Search results for: maximum period nonlinear CA
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 10226

Search results for: maximum period nonlinear CA

10226 Achieving Better Security by Using Nonlinear Cellular Automata as a Cryptographic Primitive

Authors: Swapan Maiti, Dipanwita Roy Chowdhury

Abstract:

Nonlinear functions are essential in different cryptoprimitives as they play an important role on the security of the cipher designs. Rule 30 was identified as a powerful nonlinear function for cryptographic applications. However, an attack (MS attack) was mounted against Rule 30 Cellular Automata (CA). Nonlinear rules as well as maximum period CA increase randomness property. In this work, nonlinear rules of maximum period nonlinear hybrid CA (M-NHCA) are studied and it is shown to be a better crypto-primitive than Rule 30 CA. It has also been analysed that the M-NHCA with single nonlinearity injection proposed in the literature is vulnerable against MS attack, whereas M-NHCA with multiple nonlinearity injections provide maximum length cycle as well as better cryptographic primitives and they are also secure against MS attack.

Keywords: cellular automata, maximum period nonlinear CA, Meier and Staffelbach attack, nonlinear functions

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10225 Nonlinear Heat Transfer in a Spiral Fin with a Period Base Temperature

Authors: Kuo-Teng Tsai, You-Min Huang

Abstract:

In this study, the problem of a spiral fin with a period base temperature is analyzed by using the Adomian decomposition method. The Adomian decomposition method is a useful and practice method to solve the nonlinear energy equation which are associated with the heat radiation. The period base temperature is around a mean value. The results including the temperature distribution and the heat flux from the spiral fin base can be calculated directly. The results also discussed the effects of the dimensionless variables for the temperature variations and the total energy transferred from the spiral fin base.

Keywords: spiral fin, period, adomian decomposition method, nonlinear

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10224 Residual Life Estimation Based on Multi-Phase Nonlinear Wiener Process

Authors: Hao Chen, Bo Guo, Ping Jiang

Abstract:

Residual life (RL) estimation based on multi-phase nonlinear Wiener process was studied in this paper, which is significant for complicated products with small samples. Firstly, nonlinear Wiener model with random parameter was introduced and multi-phase nonlinear Wiener model was proposed to model degradation process of products that were nonlinear and separated into different phases. Then the multi-phase RL probability density function based on the presented model was derived approximately in a closed form and parameters estimation was achieved with the method of maximum likelihood estimation (MLE). Finally, the method was applied to estimate the RL of high voltage plus capacitor. Compared with the other three different models by log-likelihood function (Log-LF) and Akaike information criterion (AIC), the results show that the proposed degradation model can capture degradation process of high voltage plus capacitors in a better way and provide a more reliable result.

Keywords: multi-phase nonlinear wiener process, residual life estimation, maximum likelihood estimation, high voltage plus capacitor

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10223 X-Ray Dynamical Diffraction 'Third Order Nonlinear Renninger Effect'

Authors: Minas Balyan

Abstract:

Nowadays X-ray nonlinear diffraction and nonlinear effects are investigated due to the presence of the third generation synchrotron sources and XFELs. X-ray third order nonlinear dynamical diffraction is considered as well. Using the nonlinear model of the usual visible light optics the third-order nonlinear Takagi’s equations for monochromatic waves and the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses are obtained by the author in previous papers. The obtained equations show, that even if the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero (forbidden reflection), the dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus, in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well-known Renninger effect takes place. In this work, the 'third order nonlinear Renninger effect' is considered theoretically.

Keywords: Bragg diffraction, nonlinear Takagi’s equations, nonlinear Renninger effect, third order nonlinearity

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10222 Study on Optimal Control Strategy of PM2.5 in Wuhan, China

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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10221 Shock Response Analysis of Soil-Structure Systems Induced by Near-Fault Pulses

Authors: H. Masaeli, R. Ziaei, F. Khoshnoudian

Abstract:

Shock response analysis of the soil–structure systems induced by near–fault pulses is investigated. Vibration transmissibility of the soil–structure systems is evaluated by Shock Response Spectra (SRS). Medium–to–high rise buildings with different aspect ratios located on different soil types as well as different foundations with respect to vertical load bearing safety factors are studied. Two types of mathematical near–fault pulses, i.e. forward directivity and fling step, with different pulse periods as well as pulse amplitudes are selected as incident ground shock. Linear versus nonlinear Soil–Structure Interaction (SSI) condition are considered alternatively and the corresponding results are compared. The results show that nonlinear SSI is likely to amplify the acceleration responses when subjected to long–period incident pulses with normalized period exceeding a threshold. It is also shown that this threshold correlates with soil type, so that increased shear–wave velocity of the underlying soil makes the threshold period decrease.

Keywords: nonlinear soil–structure interaction, shock response spectrum, near–fault ground shock, rocking isolation

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10220 Study of Two MPPTs for Photovoltaic Systems Using Controllers Based in Fuzzy Logic and Sliding Mode

Authors: N. Ould cherchali, M. S. Boucherit, L. Barazane, A. Morsli

Abstract:

Photovoltaic power is widely used to supply isolated or unpopulated areas (lighting, pumping, etc.). Great advantage is that this source is inexhaustible, it offers great safety in use and it is clean. But the dynamic models used to describe a photovoltaic system are complicated and nonlinear and due to nonlinear I-V and P–V characteristics of photovoltaic generators, a maximum power point tracking technique (MPPT) is required to maximize the output power. In this paper, two online techniques of maximum power point tracking using robust controller for photovoltaic systems are proposed, the first technique use fuzzy logic controller (FLC) and the second use sliding mode controller (SMC) for photovoltaic systems. The two maximum power point tracking controllers receive the partial derivative of power as inputs, and the output is the duty cycle corresponding to maximum power. A Photovoltaic generator with Boost converter is developed using MATLAB/Simulink to verify the preferences of the proposed techniques. SMC technique provides a good tracking speed in fast changing irradiation and when the irradiation changes slowly or is constant the panel power of FLC technique presents a much smoother signal with less fluctuations.

Keywords: fuzzy logic controller, maximum power point, photovoltaic system, tracker, sliding mode controller

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10219 Exact Solutions of a Nonlinear Schrodinger Equation with Kerr Law Nonlinearity

Authors: Muna Alghabshi, Edmana Krishnan

Abstract:

A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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10218 A New Nonlinear State-Space Model and Its Application

Authors: Abdullah Eqal Al Mazrooei

Abstract:

In this work, a new nonlinear model will be introduced. The model is in the state-space form. The nonlinearity of this model is in the state equation where the state vector is multiplied by its self. This technique makes our model generalizes many famous models as Lotka-Volterra model and Lorenz model which have many applications in the real life. We will apply our new model to estimate the wind speed by using a new nonlinear estimator which suitable to work with our model.

Keywords: nonlinear systems, state-space model, Kronecker product, nonlinear estimator

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10217 Comparison of the Seismic Response of Planar Regular and Irregular Steel Frames

Authors: Robespierre Chavez, Eden Bojorquez, Alfredo Reyes-Salazar

Abstract:

This study compares the seismic response of regular and vertically irregular steel frames determined by nonlinear time history analysis and by using several sets of earthquake records, which are divided in two categories: The first category having 20 stiff-soil ground motion records obtained from the NGA database, and the second category having 30 soft-soil ground motions recorded in the Lake Zone of Mexico City and exhibiting a dominant period (Ts) of two seconds. The steel frames in both format regular and irregular were designed according to the Mexico City Seismic Design Provisions (MCSDP). The effects of irregularity throught the height on the maximum interstory drifts are estimated.

Keywords: irregular steel frames, maximum interstory drifts, seismic response, seismic records

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10216 Seismic Hazard Study and Strong Ground Motion in Southwest Alborz, Iran

Authors: Fereshteh Pourmohammad, Mehdi Zare

Abstract:

The city of Karaj, having a population of 2.2 millions (est. 2022) is located in the South West of Alborz Mountain Belt in Northern Iran. The region is known to be a highly active seismic zone. This study is focused on the geological and seismological analyses within a radius of 200 km from the center of Karaj. There are identified five seismic zones and seven linear seismic sources. The maximum magnitude was calculated for the seismic zones. Scine tghe seismicity catalog is incomplete, we have used a parametric-historic algorithm and the Kijko and Sellevoll (1992) method was used to calculate seismicity parameters, and the return periods and the probability frequency of recurrence of the earthquake magnitude in each zone obtained for 475-years return period. According to the calculations, the highest and lowest earthquake magnitudes of 7.6 and 6.2 were respectively obtained in Zones 1 and 4. This result is a new and extremely important in view point of earthquake risk in a densely population city. The maximum strong horizontal ground motion for the 475-years return period 0.42g and for 2475-year return period 0.70g also the maximum strong vertical ground motion for 475-years return period 0.25g and 2475-years return period 0.44g was calculated using attenuation relationships. These acceleration levels are new, and are obtained to be about 25% higher than presented values in the Iranian building code.

Keywords: seismic zones, ground motion, return period, hazard analysis

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10215 Nonlinear Observer Canonical Form for Genetic Regulation Process

Authors: Bououden Soraya

Abstract:

This paper aims to study the existence of the change of coordinates which permits to transform a class of nonlinear dynamical systems into the so-called nonlinear observer canonical form (NOCF). Moreover, an algorithm to construct such a change of coordinates is given. Based on this form, we can design an observer with a linear error dynamic. This enables us to estimate the state of a nonlinear dynamical system. A concrete example (biological model) is provided to illustrate the feasibility of the proposed results.

Keywords: nonlinear observer canonical form, observer, design, gene regulation, gene expression

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10214 Comprehensive Investigation of Solving Analytical of Nonlinear Differential Equations at Chemical Reactions to Design of Reactors by New Method “AGM”

Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza khalili, Sara Akbari, Davood Domiri Ganji

Abstract:

In this symposium, our aims are accuracy, capabilities and power at solving of the complicate non-linear differential at the reaction chemical in the catalyst reactor (heterogeneous reaction). Our purpose is to enhance the ability of solving the mentioned nonlinear differential equations at chemical engineering and similar issues with a simple and innovative approach which entitled ‘’Akbari-Ganji's Method’’ or ‘’AGM’’. In this paper we solve many examples of nonlinear differential equations of chemical reactions and its investigate. The chemical reactor with the energy changing (non-isotherm) in two reactors of mixed and plug are separately studied and the nonlinear differential equations obtained from the reaction behavior in these systems are solved by a new method. Practically, the reactions with the energy changing (heat or cold) have an important effect on designing and function of the reactors. This means that possibility of reaching the optimal conditions of operation for the maximum conversion depending on nonlinear nature of the reaction velocity toward temperature, results in the complexity of the operation in the reactor. In this case, the differential equation set which governs the reactors can be obtained simultaneous solution of mass equilibrium and energy and temperature changing at concentration.

Keywords: new method (AGM), nonlinear differential equation, tubular and mixed reactors, catalyst bed

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10213 Characterization of Ultrasonic Nonlinearity in Concrete under Cyclic Change of Prestressing Force

Authors: Gyu-Jin Kim, Hyo-Gyoung Kwak

Abstract:

In this research, the effect of prestressing force on the nonlinearity of concrete was investigated by an experimental study. For the measurement of ultrasonic nonlinearity, a prestressed concrete beam was prepared and a nonlinear resonant ultrasound method was adopted. When the prestressing force changes, the stress state of the concrete inside the beam is affected, which leads to the occurrence of micro-cracks and changes in mechanical properties. Therefore, it is necessary to introduce nonlinear ultrasonic technology which sensitively reflects microstructural changes. Repetitive prestressing load history, including maximum levels of 45%, 60% and 75%, depending on the compressive strength, is designed to evaluate the impact of loading levels on the nonlinearity. With the experimental results, the possibility of ultrasonic nonlinearity as a trial indicator of stress was evaluated.

Keywords: micro crack, nonlinear ultrasonic resonant spectroscopy, prestressed concrete beam, prestressing force, ultrasonic nonlinearity

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10212 X-Ray Dynamical Diffraction Rocking Curves in Case of Third Order Nonlinear Renninger Effect

Authors: Minas Balyan

Abstract:

In the third-order nonlinear Takagi’s equations for monochromatic waves and in the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses for forbidden reflections the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero. The dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well known Renninger effect takes place. In this work, the ‘third order nonlinear Renninger effect’ is considered theoretically and numerically. If the reflection exactly is forbidden the diffracted wave’s amplitude is zero both in Laue and Bragg cases since the boundary conditions and dynamical diffraction equations are compatible with zero solution. But in real crystals due to some percent of dislocations and other localized defects, the atoms are displaced with respect to their equilibrium positions. Thus in real crystals susceptibilities of forbidden reflection are by some order small than for usual not forbidden reflections but are not exactly equal to zero. The numerical calculations for susceptibilities two order less than for not forbidden reflection show that in Bragg geometry case the nonlinear reflection curve’s behavior is the same as for not forbidden reflection, but for forbidden reflection the rocking curves’ width, center and boundaries are two order sensitive on the input intensity value. This gives an opportunity to investigate third order nonlinear X-ray dynamical diffraction for not intense beams – 0.001 in the units of critical intensity.

Keywords: third order nonlinearity, Bragg diffraction, nonlinear Renninger effect, rocking curves

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10211 A Filtering Algorithm for a Nonlinear State-Space Model

Authors: Abdullah Eqal Al Mazrooei

Abstract:

Kalman filter is a famous algorithm that utilizes to estimate the state in the linear systems. It has numerous applications in technology and science. Since of the most of applications in real life can be described by nonlinear systems. So, Kalman filter does not work with the nonlinear systems because it is suitable to linear systems only. In this work, a nonlinear filtering algorithm is presented which is suitable to use with the special kinds of nonlinear systems. This filter generalizes the Kalman filter. This means that this filter also can be used for the linear systems. Our algorithm depends on a special linearization of the second degree. We introduced the nonlinear algorithm with a bilinear state-space model. A simulation example is presented to illustrate the efficiency of the algorithm.

Keywords: Kalman filter, filtering algorithm, nonlinear systems, state-space model

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10210 Nonlinear Impact Responses for a Damped Frame Supported by Nonlinear Springs with Hysteresis Using Fast FEA

Authors: T. Yamaguchi, M. Watanabe, M. Sasajima, C. Yuan, S. Maruyama, T. B. Ibrahim, H. Tomita

Abstract:

This paper deals with nonlinear vibration analysis using finite element method for frame structures consisting of elastic and viscoelastic damping layers supported by multiple nonlinear concentrated springs with hysteresis damping. The frame is supported by four nonlinear concentrated springs near the four corners. The restoring forces of the springs have cubic non-linearity and linear component of the nonlinear springs has complex quantity to represent linear hysteresis damping. The damping layer of the frame structures has complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. Comparing shares of strain energy of the elastic frame, the damping layer and the springs, we evaluate the influences of the damping couplings on the linear and nonlinear impact responses. We also investigate influences of damping changed by stiffness of the elastic frame on the nonlinear coupling in the damped impact responses.

Keywords: dynamic response, nonlinear impact response, finite element analysis, numerical analysis

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10209 Second Order MIMO Sliding Mode Controller for Nonlinear Modeled Wind Turbine

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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10208 One Period Loops of Memristive Circuits with Mixed-Mode Oscillations

Authors: Wieslaw Marszalek, Zdzislaw Trzaska

Abstract:

Interesting properties of various one-period loops of singularly perturbed memristive circuits with mixed-mode oscillations (MMOs) are analyzed in this paper. The analysis is mixed, both analytical and numerical and focused on the properties of pinched hysteresis of the memristive element and other one-period loops formed by pairs of time-series solutions for various circuits' variables. The memristive element is the only nonlinear element in the two circuits. A theorem on periods of mixed-mode oscillations of the circuits is formulated and proved. Replacements of memristors by parallel G-C or series R-L circuits for a MMO response with equivalent RMS values is also discussed.

Keywords: mixed-mode oscillations, memristive circuits, pinched hysteresis, one-period loops, singularly perturbed circuits

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10207 Estimation of the Effect of Initial Damping Model and Hysteretic Model on Dynamic Characteristics of Structure

Authors: Shinji Ukita, Naohiro Nakamura, Yuji Miyazu

Abstract:

In considering the dynamic characteristics of structure, natural frequency and damping ratio are useful indicator. When performing dynamic design, it's necessary to select an appropriate initial damping model and hysteretic model. In the linear region, the setting of initial damping model influences the response, and in the nonlinear region, the combination of initial damping model and hysteretic model influences the response. However, the dynamic characteristics of structure in the nonlinear region remain unclear. In this paper, we studied the effect of setting of initial damping model and hysteretic model on the dynamic characteristics of structure. On initial damping model setting, Initial stiffness proportional, Tangent stiffness proportional, and Rayleigh-type were used. On hysteretic model setting, TAKEDA model and Normal-trilinear model were used. As a study method, dynamic analysis was performed using a lumped mass model of base-fixed. During analysis, the maximum acceleration of input earthquake motion was gradually increased from 1 to 600 gal. The dynamic characteristics were calculated using the ARX model. Then, the characteristics of 1st and 2nd natural frequency and 1st damping ratio were evaluated. Input earthquake motion was simulated wave that the Building Center of Japan has published. On the building model, an RC building with 30×30m planes on each floor was assumed. The story height was 3m and the maximum height was 18m. Unit weight for each floor was 1.0t/m2. The building natural period was set to 0.36sec, and the initial stiffness of each floor was calculated by assuming the 1st mode to be an inverted triangle. First, we investigated the difference of the dynamic characteristics depending on the difference of initial damping model setting. With the increase in the maximum acceleration of the input earthquake motions, the 1st and 2nd natural frequency decreased, and the 1st damping ratio increased. Then, in the natural frequency, the difference due to initial damping model setting was small, but in the damping ratio, a significant difference was observed (Initial stiffness proportional≒Rayleigh type>Tangent stiffness proportional). The acceleration and the displacement of the earthquake response were largest in the tangent stiffness proportional. In the range where the acceleration response increased, the damping ratio was constant. In the range where the acceleration response was constant, the damping ratio increased. Next, we investigated the difference of the dynamic characteristics depending on the difference of hysteretic model setting. With the increase in the maximum acceleration of the input earthquake motions, the natural frequency decreased in TAKEDA model, but in Normal-trilinear model, the natural frequency didn’t change. The damping ratio in TAKEDA model was higher than that in Normal-trilinear model, although, both in TAKEDA model and Normal-trilinear model, the damping ratio increased. In conclusion, in initial damping model setting, the tangent stiffness proportional was evaluated the most. In the hysteretic model setting, TAKEDA model was more appreciated than the Normal-trilinear model in the nonlinear region. Our results would provide useful indicator on dynamic design.

Keywords: initial damping model, damping ratio, dynamic analysis, hysteretic model, natural frequency

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10206 Analysis of Nonlinear Pulse Propagation Characteristics in Semiconductor Optical Amplifier for Different Input Pulse Shapes

Authors: Suchi Barua, Narottam Das, Sven Nordholm, Mohammad Razaghi

Abstract:

This paper presents nonlinear pulse propagation characteristics for different input optical pulse shapes with various input pulse energy levels in semiconductor optical amplifiers. For simulation of nonlinear pulse propagation, finite-difference beam propagation method is used to solve the nonlinear Schrödinger equation. In this equation, gain spectrum dynamics, gain saturation are taken into account which depends on carrier depletion, carrier heating, spectral-hole burning, group velocity dispersion, self-phase modulation and two photon absorption. From this analysis, we obtained the output waveforms and spectra for different input pulse shapes as well as for different input energies. It shows clearly that the peak position of the output waveforms are shifted toward the leading edge which due to the gain saturation of the SOA for higher input pulse energies. We also analyzed and compared the normalized difference of full-width at half maximum for different input pulse shapes in the SOA.

Keywords: finite-difference beam propagation method, pulse shape, pulse propagation, semiconductor optical amplifier

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10205 Direct Design of Steel Bridge Using Nonlinear Inelastic Analysis

Authors: Boo-Sung Koh, Seung-Eock Kim

Abstract:

In this paper, a direct design using a nonlinear inelastic analysis is suggested. Also, this paper compares the load carrying capacity obtained by a nonlinear inelastic analysis with experiment results to verify the accuracy of the results. The allowable stress design results of a railroad through a plate girder bridge and the safety factor of the nonlinear inelastic analysis were compared to examine the safety performance. As a result, the load safety factor for the nonlinear inelastic analysis was twice as high as the required safety factor under the allowable stress design standard specified in the civil engineering structure design standards for urban magnetic levitation railways, which further verified the advantages of the proposed direct design method.

Keywords: direct design, nonlinear inelastic analysis, residual stress, initial geometric imperfection

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10204 Optimizing Operation of Photovoltaic System Using Neural Network and Fuzzy Logic

Authors: N. Drir, L. Barazane, M. Loudini

Abstract:

It is well known that photovoltaic (PV) cells are an attractive source of energy. Abundant and ubiquitous, this source is one of the important renewable energy sources that have been increasing worldwide year by year. However, in the V-P characteristic curve of GPV, there is a maximum point called the maximum power point (MPP) which depends closely on the variation of atmospheric conditions and the rotation of the earth. In fact, such characteristics outputs are nonlinear and change with variations of temperature and irradiation, so we need a controller named maximum power point tracker MPPT to extract the maximum power at the terminals of photovoltaic generator. In this context, the authors propose here to study the modeling of a photovoltaic system and to find an appropriate method for optimizing the operation of the PV generator using two intelligent controllers respectively to track this point. The first one is based on artificial neural networks and the second on fuzzy logic. After the conception and the integration of each controller in the global process, the performances are examined and compared through a series of simulation. These two controller have prove by their results good tracking of the MPPT compare with the other method which are proposed up to now.

Keywords: maximum power point tracking, neural networks, photovoltaic, P&O

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10203 Soliton Solutions of the Higher-Order Nonlinear Schrödinger Equation with Dispersion Effects

Authors: H. Triki, Y. Hamaizi, A. El-Akrmi

Abstract:

We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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10202 Using the Simple Fixed Rate Approach to Solve Economic Lot Scheduling Problem under the Basic Period Approach

Authors: Yu-Jen Chang, Yun Chen, Hei-Lam Wong

Abstract:

The Economic Lot Scheduling Problem (ELSP) is a valuable mathematical model that can support decision-makers to make scheduling decisions. The basic period approach is effective for solving the ELSP. The assumption for applying the basic period approach is that a product must use its maximum production rate to be produced. However, a product can lower its production rate to reduce the average total cost when a facility has extra idle time. The past researches discussed how a product adjusts its production rate under the common cycle approach. To the best of our knowledge, no studies have addressed how a product lowers its production rate under the basic period approach. This research is the first paper to discuss this topic. The research develops a simple fixed rate approach that adjusts the production rate of a product under the basic period approach to solve the ELSP. Our numerical example shows our approach can find a better solution than the traditional basic period approach. Our mathematical model that applies the fixed rate approach under the basic period approach can serve as a reference for other related researches.

Keywords: economic lot, basic period, genetic algorithm, fixed rate

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10201 State Estimation Method Based on Unscented Kalman Filter for Vehicle Nonlinear Dynamics

Authors: Wataru Nakamura, Tomoaki Hashimoto, Liang-Kuang Chen

Abstract:

This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: state estimation, control systems, observer systems, nonlinear systems

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10200 Vibration Analysis of Pendulum in a Viscous Fluid by Analytical Methods

Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

Abstract:

In this study, a vibrational differential equation governing on swinging single-degree-of-freedom pendulum in a viscous fluid has been investigated. The damping process is characterized according to two different regimes: at first, damping in stationary viscous fluid, in the second, damping in flowing viscous fluid with constant velocity. Our purpose is to enhance the ability of solving the mentioned nonlinear differential equation with a simple and innovative approach. Comparisons are made between new method and Numerical Method (rkf45). The results show that this method is very effective and simple and can be applied for other nonlinear problems.

Keywords: oscillating systems, angular frequency and damping ratio, pendulum at fluid, locus of maximum

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10199 Numerical Iteration Method to Find New Formulas for Nonlinear Equations

Authors: Kholod Mohammad Abualnaja

Abstract:

A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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10198 Inference for Compound Truncated Poisson Lognormal Model with Application to Maximum Precipitation Data

Authors: M. Z. Raqab, Debasis Kundu, M. A. Meraou

Abstract:

In this paper, we have analyzed maximum precipitation data during a particular period of time obtained from different stations in the Global Historical Climatological Network of the USA. One important point to mention is that some stations are shut down on certain days for some reason or the other. Hence, the maximum values are recorded by excluding those readings. It is assumed that the number of stations that operate follows zero-truncated Poisson random variables, and the daily precipitation follows a lognormal random variable. We call this model a compound truncated Poisson lognormal model. The proposed model has three unknown parameters, and it can take a variety of shapes. The maximum likelihood estimators can be obtained quite conveniently using Expectation-Maximization (EM) algorithm. Approximate maximum likelihood estimators are also derived. The associated confidence intervals also can be obtained from the observed Fisher information matrix. Simulation results have been performed to check the performance of the EM algorithm, and it is observed that the EM algorithm works quite well in this case. When we analyze the precipitation data set using the proposed model, it is observed that the proposed model provides a better fit than some of the existing models.

Keywords: compound Poisson lognormal distribution, EM algorithm, maximum likelihood estimation, approximate maximum likelihood estimation, Fisher information, skew distribution

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10197 Simulation of Propagation of Cos-Gaussian Beam in Strongly Nonlocal Nonlinear Media Using Paraxial Group Transformation

Authors: A. Keshavarz, Z. Roosta

Abstract:

In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: paraxial group transformation, nonlocal nonlinear media, cos-Gaussian beam, ABCD law

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