Search results for: NARX (Nonlinear Autoregressive Exogenous Model)

Authors: A. Oukaci, R. Toufouti, D. Dib, l. Atarsia

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This article presents a multitude of alternative techniques to control the vector control, namely the nonlinear control and sliding mode control. Moreover, the implementation of their control law applied to the high-performance to the induction motor with the objective to improve the tracking control, ensure stability robustness to parameter variations and disturbance rejection. Tests are performed numerical simulations in the Matlab/Simulink interface, the results demonstrate the efficiency and dynamic performance of the proposed strategy.

Keywords: Induction Motor (IM), Non-linear Control (NLC), Sliding Mode Control (SMC), nonlinear sliding surface

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Authors: Jan Henrik Wosnitza

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The logistic regression has developed into a standard approach for estimating conditional probabilities in a wide range of applications including credit risk prediction. The article at hand contributes to the current literature on logistic regression fourfold: First, it is demonstrated that the binary logistic regression automatically meets its model assumptions under very general conditions. This result explains, at least in part, the logistic regression's popularity. Second, the requirement of homoscedasticity in the context of binary logistic regression is theoretically substantiated. The variances among the groups of defaulted and non-defaulted obligors have to be the same across the level of the aggregated default indicators in order to achieve linear logits. Third, this article sheds some light on the question why nonlinear logits might be superior to linear logits in case of a small amount of data. Fourth, an innovative methodology for estimating correlations between obligor-specific log-odds is proposed. In order to crystallize the key ideas, this paper focuses on the example of credit risk prediction. However, the results presented in this paper can easily be transferred to any other field of application.

Keywords: correlation, credit risk estimation, default correlation, homoscedasticity, logistic regression, nonlinear logistic regression

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Authors: Aid Abdelkrim

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A method of fatigue damage accumulation based upon application of energy parameters of the fatigue process is proposed in the paper. Using this model is simple, it has no parameter to be determined, it requires only the knowledge of the curve W–N (W: strain energy density N: number of cycles at failure) determined from the experimental Wöhler curve. To examine the performance of nonlinear models proposed in the estimation of fatigue damage and fatigue life of components under random loading, a batch of specimens made of 6082 T 6 aluminium alloy has been studied and some of the results are reported in the present paper. The paper describes an algorithm and suggests a fatigue cumulative damage model, especially when random loading is considered. This work contains the results of uni-axial random load fatigue tests with different mean and amplitude values performed on 6082T6 aluminium alloy specimens. The proposed model has been formulated to take into account the damage evolution at different load levels and it allows the effect of the loading sequence to be included by means of a recurrence formula derived for multilevel loading, considering complex load sequences. It is concluded that a ‘damaged stress interaction damage rule’ proposed here allows a better fatigue damage prediction than the widely used Palmgren–Miner rule, and a formula derived in random fatigue could be used to predict the fatigue damage and fatigue lifetime very easily. The results obtained by the model are compared with the experimental results and those calculated by the most fatigue damage model used in fatigue (Miner’s model). The comparison shows that the proposed model, presents a good estimation of the experimental results. Moreover, the error is minimized in comparison to the Miner’s model.

Keywords: damage accumulation, energy model, damage indicator, variable loading, random loading

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Authors: Yosra Baaziz, Moez Labidi

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Given limited research on monetary policy rules in revolutionary countries, this paper challenges the suitability of the Taylor rule in characterizing the monetary policy behavior of the Tunisian Central Bank (BCT), especially in turbulent times. More specifically, we investigate the possibility that the Taylor rule should be formulated as a threshold process and examine the validity of such nonlinear Taylor rule as a robust rule for conducting monetary policy in Tunisia. Using quarterly data from 1998:Q4 to 2013:Q4 to analyze the movement of nominal short-term interest rate of the BCT, we find that the nonlinear Taylor rule improves its performance with the advent of special events providing thus a better description of the Tunisian interest rate setting. In particular, our results show that the adoption of an appropriate nonlinear approach leads to a reduction in the errors of 150 basis points in 1999 and 2009, and 60 basis points in 2011, relative to the linear approach.

Keywords: policy rule, central bank, exchange rate, taylor rule, nonlinearity

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Authors: Mohamed Mohamed, Philip Bonello, Peter Russhard

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Blade Tip Timing (BTT) is a technology concerned with the estimation of both frequency and amplitude of rotating blades. A BTT system comprises two main parts: (a) the arrival time measurement system, and (b) the analysis algorithms. Simulators play an important role in the development of the analysis algorithms since they generate blade tip displacement data from the simulated blade vibration under controlled conditions. This enables an assessment of the performance of the different algorithms with respect to their ability to accurately reproduce the original simulated vibration. Such an assessment is usually not possible with real engine data since there is no practical alternative to BTT for blade vibration measurement. Most simulators used in the literature are based on a simple spring-mass-damper model to determine the vibration. In this work, a more realistic experimentally validated simulator based on the Finite Element (FE) model of a bladed disc (blisk) is first presented. It is then used to generate the necessary data for the assessment of different BTT algorithms. The FE modelling is validated using both a hammer test and two firewire cameras for the mode shapes. A number of autoregressive methods, fitting methods and state-of-the-art inverse methods (i.e. Russhard) are compared. All methods are compared with respect to both synchronous and asynchronous excitations with both single and simultaneous frequencies. The study assesses the applicability of each method for different conditions of vibration, amount of sampling data, and testing facilities, according to its performance and efficiency under these conditions.

Keywords: blade tip timing, blisk, finite element, vibration measurement

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Authors: L. A. Ostrovsky, Yu. A. Stepanyants

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Effect of Earth rotation on nonlinear waves is a practically important and theoretically challenging problem of fluid mechanics and geophysics. Whereas the large-scale, geostrophic processes such as Rossby waves are a classical object of oceanic and atmospheric physics, rotation effects on mesoscale waves are not well studied. In particular, the Coriolis force can radically modify the behavior of nonlinear internal gravity waves in the ocean having spatial scales of 1-10 kilometers and time durations of few hours. In the last decade, such a non-trivial behavior was observed more than once. Similar effects are possible for magnetic sound in the ionosphere. Here we outline the main physical peculiarities in the behavior of nonlinear internal waves due to the rotation effect and present some results of our recent studies. The consideration is based on the fourth-order equation derived by one of the authors as a rotation-modified Korteweg–de Vries (rKdV) equation which includes two types of dispersion: one is responsible for the finiteness of depth as in the classical KdV equation; another is due to the Coriolis effect. This equation is, in general, non-integrable; moreover, under the conditions typical of oceanic waves (positive dispersion parameter), it does not allow solitary solutions at all. In the opposite case (negative dispersion) which is possible for, e.g., magnetic sound, solitary solutions do exist and can form complex bound states (multisoliton). Another non-trivial properties of nonlinear internal waves with rotation include, to name a few, the ‘terminal’ damping of the initial KdV soliton disappearing in a finite time due to radiation losses caused by Earth’s rotation, and eventual transformation of a KdV soliton into a wave packet (an envelope soliton). The new results to be discussed refer to the interaction of a soliton with a long background wave. It is shown, in particular, that in this case internal solitons can exist since the radiation losses are compensated by energy pumping from the background wave. Finally, the relevant oceanic observations of rotation effect on internal waves are briefly described.

Keywords: Earth rotation, internal waves, nonlinear waves, solitons

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Authors: Z. Jannoo, B. W. Yap, N. Auchoybur, M. A. Lazim

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The two common approaches to Structural Equation Modeling (SEM) are the Covariance-Based SEM (CB-SEM) and Partial Least Squares SEM (PLS-SEM). There is much debate on the performance of CB-SEM and PLS-SEM for small sample size and when distributions are non-normal. This study evaluates the performance of CB-SEM and PLS-SEM under normality and non-normality conditions via a simulation. Monte Carlo Simulation in R programming language was employed to generate data based on the theoretical model with one endogenous and four exogenous variables. Each latent variable has three indicators. For normal distributions, CB-SEM estimates were found to be inaccurate for small sample size while PLS-SEM could produce the path estimates. Meanwhile, for a larger sample size, CB-SEM estimates have lower variability compared to PLS-SEM. Under non-normality, CB-SEM path estimates were inaccurate for small sample size. However, CB-SEM estimates are more accurate than those of PLS-SEM for sample size of 50 and above. The PLS-SEM estimates are not accurate unless sample size is very large.

Keywords: CB-SEM, Monte Carlo simulation, normality conditions, non-normality, PLS-SEM

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Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

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Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well-known formulas.

Keywords: conjugate gradient method, conjugate gradient coefficient, global convergence

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Authors: Gulgassyl Nugmanova, Zhanat Zhunussova, Kuralay Yesmakhanova, Galya Mamyrbekova, Ratbay Myrzakulov

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In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr\"odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields.

Keywords: Heisenberg Ferromagnet equations, soliton equations, equivalence, Lax representation

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Authors: Tasawar Hayat, Madiha Rashid, Maria Imtiaz, Ahmed Alsaedi

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This problem is about the study of flow of viscous fluid due to rotating disk in nanofluid. Effects of magnetic field, slip boundary conditions and thermal radiations are encountered. An incompressible fluid soaked the porous medium. In this model, nanoparticles of Cu is considered with water as the base fluid. For Copper-water nanofluid, graphical results are presented to describe the influences of nanoparticles volume fraction (φ) on velocity and temperature fields for the slip boundary conditions. The governing differential equations are transformed to a system of nonlinear ordinary differential equations by suitable transformations. Convergent solution of the nonlinear system is developed. The obtained results are analyzed through graphical illustrations for different parameters. Moreover, the features of the flow and heat transfer characteristics are analyzed. It is found that the skin friction coefficient and heat transfer rate at the surface are highest in copper-water nanofluid.

Keywords: MHD nanofluid, porous medium, rotating disk, slip effect

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Authors: Zeynep Karaçor, Volkan Alptekin, Gökhan Akar, Tuba Akar

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This paper aims to review the phenomenon of triplet deficit which is called interaction of budget balance that make up the overall balance of the economy, investment savings balance and current accounts balance in terms of Turkey. In this paper, triplet deficit state in Turkish economy has been analyzed with vector autoregressive model and Granger causality test using data covering the period of 1980-2010. According to VAR results, increase in current accounts is perceived on public sector borrowing requirement. These two variables influence each other bilaterally. Therefore, current accounts increase public deficit, whereas public deficit increases current accounts. It is not possible to mention the existence of a short-term Granger causality between variables at issue.

Keywords: internal and external deficit, stability, triplet deficit, Turkey economy

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Authors: Hyun-Woo Cho

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Unexpected operational events or abnormalities of industrial processes have a serious impact on the quality of final product of interest. In terms of statistical process control, fault detection and diagnosis of processes is one of the essential tasks needed to run the process safely. In this work, nonlinear representation of process measurement data is presented and evaluated using a simulation process. The effect of using different representation methods on the diagnosis performance is tested in terms of computational efficiency and data handling. The results have shown that the nonlinear representation technique produced more reliable diagnosis results and outperforms linear methods. The use of data filtering step improved computational speed and diagnosis performance for test data sets. The presented scheme is different from existing ones in that it attempts to extract the fault pattern in the reduced space, not in the original process variable space. Thus this scheme helps to reduce the sensitivity of empirical models to noise.

Keywords: fault diagnosis, nonlinear technique, process data, reduced spaces

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Authors: Sadia Arshad

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The new coronavirus disease or COVID-19 still poses an alarming situation around the world. Modeling based on the derivative of fractional order is relatively important to capture real-world problems and to analyze the realistic situation of the proposed model. Weproposed a mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. The new model is formulated in the Caputo sense and employs a nonlinear time-varying transmission rate. The existence and uniqueness solutions of the fractional order derivative have been studied using the fixed-point theory. The associated dynamical behaviors are discussed in terms of equilibrium, stability, and basic reproduction number. For the purpose of numerical implementation, an effcient approximation scheme is also employed to solve the fractional COVID-19 model. Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic. According to the comparative results with real data, we find the best value of fractional orderand justify the use of the fractional concept in the mathematical modelling, for the new fractional modelsimulates the reality more accurately than the other classical frameworks.

Keywords: fractional calculus, modeling, stability, numerical solution

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Authors: Elnaz Entezar, Reza Ezzati

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In recent decades, trade flows, capital, workforce, technology and information have increased between international borders and the globalization has turned to an undeniable process in international economics. Meanwhile, despite the positive aspects of globalization, the critics of globalization opine that the risks and costs of globalization for developing vulnerable economies and the world's impoverished people are high and significant. In this regard, this study by using the data of KOF Economic Institute and the World Bank for 113 different countries during the period 2002-2012, by taking advantage of panel smooth transition regression, and by taking the gross domestic product as transmission variables discuss the nonlinear relationship between research variables. The results have revealed that globalization in low regime (countries with low GDP) has negative impact whereas in high regime (countries with high GDP) has a positive impact. In spite of the fact that in the early stages of growth, control of corruption has a positive impact on economic growth, after a threshold has a negative impact on economic growth.

Keywords: globalization, corruption, panel smooth transition model, economic growth, threshold, economic convergence

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Authors: Cristian Baldini

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‘Diabesity’ is a term for diabetes occurring in the context of obesity. The positive effect of LCHF diets (low-carb, high-fat diets) is well documented: LCHF diets are at least as effective as other dietary strategies for reducing body weight, improving glycaemic control, and reducing both hyperinsulinaemia and blood glucose (reduction of HbA1c) in type 2 diabetes and have unique positive effects on blood lipid concentrations and cardiovascular risk factors. Also, in obese insulin-resistant women, food fried in extra-virgin olive oil significantly reduced both insulin and C-peptide responses after a meal. This case study shows that if combined, both dietary strategies produce a strong effect on blood glucose, resulting in a “forced” reduction of exogenous insulin injection to avoid the problem of hypoglycaemia. Blood tests after three months of this dietary treatment show how HbA1c, triglycerides, and blood lipid profile (LDL, HDL, Total Cholesterol) are improved despite the reduction of exogenous insulin injection of 80% with a parallel body weight decrease of 15%. For continuous glucose monitoring (CGM), the patient used FreeStyle Libre before and after the dietary treatment. In order to check general body functions and glycosuria, the patient used the urine test Multistix 10 SG Siemens.

Keywords: diabetes, obesity, diabesity, fat, fried foods

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Authors: Graziano Chesi

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The topological entropy plays a key role in linear dynamical systems, allowing one to establish the existence of stabilizing feedback controllers for linear systems in the presence of communications constraints. This paper addresses the determination of a robust value of the topological entropy in nonlinear dynamical systems, specifically the largest value of the topological entropy over all linearized models in a region of interest of the state space. It is shown that a sufficient condition for establishing upper bounds of the sought robust value of the topological entropy can be given in terms of a semidefinite program (SDP), which belongs to the class of convex optimization problems.

Keywords: non-linear system, communication constraint, topological entropy

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Authors: Mahdi Kiani, Hassan Salarieh, Aria Alasty, S. Mahdi Darbandi

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The design and implementation of the hybrid control method for a three-pole active magnetic bearing (AMB) is proposed in this paper. The system is inherently nonlinear and conventional nonlinear controllers are a little complicated, while the proposed hybrid controller has a piecewise linear form, i.e. linear in each sub-region. A state-feedback hybrid controller is designed in this study, and the unmeasurable states are estimated by an observer. The gains of the hybrid controller are obtained by the Linear Quadratic Regulator (LQR) method in each sub-region. To evaluate the performance, the designed controller is implemented on an experimental setup in static mode. The experimental results show that the proposed method can efficiently stabilize the three-pole AMB system. The simplicity of design, domain of attraction, uncomplicated control law, and computational time are advantages of this method over other nonlinear control strategies in AMB systems.

Keywords: active magnetic bearing, three pole AMB, hybrid control, Lyapunov function

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Authors: Omid Khandel, Azadeh Parvin

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An increase in accidental explosions in recent years has increased the interest on investigating the response and behavior of structures in more details. The present work focused on finite element analysis of multistory steel frame structures with different plan shapes subjected to blast loadings. In order to study the effect of the geometry of the building, three different shapes for the plan of the building were modeled and studied; Rectangular, Square and L shape plans. The nonlinear dynamic analysis was considered in this study. The relocation technique was also used to improve the behavior of structure. The accuracy of the multistory frame model was confirmed with those of the existing study in the literature and they were in good agreement. The effect of span length of the buildings was also considered. Finite element analysis of various scenarios for relocating the plastic hinges and improving the response of the structure was performed. The base shear versus displacement curves were compared to reveal the best possible scenarios to provide recommendations to designers and practitioners.

Keywords: nonlinear dynamic analysis, plastic hinge relocation, Retrofit, SAP2000

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Authors: Shaban Aly, Ali Al-Qahtani, Houari B. Khenous

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Synchronization is an important phenomenon commonly observed in nature. A system of periodically forced complex Duffings oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using impulsive synchronization techniques. We derive analytical expressions for impulsive control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.

Keywords: complex nonlinear oscillators, impulsive synchronization, chaotic systems, global exponential synchronization

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Authors: A. Boateng, La Gil-Alana, M. Lesaoana; Hj. Siweya, A. Belete

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This study examines long memory or long-range dependence in the CPI inflation rates of Ghana and South Africa using Whittle methods and autoregressive fractionally integrated moving average (ARFIMA) models. Standard I(0)/I(1) methods such as Augmented Dickey-Fuller (ADF), Philips-Perron (PP) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests were also employed. Our findings indicate that long memory exists in the CPI inflation rates of both countries. After processing fractional differencing and determining the short memory components, the models were specified as ARFIMA (4,0.35,2) and ARFIMA (3,0.49,3) respectively for Ghana and South Africa. Consequently, the CPI inflation rates of both countries are fractionally integrated and mean reverting. The implication of this result will assist in policy formulation and identification of inflationary pressures in an economy.

Keywords: Consumer Price Index (CPI) inflation rates, Whittle method, long memory, ARFIMA model

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Authors: Younghoo Choi, Yong Jun, Jinkoo Kim

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In this study seismic performance of typical reinforced concrete staggered wall system structures was evaluated through nonlinear static and incremental dynamic analyses. To this end, and 15-story SWS structures were designed and were analyzed to obtain their nonlinear force-displacement relationships. The analysis results showed that the 5-story SWS structures failed due to yielding of columns and walls located in the lower stories, whereas in the 15-story structures plastic hinges were more widely distributed throughout the stories.

Keywords: staggered wall systems, reinforced concrete, seismic performance

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Authors: Odunayo Olawuyi Fadodun

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Dielectric elastomers (DEs) are a type of intelligent materials with salient features like electromechanical coupling, lightweight, fast actuation speed, low cost and high energy density that make them good candidates for numerous engineering applications. This paper adopts a new nonlinear electroelastic constitutive theory to examine radial deformation of a pressurized thick-walled spherical shell of soft dielectric material with compliant electrodes on its inner and outer surfaces. A general formular for the internal pressure, which depends on the deformation and a potential difference between boundary electrodes or uniform surface charge distributions, is obtained in terms of special function. To illustrate the effects of an applied electric field on the mechanical behaviour of the shell, three different energy functions with distinct mechanical properties are employed for numerical purposes. The observed behaviour of the shells is preserved in the presence of an applied electric field, and the influence of the field due to a potential difference declines more slowly with the increasing deformation to that produced by a surface charge. Counterpart results are then presented for the thin-walled shell approximation as a limiting case of a thick-walled shell without restriction on the energy density. In the absence of internal pressure, it is obtained that inflation is caused by the application of an electric field. The resulting numerical solutions of the theory presented in this work are in agreement with those predicted by the generally adopted Dorfmann and Ogden model.

Keywords: constitutive theory, elastic dielectric, electroelasticity, finite deformation, nonlinear response, spherical shell

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Authors: Zahra Abdolkarimi, Naser Zourikalatehsamad,

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Up to 40 years ago, after recognition of epilepsy, it was generally believed that these attacks occurred randomly and suddenly. However, thanks to the advance of mathematics and engineering, such attacks can be predicted within a few minutes or hours. In this way, various algorithms for long-term prediction of the time and frequency of the first attack are presented. In this paper, by considering the nonlinear nature of brain signals and dynamic recorded brain signals, ANFIS model is presented to predict the brain signals, since according to physiologic structure of the onset of attacks, more complex neural structures can better model the signal during attacks. Contribution of this work is the co-evolution algorithm for optimization of ANFIS network parameters. Our objective is to predict brain signals based on time series obtained from brain signals of the people suffering from epilepsy using ANFIS. Results reveal that compared to other methods, this method has less sensitivity to uncertainties such as presence of noise and interruption in recorded signals of the brain as well as more accuracy. Long-term prediction capacity of the model illustrates the usage of planted systems for warning medication and preventing brain signals.

Keywords: co-evolution algorithms, brain signals, time series, neural networks, ANFIS model, physiologic structure, time prediction, epilepsy suffering, illustrates model

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Authors: Dehini Rachid, Ferdi Brahim

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The shunt active power filter (SAPF) is not destined only to improve the power factor, but also to compensate the unwanted harmonic currents produced by nonlinear loads. This paper presents a SAPF with identification and control method based on artificial neural network (ANN). To identify harmonics, many techniques are used, among them the conventional p-q theory and the relatively recent one the artificial neural network method. It is difficult to get satisfied identification and control characteristics by using a normal (ANN) due to the nonlinearity of the system (SAPF + fast nonlinear load variations). This work is an attempt to undertake a systematic study of the problem to equip the (SAPF) with the harmonics identification and DC link voltage control method based on (ANN). The latter has been applied to the (SAPF) with fast nonlinear load variations. The results of computer simulations and experiments are given, which can confirm the feasibility of the proposed active power filter.

Keywords: artificial neural networks (ANN), p-q theory, harmonics, total harmonic distortion

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Authors: Elena B. Cherepetskaya, Alexander A. Karabutov, Natalia B. Podymova, Ivan Sas

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Nonlinear evolution of broadband ultrasonic pulses passed through the rock specimens is studied using the apparatus ‘GEOSCAN-02M’. Ultrasonic pulses are excited by the pulses of Q-switched Nd:YAG laser with the time duration of 10 ns and with the energy of 260 mJ. This energy can be reduced to 20 mJ by some light filters. The laser beam radius did not exceed 5 mm. As a result of the absorption of the laser pulse in the special material – the optoacoustic generator–the pulses of longitudinal ultrasonic waves are excited with the time duration of 100 ns and with the maximum pressure amplitude of 10 MPa. The immersion technique is used to measure the parameters of these ultrasonic pulses passed through a specimen, the immersion liquid is distilled water. The reference pulse passed through the cell with water has the compression and the rarefaction phases. The amplitude of the rarefaction phase is five times lower than that of the compression phase. The spectral range of the reference pulse reaches 10 MHz. The cubic-shaped specimens of the Karelian gabbro are studied with the rib length 3 cm. The ultimate strength of the specimens by the uniaxial compression is (300±10) MPa. As the reference pulse passes through the area of the specimen without cracks the compression phase decreases and the rarefaction one increases due to diffraction and scattering of ultrasound, so the ratio of these phases becomes 2.3:1. After preloading some horizontal cracks appear in the specimens. Their location is found by one-sided scanning of the specimen using the backward mode detection of the ultrasonic pulses reflected from the structure defects. Using the computer processing of these signals the images are obtained of the cross-sections of the specimens with cracks. By the increase of the reference pulse amplitude from 0.1 MPa to 5 MPa the nonlinear transformation of the ultrasonic pulse passed through the specimen with horizontal cracks results in the decrease by 2.5 times of the amplitude of the rarefaction phase and in the increase of its duration by 2.1 times. By the increase of the reference pulse amplitude from 5 MPa to 10 MPa the time splitting of the phases is observed for the bipolar pulse passed through the specimen. The compression and rarefaction phases propagate with different velocities. These features of the powerful broadband ultrasonic pulses passed through the rock specimens can be described by the hysteresis model of Preisach-Mayergoyz and can be used for the location of cracks in the optically opaque materials.

Keywords: cracks, geological materials, nonlinear evolution of ultrasonic pulses, rock

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Authors: Wajih Abbassi, Zouhaier Ben Khelifa

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The present research points towards the empirical validation of three options valuation models, the ad-hoc Black-Scholes model as proposed by Berkowitz (2001), the constant elasticity of variance model of Cox and Ross (1976) and the Kou jump-diffusion model (2002). Our empirical analysis has been conducted on a sample of 26,974 options written on three indexes, the S&P 500, Nasdaq 100 and the Russell 2000 that were negotiated during the year 2007 just before the sub-prime crisis. We start by presenting the theoretical foundations of the models of interest. Then we use the technique of trust-region-reflective algorithm to estimate the structural parameters of these models from cross-section of option prices. The empirical analysis shows the superiority of the Kou jump-diffusion model. This superiority arises from the ability of this model to portray the behavior of market participants and to be closest to the true distribution that characterizes the evolution of these indices. Indeed the double-exponential distribution covers three interesting properties that are: the leptokurtic feature, the memory less property and the psychological aspect of market participants. Numerous empirical studies have shown that markets tend to have both overreaction and under reaction over good and bad news respectively. Despite of these advantages there are not many empirical studies based on this model partly because probability distribution and option valuation formula are rather complicated. This paper is the first to have used the technique of nonlinear curve-fitting through the trust-region-reflective algorithm and cross-section options to estimate the structural parameters of the Kou jump-diffusion model.

Keywords: jump-diffusion process, Kou model, Leptokurtic feature, trust-region-reflective algorithm, US index options

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

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In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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Authors: Paras Ram, Vikas Kumar

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The transmission of Malaria with seasonal were studied through the use of mathematical models. The data from the annual number of Malaria cases reported to the Division of Epidemiology, Ministry of Public Health, Thailand during the period 1997-2011 were analyzed. The transmission of Malaria with seasonal was studied by formulating a mathematical model which had been modified to describe different situations encountered in the transmission of Malaria. In our model, the population was separated into two groups: the human and vector groups, and then constructed a system of nonlinear differential equations. Each human group was divided into susceptible, infectious in hot season, infectious in rainy season, infectious in cool season and recovered classes. The vector population was separated into two classes only: susceptible and infectious vectors. The analysis of the models was given by the standard dynamical modeling.

Keywords: ferrofluid, magnetic field, porous medium, rotating disk, Neuringer-Rosensweig Model

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Authors: G. De Matteis, L. Martina, V. Turco

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The work is focused on determining and comparing special nonlinear static configurations in cholesteric liquid crystals (CLCs), confined between two parallel plates and in the presence of an external static electric/magnetic field. The solutions are stabilised by topological and non-topological conservation laws since they are described in terms of integrable or partially integrable nonlinear boundary value problems. In cholesteric liquid crystals which are subject to geometric frustration; anchoring conditions at boundaries, i.e., homeotropic conditions, are incompatible with the cholesteric twist. This aspect turns out to be essential in the admissible classes of solutions, allowing also for disclination type singularities. Within the framework of Frank-Oseen theory, we study the static configurations for CLCs. First, we find numerical solutions for isolated axisymmetric states in confined CLCs with weak homeotropic anchoring at the boundaries. These solutions describe 3-dimensional modulations, namely spherulites or cholesteric bubbles, actually observed in these systems, of standard baby skyrmions. Relations with well-known nonlinear integrable systems are found and are used to explore the asymptotic behavior of the solutions. Then we turn our attention to extended periodic static configurations called Helicoids or cholesteric fingers, described by an elliptic sine-Gordon model with appropriate boundary conditions, showing how their period and energies are determined by both the thickness of the cell and the intensity of the external electric/magnetic field. We explicitly show that helicoids with π or 2π of rotations of the molecular director are different in many aspects and are not simply algebraically related. The behaviour of the solutions, their energy and the properties of the associated disclinations are discussed in detail, both analytically and numerically.

Keywords: cholesteric liquid crystals, geometric frustration, helicoids, skyrmions

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Authors: Faramarz Khoshnoudian, Saeed Vosoughiyan

Abstract:

The main goal of this article is to clarify the soil-structure interaction (SSI) effects on the seismic performance of steel moment resisting frame buildings which are rested on soft soil and equipped with viscous fluid dampers (VFDs). For this purpose, detailed structural models of a ten-story SMRF with VFDs excluding and including the SSI are constructed first. In order to simulate the dynamic response of the foundation, in this paper, the simple cone model is applied. Then, the nonlinear time-history analysis of the models is conducted using three kinds of earthquake excitations with different intensities. The analysis results have demonstrated that the SSI effects on the seismic performance of a structure equipped with VFDs and supported by rigid foundation on soft soil need to be considered. Also VFDs designed based on rigid foundation hypothesis fail to achieve the expected seismic objective while SSI goes into effect.

Keywords: nonlinear time-history analysis, soil-structure interaction, steel moment resisting frame building, viscous fluid dampers

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