Search results for: nonlinear dynamics

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

Abstract:

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

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

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Authors: Seong-Ho Song, Ki-Seob Kim, Seop-Hyeong Park, Seon-Woo Lee

Abstract:

In this paper, the data correction algorithm is suggested when the environmental air temperature varies. To correct the infrared data in this paper, the initial temperature or the initial infrared image data is used so that a target source system may not be necessary. The temperature data obtained from infrared detector show nonlinear property depending on the surface temperature. In order to handle this nonlinear property, Taylor series approach is adopted. It is shown that the proposed algorithm can reduce the influence of environmental temperature on the components in the board. The main advantage of this algorithm is to use only the initial temperature of the components on the board rather than using other reference device such as black body sources in order to get reference temperatures.

Keywords: Infrared camera, Temperature Data compensation, Environmental Ambient Temperature, Electric Component

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Authors: H. Sayyaadi, N. Shokouhi

Abstract:

In rail vehicles, air springs are very important isolating component, which guarantee good ride comfort for passengers during their trip. In the most new rail–vehicle models, developed by researchers, the thermo–dynamical effects of air springs are ignored and secondary suspension is modeled by simple springs and dampers. As the performance of suspension components have significant effects on rail–vehicle dynamics and ride comfort of passengers, a complete nonlinear thermo–dynamical air spring model, which is a combination of two different models, is introduced. Result from field test shows remarkable agreement between proposed model and experimental data. Effects of air suspension parameters on the system performances are investigated here and then these parameters are tuned to minimize Sperling ride comfort index during the trip. Results showed that by modification of air suspension parameters, passengers comfort is improved and ride comfort index is reduced about 10%.

Keywords: Air spring, Ride comfort improvement, Thermo– dynamical effects.

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Authors: Keigo Matsuura, Isao Tomita

Abstract:

We have studied a method to widen the spectrum of optical pulses that pass through an InGaAsP waveguide for application to broadband optical communication. In particular, we have investigated the competitive effect between spectral broadening arising from nonlinear refraction (optical Kerr effect) and shrinking due to two photon absorption in the InGaAsP waveguide with χ(3) nonlinearity. The shrunk spectrum recovers broadening by the enhancement effect of the nonlinear refractive index near the bandgap of InGaAsP with a bandgap wavelength of 1490 nm. The broadened spectral width at around 1525 nm (196.7 THz) becomes 10.7 times wider than that at around 1560 nm (192.3 THz) without the enhancement effect, where amplified optical pulses with a pulse width of ∼ 2 ps and a peak power of 10 W propagate through a 1-cm-long InGaAsP waveguide with a cross-section of 4 (μm)2.

Keywords: InGaAsP Waveguide, χ(3) Nonlinearity, Spectral Broadening.

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Authors: R. Pilafkan, M. Kaffash Irzarahimi, S. F. Asbaghian Namin

Abstract:

The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into classical plate theory (CLPT). A Generalized Differential Quadrature Method (GDQM) approach is utilized and numerical solutions for the critical buckling loads are obtained. Then, molecular dynamics (MD) simulations are performed for a series of zigzag SLGSs with different side-lengths and with various boundary conditions, the results of which are matched with those obtained by the nonlocal plate model to numerical the appropriate values of nonlocal parameter relevant to each type of boundary conditions.

Keywords: Biaxial buckling, single-layered graphene sheets, nonlocal elasticity, molecular dynamics simulation, classical plate theory.

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Authors: Jose D. Herrera, Mario A. Rios

Abstract:

This paper deals with the coordinated tuning of the Power System Stabilizer (PSS) controller and Power Oscillation Damping (POD) Controller of Flexible AC Transmission System (FACTS) in a multi-machine power systems. The coordinated tuning is based on the critical eigenvalues of the power system and a model reduction technique where the Hankel Singular Value method is applied. Through the linearized system model and the parameter-constrained nonlinear optimization algorithm, it can compute the parameters of both controllers. Moreover, the parameters are optimized simultaneously obtaining the gains of both controllers. Then, the nonlinear simulation to observe the time response of the controller is performed.

Keywords: Balanced realization, controllability Grammian, electromechanical oscillations, FACTS, Hankel singular values, observability Grammian, POD, PSS.

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Authors: D.Toghraie, A.R.Azimian

Abstract:

Molecular dynamics simulation of annular flow boiling in a nanochannel with 70000 particles is numerically investigated. In this research, an annular flow model is developed to predict the superheated flow boiling heat transfer characteristics in a nanochannel. To characterize the forced annular boiling flow in a nanochannel, an external driving force F ext ranging from 1to12PN (PN= Pico Newton) is applied along the flow direction to inlet fluid particles during the simulation. Based on an annular flow model analysis, it is found that saturation condition and superheat degree have great influences on the liquid-vapor interface. Also, the results show that due to the relatively strong influence of surface tension in small channel, the interface between the liquid film and vapor core is fairly smooth, and the mean velocity along the stream-wise direction does not change anymore.

Keywords: Lennard-Jones Potential, Molecular DynamicsSimulation, Periodic Boundary Conditions (PBC), Non-EquilibriumMolecular Dynamics (NEMD), Annular Flow Boiling

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Authors: M. F. Haroun, T. A. Gulliver

Abstract:

In this paper, an encryption algorithm is proposed for real-time image encryption. The scheme employs a dual chaotic generator based on a three dimensional (3D) discrete Lorenz attractor. Encryption is achieved using non-autonomous modulation where the data is injected into the dynamics of the master chaotic generator. The second generator is used to permute the dynamics of the master generator using the same approach. Since the data stream can be regarded as a random source, the resulting permutations of the generator dynamics greatly increase the security of the transmitted signal. In addition, a technique is proposed to mitigate the error propagation due to the finite precision arithmetic of digital hardware. In particular, truncation and rounding errors are eliminated by employing an integer representation of the data which can easily be implemented. The simple hardware architecture of the algorithm makes it suitable for secure real-time applications.

Keywords: Chaotic systems, image encryption, 3D Lorenz attractor, non-autonomous modulation, FPGA.

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Authors: Ramandeep Behl, S. S. Motsa

Abstract:

The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: Basins of attraction, nonlinear equations, simple roots, Super-Halley.

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Authors: Mohammad Akbarpour, Reza Nasiri Mahalati, Caro Lucas

Abstract:

The existence of many biological systems, especially human societies, is based on cooperative behavior [1, 2]. If natural selection favors selfish individuals, then what mechanism is at work that we see so many cooperative behaviors? One answer is the effect of network structure. On a graph, cooperators can evolve by forming network bunches [2, 3, 4]. In a research, Ohtsuki et al used the idea of iterated prisoners- dilemma on a graph to model an evolutionary game. They showed that the average number of neighbors plays an important role in determining whether cooperation is the ESS of the system or not [3]. In this paper, we are going to study the dynamics of evolution of cooperation in a social network. We show that during evolution, the ratio of cooperators among individuals with fewer neighbors to cooperators among other individuals is greater than unity. The extent to which the fitness function depends on the payoff of the game determines this ratio.

Keywords: Evolution of cooperation, Iterated prisoner's dilemma, Model dynamics, Social network structure, Intensity of selection.

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Authors: Reza Abazari, Rasool Abazari

Abstract:

In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.

Keywords: Coupled Korteweg-de Vries(KdV) equation, Coupled Burgers equation, Coupled Schrödinger equation, differential transformation method.

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Authors: G. Trigui, B. Laroche, M. Miquel, B. Dubreucq, A. Trubuil

Abstract:

The subcellular organelles called oil bodies (OBs) are lipid-filled quasi-spherical droplets produced from the endoplasmic reticulum (ER) and then released into the cytoplasm during seed development. It is believed that an OB grows by coalescence with other OBs and that its stability depends on the composition of oleosins, major proteins inserted in the hemi membrane that covers OBs. In this study, we measured the OB-volume distribution from different genotypes of A. thaliana after 7, 8, 9, 10 and 11 days of seed development. In order to test the hypothesis of OBs dynamics, we developed a simple mathematical model using non-linear differential equations inspired from the theory of coagulation. The model describes the evolution of OB-volume distribution during the first steps of seed development by taking into consideration the production of OBs, the increase of triacylglycerol volume to be stored, and the growth by coalescence of OBs. Fitted parameters values show an increase in the OB production and coalescence rates in A. thaliana oleosin mutants compared to wild type.

Keywords: Biogenesis, coalescence, oil body, oleosin, population dynamics.

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Authors: Marco Kennemann, Steffen C. Eickemeyer, Peter Nyhuis

Abstract:

An increasingly dynamic and complex environment poses huge challenges to production enterprises, especially with regards to logistics. The Logistic Operating Curve Theory, developed at the Institute of Production Systems and Logistics (IFA) of the Leibniz University of Hanover, is a recognized approach to describing logistic interactions, nevertheless, it reaches its limits when it comes to the dynamic aspects. In order to facilitate a timely and optimal Logistic Positioning a method is developed for quickly and reliably identifying dynamic processing states.

Keywords: Dynamics, Logistic Operating Curves, Production Logistics, Production Planning and Control

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Authors: Petia Georgieva, Sebastião Feyo de Azevedo

Abstract:

This paper is focused on issues of nonlinear dynamic process modeling and model-based predictive control of a fed-batch sugar crystallization process applying the concept of artificial neural networks as computational tools. The control objective is to force the operation into following optimal supersaturation trajectory. It is achieved by manipulating the feed flow rate of sugar liquor/syrup, considered as the control input. A feed forward neural network (FFNN) model of the process is first built as part of the controller structure to predict the process response over a specified (prediction) horizon. The predictions are supplied to an optimization procedure to determine the values of the control action over a specified (control) horizon that minimizes a predefined performance index. The control task is rather challenging due to the strong nonlinearity of the process dynamics and variations in the crystallization kinetics. However, the simulation results demonstrated smooth behavior of the control actions and satisfactory reference tracking.

Keywords: Feed forward neural network, process modelling, model predictive control, crystallization process.

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Authors: Magdi M. Nabi, Ding-Li Yu

Abstract:

Control of a semi-batch polymerization reactor using an adaptive radial basis function (RBF) neural network method is investigated in this paper. A neural network inverse model is used to estimate the valve position of the reactor; this method can identify the controlled system with the RBF neural network identifier. The weights of the adaptive PID controller are timely adjusted based on the identification of the plant and self-learning capability of RBFNN. A PID controller is used in the feedback control to regulate the actual temperature by compensating the neural network inverse model output. Simulation results show that the proposed control has strong adaptability, robustness and satisfactory control performance and the nonlinear system is achieved.

Keywords: Chylla-Haase polymerization reactor, RBF neural networks, feed-forward and feedback control.

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Authors: Farhad Namdari, Reza Sedaghati

Abstract:

Economic dispatch (ED) has been considered to be one of the key functions in electric power system operation which can help to build up effective generating management plans. The practical ED problem has non-smooth cost function with nonlinear constraints which make it difficult to be effectively solved. This paper presents a novel heuristic and efficient optimization approach based on the new Bat algorithm (BA) to solve the practical non-smooth economic dispatch problem. The proposed algorithm easily takes care of different constraints. In addition, two newly introduced modifications method is developed to improve the variety of the bat population when increasing the convergence speed simultaneously. The simulation results obtained by the proposed algorithms are compared with the results obtained using other recently develop methods available in the literature.

Keywords: Non-smooth, economic dispatch, bat-inspired, nonlinear practical constraints, modified bat algorithm.

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Authors: Behnam Mehrkian, Arash Bahar, Ali Chaibakhsh

Abstract:

Magneto-rheological (MR) fluid damper is a semiactive control device that has recently received more attention by the vibration control community. But inherent hysteretic and highly nonlinear dynamics of MR fluid damper is one of the challenging aspects to employ its unique characteristics. The combination of artificial neural network (ANN) and fuzzy logic system (FLS) have been used to imitate more precisely the behavior of this device. However, the derivative-based nature of adaptive networks causes some deficiencies. Therefore, in this paper, a novel approach that employ genetic algorithm, as a free-derivative algorithm, to enhance the capability of fuzzy systems, is proposed. The proposed method used to model MR damper. The results will be compared with adaptive neuro-fuzzy inference system (ANFIS) model, which is one of the well-known approaches in soft computing framework, and two best parametric models of MR damper. Data are generated based on benchmark program by applying a number of famous earthquake records.

Keywords: Benchmark program, earthquake record filtering, fuzzy logic, genetic algorithm, MR damper.

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Authors: M. Kidouche, H. Habbi, M. Zelmat, S. Grouni

Abstract:

In analyzing large scale nonlinear dynamical systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solutions properties of the large scale system are then deduced from the solution properties of the individual subsystems and the nature of the interconnections. In this paper a new approach is proposed for the stability analysis of large scale systems, which is based upon the concept of vector Lyapunov functions and the decomposition methods. The present results make use of graph theoretic decomposition techniques in which the overall system is partitioned into a hierarchy of strongly connected components. We show then, that under very reasonable assumptions, the overall system is stable once the strongly connected subsystems are stables. Finally an example is given to illustrate the constructive methodology proposed.

Keywords: Comparison principle, First integral, Large scale system, Lyapunov stability.

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Authors: Jixiang Zhang, Guocheng Wang

Abstract:

A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.

Keywords: Bertrand duopoly model, Discrete dynamical system, Heterogeneous expectations, Nash equilibrium.

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Authors: S. Farzi

Abstract:

Recently, a lot of attention has been devoted to advanced techniques of system modeling. PNN(polynomial neural network) is a GMDH-type algorithm (Group Method of Data Handling) which is one of the useful method for modeling nonlinear systems but PNN performance depends strongly on the number of input variables and the order of polynomial which are determined by trial and error. In this paper, we introduce GPNN (genetic polynomial neural network) to improve the performance of PNN. GPNN determines the number of input variables and the order of all neurons with GA (genetic algorithm). We use GA to search between all possible values for the number of input variables and the order of polynomial. GPNN performance is obtained by two nonlinear systems. the quadratic equation and the time series Dow Jones stock index are two case studies for obtaining the GPNN performance.

Keywords: GMDH, GPNN, GA, PNN.

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Authors: A. K. Sharma, N. P. Patidar, G. Agnihotri, D. K. Palwalia

Abstract:

This paper presents the performance state analysis of Self-Excited Induction Generator (SEIG) using Artificial Bee Colony (ABC) optimization technique. The total admittance of the induction machine is minimized to calculate the frequency and magnetizing reactance corresponding to any rotor speed, load impedance and excitation capacitance. The performance of SEIG is calculated using the optimized parameter found. The results obtained by ABC algorithm are compared with results from numerical method. The results obtained coincide with the numerical method results. This technique proves to be efficient in solving nonlinear constrained optimization problems and analyzing the performance of SEIG.

Keywords: Artificial bee colony, Steady state analysis, Selfexcited induction generator, Nonlinear constrained optimization.

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Authors: D. Toghraie, A. R. Azimian

Abstract:

In this paper, the Lennard -Jones potential is applied to molecules of liquid argon as well as its vapor and platinum as solid surface in order to perform a non-equilibrium molecular dynamics simulation to study the microscopic aspects of liquid-vapor-solid interactions. The channel is periodic in x and y directions and along z direction it is bounded by atomic walls. It was found that density of the liquids near the solid walls fluctuated greatly and that the structure was more like a solid than a liquid. This indicates that the interactions of solid and liquid molecules are very strong. The resultant surface tension, liquid density and vapor density are found to be well predicted when compared with the experimental data for argon. Liquid and vapor densities were found to depend on the cutoff radius which induces the use of P3M (particle-particle particle-mesh) method which was implemented for evaluation of force and surface tension.

Keywords: Lennard-Jones Potential, Molecular DynamicsSimulation, Periodic Boundary Conditions (PBC), Non-EquilibriumMolecular Dynamics (NEMD).

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Authors: Seema Chopra, R. Mitra, Vijay Kumar

Abstract:

A neurofuzzy approach for a given set of input-output training data is proposed in two phases. Firstly, the data set is partitioned automatically into a set of clusters. Then a fuzzy if-then rule is extracted from each cluster to form a fuzzy rule base. Secondly, a fuzzy neural network is constructed accordingly and parameters are tuned to increase the precision of the fuzzy rule base. This network is able to learn and optimize the rule base of a Sugeno like Fuzzy inference system using Hybrid learning algorithm, which combines gradient descent, and least mean square algorithm. This proposed neurofuzzy system has the advantage of determining the number of rules automatically and also reduce the number of rules, decrease computational time, learns faster and consumes less memory. The authors also investigate that how neurofuzzy techniques can be applied in the area of control theory to design a fuzzy controller for linear and nonlinear dynamic systems modelling from a set of input/output data. The simulation analysis on a wide range of processes, to identify nonlinear components on-linely in a control system and a benchmark problem involving the prediction of a chaotic time series is carried out. Furthermore, the well-known examples of linear and nonlinear systems are also simulated under the Matlab/Simulink environment. The above combination is also illustrated in modeling the relationship between automobile trips and demographic factors.

Keywords: Fuzzy control, neuro-fuzzy techniques, fuzzy subtractive clustering, extraction of rules, and optimization of membership functions.

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Authors: Mohammad R. Jalali, Mohammad M. Jalali

Abstract:

The earliest theories of sloshing waves and solitary waves based on potential theory idealisations and irrotational flow have been extended to be applicable to more realistic domains. To this end, the computational fluid dynamics (CFD) methods are widely used. Three-dimensional CFD methods such as Navier-Stokes solvers with volume of fluid treatment of the free surface and Navier-Stokes solvers with mappings of the free surface inherently impose high computational expense; therefore, considerable effort has gone into developing depth-averaged approaches. Examples of such approaches include Green–Naghdi (GN) equations. In Cartesian system, GN velocity profile depends on horizontal directions, x-direction and y-direction. The effect of vertical direction (z-direction) is also taken into consideration by applying weighting function in approximation. GN theory considers the effect of vertical acceleration and the consequent non-hydrostatic pressure. Moreover, in GN theory, the flow is rotational. The present study illustrates the application of GN equations to propagation of sloshing waves and solitary waves. For this purpose, GN equations solver is verified for the benchmark tests of Gaussian hump sloshing and solitary wave propagation in shallow basins. Analysis of the free surface sloshing of even harmonic components of an initial Gaussian hump demonstrates that the GN model gives predictions in satisfactory agreement with the linear analytical solutions. Discrepancies between the GN predictions and the linear analytical solutions arise from the effect of wave nonlinearities arising from the wave amplitude itself and wave-wave interactions. Numerically predicted solitary wave propagation indicates that the GN model produces simulations in good agreement with the analytical solution of the linearised wave theory. Comparison between the GN model numerical prediction and the result from perturbation analysis confirms that nonlinear interaction between solitary wave and a solid wall is satisfactorilly modelled. Moreover, solitary wave propagation at an angle to the x-axis and the interaction of solitary waves with each other are conducted to validate the developed model.

Keywords: Even harmonic components of sloshing waves, Green–Naghdi equations, nonlinearity, solitary waves.

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Authors: J.Yojina, W. Ngamsaad, N. Nuttavut, D.Triampo, Y. Lenbury, W. Triampo, P. Kanthang, S.Sriyab

Abstract:

The dynamics of Min proteins plays a center role in accurate cell division. Although the nucleoids may presumably play an important role in prokaryotic cell division, there is a lack of models to account for its participation. In this work, we apply the lattice Boltzmann method to investigate protein oscillation based on a mesoscopic model that takes into account the nucleoid-s role. We found that our numerical results are in reasonably good agreement with the previous experimental results On comparing with the other computational models without the presence of nucleoids, the highlight of our finding is that the local densities of MinD and MinE on the cytoplasmic membrane increases, especially along the cell width, when the size of the obstacle increases, leading to a more distinct cap-like structure at the poles. This feature indicated the realistic pattern and reflected the combination of Min protein dynamics and nucleoid-s role.

Keywords: lattice Boltzmann method, cell division, Minproteins oscillation, nucleoid

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Authors: López-Gutiérrez R.M., Rodríguez-Orozco E., Cruz-Hernández C., Inzunza-González E., Posadas-Castillo C., García-Guerrero E.E., Cardoza-Avendaño L.

Abstract:

In this paper, we use Generalized Hamiltonian systems approach to synchronize a modified sixth-order Chua's circuit, which generates hyperchaotic dynamics. Synchronization is obtained between the master and slave dynamics with the slave being given by an observer. We apply this approach to transmit private information (analog and binary), while the encoding remains potentially secure.

Keywords: Hyperchaos synchronization, sixth-order Chua's circuit, observers, simulation, secure communication.

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Authors: Yi Liu

Abstract:

In this paper, computational fluid dynamics (CFD) is utilized to characterize a prototype biolistic delivery system, the biomedical device based on the contoured-shock-tube design (CST), with the aim at investigating shocks induced flow instabilities within the contoured shock tube. The shock/interface interactions, the growth of perturbation at an interface between two fluids of different density are interrogated. The key features of the gas dynamics and gas-particle interaction are discussed

Keywords: Simulation, Shock wave, Particle, Interface, Supersonic, Richtmyer-Meshkov Instability

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Authors: Karandeep Singh, Baibing Li

Abstract:

Traffic density, an indicator of traffic conditions, is one of the most critical characteristics to Intelligent Transport Systems (ITS). This paper investigates recursive traffic density estimation using the information provided from inductive loop detectors. On the basis of the phenomenological relationship between speed and density, the existing studies incorporate a state space model and update the density estimate using vehicular speed observations via the extended Kalman filter, where an approximation is made because of the linearization of the nonlinear observation equation. In practice, this may lead to substantial estimation errors. This paper incorporates a suitable transformation to deal with the nonlinear observation equation so that the approximation is avoided when using Kalman filter to estimate the traffic density. A numerical study is conducted. It is shown that the developed method outperforms the existing methods for traffic density estimation.

Keywords: Density estimation, Kalman filter, speed-densityrelationship, Traffic surveillance.

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Authors: H. Ghanbarpour Asl, S. H. Pourtakdoust

Abstract:

Extended Kalman Filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, not only it has difficulties arising from linearization but also many times it becomes numerically unstable because of computer round off errors that occur in the process of its implementation. To overcome linearization limitations, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. Kalman filter that uses UT for calculation of the first two statistical moments is called Unscented Kalman Filter (UKF). Square-root form of UKF (SRUKF) developed by Rudolph van der Merwe and Eric Wan to achieve numerical stability and guarantee positive semi-definiteness of the Kalman filter covariances. This paper develops another implementation of SR-UKF for sequential update measurement equation, and also derives a new UD covariance factorization filter for the implementation of UKF. This filter is equivalent to UKF but is computationally more efficient.

Keywords: Unscented Kalman filter, Square-root unscentedKalman filter, UD covariance factorization, Target tracking.

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Authors: M. Palizvan, M. T. Abadi, M. H. Sadr

Abstract:

Due to variations in damage mechanisms in the microscale, the behavior of fiber-reinforced composites is nonlinear and difficult to model. To make use of computational advantages, homogenization method is applied to the micro-scale model in order to minimize the cost at the expense of detail of local microscale phenomena. In this paper, the effective stiffness is calculated using the homogenization of nonlinear behavior of a composite representative volume element (RVE) containing fiber-matrix debonding. The damage modes for the RVE are considered by using cohesive elements and contacts for the cohesive behavior of the interface between fiber and matrix. To predict more realistic responses of composite materials, different random distributions of fibers are proposed besides square and hexagonal arrays. It was shown that in some cases, there is quite different damage behavior in different fiber distributions. A comprehensive comparison has been made between different graphs.

Keywords: Homogenization, cohesive zone model, fiber-matrix debonding, RVE.

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