Search results for: Partial shading condition

Authors: K. Divya, G. Sugumaran

Abstract:

This paper proposes an improved Maximum Power Point Tracking of PhotoVoltaic system using Deterministic Partical Swarm Optimization technique. This method has the ability to track the maximum power under varying environmental conditions i.e. partial shading conditions. The advantage of this method, particles moves in the restricted value of velocity to achieve the maximum power. SEPIC converter is employed to boost up the voltage of PV system. To estimate the value of the proposed method, MATLAB simulation carried out under partial shading condition.

Keywords: DPSO, Partial shading condition, P&O, PV, SEPIC.

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Authors: R. Ramaprabha

Abstract:

This paper presents an extraction of maximum energy from Solar Photovoltaic Array (SPVA) under partial shaded conditions by optimum selection of array size using Particle Swarm Optimization (PSO) technique. In this paper a detailed study on the output reduction of different SPVA configurations under partial shaded conditions have been carried out. A generalized MATLAB M-code based software model has been used for any required array size, configuration, shading patterns and number of bypass diodes. Comparative study has been carried out on different configurations by testing several shading scenarios. While the number of shading patterns and the rate of change are very low for stationary SPVA but these may be quite large for SPVA mounted on a mobile platforms. This paper presents the suitability of PSO technique to select optimum configuration for mobile arrays by calculating the global peak (GP) of different configurations and to transfer maximum power to the load.

Keywords: Global peak, Mobile PV arrays, Partial shading, optimization, PSO.

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Authors: Saad F. Al Nuaimi

Abstract:

Energy consumption is a very important topic these days especially regarding air conditioning in residential buildings, since this takes the biggest amount of energy in buildings total consumption, residential buildings constitute the biggest percentage of energy consumption in Bahrain. This research reflects on the effects of shading percentage in different solar orientations on the energy consumption inside residential buildings (domestic dwellings). The research as found that, there are different effects of shading in changing building orientation: • 0.69% for the shading percentage 25% when the building is oriented to the north (0º); • 18.59% for 75% of shading in north-west orientation (325º); • The best effect for shading is in north-west orientation (315º); • The less effect for shading was in case of the building orientation is the north (0º).

Keywords: Bahraini buildings, Building shading, energy consumption, residential buildings, shading effects.

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Authors: Jian Yao

Abstract:

To investigate the energy performance of solar shading devices, this paper carried out a survey on the current status of solar shading utilization in buildings in Ningbo and performed building simulations to evaluate the energy savings potential by adopting different solar shading devices. Results show that solar shading utilization in this area is not popular and effective, and should be considered firstly in the design stage since the potential for energy savings is up to 6.8% for residential buildings and 9.4% for commercial buildings.

Keywords: Solar shading, Energy savings, Building design.

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Authors: Hla Hla Khaing, Yit Jian Liang, Nant Nyein Moe Htay, Jiang Fan

Abstract:

Partial shadowing is one of the problems that are always faced in terrestrial applications of solar photovoltaic (PV). The effects of partial shadow on the energy yield of conventional mono-crystalline and multi-crystalline PV modules have been researched for a long time. With deployment of new thin-film solar PV modules in the market, it is important to understand the performance of new PV modules operating under the partial shadow in the tropical zone. This paper addresses the impacts of different partial shadowing on the operating characteristics of four different types of solar PV modules that include multi-crystalline, amorphous thin-film, CdTe thin-film and CIGS thin-film PV modules.

Keywords: Partial shade, CdTe, CIGS, multi-crystalline (mc-Si), amorphous silicon (a-Si), bypass diode.

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Authors: N. Tuaycharoen, W. Konisranukul

Abstract:

The main aim of this research was to investigate a prototype bamboo shading device. There were two objectives to this study: first, to investigate the effects of non-chemical treatments on bamboo shading devices damaged by powder-post beetles and fungi, and second to develop a prototype bamboo shading device. This study of the effects of non-chemical treatments on bamboo shading devices damage by powder-post beetles in the laboratory showed that, among seven treatments tested, wood vinegar treatment can protect powder-post beetles better than the original method by up to 92.91%. It was also found that wood vinegar treatment shows the best performance in fungi protection and works better than the original method by up to 40%. A second experiment was carried out by constructing four bamboo shading devices and installing them on a building for 28 days. All aspects of shading device were investigated in terms of their beauty, durability, and ease of construction and assembly. The final prototype was developed from the lessons learned from the test results. In conclusion, this study showed the effectiveness of some natural preservatives against insect and fungi damage, and it also illustrated the characteristics of a prototype bamboo shading device that can be constructed by rural workers within one week.

Keywords: Bamboo, shading device, energy conservation, alternative materials.

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Authors: Jian Yao, Chengwen Yan

Abstract:

Solar shading designs are important for reduction of building energy consumption and improvement of indoor thermal environment. This paper carried out a number of building simulations for evaluation of the energy performance of different shading devices based on incremental costs. The results show that movable shading devices lower incremental costs by up to 50% compared with fixed ones for the same building energy efficiency for residential buildings, and wing panel shadings are much more suitable in commercial buildings than baring screen ones and overhangs for commercial buildings.

Keywords: Solar shading, Incremental costs, Building energy consumption.

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Authors: Jian Yao

Abstract:

The purpose of this paper is to investigate the adjust- ment of solar shading devices in office buildings in two different seasons by occupants, and its influence on the lighting control and indoor illuminance levels. The results show that occupants take inappropriate measures both in reducing solar radiation in summer and in admitting solar gains in winter, resulting in an increase in lighting energy and a reduction in indoor illuminance. Therefore, movable shading devices, controlled automatically, are suitable for building applications to reduce energy consumption.

Keywords: Solar shading, adjustment, lighting control, indoor illuminance.

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Authors: Qasim Khan, Furkan Ahmad, Asfar A. Khan, M. Saad Alam, Faiz Ahmad

Abstract:

In this paper, partial discharge analysis is performed in cavities artificially created in insulation. The setup is according with Cigre-II Method. Circular Samples created from Perspex Sheet with different configuration with changing number of cavities. Assessment of insulation health can be performed by Partial Discharge measurement as this has been found to be important means of condition monitoring. The experiments are done using MPD 540, which is a modern partial discharge measurement system. By analyzing the PD activity obtained for various voids/cavities, it is observed that the PD voltages show variation for cavity’s diameter, depth even for its ratios. This can be employed for scrutiny of insulation system.

Keywords: Partial discharges, condition monitoring, MPD 540, cavities/defects, degradation and corrosion, PMMA.

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Authors: Vu Ngoc Pi

Abstract:

This paper presents a new study on the applications of optimization and regression analysis techniques for optimal calculation of partial ratios of four-step helical gearboxes for getting minimal gearbox length. In the paper, basing on the moment equilibrium condition of a mechanic system including four gear units and their regular resistance condition, models for determination of the partial ratios of the gearboxes are proposed. In particular, explicit models for calculation of the partial ratios are proposed by using regression analysis. Using these models, the determination of the partial ratios is accurate and simple.

Keywords: Gearbox design; optimal design; helical gearbox, transmission ratio.

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Authors: Vu Ngoc Pi

Abstract:

In this paper, a study on the applications of the optimization and regression techniques for optimal calculation of partial ratios of helical gearboxes with second-step double gear-sets for minimal cross section dimension is introduced. From the condition of the moment equilibrium of a mechanic system including three gear units and their regular resistance condition, models for calculation of the partial ratios of helical gearboxes with second-step double gear-sets were given. Especially, by regression analysis, explicit models for calculation of the partial ratios are introduced. These models allow determining the partial ratios accurately and simply.

Keywords: Gearbox design, optimal design, helical gearbox, transmission ratio.

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Authors: Mei Shan Ngan, Chee Wei Tan

Abstract:

Due to the non-linear characteristics of photovoltaic (PV) array, PV systems typically are equipped with the capability of maximum power point tracking (MPPT) feature. Moreover, in the case of PV array under partially shaded conditions, hotspot problem will occur which could damage the PV cells. Partial shading causes multiple peaks in the P-V characteristic curves. This paper presents a hybrid algorithm of Particle Swarm Optimization (PSO) and Artificial Neural Network (ANN) MPPT algorithm for the detection of global peak among the multiple peaks in order to extract the true maximum energy from PV panel. The PV system consists of PV array, dc-dc boost converter controlled by the proposed MPPT algorithm and a resistive load. The system was simulated using MATLAB/Simulink package. The simulation results show that the proposed algorithm performs well to detect the true global peak power. The results of the simulations are analyzed and discussed.

Keywords: Photovoltaic (PV), Partial Shading, Maximum Power Point Tracking (MPPT), Particle Swarm Optimization (PSO) and Artificial Neural Network (ANN)

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Authors: Yaw-Juen Wang, Po-Chun Hsu

Abstract:

This paper presents an equivalent circuit model based on piecewise linear parallel branches (PLPB) to study solar cell modules which are partially shaded. The PLPB model can easily be used in circuit simulation software such as the ElectroMagnetic Transients Program (EMTP). This PLPB model allows the user to simulate several different configurations of solar cells, the influence of partial shadowing on a single or multiple cells, the influence of the number of solar cells protected by a bypass diode and the effect of the cell connection configuration on partial shadowing.

Keywords: Cell Connection Configurations, EMTP, Equivalent Circuit, Partial Shading, Photovoltaic Module

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Authors: Ammar Anwar Khan, Nissar R. Wani, Nazar Malik, Abdulrehman Al-Arainy, and Saad Alghuwainem

Abstract:

Power cables are vulnerable to failure due to aging or defects that occur with the passage of time under continuous operation and loading stresses. PD detection and characterization provide information on the location, nature, form and extent of the degradation. As a result, PD monitoring has become an important part of condition based maintenance (CBM) program among power utilities. Online partial discharge (PD) localization of defect sources in power cable system is possible using the time of flight method. The information regarding the time difference between the main and reflected pulses and cable length can help in locating the partial discharge source along the cable length. However, if the length of the cable is not known and the defect source is located at the extreme ends of the cable or in the middle of the cable, then double ended measurement is required to indicate the location of PD source. Use of multiple sensors can also help in discriminating the cable PD or local/ external PD. This paper presents the experience and results from online partial discharge measurements conducted in the laboratory and the challenges in partial discharge source localization.

Keywords: Power cables, partial discharge localization, HFCT, condition based monitoring.

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Authors: Jalal M. Abdallah

Abstract:

There is a great problem in testing and investigations the reliability of different type of transformers insulation materials. It summarized in how to create and simulate the real conditions of working transformer and testing its insulation materials for Partial Discharge PD, typically as in the working mode. A lot of tests may give untrue results as the physical behavior of the insulation material differs under tests from its working condition. In this work, the real working conditions were simulated, and a large number of specimens have been tested. The investigations first stage, begin with choosing samples of different types of insulation materials (papers, pressboards, etc.). The second stage, the samples were dried in ovens at 105 C⁰and 0.01bar for 48 hours, and then impregnated with dried and gasless oil (the water content less than 6 ppm.) at 105 C⁰and 0.01bar for 48 hours, after so specimen cooling at room pressure and temperature for 24 hours. The third stage is investigating PD for the samples using ICM PD measuring device. After that, a continuous test on oil-impregnated insulation materials (paper, pressboards) was developed, and the phase resolved partial discharge pattern of PD signals was measured. The important of this work in providing the industrial sector with trusted high accurate measuring results based on real simulated working conditions. All the PD patterns (results) associated with a discharge produced in well-controlled laboratory condition. They compared with other previous and other laboratory results. In addition, the influence of different temperatures condition on the partial discharge activities was studied.

Keywords: Transformers, insulation materials, voids, partial discharge (PD).

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Authors: Nicoletta Adamo-Villani, Joe Kasenga, Tiffany Jen, Bryan Colbourn

Abstract:

The goal of the study reported in the paper was to determine whether Ambient Occlusion Shading (AOS) has a significant effect on users' perception of American Sign Language (ASL) finger spelling animations. Seventy-one (71) subjects participated in the study; all subjects were fluent in ASL. The participants were asked to watch forty (40) sign language animation clips representing twenty (20) finger spelled words. Twenty (20) clips did not show ambient occlusion, whereas the other twenty (20) were rendered using ambient occlusion shading. After viewing each animation, subjects were asked to type the word being finger-spelled and rate its legibility. Findings show that the presence of AOS had a significant effect on the subjects perception of the signed words. Subjects were able to recognize the animated words rendered with AOS with higher level of accuracy, and the legibility ratings of the animations showing AOS were consistently higher across subjects.

Keywords: Sign Language, Animation, Ambient Occlusion Shading, Deaf Education

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Authors: A. Sherif, H. Sabry, A. Elzafarany, M. Gadelhak, R. Arafa, M. Aly

Abstract:

This paper addresses the design of hospital Intensive Care Unit windows for the achievement of visual comfort and energy savings. The aim was to identify the window size and shading system configurations that could fulfill daylighting adequacy, avoid glare and reduce energy consumption. The study focused on addressing the effect of utilizing different shading systems in association with a range of Window-to-Wall Ratios (WWR) in different orientations under the desert clear-sky of Cairo, Egypt. The results of this study demonstrated that solar penetration is a critical concern affecting the design of ICU windows in desert locations, as in Cairo, Egypt. Use of shading systems was found to be essential in providing acceptable daylight performance and energy saving. Careful positioning of the ICU window towards a proper orientation can dramatically improve performance. It was observed that ICU windows facing the north direction enjoyed the widest range of successful window configuration possibilities at different WWRs. ICU windows facing south enjoyed a reasonable number of configuration options as well. By contrast, the ICU windows facing the east orientation had a very limited number of options that provide acceptable performance. These require additional local shading measures at certain times due to glare incidence. Moreover, use of horizontal sun breakers and solar screens to protect the ICU windows proved to be more successful than the other alternatives in a wide range of Window to Wall Ratios. By contrast, the use of light shelves and vertical shading devices seemed questionable.

Keywords: Daylighting, Desert, Energy Efficiency, Shading.

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Authors: Hankun Lin, Yiqiang Xiao, Qiaosheng Zhan

Abstract:

Shading devices (SDs) are widely used in buildings in the hot-humid climate areas for reducing cooling energy consumption for interior temperature, as the result of reducing the solar radiation directly. Contrasting the surface temperature of materials of SDs to the glass on the building façade could give more analysis for the shading effect. On the other side, SDs are much more used as the independence system on building façade in hot-humid area. This typical construction could have some impacts on building ventilation as well. This paper discusses the outdoor SDs’ effects on the building thermal environment and ventilation, through a set of measurements on a 2-floors office building in Guangzhou, China, which install a dynamic aluminum SD-system around the façade on 2^nd-floor. The measurements recorded the in/outdoor temperature, relative humidity, velocity, and the surface temperature of the aluminum panel and the glaze. After that, a CFD simulation was conducted for deeper discussion of ventilation. In conclusion, this paper reveals the temperature differences on the different material of the façade, and finds that the velocity of indoor environment could be reduced by the outdoor SDs.

Keywords: Outdoor shading devices, hot-humid area, temperature, ventilation, measurement, CFD.

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Authors: T. Abdelkrim, K. Ben seddik, B. Bezza, K. Benamrane, Aeh. Benkhelifa

Abstract:

This paper proposes an implementation of boost converter for a resistive load using photovoltaic energy as a source. The model of photovoltaic cell and operating principle of boost converter are presented. A PIC microcontroller is used in the close loop control to generate pulses for controlling the converter circuit. To performance evaluation of boost converter, a variation of output voltage of PV panel is done by shading one and two cells.

Keywords: Boost converter, Microcontroller, Photovoltaic power generation, Shading cells.

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Authors: Saad Odeh

Abstract:

Thermal performance is considered to be a key measure in building sustainability. One of the technologies used in the current building sustainable design is the rooftop solar PV power generators. The application of this type of technology has expanded vastly during the last five years in many countries. This paper studies the effect of roof shading developed by the solar PV panels on dwellings’ thermal performance. The analysis in this work is performed by using two types of packages: “AccuRate Sustainability” for rating the energy efficiency of residential building design, and “PVSYST” for the solar PV power system design. The former package is used to calculate the annual heating and cooling load, and the later package is used to evaluate the power production from the roof top PV system. The analysis correlates the electrical energy generated from the PV panels to the change in the heating and cooling load due to roof shading. Different roof orientation, roof inclination, roof insulation, as well as PV panel area are considered in this study. The analysis shows that the drop in energy efficiency due to the shaded area of the roof by PV panels is negligible compared to the energy generated by these panels.

Keywords: Energy efficiency, roof shading, thermal performance, PV panel.

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Authors: Mansour Nikpour, Mohd Zin kandar, Mohammad Ghomeshi, Nima Moeinzadeh, Mohsen Ghasemi

Abstract:

So much energy is used in high rise buildings to fulfill the basic needs of users such as lighting and thermal comfort. Malaysia has hot and humid climate, buildings especially high rise buildings receive unnecessary solar radiation that cause more solar heat gain. Energy use specially electricity consumption in high rise buildings has increased. There have been growing concerns about energy consumption and its effect on environment. Building, energy and the environment are important issues that the designers should consider to them. Self protected form is one of possible ways against the impact of solar radiation in high rise buildings. The Energy performance of building envelopes was investigated in term of the Overall Thermal Transfer Value (OTTV ).In this paper, the amount of OTTV reduction was calculated through OTTV Equations to clear the effectiveness of self shading strategy on minimizing energy consumption for cooling interior spaces in high rise buildings which has considerable envelope areas against solar radiation. Also increasing the optimum window area was investigated using self-shading strategy in designing high rise buildings. As result, the significant reduction in OTTV was shown based on WWR.In addition slight increase was demonstrated in WWR that can influence on visible comfort interior spaces.

Keywords: Self-shading strategy, high rise buildings, Overall thermal transfer value (OTTV ), Window to wall ratio (WWR).

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Authors: A. Sherif, A. El Zafarany, R. Arafa

Abstract:

Hospitals, everywhere, are considered heavy energy consumers. Hospital Intensive Care Unit spaces pose a special challenge, where design guidelines requires the provision of external windows for daylighting and external view. Window protection strategies could be employed to reduce energy loads without detriment effect on comfort or health care. This paper addresses the effectiveness of using various window strategies on the annual cooling, heating and lighting energy use of a typical Hospital Intensive Unit space. Series of experiments were performed using the EnergyPlus simulation software for a typical Intensive Care Unit (ICU) space in Cairo, located in the Egyptian desert. This study concluded that the use of shading systems is more effective in conserving energy in comparison with glazing of different types, in the Cairo ICUs. The highest energy savings in the West and South orientations were accomplished by external perforated solar screens, followed by overhangs positioned at a protection angle of 45°.

Keywords: Energy, Hospital, Intensive Care Units, Shading.

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Authors: R. H. Khawaja, T. R. Blackburn, M. Rehan Arif

Abstract:

The power transformer is the most expensive, indispensable and arguably the most important equipment item in a power system Insulation failure in transformers can cause long term interruption to supply and loss of revenue and the condition assessment of the insulation is thus an important maintenance procedure. Oil-impregnated transformer insulation consists of mainly organic materials including mineral oil and cellulose-base paper and pressboard. The operating life of cellulose-based insulation, as with most organic insulation, depends heavily on its operating temperature rise above ambient. This paper reports results of a laboratory-based experimental investigation of partial discharge (PD) activity at high temperature in oil-impregnated insulation. The experiments reported here are part an on-going programme aimed at investigating the way in which insulation deterioration can be monitored and quantified by use of partial discharge diagnostics. Partial discharge patterns were recorded and analysed during increasing and decreasing phases of the temperature. The effect of ageing of the insulation on the PD patterns in oil and oil-impregnated insulation are also considered.

Keywords: Ageing, high temperature, PD, oil-impregnated insulation.

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Authors: Viridiana Edith Ardura Perea, José Luis Bermúdez Alcocer

Abstract:

The purpose of this paper is to establish the influence of shading on a Building Integrated Photovoltaic (BIPV) system´s performance in an urban context. The PV systems of the Science Center of Complexity (Centro de Ciencias de la Complejidad) Building based in the Main Campus of the National and Autonomous University of Mexico (UNAM) in Mexico City was taken as case study.  The PV systems are placed on the rooftop and on the south façade of the building.  The south-façade PV system, operating as sunshades, consists of two strings:  one at the ground floor and the other one at the first floor.  According to the building’s facility manager, the south-façade PV system generates 42% less electricity per kilowatt peak (kWp) installed than the one on the roof.  The methods applied in this study were Solar Radiation Analysis (SRA) simulations performed with the Insight 360 Plug-in from Revit 2018^® and an on-site measurement using specialized tools.  The results of the SRA simulations showed that the shading casted by the PV system placed on the first floor on top of the PV system of the ground floor decreases its solar incident radiation over 50%.  The simulation outcome was compared and validated to the measured data obtained from the on-site measurement.  In conclusion, the loss factor achieved from the shading of the PVs is due to the surroundings and the PV system´s own design.  The south-façade BIPV system’s deficient design generates critical losses on its performance and decreases its profitability.

Keywords: Building integrated photovoltaics (BIPV) design, energy analysis software, shading losses, solar radiation analysis.

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Authors: Seifedine Kadry

Abstract:

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.

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Authors: Ping He

Abstract:

This paper addresses the problem of the partial state feedback stabilization of a class of nonlinear systems. In order to stabilization this class systems, the especial place of this paper is to reverse designing the state feedback control law from the method of judging system stability with the center manifold theory. First of all, the center manifold theory is applied to discuss the stabilization sufficient condition and design the stabilizing state control laws for a class of nonlinear. Secondly, the problem of partial stabilization for a class of plane nonlinear system is discuss using the lyapunov second method and the center manifold theory. Thirdly, we investigate specially the problem of the stabilization for a class of homogenous plane nonlinear systems, a class of nonlinear with dual-zero eigenvalues and a class of nonlinear with zero-center using the method of lyapunov function with homogenous derivative, specifically. At the end of this paper, some examples and simulation results are given show that the approach of this paper to this class of nonlinear system is effective and convenient.

Keywords: Partial stabilization, Nonlinear critical systems, Centermanifold theory, Lyapunov function, System reduction.

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Authors: H. B. Kekre, Sudeep D. Thepade

Abstract:

The automatic construction of large, high-resolution image vistas (mosaics) is an active area of research in the fields of photogrammetry [1,2], computer vision [1,4], medical image processing [4], computer graphics [3] and biometrics [8]. Image stitching is one of the possible options to get image mosaics. Vista Creation in image processing is used to construct an image with a large field of view than that could be obtained with a single photograph. It refers to transforming and stitching multiple images into a new aggregate image without any visible seam or distortion in the overlapping areas. Vista creation process aligns two partial images over each other and blends them together. Image mosaics allow one to compensate for differences in viewing geometry. Thus they can be used to simplify tasks by simulating the condition in which the scene is viewed from a fixed position with single camera. While obtaining partial images the geometric anomalies like rotation, scaling are bound to happen. To nullify effect of rotation of partial images on process of vista creation, we are proposing rotation invariant vista creation algorithm in this paper. Rotation of partial image parts in the proposed method of vista creation may introduce some missing region in the vista. To correct this error, that is to fill the missing region further we have used image inpainting method on the created vista. This missing view regeneration method also overcomes the problem of missing view [31] in vista due to cropping, irregular boundaries of partial image parts and errors in digitization [35]. The method of missing view regeneration generates the missing view of vista using the information present in vista itself.

Keywords: Vista, Overlap Estimation, Rotation Invariance, Missing View Regeneration.

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Authors: B. Rajesh Kamath, J. Sundara Rajan

Abstract:

Partial Discharge measurement is a very important means of assessing the integrity of insulation systems in a High Voltage apparatus. In compressed gas insulation systems, floating particles can initiate partial discharge activities which adversely affect the working of insulation. Partial Discharges below the inception voltage also plays a crucial in damaging the integrity of insulation over a period of time. This paper discusses the effect of loose and fixed Copper and Nichrome wire particles on the PD characteristics in SF6-N2 (10:90) gas mixtures at a pressure of 0.4MPa. The Partial Discharge statistical parameters and their correlation to the observed results are discussed.

Keywords: Gas Insulated transmission Line, Sulphur HexaFlouride, metallic Particles, Partial Discharge (PD), InceptionVoltage (Vi), Extinction Voltage (Ve), PD Statistical parameters.

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Authors: Dursun Aydın

Abstract:

In this paper, estimation of the linear regression model is made by ordinary least squares method and the partially linear regression model is estimated by penalized least squares method using smoothing spline. Then, it is investigated that differences and similarity in the sum of squares related for linear regression and partial linear regression models (semi-parametric regression models). It is denoted that the sum of squares in linear regression is reduced to sum of squares in partial linear regression models. Furthermore, we indicated that various sums of squares in the linear regression are similar to different deviance statements in partial linear regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the partial linear regression model. For this aim, it is made two different applications. A simulated and a real data set are considered to prove the claim mentioned here. In this way, this study is supported with a simulation and a real data example.

Keywords: Partial Linear Regression Model, Linear RegressionModel, Residuals, Deviance, Smoothing Spline.

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Authors: Mohd Agos Salim Nasir, Ros Fadilah Deraman, Siti Salmah Yasiran

Abstract:

The Goursat partial differential equation arises in linear and non linear partial differential equations with mixed derivatives. This equation is a second order hyperbolic partial differential equation which occurs in various fields of study such as in engineering, physics, and applied mathematics. There are many approaches that have been suggested to approximate the solution of the Goursat partial differential equation. However, all of the suggested methods traditionally focused on numerical differentiation approaches including forward and central differences in deriving the scheme. An innovation has been done in deriving the Goursat partial differential equation scheme which involves numerical integration techniques. In this paper we have developed a new scheme to solve the Goursat partial differential equation based on the Adomian decomposition (ADM) and associated with Boole-s integration rule to approximate the integration terms. The new scheme can easily be applied to many linear and non linear Goursat partial differential equations and is capable to reduce the size of computational work. The accuracy of the results reveals the advantage of this new scheme over existing numerical method.

Keywords: Goursat problem, partial differential equation, Adomian decomposition method, Boole's integration rule.

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