Search results for: motion vector
674 Face Recognition using Features Combination and a New Non-linear Kernel
Authors: Essam Al Daoud
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To improve the classification rate of the face recognition, features combination and a novel non-linear kernel are proposed. The feature vector concatenates three different radius of local binary patterns and Gabor wavelet features. Gabor features are the mean, standard deviation and the skew of each scaling and orientation parameter. The aim of the new kernel is to incorporate the power of the kernel methods with the optimal balance between the features. To verify the effectiveness of the proposed method, numerous methods are tested by using four datasets, which are consisting of various emotions, orientations, configuration, expressions and lighting conditions. Empirical results show the superiority of the proposed technique when compared to other methods.Keywords: Face recognition, Gabor wavelet, LBP, Non-linearkerner
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1533673 Performance of Block Codes Using the Eigenstructure of the Code Correlation Matrixand Soft-Decision Decoding of BPSK
Authors: Vitalice K. Oduol, C. Ardil
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A method is presented for obtaining the error probability for block codes. The method is based on the eigenvalueeigenvector properties of the code correlation matrix. It is found that under a unary transformation and for an additive white Gaussian noise environment, the performance evaluation of a block code becomes a one-dimensional problem in which only one eigenvalue and its corresponding eigenvector are needed in the computation. The obtained error rate results show remarkable agreement between simulations and analysis.
Keywords: bit error rate, block codes, code correlation matrix, eigenstructure, soft-decision decoding, weight vector.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1774672 Gauss-Seidel Iterative Methods for Rank Deficient Least Squares Problems
Authors: Davod Khojasteh Salkuyeh, Sayyed Hasan Azizi
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We study the semiconvergence of Gauss-Seidel iterative methods for the least squares solution of minimal norm of rank deficient linear systems of equations. Necessary and sufficient conditions for the semiconvergence of the Gauss-Seidel iterative method are given. We also show that if the linear system of equations is consistent, then the proposed methods with a zero vector as an initial guess converge in one iteration. Some numerical results are given to illustrate the theoretical results.Keywords: rank deficient least squares problems, AOR iterativemethod, Gauss-Seidel iterative method, semiconvergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1922671 A Review on Important Aspects of Information Retrieval
Authors: Yogesh Gupta, Ashish Saini, A.K. Saxena
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Information retrieval has become an important field of study and research under computer science due to explosive growth of information available in the form of full text, hypertext, administrative text, directory, numeric or bibliographic text. The research work is going on various aspects of information retrieval systems so as to improve its efficiency and reliability. This paper presents a comprehensive study, which discusses not only emergence and evolution of information retrieval but also includes different information retrieval models and some important aspects such as document representation, similarity measure and query expansion.
Keywords: Information Retrieval, query expansion, similarity measure, query expansion, vector space model.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3329670 Enhanced Gram-Schmidt Process for Improving the Stability in Signal and Image Processing
Authors: Mario Mastriani, Marcelo Naiouf
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The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors) into an orthonormal basis (a set of orthogonal, unit-length vectors). The process consists of taking each vector and then subtracting the elements in common with the previous vectors. This paper introduces an Enhanced version of the Gram-Schmidt Process (EGSP) with inverse, which is useful for signal and image processing applications.
Keywords: Digital filters, digital signal and image processing, Gram-Schmidt Process, orthonormalization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2878669 A609 Modeling of AC Servomotor Using Genetic Algorithm and Tests for Control of a Robotic Joint
Authors: J. G. Batista, T. S. Santiago, E. A. Ribeiro, ¬G. A. P. Thé
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This work deals with parameter identification of permanent magnet motors, a class of ac motor which is particularly important in industrial automation due to characteristics like applications high performance, are very attractive for applications with limited space and reducing the need to eliminate because they have reduced size and volume and can operate in a wide speed range, without independent ventilation. By using experimental data and genetic algorithm we have been able to extract values for both the motor inductance and the electromechanical coupling constant, which are then compared to measure and/or expected values.
Keywords: Modeling, AC servomotor, Permanent Magnet Synchronous Motor-PMSM, Genetic Algorithm, Vector Control, Robotic Manipulator, Control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2480668 Modeling and Analysis of SVPWM Based Dynamic Voltage Restorer
Authors: Ahmed Helal, Sherif Zain Elabideen, Ahmed Lotfy
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In this paper the modeling and analysis of Space Vector Pulse Width Modulation (SVPWM) based Dynamic Voltage Restorer (DVR) using PSCAD/EMTDC software will be presented in details. The simulation includes full modeling of the SVPWM technique used to control the DVR inverter. A test power system composed of three phase voltage source, sag generator, DVR and three phase resistive load is used to demonstrate restoration capability of the DVR. The simulation results of the presented DVR proved excellent voltage sag mitigation to protect sensitive loads.Keywords: Dynamic voltage restorer, power quality, simulationand modeling, voltage sag.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3706667 Unsupervised Texture Segmentation via Applying Geodesic Active Regions to Gaborian Feature Space
Authors: Yuan He, Yupin Luo, Dongcheng Hu
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In this paper, we propose a novel variational method for unsupervised texture segmentation. We use a Gabor filter bank to extract texture features. Some of the filtered channels form a multidimensional Gaborian feature space. To avoid deforming contours directly in a vector-valued space we use a Gaussian mixture model to describe the statistical distribution of this space and get the boundary and region probabilities. Then a framework of geodesic active regions is applied based on them. In the end, experimental results are presented, and show that this method can obtain satisfied boundaries between different texture regions.
Keywords: Texture segmentation, Gabor filter, snakes, Geodesicactive regions
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1765666 Local Dynamic Mechanical Properties of Native Porcine Endplate
Authors: J. Sepitka, J. Lukes, J. Reznicek
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Hysitron TriboIndenterTM TI 950 system has been used for studying the local viscoelastic properties of porcine intervertebral disc end plate by means of nanoscale mechanical dynamic analysis. The specimen of an endplate was cut from fresh porcine vertebra dissected from 16 month animal. The lumbar spine motion segments were dissected and 5 millimeter thick plates of vertebral body, endplate and annulus fibrosus were prepared for nanoindentation. The surface of the sample was kept in physiological solution during nanoindentation experiment. We obtained mechanical characteristics of different areas of native endplate (endplate middle and vertebra and annulus fibrosus boundary).Keywords: nanoindentation, DMA, endplate, cartilage
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1833665 Study of a BVAR(p) Process Applied to U.S. Commodity Market Data
Authors: Jan Sindelar
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The paper presents an applied study of a multivariate AR(p) process fitted to daily data from U.S. commodity futures markets with the use of Bayesian statistics. In the first part a detailed description of the methods used is given. In the second part two BVAR models are chosen one with assumption of lognormal, the second with normal distribution of prices conditioned on the parameters. For a comparison two simple benchmark models are chosen that are commonly used in todays Financial Mathematics. The article compares the quality of predictions of all the models, tries to find an adequate rate of forgetting of information and questions the validity of Efficient Market Hypothesis in the semi-strong form.
Keywords: Vector auto-regression, forecasting, financial, Bayesian, efficient markets.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1192664 An Efficient Method of Shot Cut Detection
Authors: Lenka Krulikovská, Jaroslav Polec
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In this paper we present a method of abrupt cut detection with a novel logic of frames- comparison. Actual frame is compared with its motion estimated prediction instead of comparison with successive frame. Four different similarity metrics were employed to estimate the resemblance of compared frames. Obtained results were evaluated by standard used measures of test accuracy and compared with existing approach. Based on the results, we claim the proposed method is more effective and Pearson correlation coefficient obtained the best results among chosen similarity metrics.
Keywords: Abrupt cut, mutual information, shot cut detection, Pearson correlation coefficient.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1926663 A High Bitrate Information Hiding Algorithm for Video in Video
Authors: Wang Shou-Dao, Xiao Chuang-Bai, Lin Yu
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In high bitrate information hiding techniques, 1 bit is embedded within each 4 x 4 Discrete Cosine Transform (DCT) coefficient block by means of vector quantization, then the hidden bit can be effectively extracted in terminal end. In this paper high bitrate information hiding algorithms are summarized, and the scheme of video in video is implemented. Experimental result shows that the host video which is embedded numerous auxiliary information have little visually quality decline. Peak Signal to Noise Ratio (PSNR)Y of host video only degrades 0.22dB in average, while the hidden information has a high percentage of survives and keeps a high robustness in H.264/AVC compression, the average Bit Error Rate(BER) of hiding information is 0.015%.Keywords: Information Hiding, Embed, Quantification, Extract
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1892662 Trade Policy and Economic Growth of Turkey in Global Economy: New Empirical Evidences
Authors: Pınar Yardımcı
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This paper tries to answer to the questions whether or not trade openness causes economic growth and trade policy changes are good for Turkey as a developing country in global economy before and after 1980. We employ Johansen co-integration and Granger causality tests with error correction modeling based on vector autoregressive. Using WDI data from the pre-1980 and the post-1980, we find that trade openness and economic growth are cointegrated in the second term only. Also the results suggest a lack of long-run causality between our two variables. These findings may imply that trade policy of Turkey should concentrate more on extra complementary economic reforms.Keywords: Globalization, Trade Policy, Economic Growth, Openness, Co-integration, Turkey.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1945661 Nonlinear Simulation of Harmonically Coupled Two-Beam Free-Electron Laser
Authors: M. Zahedian, B. Maraghechi, M. H. Rouhani
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A nonlinear model of two-beam free-electron laser (FEL) in the absence of slippage is presented. The two beams are assumed to be cold with different energies and the fundamental resonance of the higher energy beam is at the third harmonic of lower energy beam. By using Maxwell-s equations and full Lorentz force equations of motion for the electron beams, coupled differential equations are derived and solved numerically by the fourth order Runge–Kutta method. In this method a considerable growth of third harmonic electromagnetic field in the XUV and X-ray regions is predicted.Keywords: Free-electron laser, Higher energy beam, Lowerenergy beam, Two-beam
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1340660 A Coherent Relationship between EconomicGrowth and Unemployment: An Empirical Evidence from Pakistan
Authors: T. Hussain, M. W. Siddiqi, A. Iqbal
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The study is aimed to test causal relationship between growth and unemployment, using time series data for Pakistan from 1972 to 2006. Growth is considered to be a pathway to decrease the level of unemployment. Unemployment is a social and political issue. It is a phenomenon where human resources are wasted leading to deacceleration in growth. Johanson Cointegration shows that there is long run relationship between growth and unemployment. For short run dynamics and causality, the study utilizes Vector Error Correction Model (VECM). The results of VECM indicate that there is short and long run causal relation between growth and unemployment including capital, labor and human capital as explanatory variables.Keywords: Economic Growth, Unemployment, Cointegrationand Causality.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3165659 Delay-range-Dependent Exponential Synchronization of Lur-e Systems with Markovian Switching
Authors: Xia Zhou, Shouming Zhong
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The problem of delay-range-dependent exponential synchronization is investigated for Lur-e master-slave systems with delay feedback control and Markovian switching. Using Lyapunov- Krasovskii functional and nonsingular M-matrix method, novel delayrange- dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes all the features of interval systems, Itˆo equations, Markovian switching, time-varying delay, as well as the environmental noise, into account. Finally, an example is given to show the validity of the main result.
Keywords: Synchronization, delay-range-dependent, Markov chain, generalized Itō's formula, brownian motion, M-matrix.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1562658 A Comparative Study of Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) for Airflow Measurement
Authors: Sijie Fu, Pascal-Henry Biwolé, Christian Mathis
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Among modern airflow measurement methods, Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV), as visualized and non-instructive measurement techniques, are playing more important role. This paper conducts a comparative experimental study for airflow measurement employing both techniques with the same condition. Velocity vector fields, velocity contour fields, voticity profiles and turbulence profiles are selected as the comparison indexes. The results show that the performance of both PIV and PTV techniques for airflow measurement is satisfied, but some differences between the both techniques are existed, it suggests that selecting the measurement technique should be based on a comprehensive consideration.
Keywords: PIV, PTV, airflow measurement.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4299657 Tool Path Generation and Manufacturing Process for Blades of a Compressor Rotor
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This paper presents a complete procedure for tool path planning and blade machining in 5-axis manufacturing. The actual cutting contact and cutter locations can be determined by lead and tilt angles. The tool path generation is implemented by piecewise curved approximation and chordal deviation detection. An application about drive surface method promotes flexibility of tool control and stability of machine motion. A real manufacturing process is proposed to separate the operation into three regions with five stages and to modify the local tool orientation with an interactive algorithm.Keywords: 5-axis machining, tool orientation, lead and tilt angles, tool path generation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2260656 SVPWM Based Two Level VSI for Micro Grids
Authors: P. V. V. Rama Rao, M. V. Srikanth, S. Dileep Kumar Varma
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With advances in solid-state power electronic devices and microprocessors, various pulse-width-modulation (PWM) techniques have been developed for industrial applications. This paper presents the comparison of two different PWM techniques, the sinusoidal PWM (SPWM) technique and the space-vector PWM (SVPWM) technique applied to two level VSI for micro grid applications. These two methods are compared by discussing their ease of implementation and by analyzing the output harmonic spectra of various output voltages (line-to-neutral voltages, and line-to-line voltages) and their total harmonic distortion (THD). The SVPWM technique in the under-modulation region can increase the fundamental output voltage by 15.5% over the SPWM technique.
Keywords: SPWM, SVPWM, VSI, Modulation Index.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3223655 Development of a Speed Sensorless IM Drives
Authors: Dj. Cherifi, Y. Miloud, A. Tahri
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The primary objective of this paper is to elimination of the problem of sensitivity to parameter variation of induction motor drive. The proposed sensorless strategy is based on an algorithm permitting a better simultaneous estimation of the rotor speed and the stator resistance including an adaptive mechanism based on the lyaponov theory. To study the reliability and the robustness of the sensorless technique to abnormal operations, some simulation tests have been performed under several cases.
The proposed sensorless vector control scheme showed a good performance behavior in the transient and steady states, with an excellent disturbance rejection of the load torque.
Keywords: Induction Motor Drive, field-oriented control, adaptive speed observer, stator resistance estimation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2019654 New Multipath Node-Disjoint Routing Based on AODV Protocol
Authors: V. Zangeneh, S. Mohammadi
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Today, node-disjoint routing becomes inessential technique in communication of packets among various nodes in networks. Meanwhile AODV (Ad Hoc On-demand Multipath Distance Vector) creates single-path route between a pair of source and destination nodes. Some researches has done so far to make multipath node-disjoint routing based on AODV protocol. But however their overhead and end-to-end delay are relatively high, while the detail of their code is not available too. This paper proposes a new approach of multipath node-disjoint routing based on AODV protocol. Then the algorithm of analytical model is presented. The extensive results of this algorithm will be presented in the next paper.Keywords: AODV; MANET; Multipath Routing; Node-disjoint;transmission delay.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3071653 Design a Three-dimensional Pursuit Guidance Law with Feedback Linearization Method
Authors: Chien-Chun Kung, Feng-Lung Chiang, Kuei-Yi Chen
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In this paper, we will implement three-dimensional pursuit guidance law with feedback linearization control method and study the effects of parameters. First, we introduce guidance laws and equations of motion of a missile. Pursuit guidance law is our highlight. We apply feedback linearization control method to obtain the accelerations to implement pursuit guidance law. The solution makes warhead direction follow with line-of-sight. Final, the simulation results show that the exact solution derived in this paper is correct and some factors e.g. control gain, time delay, are important to implement pursuit guidance law.
Keywords: Pursuit guidance law, feedback linearization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2521652 Design and Implementation of an Image Based System to Enhance the Security of ATM
Authors: Seyed Nima Tayarani Bathaie
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In this paper, an image-receiving system was designed and implemented through optimization of object detection algorithms using Haar features. This optimized algorithm served as face and eye detection separately. Then, cascading them led to a clear image of the user. Utilization of this feature brought about higher security by preventing fraud. This attribute results from the fact that services will be given to the user on condition that a clear image of his face has already been captured which would exclude the inappropriate person. In order to expedite processing and eliminating unnecessary ones, the input image was compressed, a motion detection function was included in the program, and detection window size was confined.
Keywords: Face detection algorithm, Haar features, Security of ATM.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2103651 Design of Multiplier-free State-Space Digital Filters
Authors: Tamal Bose, Zhurun Zhang, Miloje Radenkovic, Ojas Chauhan
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In this paper, a novel approach is presented for designing multiplier-free state-space digital filters. The multiplier-free design is obtained by finding power-of-2 coefficients and also quantizing the state variables to power-of-2 numbers. Expressions for the noise variance are derived for the quantized state vector and the output of the filter. A “structuretransformation matrix" is incorporated in these expressions. It is shown that quantization effects can be minimized by properly designing the structure-transformation matrix. Simulation results are very promising and illustrate the design algorithm.Keywords: Digital filters, minimum noise, multiplier-free, quantization, state-space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1527650 Comparing Emotion Recognition from Voice and Facial Data Using Time Invariant Features
Authors: Vesna Kirandziska, Nevena Ackovska, Ana Madevska Bogdanova
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The problem of emotion recognition is a challenging problem. It is still an open problem from the aspect of both intelligent systems and psychology. In this paper, both voice features and facial features are used for building an emotion recognition system. A Support Vector Machine classifiers are built by using raw data from video recordings. In this paper, the results obtained for the emotion recognition are given, and a discussion about the validity and the expressiveness of different emotions is presented. A comparison between the classifiers build from facial data only, voice data only and from the combination of both data is made here. The need for a better combination of the information from facial expression and voice data is argued.
Keywords: Emotion recognition, facial recognition, signal processing, machine learning.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2012649 Investigation of Enhancement of Heat Transfer in Natural Convection Utilizing of Nanofluids
Authors: S. Etaig, R. Hasan, N. Perera
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This paper analyses the heat transfer performance and fluid flow using different nanofluids in a square enclosure. The energy equation and Navier-Stokes equation are solved numerically using finite volume scheme. The effect of volume fraction concentration on the enhancement of heat transfer has been studied icorporating the Brownian motion; the influence of effective thermal conductivity on the enhancement was also investigated for a range of volume fraction concentration. The velocity profile for different Rayleigh number. Water-Cu, water AL2O3 and water-TiO2 were tested.Keywords: Computational fluid Dynamics, Natural convection, Nanofluid and Thermal conductivity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1833648 An Estimation of the Performance of HRLS Algorithm
Authors: Shazia Javed, Noor Atinah Ahmad
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The householder RLS (HRLS) algorithm is an O(N2) algorithm which recursively updates an arbitrary square-root of the input data correlation matrix and naturally provides the LS weight vector. A data dependent householder matrix is applied for such an update. In this paper a recursive estimate of the eigenvalue spread and misalignment of the algorithm is presented at a very low computational cost. Misalignment is found to be highly sensitive to the eigenvalue spread of input signals, output noise of the system and exponential window. Simulation results show noticeable degradation in the misalignment by increase in eigenvalue spread as well as system-s output noise, while exponential window was kept constant.Keywords: HRLS algorithm, eigenvalue spread, misalignment.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1569647 File Format of Flow Chart Simulation Software - CFlow
Authors: Syahanim Mohd Salleh, Zaihosnita Hood, Hairulliza Mohd Judi, Marini Abu Bakar
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CFlow is a flow chart software, it contains facilities to draw and evaluate a flow chart. A flow chart evaluation applies a simulation method to enable presentation of work flow in a flow chart solution. Flow chart simulation of CFlow is executed by manipulating the CFlow data file which is saved in a graphical vector format. These text-based data are organised by using a data classification technic based on a Library classification-scheme. This paper describes the file format for flow chart simulation software of CFlow.Keywords: CFlow, flow chart, file format.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2540646 Design and Fabrication of a Miniature Railway Vehicle
Authors: Max Ti-Kuang Hou, Hui-Mei Shen, Chiang-Ni Lu, I-Jen Hsu
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We present design, fabrication, and characterization of a small (12 mm × 12 mm × 8 mm) movable railway vehicle for sensor carrying. The miniature railway vehicle (MRV) was mainly composed of a vibrational structure and three legs. A railway was designed and fabricated to power and guide the MRV. It also transmits the sensed data from the MRV to the signal processing unit. The MRV with legs on the railway was moving due to its high-frequency vibration. A model was derived to describe the motion. Besides, FEM simulations were performed to design the legs. Then, the MRV and the railway were fabricated by precision machining. Finally, an infrared sensor was carried and tested. The result shows that the MRV without loading was moving along the railway and its maximum speed was 12.2 mm/s. Moreover, the testing signal was sensed by the MRV.Keywords: Locomotion, Micro-Robot, Miniature Railway Vehicle, Stick-Slip.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1545645 Seismic Time History Analysis for Cable-Stayed Bridge Considering Different Geometrical Configuration For Near Field Earthquakes
Authors: Atul K. Desai
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To increase the maximum span of cable-stayed bridges, Uwe Starossek has developed a modified statical system. The basic idea of this new concept is the use of pairs of inclined pylon legs that spread out longitudinally from the foundation base or from the girder level. Spread-pylon cable-stayed bridge has distinct advantage like reduction of sag of cables and oscillation of cable during earthquake over traditional cable-stayed bridges. Spread-pylon also improves seismic performance of deck during strong ground motion.
Keywords: Different geometry of cable stayed bridge, seismic time history analysis, earthquake displacement ratio, response mode shape.
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