Search results for: single layer

Authors: N.Karpagam, D.Devaraj

Abstract:

Static Var Compensator (SVC) is a shunt type FACTS device which is used in power system primarily for the purpose of voltage and reactive power control. In this paper, a fuzzy logic based supplementary controller for Static Var Compensator (SVC) is developed which is used for damping the rotor angle oscillations and to improve the transient stability of the power system. Generator speed and the electrical power are chosen as input signals for the Fuzzy Logic Controller (FLC). The effectiveness and feasibility of the proposed control is demonstrated with Single Machine Infinite Bus (SMIB) system and multimachine system (WSCC System) which show improvement over the use of a fixed parameter controller.

Keywords: FLC, SVC, Transient stability, SMIB, PIDcontroller.

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Authors: N. Deepika, P. A. L. Narayana

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Linear stability analysis of double diffusive convection in a horizontal porous layer saturated with fluid is examined by considering the effects of viscous dissipation, concentration based internal heat source and vertical throughflow. The basic steady state solution for Governing equations is derived. Linear stability analysis has been implemented numerically by using shooting and Runge-kutta methods. Critical thermal Rayleigh number Rac is obtained for various values of solutal Rayleigh number Sa, vertical Peclet number Pe, Gebhart number Ge, Lewis number Le and measure of concentration based internal heat source γ. It is observed that Ge has destabilizing effect for upward throughflow and stabilizing effect for downward throughflow. And γ has considerable destabilizing effect for upward throughflow and insignificant destabilizing effect for downward throughflow.

Keywords: Porous medium, concentration based internal heat source, vertical throughflow, viscous dissipation.

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Authors: Xin-Yu Shih, Yue-Qu Liu, Hong-Ru Chou

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This paper presents a low-area and fully-reconfigurable Fast Fourier Transform (FFT) hardware design for 3GPP-LTE communication standard. It can fully support 32 different FFT sizes, up to 2048 FFT points. Besides, a special processing element is developed for making reconfigurable computing characteristics possible, while first-in first-out (FIFO) scheduling scheme design technique is proposed for hardware-friendly FIFO resource arranging. In a synthesis chip realization via TSMC 40 nm CMOS technology, the hardware circuit only occupies core area of 0.2325 mm² and dissipates 233.5 mW at maximal operating frequency of 250 MHz.

Keywords: Reconfigurable, fast Fourier transform, single-path delay feedback, 3GPP-LTE.

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Authors: Shi Qi Koo, Ahmad Beng Hong Kueh

Abstract:

In the present work, the finite element formulation for the investigation of the effects of a localized interfacial degeneration on the dynamic behavior of the [90°/0°] laminated composite plate employing the state-space technique is performed. The stiffness of the laminate is determined by assembling the stiffnesses of subelements. This includes an introduction of an interface layer adopting the virtually zero-thickness formulation to model the interfacial degeneration. Also, the kinematically consistent mass matrix and proportional damping have been formulated to complete the free vibration governing expression. To simulate the interfacial degeneration of the laminate, the degenerated areas are defined from the center propagating outwards in a localized manner. It is found that the natural frequency, damped frequency and damping ratio of the plate decreases as the degenerated area of the interface increases. On the contrary, the loss factor increases correspondingly.

Keywords: Dynamic finite element, localized interface degeneration, proportional damping, state-space modeling.

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Authors: E. T. L. Cöuras Ford, V. A. C. Vale, J. U. L. Mendes, F. A. Ribeiro

Abstract:

The study of the aerodynamics related to the improvement in the acting of airplanes and automobiles with the objective of being reduced the effect of the attrition of the air on structures, providing larger speeds and smaller consumption of fuel. The application of the knowledge of the aerodynamics not more limits to the aeronautical and automobile industries. Therefore, this research aims to design and construction of a wind tunnel to perform aerodynamic analysis in bodies of cars, seeking greater efficiency. Therefore, this research aims to design and construction of a wind tunnel to perform aerodynamic analysis in bodies of cars, seeking greater efficiency. For this, a methodology for wind tunnel type selection is designed to be built, taking into account the various existing configurations in which chose to build an open circuit tunnel, due to the lower complexity of construction and installation; operational simplicity and low cost. The guidelines for the project were teaching: the layer that limits study and analyze specimens with different geometries. For the variation of pressure in the test, section of a switched gauge used a pitot tube. Thus, it was possible to obtain quantitative and qualitative results, which proved to be satisfactory.

Keywords: Wind tunnel, Aerodynamics, Air.

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Authors: Ahmed Abdulla Ashlam, Atta Badii, Frederic Stahl

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In recent years, SQL injection attacks have been identified as being prevalent against web applications. They affect network security and user data, which leads to a considerable loss of money and data every year. This paper presents the use of classification algorithms in machine learning using a method to classify the login data filtering inputs into "SQLi" or "Non-SQLi,” thus increasing the reliability and accuracy of results in terms of deciding whether an operation is an attack or a valid operation. A method as a Web-App is developed for auto-generated data replication to provide a twin of the targeted data structure. Shielding against SQLi attacks (WebAppShield) that verifies all users and prevents attackers (SQLi attacks) from entering and or accessing the database, which the machine learning module predicts as "Non-SQLi", has been developed. A special login form has been developed with a special instance of the data validation; this verification process secures the web application from its early stages. The system has been tested and validated, and up to 99% of SQLi attacks have been prevented.

Keywords: SQL injection, attacks, web application, accuracy, database, WebAppShield.

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Authors: N. W. K. Jayatissa, R. Attalage, Prabath Hewageegana, P. A. A. Perera, M. A. Punyasena

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Per capita energy usage in any country is exponentially increasing with their development. As a result, the country’s dependence on the fossil fuels for energy generation is also increasing tremendously creating economic and environmental concerns. Tropical countries receive considerable amount of solar radiation throughout the year, use of solar energy with different energy storage and conversion methodologies is a viable solution to minimize the ever increasing demand for the depleting fossil fuels. Salinity gradient solar pond is one such solar energy application. This paper reports the characteristics and performance of a thermally insulated, experimental salinity-gradient solar pond, built at the premises of the University of Kelaniya, Sri Lanka. Particular stress is given to the behavior of the evolution of the three layer structure exist at the stable state of a salinity gradient solar pond over a long period of time, under different environmental conditions. The operational procedures required to maintain the long term thermal stability are also reported in this article.

Keywords: Salt-gradient, solar pond, solar radiation, renewable energy.

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Authors: Saqib Mahmood, Rolf Radespiel

Abstract:

This paper aims at numerically analysing the effect of an active flow control (AFC) by a vortex generator jet (VGJ) submerged in a boundary layer via Chimera Grids and Detached- Eddy Simulation (DES). The performance of DES results are judged against Reynolds-Averaged Navier-Stokes (RANS) and compared with the experiments that showed an unsteady vortex motion downstream of VGJ. Experimental results showed that the mechanism of embedding logitudinal vortex structure in the main stream flow is quite effective in increasing the near wall momentum of separated aircraft wing. In order to simulate such a flow configuration together with the VGJ, an efficient numerical approach is required. This requirement is fulfilled by performing the DES simulation over the flat plate using the DLR TAU Code. The DES predictions identify the vortex region via smooth hybrid length scale and predict the unsteady vortex motion observed in the experiments. The DES results also showed that the sufficient grid refinement in the vortex region resolves the turbulent scales downstream of the VGJ, the spatial vortex core postion and nondimensional momentum coefficient
RVx .

Keywords: VGJ, Chimera Grid, DES, RANS.

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Authors: Christhu Raj M. R., Rajeev Sukumaran

Abstract:

Underwater acoustic networks have attracted great attention in the last few years because of its numerous applications. High data rate can be achieved by efficiently modeling the physical layer in the network protocol stack. In Acoustic medium, propagation speed of the acoustic waves is dependent on many parameters such as temperature, salinity, density, and depth. Acoustic propagation speed cannot be modeled using standard empirical formulas such as Urick and Thorp descriptions. In this paper, we have modeled the acoustic channel using real time data of temperature, salinity, and speed of Bay of Bengal (Indian Coastal Region). We have modeled the acoustic channel by using Mackenzie speed equation and real time data obtained from National Institute of Oceanography and Technology. It is found that acoustic propagation speed varies between 1503 m/s to 1544 m/s as temperature and depth differs. The simulation results show that temperature, salinity, depth plays major role in acoustic propagation and data rate increases with appropriate data sets substituted in the simulated model.

Keywords: Underwater Acoustics, Mackenzie Speed Equation, Temperature, Salinity.

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Authors: Yunyong Guo, Sudhakar Ganti, Bryan Guo

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The swift proliferation of telehealth Internet of Things (IoT) devices has sparked concerns regarding energy consumption and the need for streamlined data processing. This paper presents an energy-efficient model that integrates telehealth IoT devices into a platform based on fog and cloud computing. This integrated system provides a sustainable and robust solution to address the challenges. Our model strategically utilizes fog computing as a localized data processing layer and leverages cloud computing for resource-intensive tasks, resulting in a significant reduction in overall energy consumption. The incorporation of adaptive energy-saving strategies further enhances the efficiency of our approach. Simulation analysis validates the effectiveness of our model in improving energy efficiency for telehealth IoT systems, particularly when integrated with localized fog nodes and both private and public cloud infrastructures. Subsequent research endeavors will concentrate on refining the energy-saving model, exploring additional functional enhancements, and assessing its broader applicability across various healthcare and industry sectors.

Keywords: Energy-efficient, fog computing, IoT, telehealth.

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Authors: Abdelhalim Kessal

Abstract:

This paper treats a design of combined control of a single phase power factor correction (PFC). The strategy of the proposed control is based on two parts, the first, for the outer loop (DC output regulated voltage), and the second govern the input current of the converter in order to achieve a sinusoidal form in phase with the grid voltage. Two kinds of regulators are used, Fuzzy controller for the outer loop and predictive controller for the inner loop. The controllers are verified and discussed through simulation under MATLAB/Simulink platform. Also an experimental confirmation is applied. Results present a high dynamic performance under various parameters changes.

Keywords: Boost converter, harmonic distortion, Fuzzy, prediction, unity power factor.

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Authors: Hichem Talbi, Mohamed Batouche, Amer Draa

Abstract:

In this paper we present a new approach to deal with image segmentation. The fact that a single segmentation result do not generally allow a higher level process to take into account all the elements included in the image has motivated the consideration of image segmentation as a multiobjective optimization problem. The proposed algorithm adopts a split/merge strategy that uses the result of the k-means algorithm as input for a quantum evolutionary algorithm to establish a set of non-dominated solutions. The evaluation is made simultaneously according to two distinct features: intra-region homogeneity and inter-region heterogeneity. The experimentation of the new approach on natural images has proved its efficiency and usefulness.

Keywords: Image segmentation, multiobjective optimization, quantum computing, evolutionary algorithms.

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Authors: Rami El-Hajj Mohamad, Mahmoud Skafi, Ali Massoud Haidar

Abstract:

Several meteorological parameters were used for the  prediction of monthly average daily global solar radiation on  horizontal using recurrent neural networks (RNNs). Climatological  data and measures, mainly air temperature, humidity, sunshine  duration, and wind speed between 1995 and 2007 were used to design  and validate a feed forward and recurrent neural network based  prediction systems. In this paper we present our reference system  based on a feed-forward multilayer perceptron (MLP) as well as the  proposed approach based on an RNN model. The obtained results  were promising and comparable to those obtained by other existing  empirical and neural models. The experimental results showed the  advantage of RNNs over simple MLPs when we deal with time series  solar radiation predictions based on daily climatological data.

Keywords: Recurrent Neural Networks, Global Solar Radiation, Multi-layer perceptron, gradient, Root Mean Square Error.

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Authors: Abdelheq Boukarkar, Omar Guermoua

Abstract:

In this paper, we propose a miniaturized and wideband patch antenna for C-band applications. The antenna miniaturization is obtained by loading shorting vias along one patch edge. At the same time, the wideband performance is achieved by combining two resonances using one feed line. The measured results reveal that the antenna covers the frequency band 4.32 GHz to 6.52 GHz (41%) with a peak gain and a peak efficiency of 5.5 dBi and 87%, respectively. The antenna occupies a relatively small size of only 26 x 22 x 5.6 mm³, making it suitable for compact wireless devices requiring a stable unidirectional gain over a wide frequency range.

Keywords: Miniaturized antennas, patch antennas, stable gain, wideband antennas.

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Authors: Shi Chen, Zi Y. Chen, Jian K. Dan, Jian F. Li

Abstract:

Evolution of one-dimensional electron system under high-energy-density (HED) conditions is investigated, using the principle of least-action and variational method. In a single-mode modulation model, the amplitude and spatial wavelength of the modulation are chosen to be general coordinates. Equations of motion are derived by considering energy conservation and force balance. Numerical results show that under HED conditions, electron density modulation could exist. Time dependences of amplitude and wavelength are both positively related to the rate of energy input. Besides, initial loading speed has a significant effect on modulation amplitude, while wavelength relies more on loading duration.

Keywords: Electron density modulation, HED, nonlinearevolution, plasmas.

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Authors: S. Ntalampiras, I. Potamitis, N. Fakotakis, S. Kouzoupis

Abstract:

The present work faces the problem of automatic enumeration and recognition of an unknown and time-varying number of environmental sound sources while using a single microphone. The assumption that is made is that the sound recorded is a realization of sound sources belonging to a group of audio classes which is known a-priori. We describe two variations of the same principle which is to calculate the distance between the current unknown audio frame and all possible combinations of the classes that are assumed to span the soundscene. We concentrate on categorizing environmental sound sources, such as birds, insects etc. in the task of monitoring the biodiversity of a specific habitat.

Keywords: automatic recognition of multiple sound sources, enumeration of sound sources, computational ecology.

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Authors: Mahdi Fakoor, Seyed Mohammad Navid Ghoreishi

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Composite patching is a common way for reinforcing the cracked pipes and cylinders. The effects of composite patch reinforcement on fracture parameters of a cracked pipe depend on a variety of parameters such as number of layers, angle, thickness, and material of each layer. Therefore, stacking sequence optimization of composite patch becomes crucial for the applications of cracked pipes. In this study, in order to obtain the optimal stacking sequence for a composite patch that has minimum weight and maximum resistance in propagation of cracks, a coupled Multi-Objective Genetic Algorithm (MOGA) and Finite Element Method (FEM) process is proposed. This optimization process has done for longitudinal and transverse semi-elliptical cracks and optimal stacking sequences and Pareto’s front for each kind of cracks are presented. The proposed algorithm is validated against collected results from the existing literature.

Keywords: Multi objective optimization, Pareto front, composite patch, cracked pipe.

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Authors: Yue-Der Lin, Ya-Hsueh Chien, Yen-Ting Lin, Shih-Fan Wang, Cheng-Lun Tsai, Ching-Che Tsai

Abstract:

Capacitive electrocardiogram (ECG) measurement is an attractive approach for long-term health monitoring. However, there is little literature available on its implementation, especially for multichannel system in standard ECG leads. This paper begins from the design criteria for capacitive ECG measurement and presents a multichannel limb-lead capacitive ECG system with conductive fabric tapes pasted on a double layer PCB as the capacitive sensors. The proposed prototype system incorporates a capacitive driven-body (CDB) circuit to reduce the common-mode power-line interference (PLI). The presented prototype system has been verified to be stable by theoretic analysis and practical long-term experiments. The signal quality is competitive to that acquired by commercial ECG machines. The feasible size and distance of capacitive sensor have also been evaluated by a series of tests. From the test results, it is suggested to be greater than 60 cm2 in sensor size and be smaller than 1.5 mm in distance for capacitive ECG measurement.

Keywords: capacitive driven-body (CDB) circuit, capacitive electrocardiogram (ECG) measurement, capacitive sensor, conductive fabric tape, power-line interference (PLI).

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Authors: Aleš Florian, Lenka Ševelová, Rudolf Hela

Abstract:

Complex statistical analysis of stresses in concrete slab of the real type of rigid pavement is performed. The computational model of the pavement is designed as a spatial (3D) model, is based on a nonlinear variant of the finite element method that respects the structural nonlinearity, enables to model different arrangement of joints, and the entire model can be loaded by the thermal load. Interaction of adjacent slabs in joints and contact of the slab and the subsequent layer are modeled with help of special contact elements. Four concrete slabs separated by transverse and longitudinal joints and the additional subgrade layers and soil to the depth of about 3m are modeled. The thickness of individual layers, physical and mechanical properties of materials, characteristics of joints, and the temperature of the upper and lower surface of slabs are supposed to be random variables. The modern simulation technique Updated Latin Hypercube Sampling with 20 simulations is used for statistical analysis. As results, the estimates of basic statistics of the principal stresses s1 and s3 in 53 points on the upper and lower surface of the slabs are obtained.

Keywords: concrete, FEM, pavement, simulation.

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Authors: Muhibul Haque Bhuyan, Quazi D. M. Khosru

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Carrier scatterings in the inversion channel of MOSFET dominates the carrier mobility and hence drain current. This paper presents an analytical model of the subthreshold drain current incorporating the effective electron mobility model of the pocket implanted nano scale n-MOSFET. The model is developed by assuming two linear pocket profiles at the source and drain edges at the surface and by using the conventional drift-diffusion equation. Effective electron mobility model includes three scattering mechanisms, such as, Coulomb, phonon and surface roughness scatterings as well as ballistic phenomena in the pocket implanted n-MOSFET. The model is simulated for various pocket profile and device parameters as well as for various bias conditions. Simulation results show that the subthreshold drain current data matches the experimental data already published in the literature.

Keywords: Linear Pocket Profile, Pocket Implanted n-MOSFET, Subthreshold Drain Current and Effective Mobility Model.

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Authors: Zhang Lei, Zhan Haiyang, Gu Miao

Abstract:

A universal software platform is developed for improving the defects in the practical one. This software platform has distinct advantages in modularization, information management, and the interfaces. Several technologies such as computer technology, virtualization technology, network technology, etc. are combined together in this software platform, and four working modes are introduced in this article including single mode, distributed mode, cloud mode, and the centralized mode. The application area of the software platform is extended through the switch between these working modes. The software platform can arrange the thermal vacuum test process automatically. This function can improve the reliability of thermal vacuum test.

Keywords: Software platform, thermal vacuum test, control and measurement, work mode.

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Authors: K. M. Rabiul Karim

Abstract:

The purpose of this study was to examine the reliability and validity of the Masculine Subordination-to-women Stress Scale (MSS) in the rural Bangladeshi population. The scale was validated using a sample of 342 Bangladeshi married men from 5 northwest villages of the country. Exploratory factor analysis revealed a single-factorial structure of the scale: masculine subordination-to-women stress. The MSS also showed adequate reliability and concurrent validity. It appears that the MSS is a reliable and valid instrument to measure masculine subordination-to-women stress for Bangladeshi men. However, further study of the scale is imperative.

Keywords: Reliability, Validity, Masculine Subordination-to-women Stress, and Bangladeshi Rural Men.

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Authors: Vasundara Patel K. S., Harsha N. Bhushan, Kiran G. Gadag, Nischal Prasad B. N., Mohmmed Haroon

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The most widely used semiconductor memory types are the Dynamic Random Access Memory (DRAM) and Static Random Access memory (SRAM). Competition among memory manufacturers drives the need to decrease power consumption and reduce the probability of read failure. A technology that is relatively new and has not been explored is the FinFET technology. In this paper, a single cell Schmitt Trigger Based Static RAM using FinFET technology is proposed and analyzed. The accuracy of the result is validated by means of HSPICE simulations with 32nm FinFET technology and the results are then compared with 6T SRAM using the same technology.

Keywords: Schmitt trigger based SRAM, FinFET, and Static Noise Margin.

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Authors: M. Kucukali Ozturk, B. Nergis, C. Candan

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Air permeability plays an important role for applications such as filtration, thermal and acoustic insulation. The study discussed in this paper was conducted in an attempt to investigate air permeability property of various combinations of nonwovens. The PROWHITE air permeability tester was used for the measurement of the air permeability of the samples in accordance with the relevant standards and a comparative study of the results were made. It was found that the fabric mass per unit area was closely related to the air-permeability. The air permeability decreased with the increase in mass per unit area. Additionally, the air permeability of nonwoven fabrics decreased with the increase in thickness. Moreover, air permeability of multilayered SMS nonwoven structures was lower than those of single layered ones.

Keywords: Air permeability, mass per unit area, nonwoven structure, polypropylene nonwoven, thickness.

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Authors: Ollie Hall, Salma ElSayed

Abstract:

Affective adaptation is a creative way for game designers to add an extra layer of engagement to their productions. When player’s emotions are an explicit factor in mechanics design, endless possibilities for imaginative gameplay emerge. Whilst gaining popularity, existing affective game research mostly runs controlled experiments in restrictive settings and rely on one or more specialist devices for measuring player’s emotional state. These conditions albeit effective, are not necessarily realistic. Moreover, the simplified narrative and intrusive wearables may not be suitable for players. This exploratory study investigates delivering an immersive affective experience in the wild with minimal requirements, in an attempt for the average developer to reach the average player. A puzzle game is created with rich narrative and creative mechanics. It employs both explicit and implicit adaptation and only requires a web camera. Participants played the game on their own machines in various settings. Whilst it was rated feasible, very engaging and enjoyable, it remains questionable whether a fully immersive experience was delivered due to the limited sample size.

Keywords: affective games, dynamic adaptation, emotion recognition, game design

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Authors: Abduladheem A. Ali, Easa A. Abd

Abstract:

The robot is a repeated task plant. The control of such a plant under parameter variations and load disturbances is one of the important problems. The aim of this work is to design Geno-Fuzzy controller suitable for online applications to control single link rigid robot arm plant. The genetic-fuzzy online controller (indirect controller) has two genetic-fuzzy blocks, the first as controller, the second as identifier. The identification method is based on inverse identification technique. The proposed controller it tested in normal and load disturbance conditions.

Keywords: Fuzzy network, genetic algorithm, robot control, online genetic control, parameter identification.

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Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin

Abstract:

Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.

Keywords: Gravity gradient, accelerometer, gravity gradient sensor, single-axis rotation modulation.

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Authors: Hongjun Liu, Qibing Sun, Nan Huang, Shaolan Zhu, Wei Zhao

Abstract:

A high energy dual-wavelength extracavity KTA optical parametric oscillator (OPO) with excellent stability and beam quality, which is pumped by a Q-switched single-longitudinal-mode Nd:YAG laser, has been demonstrated based on a type II noncritical phase matching (NCPM) KTA crystal. The maximum pulse energy of 10.2 mJ with the output stability of better than 4.1% rms at 3.467 μm is obtained at the repetition rate of 10 Hz and pulse width of 2 ns, and the 11.9 mJ of 1.535 μm radiation is obtained simultaneously. This extracavity NCPM KTA OPO is very useful when high energy, high beam quality and smooth time domain are needed.

Keywords: mid-infrared laser, OPO, dual-wavelength laser

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Authors: Shaharin A. Sulaiman, Mizuan Minhat

Abstract:

This paper presents development of an ignition system using spark electrodes for application in a research explosion vessel. A single spark is aimed to be discharged with quantifiable ignition energy. The spark electrode system would enable study of flame propagation, ignitability of fuel-air mixtures and other fundamental characteristics of flames. The principle of the capacitive spark circuit of ASTM is studied to charge an appropriate capacitance connected across the spark gap through a large resistor by a high voltage from the source of power supply until the initiation of spark. Different spark energies could be obtained mainly by varying the value of the capacitance and the supply current. The spark sizes produced are found to be affected by the spark gap, electrode size, input voltage and capacitance value.

Keywords: Ignition, Spark Electrode, Flame

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Authors: M. Ziółkowska, J. T. Duda, J. Milewska-Duda

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This paper describes an approach to the adsorption phenomena modeling aimed at specifying the adsorption mechanisms on localized or nonlocalized adsorbent sites, when applied to the nanocarbons. The concept comes from the fundamental thermodynamic description of adsorption equilibrium and is based on numerical calculations of the hydrogen adsorbed particles volume on the surface of selected nanocarbons: single-walled nanotube and nanocone. This approach enables to obtain information on adsorption mechanism and then as a consequence to take appropriate mathematical adsorption model, thus allowing for a more reliable identification of the material porous structure. Theoretical basis of the approach is discussed and newly derived results of the numerical calculations are presented for the selected nanocarbons.

Keywords: Adsorption, mathematical modeling, nanocarbons, numerical analysis.

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