Search results for: green's function
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2589

Search results for: green's function

1539 A User - Requirements Approach in Medical Devices Maintenance System Development: A Case Study from an Industry Perspective

Authors: Manar AlJazzazi, Mohammed Rawashdeh, Tariq Alshawaheen, Aktham Malkawi

Abstract:

This paper is a part of research, in which the way the biomedical engineers follow in their work is analyzed. The goal of this paper is to present a method for specification of user requirements in the medical devices maintenance process. Data Gathering Methods, Research Model Phases and Descriptive Analysis is presented. These technology and verification rules can be implemented in Medical devices maintenance management process to the maintenance process.

Keywords: Quality Function Deployment (QFD), User - requirements approach.

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1538 Order Reduction using Modified Pole Clustering and Pade Approximations

Authors: C.B. Vishwakarma

Abstract:

The authors present a mixed method for reducing the order of the large-scale dynamic systems. In this method, the denominator polynomial of the reduced order model is obtained by using the modified pole clustering technique while the coefficients of the numerator are obtained by Pade approximations. This method is conceptually simple and always generates stable reduced models if the original high-order system is stable. The proposed method is illustrated with the help of the numerical examples taken from the literature.

Keywords: Modified pole clustering, order reduction, padeapproximation, stability, transfer function.

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1537 Robust BIBO Stabilization Analysis for Discrete-time Uncertain System

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

Abstract:

The discrete-time uncertain system with time delay is investigated for bounded input bounded output (BIBO). By constructing an augmented Lyapunov function, three different sufficient conditions are established for BIBO stabilization. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Two numerical examples are provided to demonstrate the effectiveness of the derived results.

Keywords: Robust BIBO stabilization, delay-dependent stabilization, discrete-time system, time delay.

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1536 Kinetics of Aggregation in Media with Memory

Authors: A. Brener, B. Balabekov, N. Zhumataev

Abstract:

In the paper we submit the non-local modification of kinetic Smoluchowski equation for binary aggregation applying to dispersed media having memory. Our supposition consists in that that intensity of evolution of clusters is supposed to be a function of the product of concentrations of the lowest orders clusters at different moments. The new form of kinetic equation for aggregation is derived on the base of the transfer kernels approach. This approach allows considering the influence of relaxation times hierarchy on kinetics of aggregation process in media with memory.

Keywords: Binary aggregation, Media with memory, Non-local model, Relaxation times

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1535 Effect of Crashed Stone on Properties of Fly Ash Based-Geopolymer Concrete with Local Alkaline Activator in Egypt

Authors: O. M. Omar, G. D. Abd Elhameed, A. M. Heniegal H. A. Mohamadien

Abstract:

Green concrete are generally composed of recycling materials as hundred or partial percent substitutes for aggregate, cement, and admixture in concrete. To reduce greenhouse gas emissions, efforts are needed to develop environmentally friendly construction materials. Using of fly ash based geopolymer as an alternative binder can help reduce CO2 emission of concrete. The binder of geopolymer concrete is different from the ordinary Portland cement concrete. Geopolymer Concrete specimens were prepared with different concentration of NaOH solution M10, M14, and, M16 and cured at 60ºC in duration of 24 hours and 8 hours, in addition to the curing in direct sunlight. Thus, it is necessary to study the effects of the geopolymer binder on the behavior of concrete. Concrete is made by using geopolymer technology is environmental friendly and could be considered as part of the sustainable development. In this study, the Local Alkaline Activator in Egypt and crashed stone as coarse aggregate in fly ash based-geopolymer concrete was investigated. This paper illustrates the development of mechanical properties. Since the gained compressive strength for geopolymer concrete at 28 days was in the range of 22.5MPa – 43.9MPa.

Keywords: Geopolymer, molarity, sodium hydroxide, sodium silicate.

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1534 Medical Imaging Techniques in Clinical Medicine

Authors: Sharan Badiger, Prema T. Akkasaligar

Abstract:

Medical imaging technology has experienced a dramatic change in the last few years. Medical imaging refers to the techniques and processes used to create images of the human body (or parts thereof) for various clinical purposes such as medical procedures and diagnosis or medical science including the study of normal anatomy and function. With the growth of computers and image technology, medical imaging has greatly influenced the medical field. The diagnosis of a health problem is now highly dependent on the quality and the credibility of the image analysis. This paper deals with the various aspects and types of medical imaging.

Keywords: Computed Tomography, Echocardiography, Medical Imaging, Magnetic Resonance, Ultrasound Imaging.

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1533 Considering Assembly Operations and Product Structure for Manufacturing Cell Formation

Authors: M.B. Aryanezhad, J. Aliabadi

Abstract:

This paper considers the integration of assembly operations and product structure to Cellular Manufacturing System (CMS) design so that to correct the drawbacks of previous researches in the literature. For this purpose, a new mathematical model is developed which dedicates machining and assembly operations to manufacturing cells while the objective function is to minimize the intercellular movements resulting due to both of them. A linearization method is applied to achieve optimum solution through solving aforementioned nonlinear model by common programming language such as Lingo. Then, using different examples and comparing the results, the importance of integrating assembly considerations is demonstrated.

Keywords: Assembly operations and Product structure, CellFormation, Genetic Algorithm.

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1532 On the Efficiency of Five Step Approximation Method for the Solution of General Third Order Ordinary Differential Equations

Authors: N. M. Kamoh, M. C. Soomiyol

Abstract:

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

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1531 Flow and Heat Transfer of a Nanofluid over a Shrinking Sheet

Authors: N. Bachok, N. L. Aleng, N. M. Arifin, A. Ishak, N. Senu

Abstract:

The problem of laminar fluid flow which results from the shrinking of a permeable surface in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the mass suction parameter S, Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. It was found that the reduced Nusselt number is decreasing function of each dimensionless number.

Keywords: Boundary layer, Nanofluid, Shrinking sheet, Brownian motion, Thermophoresis, Similarity solution.

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1530 Contrast Enhancement of Color Images with Color Morphing Approach

Authors: Javed Khan, Aamir Saeed Malik, Nidal Kamel, Sarat Chandra Dass, Azura Mohd Affandi

Abstract:

Low contrast images can result from the wrong setting of image acquisition or poor illumination conditions. Such images may not be visually appealing and can be difficult for feature extraction. Contrast enhancement of color images can be useful in medical area for visual inspection. In this paper, a new technique is proposed to improve the contrast of color images. The RGB (red, green, blue) color image is transformed into normalized RGB color space. Adaptive histogram equalization technique is applied to each of the three channels of normalized RGB color space. The corresponding channels in the original image (low contrast) and that of contrast enhanced image with adaptive histogram equalization (AHE) are morphed together in proper proportions. The proposed technique is tested on seventy color images of acne patients. The results of the proposed technique are analyzed using cumulative variance and contrast improvement factor measures. The results are also compared with decorrelation stretch. Both subjective and quantitative analysis demonstrates that the proposed techniques outperform the other techniques.

Keywords: Contrast enhancement, normalized RGB, adaptive histogram equalization, cumulative variance.

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1529 Ethics in the Technology Driven Enterprise

Authors: Bobbie Green, James A. Nelson

Abstract:

Innovations in technology have created new ethical challenges. Essential use of electronic communication in the workplace has escalated at an astronomical rate over the past decade. As such, legal and ethical dilemmas confronted by both the employer and the employee concerning managerial control and ownership of einformation have increased dramatically in the USA. From the employer-s perspective, ownership and control of all information created for the workplace is an undeniable source of economic advantage and must be monitored zealously. From the perspective of the employee, individual rights, such as privacy, freedom of speech, and freedom from unreasonable search and seizure, continue to be stalwart legal guarantees that employers are not legally or ethically entitled to abridge in the workplace. These issues have been the source of great debate and the catalyst for legal reform. The fine line between ethical and legal has been complicated by emerging technologies. This manuscript will identify and discuss a number of specific legal and ethical issues raised by the dynamic electronic workplace and conclude with suggestions that employers should follow to respect the delicate balance between employees- legal rights to privacy and the employer's right to protect its knowledge systems and infrastructure.

Keywords: Information, ethics, legal, privacy

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1528 Supply Chain Decarbonisation – A Cost-Based Decision Support Model in Slow Steaming Maritime Operations

Authors: Eugene Y. C. Wong, Henry Y. K. Lau, Mardjuki Raman

Abstract:

CO2 emissions from maritime transport operations represent a substantial part of the total greenhouse gas emission. Vessels are designed with better energy efficiency. Minimizing CO2 emission in maritime operations plays an important role in supply chain decarbonisation. This paper reviews the initiatives on slow steaming operations towards the reduction of carbon emission. It investigates the relationship and impact among slow steaming cost reduction, carbon emission reduction, and shipment delay. A scenario-based cost-driven decision support model is developed to facilitate the selection of the optimal slow steaming options, considering the cost on bunker fuel consumption, available speed, carbon emission, and shipment delay. The incorporation of the social cost of cargo is reviewed and suggested. Additional measures on the effect of vessels sizes, routing, and type of fuels towards decarbonisation are discussed.

Keywords: Slow steaming, carbon emission, maritime logistics, sustainability, green supply chain.

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1527 Clogging Reduction Design Factor for Geosynthetics Used in Sustainable Urban Drainage Systems and Roads

Authors: Jaime Carpio-García, Elena Blanco-Fernández, Javier González-Fernández, Daniel Castro-Fresno

Abstract:

Sustainable urban drainage systems (SUDS) are more often used in order to prevent floods, water treatment, fight against pollution, urban heat island effect, and global warming in applications like green roofs, permeable pavements, and others. Furthermore, geosynthetics are also worldwide used as a part of drainage systems in road construction. Geotextiles are an essential part of both, and one of the main geotextile properties in those applications is permeability, whose behavior is not well established along its service life. In this paper, clogging reduction design factors for an estimated service life of 25 years are experimentally obtained for five different geotextiles used in SUDS and roads combined with two different soils and with two pollutants, motor oil, and lime, in order to evaluate chemical clogging, too. The effect of characteristic opening size and other characteristics of the geosynthetics are also discussed in order to give civil engineers, together with the clogging reduction factors, a better long-time design of geotextiles used in their SUDS and roads.

Keywords: Geotextiles, drainage, clogging, reduction factor.

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1526 Assessing the Impact of High Fidelity Human Patient Simulation on Teamwork among Nursing, Medicine and Pharmacy Undergraduate Students

Authors: S. MacDonald, A. Manuel, R. Law, N. Bandruak, A. Dubrowski, V. Curran, J. Smith-Young, K. Simmons, A. Warren

Abstract:

High fidelity human patient simulation has been used for many years by health sciences education programs to foster critical thinking, engage learners, improve confidence, improve communication, and enhance psychomotor skills. Unfortunately, there is a paucity of research on the use of high fidelity human patient simulation to foster teamwork among nursing, medicine and pharmacy undergraduate students. This study compared the impact of high fidelity and low fidelity simulation education on teamwork among nursing, medicine and pharmacy students. For the purpose of this study, two innovative teaching scenarios were developed based on the care of an adult patient experiencing acute anaphylaxis: one high fidelity using a human patient simulator and one low fidelity using case based discussions. A within subjects, pretest-posttest, repeated measures design was used with two-treatment levels and random assignment of individual subjects to teams of two or more professions. A convenience sample of twenty-four (n=24) undergraduate students participated, including: nursing (n=11), medicine (n=9), and pharmacy (n=4). The Interprofessional Teamwork Questionnaire was used to assess for changes in students’ perception of their functionality within the team, importance of interprofessional collaboration, comprehension of roles, and confidence in communication and collaboration. Student satisfaction was also assessed. Students reported significant improvements in their understanding of the importance of interprofessional teamwork and of the roles of nursing and medicine on the team after participation in both the high fidelity and the low fidelity simulation. However, only participants in the high fidelity simulation reported a significant improvement in their ability to function effectively as a member of the team. All students reported that both simulations were a meaningful learning experience and all students would recommend both experiences to other students. These findings suggest there is merit in both high fidelity and low fidelity simulation as a teaching and learning approach to foster teamwork among undergraduate nursing, medicine and pharmacy students. However, participation in high fidelity simulation may provide a more realistic opportunity to practice and function as an effective member of the interprofessional health care team.

Keywords: Acute anaphylaxis, high fidelity human patient simulation, low fidelity simulation, interprofessional education.

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1525 A Self-Consistent Scheme for Elastic-Plastic Asperity Contact

Authors: Xu Jianguo

Abstract:

In this paper, a generalized self-consistent scheme, or “three phase model", is used to set up a micro-mechanics model for rough surface contact with randomly distributed asperities. The dimensionless average real pressure p is obtained as function of the ratio of the real contact area to the apparent contact area, 0 A / A r . Both elastic and plastic materials are considered, and the influence of the plasticity of material on p is discussed. Both two-dimensional and three-dimensional rough surface contact problems are considered.

Keywords: Contact mechanics, plastic deformation, self-consistent scheme.

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1524 Strategic Maintenance Management of Built Facilities in an Organisation

Authors: Anita D. Adamu, Winston M. W. Shakantu

Abstract:

Maintenance management is no longer a stand-alone activity. It has now assumed a strategic position in many organisations that have recognised its importance in achieving primary goals and a key aspect of effective management of facilities. This paper aims at providing an understanding of the role and function of strategic management in creating and sustaining an effective maintenance management system in an organisation. The background provides an articulated concept and principles of strategic management. The theoretical concepts paved way for a conceptual framework for which strategic management can be integrated into the maintenance management system of an organisation to improve effectiveness in the maintenance of facilities.

Keywords: Facilities, maintenance management, organisations, strategic management.

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1523 Scalable Deployment and Configuration of High-Performance Virtual Clusters

Authors: Kyrre M Begnum, Matthew Disney

Abstract:

Virtualization and high performance computing have been discussed from a performance perspective in recent publications. We present and discuss a flexible and efficient approach to the management of virtual clusters. A virtual machine management tool is extended to function as a fabric for cluster deployment and management. We show how features such as saving the state of a running cluster can be used to avoid disruption. We also compare our approach to the traditional methods of cluster deployment and present benchmarks which illustrate the efficiency of our approach.

Keywords: Cluster management, clusters, high-performance, virtual machines, Xen

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1522 Microstructural Properties of the Interfacial Transition Zone and Strength Development of Concrete Incorporating Recycled Concrete Aggregate

Authors: S. Boudali, A. M. Soliman, B. Abdulsalam, K. Ayed, D. E. Kerdal, S. Poncet

Abstract:

This study investigates the potential of using crushed concrete as aggregates to produce green and sustainable concrete. Crushed concrete was sieved to powder fine recycled aggregate (PFRA) less than 80 µm and coarse recycled aggregates (CRA). Physical, mechanical, and microstructural properties for PFRA and CRA were evaluated. The effect of the additional rates of PFRA and CRA on strength development of recycled aggregate concrete (RAC) was investigated. Additionally, the characteristics of interfacial transition zone (ITZ) between cement paste and recycled aggregate were also examined. Results show that concrete mixtures made with 100% of CRA and 40% PFRA exhibited similar performance to that of the control mixture prepared with 100% natural aggregate (NA) and 40% natural pozzolan (NP). Moreover, concrete mixture incorporating recycled aggregate exhibited a slightly higher later compressive strength than that of the concrete with NA. This was confirmed by the very dense microstructure for concrete mixture incorporating recycled concrete aggregates compared to that of conventional concrete mixture.

Keywords: Compressive strength, recycled concrete aggregates, microstructure, interfacial transition zone, powder fine recycled aggregate.

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1521 Evaluation of a Surrogate Based Method for Global Optimization

Authors: David Lindström

Abstract:

We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cyclic parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

Keywords: Expensive function, infill sampling criterion, kriging, global optimization, response surface, Runge phenomenon.

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1520 Enhanced Traveling Salesman Problem Solving by Genetic Algorithm Technique (TSPGA)

Authors: Buthainah Fahran Al-Dulaimi, Hamza A. Ali

Abstract:

The well known NP-complete problem of the Traveling Salesman Problem (TSP) is coded in genetic form. A software system is proposed to determine the optimum route for a Traveling Salesman Problem using Genetic Algorithm technique. The system starts from a matrix of the calculated Euclidean distances between the cities to be visited by the traveling salesman and a randomly chosen city order as the initial population. Then new generations are then created repeatedly until the proper path is reached upon reaching a stopping criterion. This search is guided by a solution evaluation function.

Keywords: Genetic algorithms, traveling salesman problem solving, optimization.

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1519 Preparation and Characterization of M. × Piperita L. Oil Based Gel Formulation

Authors: Peeyush Kumar, Sapna Mishra, Anushree Malik, Santosh Satya

Abstract:

The essential oil of M. × piperita L. was formulated into a topical gel. The prepared gel was characterized for its pH, viscosity, spreadiblity, consistency and extrudiblity, while its stability was evaluated under different temperature conditions. The prepared M. × piperita oil gel was clear and transparent. The pH value of developed gel was 6.6, while its viscosity was 1200 cP. Spreadability and consistency of the M. × piperita oil gel was 10.7 g.cm/sec and 7 mm, respectively. The prepared gel showed good extrudiblity. During the stability studies, no significant change in pH and viscosity as a function of time for gel was observed, indicating stability of prepared formulation. The gel developed in this study is expected to forward the usage of M. × piperita essential towards commercial application.

Keywords: M. × piperita L., formulation, gel, characterization, stability

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1518 New Data Reuse Adaptive Filters with Noise Constraint

Authors: Young-Seok Choi

Abstract:

We present a new framework of the data-reusing (DR) adaptive algorithms by incorporating a constraint on noise, referred to as a noise constraint. The motivation behind this work is that the use of the statistical knowledge of the channel noise can contribute toward improving the convergence performance of an adaptive filter in identifying a noisy linear finite impulse response (FIR) channel. By incorporating the noise constraint into the cost function of the DR adaptive algorithms, the noise constrained DR (NC-DR) adaptive algorithms are derived. Experimental results clearly indicate their superior performance over the conventional DR ones.

Keywords: Adaptive filter, data-reusing, least-mean square (LMS), affine projection (AP), noise constraint.

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1517 Analysis on Fractals in Intuitionistic Fuzzy Metric Spaces

Authors: R. Uthayakumar, D. Easwaramoorthy

Abstract:

This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we analyze some results on intuitionistic fuzzy fractals in the standard intuitionistic fuzzy metric spaces with respect to the Hausdorff intuitionistic fuzzy metrics.

Keywords: Fractal Analysis, Fixed Point, Contraction, Iterated Function System, Intuitionistic Fuzzy Metric Space.

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1516 Statistical Analysis of First Order Plus Dead-time System using Operational Matrix

Authors: Pham Luu Trung Duong, Moonyong Lee

Abstract:

To increase precision and reliability of automatic control systems, we have to take into account of random factors affecting the control system. Thus, operational matrix technique is used for statistical analysis of first order plus time delay system with uniform random parameter. Examples with deterministic and stochastic disturbance are considered to demonstrate the validity of the method. Comparison with Monte Carlo method is made to show the computational effectiveness of the method.

Keywords: First order plus dead-time, Operational matrix, Statistical analysis, Walsh function.

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1515 Selective Minterms Based Tabular Method for BDD Manipulations

Authors: P. W. C. Prasad, A. Assi, M. Raseen, A. Harb

Abstract:

The goal of this work is to describe a new algorithm for finding the optimal variable order, number of nodes for any order and other ROBDD parameters, based on a tabular method. The tabular method makes use of a pre-built backend database table that stores the ROBDD size for selected combinations of min-terms. The user uses the backend table and the proposed algorithm to find the necessary ROBDD parameters, such as best variable order, number of nodes etc. Experimental results on benchmarks are given for this technique.

Keywords: Tabular Method, Binary Decision Diagram, BDD Manipulation, Boolean Function.

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1514 Ranking of Performance Measures of GSCM towards Sustainability: Using Analytic Hierarchy Process

Authors: Dixit Garg, S. Luthra, A. Haleem

Abstract:

During recent years, the natural environment has become a challenging topic that business organizations must consider due to the economic and ecological impacts and increasing awareness of environment protection among society. Organizations are trying to achieve the goals of improvement in environment, low cost, high quality, flexibility and more customer satisfaction. Performance measurement frameworks are very useful to monitor the performance of any organization. The basic goal of this paper is to identify performance measures and ranking of these performance measures of GSCM performance measurement towards sustainability framework. Five perspectives (Environment, Economic, Social, Operational and Cost performances) and nineteen performance measures of GSCM performance towards sustainability have been have been identified from extensive literature review. Analytical Hierarchy Process (AHP) technique has been utilized for ranking of these performance perspectives and measures. All pair comparisons in AHP have been made on the basis on the experts’ opinions (selected from academia and industry). Ranking of these performance perspectives and measures will help to understand the importance of environmental, economic, social, operational performances and cost performances in the supply chain.

Keywords: Analytical Hierarchy Process (AHP), Green Supply Chain Management, Performance Measures (PM), Sustainability.

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1513 A Real Time Comparison of Standalone and Grid Connected Solar Photovoltaic Generation Systems

Authors: Sachin Vrajlal Rajani, Vivek Pandya, Ankit Suvariya

Abstract:

Green and renewable energy is getting extraordinary consideration today, because of ecological concerns made by blazing of fossil powers. Photovoltaic and wind power generation are the basic decisions for delivering power in this respects. Producing power by the sun based photovoltaic systems is known to the world, yet control makers may get confounded to pick between on-grid and off-grid systems. In this exploration work, an endeavor is made to compare the off-grid (stand-alone) and on-grid (grid-connected) frameworks. The work presents relative examination, between two distinctive PV frameworks situated at V.V.P. Engineering College, Rajkot. The first framework is 100 kW remain solitary and the second is 60 kW network joined. The real-time parameters compared are; output voltage, load current, power in-flow, power output, performance ratio, yield factor, and capacity factor. The voltage changes and the power variances in both frameworks are given exceptional consideration and the examination is made between the two frameworks to judge the focal points and confinements of both the frameworks.

Keywords: Standalone PV systems, grid connected PV systems, comparison, real time data analysis.

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1512 Grid Artifacts Suppression in Computed Radiographic Images

Authors: Igor Belykh

Abstract:

Anti-scatter grids used in radiographic imaging for the contrast enhancement leave specific artifacts. Those artifacts may be visible or may cause Moiré effect when digital image is resized on a diagnostic monitor. In this paper we propose an automated grid artifactsdetection and suppression algorithm which is still an actual problem. Grid artifacts detection is based on statistical approach in spatial domain. Grid artifacts suppression is based on Kaiser bandstop filter transfer function design and application avoiding ringing artifacts. Experimental results are discussed and concluded with description of advantages over existing approaches.

Keywords: Computed radiography, grid artifacts, image filtering.

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1511 Foil Bearing Stiffness Estimation with Pseudospectral Scheme

Authors: Balaji Sankar, Sadanand Kulkarni

Abstract:

Compliant foil gas lubricated bearings are used for the support of light loads in the order of few kilograms at high speeds, in the order of 50,000 RPM. The stiffness of the foil bearings depends both on the stiffness of the compliant foil and on the lubricating gas film. The stiffness of the bearings plays a crucial role in the stable operation of the supported rotor over a range of speeds. This paper describes a numerical approach to estimate the stiffness of the bearings using pseudo spectral scheme. Methodology to obtain the stiffness of the foil bearing as a function of weight of the shaft is given and the results are presented.

Keywords: Foil bearing, simulation, numerical, stiffness estimation.

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1510 An Overview of Some High Order and Multi-Level Finite Difference Schemes in Computational Aeroacoustics

Authors: Appanah Rao Appadu, Muhammad Zaid Dauhoo

Abstract:

In this paper, we have combined some spatial derivatives with the optimised time derivative proposed by Tam and Webb in order to approximate the linear advection equation which is given by = 0. Ôêé Ôêé + Ôêé Ôêé x f t u These spatial derivatives are as follows: a standard 7-point 6 th -order central difference scheme (ST7), a standard 9-point 8 th -order central difference scheme (ST9) and optimised schemes designed by Tam and Webb, Lockard et al., Zingg et al., Zhuang and Chen, Bogey and Bailly. Thus, these seven different spatial derivatives have been coupled with the optimised time derivative to obtain seven different finite-difference schemes to approximate the linear advection equation. We have analysed the variation of the modified wavenumber and group velocity, both with respect to the exact wavenumber for each spatial derivative. The problems considered are the 1-D propagation of a Boxcar function, propagation of an initial disturbance consisting of a sine and Gaussian function and the propagation of a Gaussian profile. It is known that the choice of the cfl number affects the quality of results in terms of dissipation and dispersion characteristics. Based on the numerical experiments solved and numerical methods used to approximate the linear advection equation, it is observed in this work, that the quality of results is dependent on the choice of the cfl number, even for optimised numerical methods. The errors from the numerical results have been quantified into dispersion and dissipation using a technique devised by Takacs. Also, the quantity, Exponential Error for Low Dispersion and Low Dissipation, eeldld has been computed from the numerical results. Moreover, based on this work, it has been found that when the quantity, eeldld can be used as a measure of the total error. In particular, the total error is a minimum when the eeldld is a minimum.

Keywords: Optimised time derivative, dissipation, dispersion, cfl number, Nomenclature: k : time step, h : spatial step, β :advection velocity, r: cfl/Courant number, hkrβ= , w =θ, h : exact wave number, n :time level, RPE : Relative phase error per unit time step, AFM :modulus of amplification factor

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