Search results for: Wave Vortex Parameters

Authors: M. Aslam, Farrukh, A. R. Gardezi, Nasir Hayat

Abstract:

Automated material handling is given prime importance in the semi automated and automated facilities since it provides solution to the gigantic problems related to inventory and also support the latest philosophies like just in time production JIT and lean production. Automated storage and retrieval system is an antidote (if designed properly) to the facility sufferings like getting the right material , materials getting perished, long cycle times or many other similar kind of problems. A working model of automated storage and retrieval system (AS/RS) is designed and developed under the design parameters specified by Material Handling Industry of America (MHIA). Later on analysis was carried out to calculate the throughput and size of the machine. The possible implementation of this technology in local scenario is also discussed in this paper.

Keywords: Automated storage and retrieval system (AS/RS), Material handling, Computer integrated manufacturing (CIM), Lightdependent resistor (LDR)

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Authors: Alexandros Leontitsis, Archana P. Sangole

Abstract:

This article presents a short discussion on optimum neighborhood size selection in a spherical selforganizing feature map (SOFM). A majority of the literature on the SOFMs have addressed the issue of selecting optimal learning parameters in the case of Cartesian topology SOFMs. However, the use of a Spherical SOFM suggested that the learning aspects of Cartesian topology SOFM are not directly translated. This article presents an approach on how to estimate the neighborhood size of a spherical SOFM based on the data. It adopts the L-curve criterion, previously suggested for choosing the regularization parameter on problems of linear equations where their right-hand-side is contaminated with noise. Simulation results are presented on two artificial 4D data sets of the coupled Hénon-Ikeda map.

Keywords: Parameter estimation, self-organizing feature maps, spherical topology.

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

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The problem of exponential stability and periodicity for a class of cellular neural networks (DCNNs) with time-varying delays is investigated. By dividing the network state variables into subgroups according to the characters of the neural networks, some sufficient conditions for exponential stability and periodicity are derived via the methods of variation parameters and inequality techniques. These conditions are represented by some blocks of the interconnection matrices. Compared with some previous methods, the method used in this paper does not resort to any Lyapunov function, and the results derived in this paper improve and generalize some earlier criteria established in the literature cited therein. Two examples are discussed to illustrate the main results.

Keywords: Cellular neural networks, exponential stability, time varying delays, partitioned matrices, periodic solution.

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Authors: Vineet Srivastava, Pulak M. Pandey

Abstract:

Electrical discharge machining (EDM) is well established machining technique mainly used to machine complex geometries on difficult-to-machine materials and high strength temperature resistant alloys. In the present research, the objective is to study the shape of the electrode and establish the application of liquid nitrogen in reducing distortion of the electrode during electrical discharge machining of M2 grade high speed steel using copper electrodes. Study of roundness was performed on the electrode to observe the shape of the electrode for both conventional EDM and EDM with cryogenically cooled electrode. Scanning Electron Microscope (SEM) has been used to study the shape of electrode tip. The effect of various parameters such as discharge current and pulse on time has been studied to understand the behavior of distortion of electrode. It has been concluded that the shape retention is better in case of liquid nitrogen cooled electrode.

Keywords: cryogenic cooling, EDM, electrode shape, out of roundness.

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Authors: Arun Jacob, Leena R., Krishnakumar T.S., Jose Prakash M.

Abstract:

Effective cooling of electronic equipment has emerged as a challenging and constraining problem of the new century. In the present work the feasibility and effectiveness of jet impingement cooling on electronics were investigated numerically and experimentally. Studies have been conducted to see the effect of the geometrical parameters such as jet diameter (D), jet to target spacing (Z) and ratio of jet spacing to jet diameter (Z/D) on the heat transfer characteristics. The values of Reynolds numbers considered are in the range 7000 to 42000. The results obtained from the numerical studies are validated by conducting experiments. From the studies it is found that the optimum value of Z/D ratio is 5. For a given Reynolds number, the Nusselt number increases by about 28% if the diameter of the nozzle is increased from 1mm to 2mm. Correlations are proposed for Nusselt number in terms of Reynolds number and these are valid for air as the cooling medium.

Keywords: CFD, heat transfer coefficient, Nusselt number, ratio of jet diameter to jet spacing (Z/D), Reynolds number, turbulence model.

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Authors: Mircea Ivanescu, Nirvana Popescu, Decebal Popescu, Dorin Popescu

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This paper addresses the control problem of a class of hyper-redundant arms. In order to avoid discrepancy between the mathematical model and the actual dynamics, the dynamic model with uncertain parameters of this class of manipulators is inferred. A procedure to design a feedback controller which stabilizes the uncertain system has been proposed. A PD boundary control algorithm is used in order to control the desired position of the manipulator. This controller is easy to implement from the point of view of measuring techniques and actuation. Numerical simulations verify the effectiveness of the presented methods. In order to verify the suitability of the control algorithm, a platform with a 3D flexible manipulator has been employed for testing. Experimental tests on this platform illustrate the applications of the techniques developed in the paper.

Keywords: Distributed model, flexible manipulator, observer, robot control.

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Authors: Tusharkanta Das, Tumbanath Samantara, Sukanta Kumar Sahoo

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Unsteady effects of MHD free convection flow past in an infinite vertical plate with heat source in presence of radiation with reference to all critical parameters that appear in field equations are studied in this paper. The governing equations are developed by usual Boussinesq’s approximation. The problem is solved by using perturbation technique. The results are obtained for velocity, temperature, Nusselt number and skin-friction. The effects of magnetic parameter, prandtl number, Grashof number, permeability parameter, heat source/sink parameter and radiation parameter are discussed on flow characteristics and shown by means of graphs and tables.

Keywords: Heat transfer, radiation, MHD, free convection, porous medium, suction.

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Authors: S. A. Razavian Amrei, G.Ghodrati Amiri, D. Rezaei

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This paper presents probabilistic horizontal seismic hazard assessment of Naghan, Iran. It displays the probabilistic estimate of Peak Ground Horizontal Acceleration (PGHA) for the return period of 475, 950 and 2475 years. The output of the probabilistic seismic hazard analysis is based on peak ground acceleration (PGA), which is the most common criterion in designing of buildings. A catalogue of seismic events that includes both historical and instrumental events was developed and covers the period from 840 to 2009. The seismic sources that affect the hazard in Naghan were identified within the radius of 200 km and the recurrence relationships of these sources were generated by Kijko and Sellevoll. Finally Peak Ground Horizontal Acceleration (PGHA) has been prepared to indicate the earthquake hazard of Naghan for different hazard levels by using SEISRISK III software.

Keywords: Seismic Hazard Assessment, Seismicity Parameters, PGA, Naghan, Iran

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Authors: Dileep Malkhede, Bhartendu Seth

Abstract:

In this paper, the full state feedback controllers capable of regulating and tracking the speed trajectory are presented. A fourth order nonlinear mean value model of a 448 kW turbocharged diesel engine published earlier is used for the purpose. For designing controllers, the nonlinear model is linearized and represented in state-space form. Full state feedback controllers capable of meeting varying speed demands of drivers are presented. Main focus here is to investigate sensitivity of the controller to the perturbations in the parameters of the original nonlinear model. Suggested controller is shown to be highly insensitive to the parameter variations. This indicates that the controller is likely perform with same accuracy even after significant wear and tear of engine due to its use for years.

Keywords: Diesel engine model, Engine speed control, State feedback controller, Controller robustness.

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Authors: Yasuo Obikane

Abstract:

The frequency dependence of the phase field model(PFM) is studied. A simple PFM is proposed, and is tested in a laminar boundary layer. The Blasius-s laminar boundary layer solution on a flat plate is used for the flow pattern, and several frequencies are imposed on the PFM, and the decay times of the interfaces are obtained. The computations were conducted for three cases: 1) no-flow, and 2) a half ball on the laminar boundary layer, 3) a line of mass sources in the laminar boundary layer. The computations show the decay time becomes shorter as the frequency goes larger, and also show that it is sensitive to both background disturbances and surface tension parameters. It is concluded that the proposed simple PFM can describe the properties of decay process, and could give the fundamentals for the decay of the interface in turbulent flows.

Keywords: Phase field model, two phase flows, Laminarboundary Layer

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Authors: Guy Leshem, Ya'acov Ritov

Abstract:

Traffic Management and Information Systems, which rely on a system of sensors, aim to describe in real-time traffic in urban areas using a set of parameters and estimating them. Though the state of the art focuses on data analysis, little is done in the sense of prediction. In this paper, we describe a machine learning system for traffic flow management and control for a prediction of traffic flow problem. This new algorithm is obtained by combining Random Forests algorithm into Adaboost algorithm as a weak learner. We show that our algorithm performs relatively well on real data, and enables, according to the Traffic Flow Evaluation model, to estimate and predict whether there is congestion or not at a given time on road intersections.

Keywords: Machine Learning, Boosting, Classification, TrafficCongestion, Data Collecting, Magnetic Loop Detectors, SignalizedIntersections, Traffic Signal Timing Optimization.

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Authors: Bashir Ahmmad, Kensaku Kanomata, Fumihiko Hirose

Abstract:

The effect of carbon materials on TiO₂ for the photocatalytic hydrogen gas production from water / alcohol mixtures was investigated. Single walled carbon nanotubes (SWNTs), multi walled carbon nanotubes (MWNTs), carbon nanofiber (CNF), fullerene (FLN), graphite (GP), and graphite silica (GS) were used as co-catalysts by directly mixing with TiO₂. Drastic synergy effects were found with increase in the amount of hydrogen gas by a factor of ca. 150 and 100 for SWNTs and GS with TiO₂, respectively. Moreover, the increment factor of hydrogen production reached to 180, when the mixture of SWNTs and TiO₂ were smashed in an agate mortar before photocatalytic reactions. The order of H₂ gas production for these carbon materials was SWNTs > GS >> MWNTs > FLN > CNF > GP. To maximize the hydrogen production from SWNTs/TiO₂, various parameters of experimental condition were changed. Also, a comparison between Pt/TiO₂, SWNTs/TiO₂ and GS/TiO₂ was made for the amount of H₂ gas production. Finally, the recyclability of SWNTs/TiO₂or GS/TiO₂ was tested.

Keywords: Photocatalysis, carbon materials, alcohol reforming, hydrogen production, titanium oxide.

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Authors: H. Zemmouri, H. Lounic, N. Mameri

Abstract:

The present study aims to investigate the performance of Moringa oleifera seed extract as natural coagulant in clarification of secondary wastewater treatment plant (MWWTP) located in East of Algiers, Algeria. Coagulation flocculation performance of Moringa oleifera was evaluated through supernatant residual turbidity after jar test trials. Various influence parameters namely Moringa oleifera dosage and pH have been considered. Tests on Reghaia wastewater, having 129 NTU of initial turbidity, showed a removal of 69.45% of residual turbidity with only 1.5 mg/l of Moringa oleifera. This sufficient removal capability encourages the use of this bioflocculant for treatment of turbid waters. Indeed, Moringa oleifera which is a natural resource available locally (South of Algeria) coupled to the non-toxicity, biocompatibility and biodegradability, may be a very interesting alternative to the conventional coagulants used so far.

Keywords: Coagulation flocculation, colloids, Moringa oleifera, secondary wastewater.

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Authors: Ali Al-Zughaibi, Huw Davies

Abstract:

The purpose of this paper is to present a modeling and control of a quarter-car active suspension system with unknown mass, unknown time-delay and road disturbance. The objective of designing the controller is to derive a control law to achieve stability of the system and convergence that can considerably improve ride comfort and road disturbance handling. This is accomplished by using Routh-Hurwitz criterion based on defined parameters. Mathematical proof is given to show the ability of the designed controller to ensure the target of design, implementation with the active suspension system and enhancement dispersion oscillation of the system despite these problems. Simulations were also performed to control quarter car suspension, where the results obtained from these simulations verify the validity of the proposed design.

Keywords: Active suspension system, disturbance rejection, dynamic uncertainty, time-delay.

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Authors: Toyoyuki Honjo, Takeshi Hayashi, Akinori Nagano, Zhi-Wei Luo

Abstract:

For stable bipedal gait generation on the level floor, efficient restoring of mechanical energy lost by heel collision at the ground is necessary. Parametric excitation principle is one of the solutions. We dealt with the robot-s total center of mass as an inverted pendulum to consider the total dynamics of the robot. Parametrically excited walking requires the use of continuous target trajectory that is close to discontinuous optimal trajectory. In this paper, we proposed the new target trajectory based on a position in the walking direction. We surveyed relations between walking performance and the parameters that form the target trajectory via numerical simulations. As a result, it was found that our target trajectory has the similar characteristics of a parametrically excited inverted pendulum.

Keywords: Dynamic Bipedal Walking, Parametric Excitation, Target Trajectory Design.

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Authors: M. J. Baum, B. Gibbes, A. Grinham, S. Albert, D. Gale, P. Fisher

Abstract:

Alongside the rapid expansion of Seawater Reverse Osmosis technologies there is a concurrent increase in the production of hypersaline brine by-products. To minimize environmental impact, these by-products are commonly disposed into open-coastal environments via submerged diffuser systems as inclined dense jet outfalls. Despite the widespread implementation of this process, diffuser designs are typically based on small-scale laboratory experiments under idealistic quiescent conditions. Studies concerning diffuser performance in the field are limited. A set of experiments were conducted to assess the near field characteristics of brine disposal at the Gold Coast Desalination Plant offshore multiport diffuser. The aim of the field experiments was to determine the trajectory and dilution characteristics of the plume under various discharge configurations with production ranging 66 – 100% of plant operative capacity. The field monitoring system employed an unprecedented static array of temperature and electrical conductivity sensors in a three-dimensional grid surrounding a single diffuser port. Complimenting these measurements, Acoustic Doppler Current Profilers were also deployed to record current variability over the depth of the water column and wave characteristics. Recorded data suggested the open-coastal environment was highly active over the experimental duration with ambient velocities ranging 0.0 – 0.5 m∙s^-1, with considerable variability over the depth of the water column observed. Variations in background electrical conductivity corresponding to salinity fluctuations of ± 1.7 g∙kg^-1 were also observed. Increases in salinity were detected during plant operation and appeared to be most pronounced 10 – 30 m from the diffuser, consistent with trajectory predictions described by existing literature. Plume trajectories and respective dilutions extrapolated from salinity data are compared with empirical scaling arguments. Discharge properties were found to adequately correlate with modelling projections. Temporal and spatial variation of background processes and their subsequent influence upon discharge outcomes are discussed with a view to incorporating the influence of waves and ambient currents in the design of brine outfalls into the future.

Keywords: Brine disposal, desalination, field study, inclined dense jets, negatively buoyant discharge.

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Authors: L. A. S. Dionel, B. A. P. Santos, V. C. P. Lopes, L. G. Vasconcelos, M. A. Soares, E. B. Morais

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This study investigated the biosorption of the azo dye reactive Black B (RBB) from aqueous solution using the nonviable biomass of Cladosporium cladosporioides LM1. The biosorption systems were carried out in batch mode considering different conditions of initial pH, contact time, temperature, initial dye concentration and biosorbent dosage. Higher removal rate of RBB was obtained at pH 2. Biosorption data were successfully described by pseudo-second-order kinetic model and Langmuir isotherm model with the maximum monolayer biosorption capacity estimated at 71.43 mg/g. The values of thermodynamic parameters such as ∆G°, ∆H° and ∆S° indicated that the biosorption of RBB onto fungal biomass was spontaneous and exothermic in nature. It can be concluded that nonviable biomass of Cladosporium cladosporioides LM1 may be an attractive low-cost biosorbent for the removal of azo dye RBB from aqueous solution.

Keywords: Color removal, isotherms and kinetics models, thermodynamic studies, fungus.

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Authors: M. S. Anton Merkulov

Abstract:

This article discusses the questions concerning of creating small packet networks for energy companies with application of high voltage power line carrier equipment (PLC) with functionality of IP traffic transmission. The main idea is to create converged PLC links between substations and dispatching centers where packet data and voice are transmitted in one data flow. The article contents description of basic conception of the network, evaluation of voice traffic transmission parameters, and discussion of header compression techniques in relation to PLC links. The results of exploration show us, that convergent packet PLC links can be very useful in the construction of small packet networks between substations in remote locations, such as deposits or low populated areas.

Keywords: packet PLC, VoIP, time delay, packet traffic, overhead compression

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Authors: Liu Dan, Wang Xue, Wang Guiqin, Qian Zhihong

Abstract:

The burst noise is a kind of noises that are destructive and frequently found in semiconductor devices and ICs, yet detecting and removing the noise has proved challenging for IC designers or users. According to the properties of burst noise, a methodological approach is presented (proposed) in the paper, by which the burst noise can be analysed and detected in time domain. In this paper, principles and properties of burst noise are expounded first, Afterwards, feasibility (viable) of burst noise detection by means of wavelet transform in the time domain is corroborated in the paper, and the multi-resolution characters of Gaussian noise, burst noise and blurred burst noise are discussed in details by computer emulation. Furthermore, the practical method to decide parameters of wavelet transform is acquired through a great deal of experiment and data statistics. The methodology may yield an expectation in a wide variety of applications.

Keywords: Burst noise, detection, wavelet transform

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Authors: Abdallah F. Abd El-Mohsen, Ahmed A. Abdelsamee, Nouby M. Ghazaly

Abstract:

Engine exhaust noise is considered one of the largest sources of vehicle exterior noise. Further reduction of noise from the vehicle exhaust system will be required, as the vehicle exterior noise regulations become stricter. Therefore, the present study has been carried out to illustrate the role of engine operating parameters and exhaust system construction factors on exhaust noise emitted. The measurements carried out using different exhaust systems, which are mainly used in today’s vehicle. The effect of engine speed on the spectra level of exhaust noise is recorded at engine speeds of 900 rpm, 1800 rpm, 2700, rpm 3600 rpm and 4500 rpm. The results indicate that the increase of engine speed causes a significant increase in the spectrum level of exhaust noise. The increase in the number of the outlet of the expansion chamber also reduces the overall level of exhaust noise.

Keywords: Exhaust system, engine speed, expansion chamber.

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Authors: Quy Dang Nguyen, Reza Nakhaie Jazar

Abstract:

The paper investigates vibration dynamics of tire-road separation for a quarter-car model; this separation model is developed to be close to the real situation considering the tire is able to separate from the ground plane. A set of piecewise linear mathematical models is developed and matches the in-contact and no-contact states to be considered as mother models for further investigations. The bound dynamics are numerically simulated in the time response and phase portraits. The separation analysis may determine which values of suspension parameters can delay and avoid the no-contact phenomenon, which results in improving ride comfort and eliminating the potentially dangerous oscillation. Finally, model verification is carried out in the MSC-ADAMS environment.

Keywords: Quarter-car vibrations, tire-road separation, separation analysis, separation dynamics, ride comfort, ADAMS validation.

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Authors: Mousaab Alrhmoun, Magali Casellas, Michel Baudu, Christophe Dagot

Abstract:

The aim of the study is to improve removal of trace organic contaminants dissolved in activated sludge by the process of filtration with membrane bioreactor combined with modified activated carbon, for a maximum removal of organic compounds characterized by low molecular weight. Special treatment was conducted in laboratory on activated carbon. Tow reaction parameters: the pH of aqueous middle and the type of granular activated carbon were very important to improve the removal and to motivate the electrostatic Interactions of organic compounds with modified activated carbon in addition to physical adsorption, ligand exchange or complexation on the surface activated carbon. The results indicate that modified activated carbon has a strong impact in removal 21 of organic contaminants and in percentage of 100% of the process.

Keywords: Activated carbon, organic contaminants, Membrane bioreactor.

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Authors: M. M. Doustdar, M. Mojtahedpoor

Abstract:

The effects of flame-holder position, the ratio of flame holder diameter to combustion chamber diameter and injection angle on fuel propulsive droplets sizing and effective mass fraction have been studied by a cold flow. We named the mass of fuel vapor inside the flammability limit as the effective mass fraction. An empty cylinder as well as a flame-holder which are a simulator for duct combustion has been considered. The airflow comes into the cylinder from one side and injection operation will be done by four nozzles which are located on the entrance of cylinder. To fulfill the calculations a modified version of KIVA-3V code which is a transient, three-dimensional, multiphase, multi component code for the analysis of chemically reacting flows with sprays, is used.

Keywords: KIVA-3V, flame-holder, duct combustion, effective mass fraction, mean diameter of droplets.

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Authors: Hyoup-Sang Yoon

Abstract:

Video-on-demand (VOD) is designed by using content delivery networks (CDN) to minimize the overall operational cost and to maximize scalability. Estimation of the viewing pattern (i.e., the relationship between the number of viewings and the ranking of VOD contents) plays an important role in minimizing the total operational cost and maximizing the performance of the VOD systems. In this paper, we have analyzed a large body of commercial VOD viewing data and found that the viewing rank distribution fits well with the parabolic fractal distribution. The weighted linear model fitting function is used to estimate the parameters (coefficients) of the parabolic fractal distribution. This paper presents an analytical basis for designing an optimal hierarchical VOD contents distribution system in terms of its cost and performance.

Keywords: VOD, CDN, parabolic fractal distribution, viewing rank, weighted linear model fitting

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Authors: Babak H. Mamamqani, Alimohammad Entezarmahdi

Abstract:

There are many researches on parameters affecting seismic behavior of steel moment frames. Great deal of these researches considers cover plate connections with or without haunch and direct beam to column connection for exterior columns. Also there are experimental results for interior connections with equal beam depth on both sides but not much research has been performed on the seismic behavior of joints with unequal beam depth. Based on previous experimental results, a series of companion analyses have been set up considering different beam height and connection detailing configuration to investigate the seismic behavior of the connections. Results of this study indicate that when the differences between beams height on both side increases, use of haunch connection system leads to significant improvement in the seismic response whereas other configurations did not provide satisfying results.

Keywords: Analytical modeling, Haunch connection, Seismic design, Unequal beam depth.

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Authors: Baki Koyuncu, Mehmet Güzel

Abstract:

The kinematics of manipulators is a central problem in the automatic control of robot manipulators. Theoretical background for the analysis of the 5 Dof Lynx-6 educational Robot Arm kinematics is presented in this paper. The kinematics problem is defined as the transformation from the Cartesian space to the joint space and vice versa. The Denavit-Harbenterg (D-H) model of representation is used to model robot links and joints in this study. Both forward and inverse kinematics solutions for this educational manipulator are presented, An effective method is suggested to decrease multiple solutions in inverse kinematics. A visual software package, named MSG, is also developed for testing Motional Characteristics of the Lynx-6 Robot arm. The kinematics solutions of the software package were found to be identical with the robot arm-s physical motional behaviors.

Keywords: Lynx 6, robot arm, forward kinematics, inverse kinematics, software, DH parameters, 5 DOF , SSC-32 , simulator.

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Authors: S. Yaman, S. Rostami

Abstract:

In this study, a black box modeling of the coupled-tank system is obtained by using fuzzy sets. The derived model is tested via adaptive neuro fuzzy inference system (ANFIS). In order to achieve a better control performance, the parameters of three different controller types, classical proportional integral controller (PID), fuzzy PID and function tuner method, are tuned by one of the evolutionary computation method, genetic algorithm. All tuned controllers are applied to the fuzzy model of the coupled-tank experimental setup and analyzed under the different reference input values. According to the results, it is seen that function tuner method demonstrates better robust control performance and guarantees the closed loop stability.

Keywords: Function tuner method, fuzzy modeling, fuzzy PID controller, genetic algorithm.

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Authors: S. Bourennane, A. Bendjama

Abstract:

This paper deals with the localization of the wideband sources. We develop a new approach for estimating the wide band sources parameters. This method is based on the high order statistics of the recorded data in order to eliminate the Gaussian components from the signals received on the various hydrophones.In fact the noise of sea bottom is regarded as being Gaussian. Thanks to the coherent signal subspace algorithm based on the cumulant matrix of the received data instead of the cross-spectral matrix the wideband correlated sources are perfectly located in the very noisy environment. We demonstrate the performance of the proposed algorithm on the real data recorded during an underwater acoustics experiments.

Keywords: Higher-order statistics, high resolution array processing techniques, localization of acoustics sources, wide band sources.

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Authors: Davood Shishebori, Mohammad Saber Fallah Nezhad, Sina Seifi

Abstract:

In this paper, a variable multiple dependent state (MDS) sampling plan is developed based on the process capability index using Bayesian approach. The optimal parameters of the developed sampling plan with respect to constraints related to the risk of consumer and producer are presented. Two comparison studies have been done. First, the methods of double sampling model, sampling plan for resubmitted lots and repetitive group sampling (RGS) plan are elaborated and average sample numbers of the developed MDS plan and other classical methods are compared. A comparison study between the developed MDS plan based on Bayesian approach and the exact probability distribution is carried out.

Keywords: MDS sampling plan, RGS plan, sampling plan for resubmitted lots, process capability index, average sample number, Bayesian approach.

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Authors: Kholod M. Abu-Alnaja

Abstract:

In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.

Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential Equations

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