Search results for: Nonlinear Modeling

Authors: Aini Hussain, M A Hannan, Azah Mohamed, Hilmi Sanusi, Burhanuddin Yeop Majlis

Abstract:

Airbag deployment has been known to be responsible for huge death, incidental injuries and broken bones due to low crash severity and wrong deployment decisions. Therefore, the authorities and industries have been looking for more innovative and intelligent products to be realized for future enhancements in the vehicle safety systems (VSSs). Although the VSSs technologies have advanced considerably, they still face challenges such as how to avoid unnecessary and untimely airbag deployments that can be hazardous and fatal. Currently, most of the existing airbag systems deploy without regard to occupant size and position. As such, this paper will focus on the occupant and crash sensing performances due to frontal collisions for the new breed of so called smart airbag systems. It intends to provide a thorough discussion relating to the occupancy detection, occupant size classification, occupant off-position detection to determine safe distance zone for airbag deployment, crash-severity analysis and airbag decision algorithms via a computer modeling. The proposed system model consists of three main modules namely, occupant sensing, crash severity analysis and decision fusion. The occupant sensing system module utilizes the weight sensor to determine occupancy, classify the occupant size, and determine occupant off-position condition to compute safe distance for airbag deployment. The crash severity analysis module is used to generate relevant information pertinent to airbag deployment decision. Outputs from these two modules are fused to the decision module for correct and efficient airbag deployment action. Computer modeling work is carried out using Simulink, Stateflow, SimMechanics and Virtual Reality toolboxes.

Keywords: Crash severity analysis, occupant size classification, smart airbag, vehicle safety system.

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Authors: Marc Sango, Olimpia Hoinaru, Christophe Gransart, Laurence Duchien

Abstract:

Ontologies offer a means for representing and sharing information in many domains, particularly in complex domains. For example, it can be used for representing and sharing information of System Requirement Specification (SRS) of complex systems like the SRS of ERTMS/ETCS written in natural language. Since this system is a real-time and critical system, generic ontologies, such as OWL and generic ERTMS ontologies provide minimal support for modeling temporal information omnipresent in these SRS documents. To support the modeling of temporal information, one of the challenges is to enable representation of dynamic features evolving in time within a generic ontology with a minimal redesign of it. The separation of temporal information from other information can help to predict system runtime operation and to properly design and implement them. In addition, it is helpful to provide a reasoning and querying techniques to reason and query temporal information represented in the ontology in order to detect potential temporal inconsistencies. To address this challenge, we propose a lightweight 3-layer temporal Quality of Service (QoS) ontology for representing, reasoning and querying over temporal and non-temporal information in a complex domain ontology. Representing QoS entities in separated layers can clarify the distinction between the non QoS entities and the QoS entities in an ontology. The upper generic layer of the proposed ontology provides an intuitive knowledge of domain components, specially ERTMS/ETCS components. The separation of the intermediate QoS layer from the lower QoS layer allows us to focus on specific QoS Characteristics, such as temporal or integrity characteristics. In this paper, we focus on temporal information that can be used to predict system runtime operation. To evaluate our approach, an example of the proposed domain ontology for handover operation, as well as a reasoning rule over temporal relations in this domain-specific ontology, are presented.

Keywords: System Requirement Specification, ERTMS/ETCS, Temporal Ontologies, Domain Ontologies.

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Authors: F. Khaber, K. Zehar, A. Hamzaoui

Abstract:

In this paper, we introduce a robust state feedback controller design using Linear Matrix Inequalities (LMIs) and guaranteed cost approach for Takagi-Sugeno fuzzy systems. The purpose on this work is to establish a systematic method to design controllers for a class of uncertain linear and non linear systems. Our approach utilizes a certain type of fuzzy systems that are based on Takagi-Sugeno (T-S) fuzzy models to approximate nonlinear systems. We use a robust control methodology to design controllers. This method not only guarantees stability, but also minimizes an upper bound on a linear quadratic performance measure. A simulation example is presented to show the effectiveness of this method.

Keywords: Takagi-Sugeno fuzzy model, state feedback, linear matrix inequalities, robust stability.

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Authors: M. Baghdasaryan, A. Sukiasyan

Abstract:

An algorithm for estimating the stable operation conditions of the synchronous motor of the ore mill electric drive is proposed. The stable operation conditions of the synchronous motor are revealed, taking into account the estimation of the q angle change and the technological factors. The stability condition obtained allows to ensure the stable operation of the motor in the synchronous mode, taking into account the nonlinear character of the mill loading. The developed algorithm gives an opportunity to present the undesirable phenomena, arising in the electric drive system. The obtained stability condition can be successfully applied for the optimal control of the electromechanical system of the mill.

Keywords: Electric drive, synchronous motor, ore mill, stability, technological factors.

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Authors: Jeong-Hwan Choi, Hyo-Sang Park, Tae-Hyung Lee

Abstract:

The transmission tower is one of the crucial lifeline structures in a modern society, and it needs to be protected against extreme loading conditions. However, the transmission tower is a very complex structure and, therefore, it is very difficult to simulate the actual damage and the collapse behavior of the tower structure. In this study, the actual collapse behavior of the transmission tower due to lateral loading conditions such as wind load is evaluated through the computational simulation. For that, a progressive collapse procedure is applied to the simulation. In this procedure, after running the simulation, if a member of the tower structure fails, the failed member is removed and the simulation run again. The 154kV transmission tower is selected for this study. The simulation is performed by nonlinear static analysis procedure, namely pushover analysis, using OpenSEES, an earthquake simulation platform. Three-dimensional finite element models of those towers are developed.

Keywords: Transmission tower, OpenSEES, pushover analysis, progressive collapse.

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Authors: E. Srinivasan, D. Ebenezer

Abstract:

Median filters with larger windows offer greater smoothing and are more robust than the median filters of smaller windows. However, the larger median smoothers (the median filters with the larger windows) fail to track low order polynomial trends in the signals. Due to this, constant regions are produced at the signal corners, leading to the loss of fine details. In this paper, an algorithm, which combines the ability of the 3-point median smoother in preserving the low order polynomial trends and the superior noise filtering characteristics of the larger median smoother, is introduced. The proposed algorithm (called the combiner algorithm in this paper) is evaluated for its performance on a test image corrupted with different types of noise and the results obtained are included.

Keywords: Image filtering, detail preservation, median filters, nonlinear filters, order statistics filtering, Rank order filtering.

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Authors: Ali Khajeh Samani, Mario M. Attard

Abstract:

Lateral expansion is a factor defining the level of confinement in reinforced concrete columns. Therefore, predicting the lateral strain relationship with axial strain becomes an important issue. Measuring lateral strains in experiments is difficult and only few report experimental lateral strains. Among the existing analytical formulations, two recent models are compared with available test results in this paper with shortcomings highlighted. A new analytical model is proposed here for lateral strain axial strain relationship and is based on the supposition that the concrete behaves linear elastic in the early stages of loading and then nonlinear hardening up to the peak stress and then volumetric expansion. The proposal for the lateral strain axial strain relationship after the peak stress is mainly based on the hypothesis that the plastic lateral strain varies linearly with the plastic axial strain and it is shown that this is related to the lateral confinement level.

Keywords: Confined Concrete, Lateral Strain, Triaxial test, Postpeak behavior

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Authors: F. Ekoue, A. Fouache d'Halloy, D. Gigon, G Plantamp, E. Zajdman

Abstract:

This work focuses on analysis of classical heat transfer equation regularized with Maxwell-Cattaneo transfer law. Computer simulations are performed in MATLAB environment. Numerical experiments are first developed on classical Fourier equation, then Maxwell-Cattaneo law is considered. Corresponding equation is regularized with a balancing diffusion term to stabilize discretizing scheme with adjusted time and space numerical steps. Several cases including a convective term in model equations are discussed, and results are given. It is shown that limiting conditions on regularizing parameters have to be satisfied in convective case for Maxwell-Cattaneo regularization to give physically acceptable solutions. In all valid cases, uniform convergence to solution of initial heat equation with Fourier law is observed, even in nonlinear case.

Keywords: Maxwell-Cattaneo heat transfers equations, fourierlaw, heat conduction, numerical solution.

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Authors: A. Pashayev, C. Ardil, R. Sadiqov

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Various methods of geofield parameters restoration (by algebraic polynoms; filters; rational fractions; interpolation splines; geostatistical methods – kriging; search methods of nearest points – inverse distance, minimum curvature, local – polynomial interpolation; neural networks) have been analyzed and some possible mistakes arising during geofield surface modeling have been presented.

Keywords: interpolation methods, geofield parameters, neural networks.

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Authors: Zhongxu Chen, Jun Yang, Heyue Mao, Xiaoyu Zheng

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Hemorrhage Disease of Grass Carp (HDGC) is a kind of commonly occurring illnesses in summer, and the extremely high death rate result in colossal losses to aquaculture. As the complex connections among each factor which influences aquiculture diseases, there-s no quit reasonable mathematical model to solve the problem at present.A BP neural network which with excellent nonlinear mapping coherence was adopted to establish mathematical model; Environmental factor, which can easily detected, such as breeding density, water temperature, pH and light intensity was set as the main analyzing object. 25 groups of experimental data were used for training and test, and the accuracy of using the model to predict the trend of HDGC was above 80%. It is demonstrated that BP neural network for predicating diseases in HDGC has a particularly objectivity and practicality, thus it can be spread to other aquiculture disease.

Keywords: Aquaculture, Hemorrhage Disease of Grass Carp, BP Neural Network

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Authors: Weifeng Wang, Xilong Chen, Xianwei Zeng

Abstract:

The cable tower of Liede Bridge is a double-column curved-lever arched-beam portal framed structure. Being novel and unique in structure, its cable tower differs in complexity from traditional ones. This paper analyzes the ultimate load capacity of cable tower by adopting the finite element calculations and model tests which indicate that constitutive relations applied here give a better simulation of actual failure process of prestressed reinforced concrete. In vertical load, horizontal load and overloading tests, the stepped loading of the tower model is of linear relationship, and the test data has good repeatability. All suggests that the cable tower has good bearing capacity, rational design and high emergency capacity.

Keywords: Cable tower of Liede Bridge, ultimate load capacity, model test, nonlinear finite element method

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Authors: Chuanjian Wang, Changfu Liu, Zhengde Dai

Abstract:

In this paper, the direct AnsAz method is used for constructing the multi-wave solutions to the (2+1)-dimensional extension of the Korteweg de-Vries (shortly EKdV) equation. A new breather type of three-wave solutions including periodic breather type soliton solution, breather type of two-solitary solution are obtained. Some cases with specific values of the involved parameters are plotted for each of the three-wave solutions. Mechanical features of resonance interaction among the multi-wave are discussed. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field.

Keywords: EKdV equation, Breather, Soliton, Bilinear form, The direct AnsAz method.

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Authors: Badr M. Alshammari, T. Guesmi

Abstract:

This study presents a modified version of the artificial bee colony (ABC) algorithm by including a local search technique for solving the non-convex economic power dispatch problem. The local search step is incorporated at the end of each iteration. Total system losses, valve-point loading effects and prohibited operating zones have been incorporated in the problem formulation. Thus, the problem becomes highly nonlinear and with discontinuous objective function. The proposed technique is validated using an IEEE benchmark system with ten thermal units. Simulation results demonstrate that the proposed optimization algorithm has better convergence characteristics in comparison with the original ABC algorithm.

Keywords: Economic power dispatch, artificial bee colony, valve-point loading effects, prohibited operating zones.

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Authors: Mohammadsadegh Zanganehfar

Abstract:

Since the introduction of fractal geometry in 1970, numerous efforts have been made by architects and researchers to transfer this area of mathematical knowledge in the discipline of architecture and postmodernist discourse. The discourse of complexity and architecture is one of the most significant ongoing discourses in the discipline of architecture from the 70's until today and has generated significant styles such as deconstructivism and parametricism in architecture. During these years, several projects were designed and presented by designers and architects using fractal geometry, but due to the lack of sufficient knowledge and appropriate comprehension of the features and characteristics of this nonlinear geometry, none of the fractal-based designs have been successful and satisfying. Fractal geometry as a geometric technology has a long presence in the history of architecture. The current research attempts to identify and discover the characteristics, features, potentials and functionality of fractals despite their aesthetic aspect by examining case studies of pre-modern architecture in Asia and investigating the function of fractals. 

Keywords: Asian architecture, fractal geometry, fractal technique, geometric properties

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Authors: M. Nekri, A. Khelladi

Abstract:

The world wide web network is a network with a complex topology, the main properties of which are the distribution of degrees in power law, A low clustering coefficient and a weak average distance. Modeling the web as a graph allows locating the information in little time and consequently offering a help in the construction of the research engine. Here, we present a model based on the already existing probabilistic graphs with all the aforesaid characteristics. This work will consist in studying the web in order to know its structuring thus it will enable us to modelize it more easily and propose a possible algorithm for its exploration.

Keywords: Clustering coefficient, preferential attachment, small world, Web community.

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Authors: A. Brener, B. Ismailov, G. Berdalieva

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In the paper we submit the modification of kinetic Smoluchowski equation for binary aggregation applying to systems with chemical reactions of first and second orders in which the main product is insoluble. The goal of this work is to create theoretical foundation and engineering procedures for calculating the chemical apparatuses in the conditions of joint course of chemical reactions and processes of aggregation of insoluble dispersed phases which are formed in working zones of the reactor.

Keywords: Binary aggregation, Clusters, Chemical reactions, Insoluble phases.

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Authors: Carlos Mendez Galindo, Toshiro Hayashikawa, Javier Gil Belda

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This paper investigates the effectiveness of the use of seismic isolation devices on the overall 3D seismic response of curved highway viaducts with an emphasis on expansion joints. Furthermore, an evaluation of the effectiveness of the use of cable restrainers is presented. For this purpose, the bridge seismic performance has been evaluated on four different radii of curvature, considering two cases: restrained and unrestrained curved viaducts. Depending on the radius of curvature, three-dimensional non-linear dynamic analysis shows the vulnerability of curved viaducts to pounding and deck unseating damage. In this study, the efficiency of using LRB supports combined with cable restrainers on curved viaducts is demonstrated, not only by reducing in all cases the possible damage, but also by providing a similar behavior in the viaducts despite of curvature radius.

Keywords: Nonlinear dynamic response, seismic design, seismic isolation, unseating prevention system.

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Authors: Tomohiro Hachino, Kenji Shimoda, Hitoshi Takata

Abstract:

This paper presents a method of model selection and identification of Hammerstein systems by hybridization of the genetic algorithm (GA) and particle swarm optimization (PSO). An unknown nonlinear static part to be estimated is approximately represented by an automatic choosing function (ACF) model. The weighting parameters of the ACF and the system parameters of the linear dynamic part are estimated by the linear least-squares method. On the other hand, the adjusting parameters of the ACF model structure are properly selected by the hybrid algorithm of the GA and PSO, where the Akaike information criterion is utilized as the evaluation value function. Simulation results are shown to demonstrate the effectiveness of the proposed hybrid algorithm.

Keywords: Hammerstein system, identification, automatic choosing function model, genetic algorithm, particle swarm optimization.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang, Yu Li

Abstract:

Utilizing echoic intension and distribution from different organs and local details of human body, ultrasonic image can catch important medical pathological changes, which unfortunately may be affected by ultrasonic speckle noise. A feature preserving ultrasonic image denoising and edge enhancement scheme is put forth, which includes two terms: anisotropic diffusion and edge enhancement, controlled by the optimum smoothing time. In this scheme, the anisotropic diffusion is governed by the local coordinate transformation and the first and the second order normal derivatives of the image, while the edge enhancement is done by the hyperbolic tangent function. Experiments on real ultrasonic images indicate effective preservation of edges, local details and ultrasonic echoic bright strips on denoising by our scheme.

Keywords: anisotropic diffusion, coordinate transformationdirectional derivatives, edge enhancement, hyperbolic tangentfunction, image denoising.

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Authors: Er. Satwinder Singh, Dr. K.S. Kahlon, Rakesh Kumar, Er. Gurjeet Singh

Abstract:

The most reliable and accurate description of the actual behavior of a software system is its source code. However, not all questions about the system can be answered directly by resorting to this repository of information. What the reverse engineering methodology aims at is the extraction of abstract, goal-oriented “views" of the system, able to summarize relevant properties of the computation performed by the program. While concentrating on reverse engineering we had modeled the C++ files by designing the translator.

Keywords: Translator, Modeling, UML, DYNO, ISVis, TED.

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Authors: Sophia Fry, Mahir Irtiza, Alexa Hoffman, Yousef Sardahi

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This study presents an intelligent control algorithm for a flexible robotic arm. Fuzzy control is used to control the motion of the arm to maintain the arm tip at the desired position while reducing vibration and increasing the system speed of response. The Fuzzy controller (FC) is based on adding the tip angular position to the arm deflection angle and using their sum as a feedback signal to the control algorithm. This reduces the complexity of the FC in terms of the input variables, number of membership functions, fuzzy rules, and control structure. Also, the design of the fuzzy controller is model-free and uses only our knowledge about the system. To show the efficacy of the FC, the control algorithm is implemented on the flexible joint manipulator (FJM) developed by Quanser. The results show that the proposed control method is effective in terms of response time, overshoot, and vibration amplitude.

Keywords: Fuzzy logic control, model-free control, flexible joint manipulators, nonlinear control.

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Authors: Xuan Sun, Mingbo Tong

Abstract:

To understand the factors which affect impact damage on composite structures, particularly the effects of impact position and ribs. In this paper, a finite element model (FEM) of low-velocity impact damage on the composite structure was established via the nonlinear finite element method, combined with the user-defined materials subroutine (VUMAT) of the ABAQUS software. The structural elements chosen for the investigation comprised a series of stiffened composite panels, representative of real aircraft structure. By impacting the panels at different positions relative to the ribs, the effect of relative position of ribs was found out. Then the simulation results and the experiments data were compared. Finally, the factors which affect impact damage on the structures were discussed. The paper was helpful for the design of stiffened composite structures.

Keywords: Stiffened, Low-velocity, Impact, Abaqus, Impact Energy.

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Authors: Taïeb Branci, Djamal Yahmi, Abdelhamid Bouchair, Eric Fourneley

Abstract:

According to current seismic codes the structures are calculated using the capacity design procedure based on the concept of shear at the base depending on several parameters including behavior factor which is considered to be the most important parameter. The behavior factor allows designing the structure when it is at its ultimate limit state taking into account its energy dissipation through its plastic deformation. The aim of the present study is to assess the basic parameters on which is composed the behavior factor among them the reduction factor due to ductility, and those due to redundancy and the overstrength for steel moment-resisting frames of different heights and regular configuration. Analyses are conducted on these frames using the nonlinear static method where the effect of some parameters on the behavior factor, such as the number of stories and the number of spans, are taken into account. The results show that the behavior factor is rather sensitive to the variation of the number of stories and bays.

Keywords: Behavior, code, frame, ductility, overstrength, redundancy, plastic.

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Authors: R. D. Kulkarni, Mayur Chaudhari, S. Mishra

Abstract:

Curing of paints by exposure to UV radiations is emerging as one of the best film forming technique as an alternative to traditional solvent borne oxidative and thermal curing coatings. The composition and chemistry of UV curable coatings and role of multifunctional and monofunctional monomers, oligomers, and photoinitiators have been discussed. The limitations imposed by thermodynamic equilibrium and tendency for acrylic double bond polymerizations during synthesis of multifunctional acrylates have been presented. Aim of present investigation was thus to explore the reaction variables associated with synthesis of multifunctional acrylates. Zirconium oxychloride was evaluated as catalyst against regular acid functional catalyst. The catalyzed synthesis of glyceryl acrylate and neopentyl glycol acrylate was conducted by variation of following reaction parameters: two different reactant molar ratios- 1:4 and 1:6; catalyst usage in % by moles on polyol- 2.5, 5.0 and 7.5 and two different reaction temperatures- 45 and 75 0C. The reaction was monitored by determination of acid value and hydroxy value at regular intervals, besides TLC, HPLC, and FTIR analysis of intermediates and products. On the basis of determination of reaction progress over 1-60 hrs, the esterification reaction was observed to follow 2nd order kinetics with rate constant varying from 1*10-4 to 7*10-4. The thermal and catalytic components of second order rate constant and energy of activation were also determined. Uses of these kinetic and thermodynamic parameters in design of reactor for manufacture of multifunctional acrylate ester have been presented. The synthesized multifunctional acrylates were used to formulate and apply UV curable clear coat followed by determination of curing characteristics and mechanical properties of cured film. The overall curing rates less than 05 min. were easily attained indicating economical viability of radiation curable system due to faster production schedules

Keywords: glyceryl acrylate, neopentyl glycol acrylate, kinetic modeling, zirconium oxychloride.

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Authors: Berardina De Carolis, Giovanni Cozzolongo

Abstract:

In this paper, we present C@sa, a multiagent system aiming at modeling, controlling and simulating the behavior of an intelligent house. The developed system aims at providing to architects, designers and psychologists a simulation and control tool for understanding which is the impact of embedded and pervasive technology on people daily life. In this vision, the house is seen as an environment made up of independent and distributed devices, controlled by agents, interacting to support user's goals and tasks.

Keywords: Ambient intelligence, agent-based systems, influence diagrams.

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Authors: Shuo-Li Hsu, Peng-Wei Gau, I-Lin Wu, Jyh-Horng Jeng

Abstract:

For most image fusion algorithms separate relationship by pixels in the image and treat them more or less independently. In addition, they have to be adjusted different parameters in different time or weather. In this paper, we propose a region–based image fusion which combines aspects of feature and pixel-level fusion method to replace only by pixel. The basic idea is to segment far infrared image only and to add information of each region from segmented image to visual image respectively. Then we determine different fused parameters according different region. At last, we adopt artificial neural network to deal with the problems of different time or weather, because the relationship between fused parameters and image features are nonlinear. It render the fused parameters can be produce automatically according different states. The experimental results present the method we proposed indeed have good adaptive capacity with automatic determined fused parameters. And the architecture can be used for lots of applications.

Keywords: Image fusion, Region-based fusion, Segmentation, Neural network, Multi-sensor.

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Authors: Mada Sanjaya, Halimatussadiyah, Dian Syah Maulana

Abstract:

The nonlinear chaotic non-autonomous fourth order system is algebraically simple but can generate complex chaotic attractors. In this paper, non-autonomous fourth order chaotic oscillator circuits were designed and simulated. Also chaotic nonautonomous Attractor is addressed suitable for chaotic masking communication circuits using Matlab® and MultiSIM® programs. We have demonstrated in simulations that chaos can be synchronized and applied to signal masking communications. We suggest that this phenomenon of chaos synchronism may serve as the basis for little known chaotic non-autonomous Attractor to achieve signal masking communication applications. Simulation results are used to visualize and illustrate the effectiveness of non-autonomous chaotic system in signal masking. All simulations results performed on nonautonomous chaotic system are verify the applicable of secure communication.

Keywords: Bidirectional chaotic synchronization, double bellattractor, secure communication

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Authors: R. Masarova, M. Juhas, B. Juhasova, Z. Sutova

Abstract:

In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: Dynamic system, transfer matrix, inverse matrix, modeling.

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Authors: Düzgün Akmaz, Hüseyin Erişti

Abstract:

In the last few years, harmonics have been occurred with the increasing use of nonlinear loads, and these harmonics have been an ever increasing problem for the line systems. This situation importantly affects the quality of power and gives large losses to the network. An efficient way to solve these problems is providing harmonic compensation through parallel active power filters. Many methods can be used in the control systems of the parallel active power filters which provide the compensation. These methods efficiently affect the performance of the active power filters. For this reason, the chosen control method is significant. In this study, Fourier analysis (FA) control method and synchronous reference frame (SRF) control method are discussed. These control methods are designed for both eliminate harmonics and perform reactive power compensation in MATLAB/Simulink pack program and are tested. The results have been compared for each two methods.

Keywords: Harmonics, Harmonic compensation, Parallel active power filters, Power quality.

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Authors: Guangyu Liu

Abstract:

In the last decade, energy based control theory has undergone a significant breakthrough in dealing with underactated mechanical systems with two successful and similar tools, controlled Lagrangians and controlled Hamiltanians (IDA-PBC). However, because of the complexity of these tools, successful case studies are lacking, in particular, MIMO cases. The seminal theoretical paper of controlled Lagrangians proposed by Bloch and his colleagues presented a benchmark example–a 4 d.o.f underactuated pendulum on a cart but a detailed and completed design is neglected. To compensate this ignorance, the note revisit their design idea by addressing explicit control functions for a similar device motivated by a vector thrust body hovering in the air. To the best of our knowledge, this system is the first MIMO, underactuated example that is stabilized by using energy based tools at the courtesy of the original design idea. Some observations are given based on computer simulation.

Keywords: Controlled Lagrangian, Energy Shaping, Spherical Inverted Pendulum, Controlled Hamiltonian.

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