production for each product type in order to gain maximum profit.

Keywords: food industry, fuzzy linear programming, fuzzy logic, linear programming

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Authors: Hazem Al-Mofleh, John Daniels, Joseph McKean

Abstract:

Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares.

Keywords: non-linear wilcoxon, robust estimation, variogram estimation, wilcoxon norm

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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, plasmonic waveguide, chalcogenide, propagation equation

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Authors: Liuyu Zhang, Di Mo, Qiang Yan, Min Liu

Abstract:

As the important equipment in the construction field, cuplock scaffold plays an important role in the construction process. As a scaffold connecting member, cuplock joint is of great importance. In order to explore the rotational stiffness nonlinear characteristics changing features of different structural forms of cuplock joint in different tightening torque condition under different conditions of load, ANSYS is used to establish four kinds of cuplock joint models with different forces to simulate the real force situation. By setting the different load conditions which means the cuplock is loaded at a certain distance from the cuplock joint in a certain direction until the cuplock is damaged and considering the gap between the cross bar joint and the vertical bar, the differences in the influence of the structural form and tightening torque on the rotation stiffness of the cuplock under different load conditions are compared. It is significantly important to improve the accuracy of calculating bearing capacity and stability of the cuplock steel pipe scaffold.

Keywords: cuplock joint, highway tunnel, non-linear characteristics, rotational stiffness, scaffold stability, theoretical analysis

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Authors: Ebrahim Hassan Kapeel, Ahmed Mohsen Kamel, Hossan Hendy, Yehia Z. Elhalwagy

Abstract:

Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control lawisdesigned for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: UAV dynamic model, attitude control, nonlinear PID, dynamic inversion

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Authors: Om Prakash Keshri, Anand Kumar, Vinod K. Gupta

Abstract:

In the present study, the effect of gravity modulation on the onset of convection in viscous fluid layer under the influence of induced magnetic field, salted from above on the boundaries, has been investigated. Linear and nonlinear stability analysis has been performed. A linear stability analysis is performed to show that the gravity modulation can significantly affect the stability limits of the system. A method based on small amplitude of the modulation is used to compute the critical value of Rayleigh number and wave number. The effect of Smith number, salute Rayleigh number and magnetic Prandtl number on the stability of the system is investigated.

Keywords: viscous fluid, induced magnetic field, gravity modulation, salute convection

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Authors: Jelena R. Pejović, Nina N. Serdar

Abstract:

This paper presents an analysis of the “Performance-Based” seismic design method, in order to overcome the perceived disadvantages and limitations of the existing seismic design approach based on force, in engineering practice. Bearing in mind, the specificity of the earthquake as a load and the fact that the seismic resistance of the structures solely depends on its behaviour in the nonlinear field, traditional seismic design approach based on force and linear analysis is not adequate. “Performance-Based” seismic design method is based on nonlinear analysis and can be used in everyday engineering practice. This paper presents the application of this method to eight-story high reinforced concrete building with combined structural system (reinforced concrete frame structural system in one direction and reinforced concrete ductile wall system in other direction). The nonlinear time-history analysis is performed on the spatial model of the structure using program Perform 3D, where the structure is exposed to forty real earthquake records. For considered building, large number of results were obtained. It was concluded that using this method we could, with a high degree of reliability, evaluate structural behavior under earthquake. It is obtained significant differences in the response of structures to various earthquake records. Also analysis showed that frame structural system had not performed well at the effect of earthquake records on soil like sand and gravel, while a ductile wall system had a satisfactory behavior on different types of soils.

Keywords: ductile wall, frame system, nonlinear time-history analysis, performance-based methodology, RC building

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Authors: Ali Raheli, Rahim Habibifar, Behzad Mohammadi-Alasti, Mahdi Abbasgholipour

Abstract:

This paper presents vibration behavior of a FGM micro-beam and its pull-in instability under a nonlinear electrostatic pressure. An exponential function has been applied to show the continuous gradation of the properties along thickness. Nonlinear integro-differential-electro-mechanical equation based on Euler–Bernoulli beam theory has been derived. The governing equation in the static analysis has been solved using Step-by-Step Linearization Method and Finite Difference Method. Fixed points or equilibrium positions and singular points have been shown in the state control space. In order to find the response to a step DC voltage, the nonlinear equation of motion has been solved using Galerkin-based reduced-order model and time histories and phase portrait for different applied voltages have been shown. The effects of electrostatic pressure on stability of FGM micro-beams having various amounts of the ceramic constituent have been investigated.

Keywords: FGM, MEMS, nonlinear vibration, electrical, dynamic pull-in voltage

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Authors: Ebrahim H. Kapeel, Ahmed M. Kamel, Hossam Hendy, Yehia Z. Elhalwagy

Abstract:

Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control law is designed for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: attitude control, nonlinear PID, dynamic inversion

Procedia PDF Downloads 83

Authors: Sandeep Singh

Abstract:

In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: Huai-Cong Liu，Tae Chul Jeong，Ju Lee

Abstract:

This paper describes characteristic analysis of a synchronous reluctance motor (SynRM)’s rotor with the Multi-segment and Multi-layer structure. The magnetic-saturation phenomenon in SynRM is often appeared. Therefore, when modeling analysis of SynRM the calculation of nonlinear magnetic field needs to be considered. An important influence factor on the convergence process is how to determine the relative permeability. An improved method, which ensures the calculation, is convergence by linear iterative method for saturated magnetic field. If there are inflection points on the magnetic curve,an optimum convergence method of solution for nonlinear magnetic field was provided. Then the equivalent magnetic circuit is calculated, and d,q-axis inductance can be got. At last, this process is applied to design a 7.5Kw SynRM and its validity is verified by comparing with the result of finite element method (FEM) and experimental test data.

Keywords: SynRM, magnetic-saturation, magnetic circuit, analytical modeling

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Authors: T. Martini, J. M. Martínez

Abstract:

An algorithmic acceleration strategy based on quasi-Newton (or secant) methods is displayed for address the practical problem of accelerating the convergence of the Newton-Lagrange method in the case of convergence to critical multipliers. Since the Newton-Lagrange iteration converges locally at a linear rate, it is natural to conjecture that quasi-Newton methods based on the so called secant equation and some minimal variation principle, could converge superlinearly, thus restoring the convergence properties of Newton's method. This strategy can also be applied to accelerate the convergence of algorithms applied to fixed-points problems. Computational experience is reported illustrating the efficiency of this strategy to solve fixed-point problems with linear convergence rate.

Keywords: algorithmic acceleration, fixed-point problems, nonlinear programming, quasi-newton method

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Authors: Mishu Gupta, Rama Gupta

Abstract:

It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.

Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

Abstract:

In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Qasim M. Kriri

Abstract:

Few Saudi Arabia production companies face financial profit issues until this moment. This work presents a linear integer programming model that solves a production problem of a Saudi Food Company in Saudi Arabia. An optimal solution to the above-mentioned problem is a Linear Programming solution. In this regard, the main purpose of this project is to maximize profit. Linear Programming Technique has been used to derive the maximum profit from production of natural juice at Saudi Food Co. The operations of production of the company were formulated and optimal results are found out by using Lindo Software that employed Sensitivity Analysis and Parametric linear programming in order develop Linear Programming. In addition, the parameter values are increased, then the values of the objective function will be increased.

Keywords: parameter linear programming, objective function, sensitivity analysis, optimize profit

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Authors: Alireza Toloei, Ahmad R. Saffary, Reza Ghasemi

Abstract:

Due to the growing need for energy and limited fossil resources, the use of renewable energy, particularly wind is strongly favored. We all wind energy can’t be saved. Betz law, 59% of the total kinetic energy of the wind turbine is extracting. Therefore turbine control to achieve maximum performance and maintain stable conditions seem necessary. In this article, we plan for a horizontal axis wind turbine variable-speed variable-pitch nonlinear controller to obtain maximum output power. The model presented in this article, including a wide range of wind turbines are horizontal axis. However, the parameters used in this model is from Vestas V29 225 kW wind turbine. We designed second order sliding mode controller, which was robust in the face of changes in wind speed and it eliminated chattering by using of super twisting algorithm. Finally, using MATLAB software to simulate the results we considered the accuracy of the simulation results.

Keywords: non linear controller, robust, sliding mode, kinetic energy

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

Abstract:

In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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Authors: Morteza Shayan Arani, Mohammadamin Esmailzadehazimi, Mohammadreza Moeini, Mohammad Toorani, Aouni A. Lakis

Abstract:

This paper investigates the nonlinear response of thin, incompressible, hyperelastic cylindrical shells in the presence of a time-varying temperature field while considering initial geometric imperfections. The governing equations of motion are derived using an improved Donnell's shallow shell theory. The hyperelastic material is modeled using the Mooney-Rivlin model with two parameters, incorporating temperature-dependent terms. The Lagrangian method is applied to obtain the equation of motion. The resulting governing equation is addressed through the Lindstedt-Poincaré and Multiple Scale methods. The linear and nonlinear models presented in this study are verified against existing open literature, demonstrating the accuracy and reliability of the presented model. The study focuses on understanding the influence of temperature variations and geometrical imperfections on the natural frequency and amplitude-frequency response of the systems. Notably, the investigation reveals the coexistence of hardening and softening peaks in the amplitude-frequency response, which vary in magnitude depending on these parameters. Additionally, resonance peaks exhibit changes as a result of temperature and geometric imperfections.

Keywords: hyperelastic material, cylindrical shell, geometrical nonlinearity, material naolinearity, initial geometric imperfection, temperature gradient, hardening and softening

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Authors: Yang Liu

Abstract:

Reinforced concrete (RC) shear wall structures are one of the most popular and efficient structural forms for medium- and high-rise buildings to resist the action of earthquake loading. Thus, it is of great significance to evaluate the seismic demands of the RC shear walls. In this paper, the application of the extend spectrum-based pushover analysis (ESPA) method on the seismic evaluation of the shear wall structure is presented. The ESPA method includes a nonlinear consecutive pushover analysis procedure and a linear elastic modal response analysis procedure to consider the combination of modes in both elastic and inelastic cases. It is found from the results of case study that the ESPA method can predict the seismic performance of shear wall structures, including internal forces and deformations very well.

Keywords: reinforced concrete shear wall, seismic performance, high mode effect, nonlinear analysis

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Authors: Sarun Phibanchon, Yuttakarn Rattanachai

Abstract:

The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.

Keywords: soliton, ion-acoustic waves, plasma, spectral method

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Authors: Hamid Nikzad, Shinta Yoshitomi

Abstract:

In this paper, nonlinear static pushover analysis is performed on 15 storied RC building structure with a shear wall to evaluate the seismic performance of the building. Section sizes of the members are obtained based on structural optimization method utilizing MATLAB frame optimizer, then the structure is simulated and designed in ETABS program conforming ACI 318-14 design code. The pushover curve has been generated by pushing the top node of the structure to the limited target displacement. Members failure due to the formation of plastic hinges, considering shear wall-frame structure was observed and the result of this study is presented based on current regulation of FEMA356, ASCE7-10, and ACI 318-14 design criteria

Keywords: structural optimization, linear static analysis, ETABS, MATLAB, RC moment frame, RC shear wall structures

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Authors: Hyun-Woo Cho

Abstract:

It is quite important to utilize right time and intelligent production monitoring and diagnosis of industrial processes in terms of quality and safety issues. When compared with monitoring task, fault diagnosis represents the task of finding process variables responsible causing a specific fault in the process. It can be helpful to process operators who should investigate and eliminate root causes more effectively and efficiently. This work focused on the active use of combining a nonlinear statistical technique with a preprocessing method in order to implement practical real-time fault identification schemes for data-rich cases. To compare its performance to existing identification schemes, a case study on a benchmark process was performed in several scenarios. The results showed that the proposed fault identification scheme produced more reliable diagnosis results than linear methods. In addition, the use of the filtering step improved the identification results for the complicated processes with massive data sets.

Keywords: diagnosis, filtering, nonlinear statistical techniques, process monitoring

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Authors: A. Zerarka, W. Djoudi

Abstract:

We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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Authors: Hendradi Hardhienata, Tony Sumaryada, Sri Setyaningsih

Abstract:

Current progress in the field of nonlinear optics has enabled precise surface characterization in semiconductor materials. Nonlinear optical techniques are favorable due to their nondestructive measurement and ability to work in nonvacuum and ambient conditions. The advance of the bond hyperpolarizability models opens a wide range of nanoscale surface investigation including the possibility to detect molecular orientation at the surface of silicon and zincblende semiconductors, investigation of electric field induced second harmonic fields at the semiconductor interface, detection of surface impurities, and very recently, study surface defects such as twin boundary in wurtzite semiconductors. In this work, we show using nonlinear optical techniques, e.g. nonlinear bond models how arbitrary polarization of the incoming electric field in Rotational Anisotropy Spectroscopy experiments can provide more information regarding the origin of the nonlinear sources in zincblende and wurtzite semiconductor structure. In addition, using hyperpolarizability consideration, we describe how the nonlinear susceptibility tensor describing SHG can be well modelled using only few parameter because of the symmetry of the bonds. We also show how the third harmonic intensity feature shows considerable changes when the incoming field polarization angle is changed from s-polarized to p-polarized. We also propose a method how to investigate surface reconstruction and defects in wurtzite and zincblende structure at the nanoscale level.

Keywords: surface characterization, bond model, rotational anisotropy spectroscopy, effective hyperpolarizability

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Authors: Shahrokh Barati

Abstract:

In this paper, we introduced AIDS disease at first, then proposed dynamic model illustrate its progress, after expression of a short history of nonlinear modeling by polynomial phasing systems, we considered the stability conditions of the systems, which contained a huge amount of researches in order to modeling and control of AIDS in dynamic nonlinear form, in this approach using a frame work of control any polynomial phasing modeling system which have been generalized by part of phasing model of T-S, in order to control the system in better way, the stability conditions were achieved based on polynomial functions, then we focused to design the appropriate controller, firstly we considered the equilibrium points of system and their conditions and in order to examine changes in the parameters, we presented polynomial phase model that was the generalized approach rather than previous Takagi Sugeno models, then with using case we evaluated the equations in both open loop and close loop and with helping the controlling feedback, the close loop equations of system were calculated, to simulate nonlinear model of AIDS disease, we used polynomial phasing controller output that was capable to make the parameters of a nonlinear system to follow a sustainable reference model properly.

Keywords: polynomial fuzzy, AIDS, nonlinear AIDS model, fuzzy control systems

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