Search results for: Natural Gas Pipe Line

Authors: Y. Sabzehmeidani, M. Mailah, M. Hussein, A. R. Tavakolpour

Abstract:

In this paper, a worm-like micro robot designed for inpipe application with intelligent active force control (AFC) capability is modelled and simulated. The motion of the micro robot is based on an impact drive mechanism (IDM) that is actuated using piezoelectric device. The trajectory tracking performance of the modelled micro robot is initially experimented via a conventional proportionalintegral- derivative (PID) controller in which the dynamic response of the robot system subjected to different input excitations is investigated. Subsequently, a robust intelligent method known as active force control with fuzzy logic (AFCFL) is later incorporated into the PID scheme to enhance the system performance by compensating the unwanted disturbances due to the interaction of the robot with its environment. Results show that the proposed AFCFL scheme is far superior than the PID control counterpart in terms of the system-s tracking capability in the wake of the disturbances.

Keywords: Active Force Control, Micro Robot, Fuzzy Logic, In-pipe Application.

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Authors: A. Bekbaev, M. Dzhamanbaev, R. Abitaeva, A. Karbozova, G. Nabyeva

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In this paper, the regression dependence of dancing intensity from wind speed and length of span was established due to the statistic data obtained from multi-year observations on line wires dancing accumulated by power systems of Kazakhstan and the Russian Federation. The lower and upper limitations of the equations parameters were estimated, as well as the adequacy of the regression model. The constructed model will be used in research of dancing phenomena for the development of methods and means of protection against dancing and for zoning plan of the territories of line wire dancing.

Keywords: Power lines, line wire dancing, dancing intensity, regression equation, dancing area intensity.

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Authors: Amany M. El-Zonkoly, Hussein Desouki

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Distance protection of transmission lines including advanced flexible AC transmission system (FACTS) devices has been a very challenging task. FACTS devices of interest in this paper are static synchronous series compensators (SSSC) and unified power flow controller (UPFC). In this paper, a new algorithm is proposed to detect and classify the fault and identify the fault position in a transmission line with respect to a FACTS device placed in the midpoint of the transmission line. Discrete wavelet transformation and wavelet entropy calculations are used to analyze during fault current and voltage signals of the compensated transmission line. The proposed algorithm is very simple and accurate in fault detection and classification. A variety of fault cases and simulation results are introduced to show the effectiveness of such algorithm.

Keywords: Entropy calculation, FACTS, SSSC, UPFC, wavelet transform.

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Authors: Khaled Alnefaie

Abstract:

In this study, rotating flexible shaft-disk system having flexible beams is considered as a dynamic system. After neglecting nonlinear terms, torsional vibration of the shaft-disk system and lateral and longitudinal vibration of the flexible beam are still coupled through the motor speed. The system has three natural frequencies; the flexible shaft-disk system torsional natural frequency, the flexible beam lateral and longitudinal natural frequencies. Eigenvalue calculations show that while the shaft speed changes, torsional natural frequency of the shaft-disk system and the beam longitudinal natural frequency are not changing but the beam lateral natural frequency changes. Beam lateral natural frequency stays the same as the nonrotating beam lateral natural frequency ωb until the motor speed ωm is equal to ωb. After then ωb increases and remains equal to the motor speed ωm until the motor speed is equal to the shaft-disk system natural frequency ωT. Then the beam lateral natural frequency ωb becomes equal to the natural frequency ωT and stays same while the motor speed ωm is increased. Modal amplitudes and phase angles of the vibrations are also plotted against the motor speed ωm.

Keywords: Rotor dynamics, beam-shaft coupling, beam vibration, flexible shaft.

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Authors: S. Woothipatanapan, S. Prakobkit

Abstract:

This paper presents a model for analysis the induced voltage of transmission lines (energized) acting on neighboring distribution lines (de-energized). From environmental restrictions, 22 kV distribution lines need to be installed under 115 kV transmission lines. With the installation of the two parallel circuits like this, they make the induced voltage which can cause harm to operators. This work was performed with the ATP-EMTP modeling to analyze such phenomenon before field testing. Simulation results are used to find solutions to prevent danger to operators who are on the pole.

Keywords: Transmission system, distribution system, induced voltage, off-line operation.

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Authors: YuLung Wu

Abstract:

In Knowledge Structure Graph, each course unit represents a phase of learning activities. Both learning portfolios and Knowledge Structure Graphs contain learning information of students and let teachers know which content are difficulties and fails. The study purposes "Dual Mode On-line Learning Diagnosis System" that integrates two search methods: learning portfolio and knowledge structure. Teachers can operate the proposed system and obtain the information of specific students without any computer science background. The teachers can find out failed students in advance and provide remedial learning resources.

Keywords: Knowledge Structure Graph, On-line LearningDiagnosis

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Authors: Jasim. A. Ghaeb

Abstract:

A high performance computer includes a fast processor and millions bytes of memory. During the data processing, huge amount of information are shuffled between the memory and processor. Because of its small size and its effectiveness speed, cache has become a common feature of high performance computers. Enhancing cache performance proved to be essential in the speed up of cache-based computers. Most enhancement approaches can be classified as either software based or hardware controlled. The performance of the cache is quantified in terms of hit ratio or miss ratio. In this paper, we are optimizing the cache performance based on enhancing the cache hit ratio. The optimum cache performance is obtained by focusing on the cache hardware modification in the way to make a quick rejection to the missed line's tags from the hit-or miss comparison stage, and thus a low hit time for the wanted line in the cache is achieved. In the proposed technique which we called Even- Odd Tabulation (EOT), the cache lines come from the main memory into cache are classified in two types; even line's tags and odd line's tags depending on their Least Significant Bit (LSB). This division is exploited by EOT technique to reject the miss match line's tags in very low time compared to the time spent by the main comparator in the cache, giving an optimum hitting time for the wanted cache line. The high performance of EOT technique against the familiar mapping technique FAM is shown in the simulated results.

Keywords: Caches, Cache performance, Hit time, Cache hit ratio, Cache mapping, Cache memory.

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Authors: Sung-Bae Choi, Sang-Yoon Yoon, Eun-Jun Yoon

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In 2011, Debiao et al. pointed out that S-3PAKE protocol proposed by Lu and Cao for password-authenticated key exchange in the three-party setting is vulnerable to an off-line dictionary attack. Then, they proposed some countermeasures to eliminate the security vulnerability of the S-3PAKE. Nevertheless, this paper points out their enhanced S-3PAKE protocol is still vulnerable to undetectable on-line dictionary attacks unlike their claim.

Keywords: Authentication, 3PAKE, password, three-party key exchange, network security, dictionary attacks.

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Authors: R. Usubamatov, M. Z. Abdulmuin

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Automated production lines with so called 'hard structures' are widely used in manufacturing. Designers segmented these lines into sections by placing a buffer between the series of machine tools to increase productivity. In real production condition the capacity of a buffer system is limited and real production line can compensate only some part of the productivity losses of an automated line. The productivity of such production lines cannot be readily determined. This paper presents mathematical approach to solving the structure of section-based automated production lines by criterion of maximum productivity.

Keywords: optimization production line, productivity, sections

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Authors: Bhaskar M., Venkataramani B.

Abstract:

In the literature, surfing technique has been proposed for single ended wave-pipelined serial interconnects to increase the data transfer rate. In this paper a novel surfing technique is proposed for differential wave-pipelined serial interconnects, which uses a 'Controllable inverter pair' for surfing. To evaluate the efficiency of this technique, a transceiver with transmitter, receiver, delay locked loop (DLL) along with 40mm metal 4 interconnects using the proposed surfing technique is implemented in UMC 180nm technology and their performances are studied through post layout simulations. From the study, it is observed that the proposed scheme permits 1.875 times higher data transmission rate compared to the single ended scheme whose maximum data transfer rate is 1.33 GB/s. The proposed scheme has the ability to receive the correct data even with stuck-at-faults in the complementary line.

Keywords: Controllable inverter pair, differential interconnect, serial link, surfing, wave pipelining.

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Authors: Qihe Li, Yupin Luo

Abstract:

Camera calibration plays an important role in the domain of the analysis of sports video. Considering soccer video, in most cases, the cross-points can be used for calibration at the center of the soccer field are not sufficient, so this paper introduces a new automatic camera calibration algorithm focus on solving this problem by using the properties of images of the center circle, halfway line and a touch line. After the theoretical analysis, a practicable automatic algorithm is proposed. Very little information used though, results of experiments with both synthetic data and real data show that the algorithm is applicable.

Keywords: Absolute conic, camera calibration, circular points, line at infinity.

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Authors: Mamta Patel, R. N. Patel

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Transmission and distribution lines are vital links between the generating unit and consumers. They are exposed to atmosphere, hence chances of occurrence of fault in transmission line is very high which has to be immediately taken care of in order to minimize damage caused by it. In this paper Discrete wavelet transform of voltage signals at the two ends of transmission lines have been analyzed. The transient energy of the detail information of level five is calculated for different fault conditions. It is observed that the variation of transient energy of healthy and faulted line can give important information which can be very useful in classifying and locating the fault.

Keywords: Wavelet, Discrete wavelet transform, Multiresolution analysis, Transient energy

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Authors: A. E. Delgado, W. Aperador

Abstract:

This study evaluated the incidence of concentrated natural fibre, as well as the effects of adding a crosslinking agent on the torque when those components are mixed with low density polyethylene (LDPE). The natural fibre has a particle size of between 0.8-1.2mm and a moisture content of 0.17%. An internal mixer was used to measure the torque required to mix the polymer with the fibre. The effect of the fibre content and crosslinking agent on the torque was also determined. A change was observed in the morphology of the mixes using SEM differential scanning microscopy.

Keywords: WPC, DCP, LDPE, natural fibre, torque.

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Authors: Israa Al-Neami, Ali J. Al-Askery, Martin Johnston, Charalampos Tsimenidis

Abstract:

In this paper, we focus on the design of a multi-line copper wire (MLCW) communication system. First, we construct our proposed MLCW channel and verify its characteristics based on the Kolmogorov-Smirnov test. In addition, we apply Middleton class A impulsive noise (IN) to the copper channel for further investigation. Second, the MIMO G.fast system is adopted utilizing the proposed MLCW channel model and is compared to a single line G-fast system. Second, the performance of the coded system is obtained utilizing concatenated interleaved Reed-Solomon (RS) code with four-dimensional trellis-coded modulation (4D TCM), and compared to the single line G-fast system. Simulations are obtained for high quadrature amplitude modulation (QAM) constellations that are commonly used with G-fast communications, the results demonstrate that the bit error rate (BER) performance of the coded MLCW system shows an improvement compared to the single line G-fast systems.

Keywords: G.fast, Middleton Class A impulsive noise, mitigation techniques, copper channel Model.

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Authors: P. Valsalal, S. Thangalakshmi

Abstract:

There is a widespread changeover in the electrical power industry universally from old-style monopolistic outline towards a horizontally distributed competitive structure to come across the demand of rising consumption. When the transmission lines of derestricted system are incapable to oblige the entire service needs, the lines are overloaded or congested. The governor between customer and power producer is nominated as Independent System Operator (ISO) to lessen the congestion without obstructing transmission line restrictions. Among the existing approaches for congestion management, the frequently used approaches are reorganizing the generation and load curbing. There is a boundary for reorganizing the generators, and further loads may not be supplemented with the prevailing resources unless more private power producers are added in the system by considerably raising the cost. Hence, congestion is relaxed by appropriate Flexible AC Transmission Systems (FACTS) devices which boost the existing transfer capacity of transmission lines. The FACTs device, namely, Unified Power Flow Controller (UPFC) is preferred, and the correct placement of UPFC is more vital and should be positioned in the highly congested line. Hence, the weak line is identified by using power flow performance index with the new objective function with proposed hybrid Fish – Bee algorithm. Further, the location of UPFC at appropriate line reduces the branch loading and minimizes the voltage deviation. The power transfer capacity of lines is determined with and without UPFC in the identified congested line of IEEE 30 bus structure and the simulated results are compared with prevailing algorithms. It is observed that the transfer capacity of existing line is increased with the presented algorithm and thus alleviating the congestion.

Keywords: Available line transfer capability, congestion management, FACTS device, hybrid fish-bee algorithm, ISO, UPFC.

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Authors: Sanath Kumar Shetty, Sanya Sinha, K. Kamalakanth Shenoy

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The posterior reference for the ala tragal line is a cause of confusion, with different authors suggesting different locations as to the superior, middle or inferior part of the tragus. This study was conducted on 200 subjects to evaluate if any correlation exists between the variation of angulation of palatal throat form and the relative parallelism of occlusal plane to ala-tragal line at different tragal levels. A custom made Occlusal Plane Analyzer was used to check the parallelism between the ala-tragal line and occlusal plane. A lateral cephalogram was shot for each subject to measure the angulation of the palatal throat form. Fisher’s exact test was used to evaluate the correlation between the angulation of the palatal throat form and the relative parallelism of occlusal plane to the ala tragal line. Also, a classification was formulated for the palatal throat form, based on confidence interval. From the results of the study, the inferior part, middle part and superior part of the tragus were seen as the reference points in 49.5%, 32% and 18.5% of the subjects respectively. Class I palatal throat form (41degree-50 degree), Class II palatal throat form (below 41 degree) and Class III palatal throat form (above 50 degree) were seen in 42%, 43% and 15% of the subjects respectively. It was also concluded that there is no significant correlation between the variation in the angulations of the palatal throat form and the relative parallelism of occlusal plane to the ala-tragal line.

Keywords: Ala-tragal line, occlusal plane, palatal throat form, cephalometry.

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Authors: Qian Wang, Sylvain Lassalle, Antony R. Mileham, Geraint W. Owen

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This paper mathematically analyses the varying magnitude of production loss, which may occur due to idle time (inprocess waiting time and traveling time) on a linear walking worker assembly line. Within this flexible and reconfigurable assembly system, each worker travels down the line carrying out each assembly task at each station; and each worker accomplishes the assembly of a unit from start to finish and then travels back to the first station to start the assembly of a new product. This strategy of system design attempts to combine the flexibility of the U-shaped moving worker assembly cell with the efficiency of the conventional fixed worker assembly line. The paper aims to evaluate the effect of idle time that may offset the labor efficiency of each walking worker providing an insight into the mechanism of such a flexible and reconfigurable assembly system.

Keywords: Production lines, manufacturing systems, assemblysystems, walking workers.

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Authors: Sergey N. Sayapin, Anatoly P. Karpenko, Suan H. Dang

Abstract:

Comparative analysis of robotic vehicles for pipe inspection is presented in this paper. The promising concept of self-propelled intelligent robotic vehicle (SPIRV) based on octahedral dodekapod for inspection and operation in active branched pipelines with variable cross-sections is reasoned. SPIRV is able to move in pipeline, regardless of its spatial orientation. SPIRV can also be used to move along the outside of the pipelines as well as in space between surfaces of annular tubes. Every one of faces of the octahedral dodekapod can clamp/unclamp a thing with a closed loop surface of various forms as well as put pressure on environmental surface of contact. These properties open new possibilities for its applications in SPIRV. We examine design principles of octahedral dodekapod as future intelligent building blocks for various robotic vehicles that can self-move and self-reconfigure.

Keywords: Modular robot, octahedral dodekapod, pipe inspection robot, spatial parallel structure.

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Authors: Renju Gangadharan, G. N. Pillai, Indra Gupta

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In this paper a novel method for finding the fault zone on a Thyristor Controlled Series Capacitor (TCSC) incorporated transmission line is presented. The method makes use of the Support Vector Machine (SVM), used in the classification mode to distinguish between the zones, before or after the TCSC. The use of Discrete Wavelet Transform is made to prepare the features which would be given as the input to the SVM. This method was tested on a 400 kV, 50 Hz, 300 Km transmission line and the results were highly accurate.

Keywords: Flexible ac transmission system (FACTS), thyristorcontrolled series-capacitor (TCSC), discrete wavelet transforms(DWT), support vector machine (SVM).

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Authors: Malik I. Al-Amayreh, Mohammad I. Kilani, Ahmed S. Al-Salaymeh

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This work presents a Computational Fluid Dynamics (CFD) simulation of a butterfly valve used to control the flow of combustible gas mixture in an industrial process setting.The work uses CFD simulation to analyze the flow characteristics in the vicinity of the valve, including the pressure distributions and Frequency spectrum of the pressure pulsations downstream the valves and the vortex shedding allow predicting the torque fluctuations acting on the valve shaft and the possibility of generating mechanical vibration and resonance.These fluctuations are due to aerodynamic torque resulting from fluid turbulence and vortex shedding in the valve vicinity. The valve analyzed is located in a pipeline between two opposing 90o elbows, which exposes the valve and the surrounding structure to the turbulence generated upstream and downstream the elbows at either end of the pipe.CFD simulations show that the best location for the valve from a vibration point of view is in the middle of the pipe joining the elbows.

Keywords: Butterfly Valve Vibration Analysis, Computational Fluid Dynamics, Fluid Flow Circuit Design, Fluid Mechanics.

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Authors: Lari Kela

Abstract:

An adaptive Helmholtz resonator was designed and adapted to hydraulics. The resonator was controlled by open- and closed-loop controls so that 20 dB attenuation of the peak-to-peak value of the pulsating pressure was maintained. The closed-loop control was noted to be better, albeit it was slower because of its low pressure and temperature variation, which caused variation in the effective bulk modulus of the hydraulic system. Low-pressure hydraulics contains air, which affects the stiffness of the hydraulics, and temperature variation changes the viscosity of the oil. Thus, an open-loop control loses its efficiency if a condition such as temperature or the amount of air changes after calibration. The instability of the low-pressure hydraulic system reduced the operational frequency range of the Helmholtz resonator when compared with the results of an analytical model. Different dampers for hydraulics are presented. Then analytical models of a hydraulic pipe and a hydraulic pipe with a Helmholtz resonator are presented. The analytical models are based on the wave equation of sound pressure. Finally, control methods and the results of experiments are presented.

Keywords: adaptive, damper, hydraulics, pressure, pulsating

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Authors: Young-Seok Choi

Abstract:

The Adaptive Line Enhancer (ALE) is widely used for enhancing narrowband signals corrupted by broadband noise. In this paper, we propose novel ALE methods to improve the enhancing capability. The proposed methods are motivated by the fact that the output of the ALE is a fine estimate of the desired narrowband signal with the broadband noise component suppressed. The proposed methods preprocess the input signal using ALE filter to regenerate a finer input signal. Thus the proposed ALE is driven by the input signal with higher signal-to-noise ratio (SNR). The analysis and simulation results are presented to demonstrate that the proposed ALE has better performance than conventional ALE’s.

Keywords: Adaptive filter, adaptive line enhancer, noise, feedback.

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Authors: N. D. Karande, G. A. Patil

Abstract:

Databases have become ubiquitous. Almost all IT applications are storing into and retrieving information from databases. Retrieving information from the database requires knowledge of technical languages such as Structured Query Language (SQL). However majority of the users who interact with the databases do not have a technical background and are intimidated by the idea of using languages such as SQL. This has led to the development of a few Natural Language Database Interfaces (NLDBIs). A NLDBI allows the user to query the database in a natural language. This paper highlights on architecture of new NLDBI system, its implementation and discusses on results obtained. In most of the typical NLDBI systems the natural language statement is converted into an internal representation based on the syntactic and semantic knowledge of the natural language. This representation is then converted into queries using a representation converter. A natural language query is translated to an equivalent SQL query after processing through various stages. The work has been experimented on primitive database queries with certain constraints.

Keywords: Natural language database interface, representation converter, syntactic and semantic knowledge

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Authors: Ashwani Kumar, Jitender Kumar

Abstract:

In this paper, an optimal power flow based approach has been applied for multi-transactions deregulated environment for ATC determination with SVC and STATCOM. The main contribution of the paper is (i) OPF based approach for evaluation of ATC with multi-transactions, (ii) ATC enhancement with FACTS devices viz. SVC and STATCOM for intact and line contingency cases, (iii) Impact of ZIP load on ATC determination and comparison of ATC obtained with SVC and STATCOM. The results have been determined for intact and line contingency cases taking simultaneous as well as single transaction cases for IEEE 24 bus RTS.

Keywords: Available transfer capability, FACTS devices, line contingency, multi-transactions, ZIP load model.

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Authors: Tosaphol Ratniyomchai, Uthai Jaithong, Thanatchai Kulworawanichpong

Abstract:

This paper presents an application of power line carrier (PLC) for electrical power telemetering. This system has a special capability of transmitting the measured values to a centralized computer via power lines. The PLC modem as a passive high-pass filter is designed for transmitting and receiving information. Its function is to send the information carrier together with transmitted data by superimposing it on the 50 Hz power frequency signal. A microcontroller is employed to function as the main processing of the modem. It is programmed for PLC control and interfacing with other devices. Each power meter, connected via a PLC modem, is assigned with a unique identification number (address) for distinguishing each device from one another.

Keywords: Power telemetering, Power line carrier, High-passfilter, Digital data transmission

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Authors: C. W. Nguong, S. N. B. Lee, D. Sujan

Abstract:

Renewable natural fibres such as oil palm, flax, and pineapple leaf can be utilized to obtain new high performance polymer materials. The reuse of waste natural fibres as reinforcement for polymer is a sustainable option to the environment. However, due to its high hydroxyl content of cellulose, natural fibres are susceptible to absorb water that affects the composite mechanical properties adversely. Research found that Nano materials such as Nano Silica Carbide (n-SiC) and Nano Clay can be added into the polymer composite to overcome this problem by enhancing its mechanical properties in wet condition. The addition of Nano material improves the tensile and wear properties, flexural stressstrain behaviour, fracture toughness, and fracture strength of polymer natural composites in wet and dry conditions.

Keywords: Natural fibres, Nano Silica Carbide, Nano Clay, Wet Condition, Polymer Composites.

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Authors: P. V. V. Rama Rao, M. V. Srikanth, S. Dileep Kumar Varma

Abstract:

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.

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Authors: Noor Mohammad

Abstract:

Environmental accounting is a recent phenomenon in the modern jurisprudence. It may reflect the corporate governance mechanisms in line with the natural resources and environmental sound management and administration systems in any country of the world. It may be a corporate focused on the improving of the environmental quality. But it is often identified that it is ignored due to some reasons such as unconsciousness, lack of ethical education etc. At present, the world community is very much concerned about the state of the environmental accounting and auditing systems as it bears sustainability on the mother earth for our generations. It is one of the important tools for understanding on the role played by the natural environment in the economy. It provides adequate data which is highlighted both in the contribution of natural resources to economic well-being as well as the costs imposed by pollution or resource degradation. It can play a critical role as on be a part of the many international environmental organizations such as IUCN, WWF, PADELIA, WRI etc.; as they have been taking many initiatives for ensuring the environmental accouting for our competent survivals. The global state actors have already taken some greening accounting initiatives under the forum of the United Nations Division for Sustainable Dedevolpment, the United Nations Statistical Division, the United Nations Conference on Environment and development known as Earth Summit in Rio de Janeiro, Johannesburg Conference 2002 etc. This study will provide an overview of the environmental accounting education consisting of 25 respondents based on the primary and secondary sources.

Keywords: Environmental Accounting, Auditing Education and Sustainable Development

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Authors: Kazeem K. Adewole, Steve J. Bull

Abstract:

Tensile armour wires provide a flexible pipe's resistance to longitudinal stresses. Flexible pipe manufacturers need to know the effect of defects such as scratches and cracks, with dimensions less than 0.2mm which is the limit of the current nondestructive detection technology, on the fracture stress and fracture strain of the wire for quality assurance purposes. Recent research involving the determination of the fracture strength of cracked wires employed laboratory testing and classical fracture mechanics approach using non-standardised fracture mechanics specimens because standard test specimens could not be manufactured from the wires owing to their sizes. In this work, the effect of miniature cracks on the fracture properties of tensile armour wires was investigated using laboratory and finite element tensile testing simulations with the phenomenological shear fracture model. The investigation revealed that the presence of cracks shallower than 0.2mm is worse on the fracture strain of the wire.

Keywords: Cracks, Finite Element Simulations, Fracture Mechanics, Shear Fracture Model, Tensile Armour Wire

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Authors: Henri Champliaud, Zhengkun Feng, Ngan Van Lê, Javad Gholipour

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In this article, a method is presented to effectively estimate the deformed shape of a thick plate due to line heating. The method uses a fifth order spline interpolation, with up to C3 continuity at specific points to compute the shape of the deformed geometry. First and second order derivatives over a surface are the resulting parameters of a given heating line on a plate. These parameters are determined through experiments and/or finite element simulations. Very accurate kriging models are fitted to real or virtual surfaces to build-up a database of maps. Maps of first and second order derivatives are then applied on numerical plate models to evaluate their evolving shapes through a sequence of heating lines. Adding an optimization process to this approach would allow determining the trajectories of heating lines needed to shape complex geometries, such as Francis turbine blades.

Keywords: Deformation, kriging, fifth order spline interpolation, first, second and third order derivatives, C3 continuity, line heating, plate forming, thermal forming.

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