Search results for: Design Algorithm

Authors: Xingping Sheng

Abstract:

Let T and S be a subspace of Cn and Cm, respectively. Then for A ∈ Cm×n satisfied AT ⊕ S = Cm, the generalized inverse A(2) T,S is given by A(2) T,S = (PS⊥APT )†. In this paper, a finite formulae is presented to compute generalized inverse A(2) T,S under the concept of restricted inner product, which defined as < A,B >T,S=< PS⊥APT,B > for the A,B ∈ Cm×n. By this iterative method, when taken the initial matrix X0 = PTA∗PS⊥, the generalized inverse A(2) T,S can be obtained within at most mn iteration steps in absence of roundoff errors. Finally given numerical example is shown that the iterative formulae is quite efficient.

Keywords: Generalized inverse A(2) T, S, Restricted inner product, Iterative method, Orthogonal projection.

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Authors: Narasimham Challa, Jayaram Pradhan

Abstract:

Cryptographic algorithms play a crucial role in the information society by providing protection from unauthorized access to sensitive data. It is clear that information technology will become increasingly pervasive, Hence we can expect the emergence of ubiquitous or pervasive computing, ambient intelligence. These new environments and applications will present new security challenges, and there is no doubt that cryptographic algorithms and protocols will form a part of the solution. The efficiency of a public key cryptosystem is mainly measured in computational overheads, key size and bandwidth. In particular the RSA algorithm is used in many applications for providing the security. Although the security of RSA is beyond doubt, the evolution in computing power has caused a growth in the necessary key length. The fact that most chips on smart cards can-t process key extending 1024 bit shows that there is need for alternative. NTRU is such an alternative and it is a collection of mathematical algorithm based on manipulating lists of very small integers and polynomials. This allows NTRU to high speeds with the use of minimal computing power. NTRU (Nth degree Truncated Polynomial Ring Unit) is the first secure public key cryptosystem not based on factorization or discrete logarithm problem. This means that given sufficient computational resources and time, an adversary, should not be able to break the key. The multi-party communication and requirement of optimal resource utilization necessitated the need for the present day demand of applications that need security enforcement technique .and can be enhanced with high-end computing. This has promoted us to develop high-performance NTRU schemes using approaches such as the use of high-end computing hardware. Peer-to-peer (P2P) or enterprise grids are proven as one of the approaches for developing high-end computing systems. By utilizing them one can improve the performance of NTRU through parallel execution. In this paper we propose and develop an application for NTRU using enterprise grid middleware called Alchemi. An analysis and comparison of its performance for various text files is presented.

Keywords: Alchemi, GridNtru, Ntru, PKCS.

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Authors: Haider K. Raad

Abstract:

In this paper, a compact wide-band, ultra-thin and flexible slot antenna intended for wearable applications is presented. The presented antenna is designed to provide Wireless Local Area Network (WLAN) and Long Term Evolution (LTE) connectivity. The presented design exhibits a relatively wide bandwidth (1600-3500 MHz below -6 dB impedance bandwidth limit). The antenna is positioned on a 33 mm x 30 mm flexible substrate with a thickness of 50 µm. Antenna properties, such as the far-field radiation patterns, scattering parameter S₁₁ are provided. The presented compact, thin and flexible design along with excellent radiation characteristics are deemed suitable for integration into flexible and wearable devices.

Keywords: Wearable Electronics, Slot Antenna, LTE, WLAN.

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Authors: R. Nagendra Babu, K. V. Ramana, K. Mallikarjuna Rao

Abstract:

Stress Concentration Factors are significant in machine design as it gives rise to localized stress when any change in the design of surface or abrupt change in the cross section occurs. Almost all machine components and structural members contain some form of geometrical or microstructural discontinuities. These discontinuities are very dangerous and lead to failure. So, it is very much essential to analyze the stress concentration factors for critical applications like Turbine Rotors. In this paper Finite Element Analysis (FEA) with extremely fine mesh in the vicinity of the blades of Steam Turbine Rotor is applied to determine stress concentration factors. A model of Steam Turbine Rotor is shown in Fig. 1.

Keywords: Stress Concentration Factors, Finite Element Analysis, and ANSYS.

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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: Tian Baoguang, Liang Chunyan, Chen Nan

Abstract:

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_i are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_i<0 is proposed.

Keywords: Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion

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Authors: Peyman Naderi, Ali Farhadi, S. Mohammad Taghi Bathaee

Abstract:

One of the best ways for achievement of conventional vehicle changing to hybrid case is trustworthy simulation result and using of driving realities. For this object, in this paper, at first sevendegree- of-freedom dynamical model of vehicle will be shown. Then by using of statically model of engine, gear box, clutch, differential, electrical machine and battery, the hybrid automobile modeling will be down and forward simulation of vehicle for pedals to wheels power transformation will be obtained. Then by design of a fuzzy controller and using the proper rule base, fuel economy and regenerative braking will be marked. Finally a series of MATLAB/SIMULINK simulation results will be proved the effectiveness of proposed structure.

Keywords: Hybrid, Driving, Fuzzy, Regeneration.

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Authors: Thirasak Panyaphirawat, Pairoj Sapsmarnwong, Teeratas Pornyungyuen

Abstract:

This paper presents the findings of an experimental investigation of important machining parameters for the horizontal boring tool modified to mouth with a horizontal lathe machine to bore an overlength workpiece. In order to verify a usability of a modified tool, design of experiment based on Taguchi method is performed. The parameters investigated are spindle speed, feed rate, depth of cut and length of workpiece. Taguchi L9 orthogonal array is selected for four factors three level parameters in order to minimize surface roughness (Ra and Rz) of S45C steel tubes. Signal to noise ratio analysis and analysis of variance (ANOVA) is performed to study an effect of said parameters and to optimize the machine setting for best surface finish. The controlled factors with most effect are depth of cut, spindle speed, length of workpiece, and feed rate in order. The confirmation test is performed to test the optimal setting obtained from Taguchi method and the result is satisfactory.

Keywords: Design of Experiment, Taguchi Design, Optimization, Analysis of Variance, Machining Parameters, Horizontal Boring Tool.

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Authors: Csaba Tóth, Éva Lakatos, László Pethő, Seoyoung Cho

Abstract:

The temperature effect on asphalt pavement structure is a crucial factor at the design stage. In this paper, by applying the German guidelines for temperature along the asphalt depth is estimated. The aim is to consider temperature profiles in different seasons in numerical modelling. The model is built with an elastic and isotropic solid element with 19 subdivisions of asphalt layers to reflect the temperature variation. Comparison with the simple three-layer pavement system (asphalt layers, base, and subgrade layers) will be followed to see the difference in result without temperature variation along with the depth. Finally, the fatigue life calculation was checked to prove the validity of the methodology of considering the temperature in the numerical modelling.

Keywords: Temperature profile, flexible pavement modelling, finite element method, temperature modelling.

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Authors: Emad Hazbkhah, Abdolreza Zahiri, Hossein Ghorbanizade Kharazi, Afshin Kiani

Abstract:

Establishing pumping stations is one of the most common ways of providing water from rivers. There are many issues involved in the design and operation of pumping stations most important of which is the problem of sedimentation. One of the significant issues which must be taken into consideration in designing pumping stations is the operation method and technical matters related to it. Safety and convenience of operation is one of the issues that must be always considered by the designer. Some of the major issues in making decisions regarding the type of design for the station are geographical condition, the location of the station and availability of experts in maintenance and operation of the station. Dimensions of the station must allow free movement for checking and operating pumps after installation of pumps and plumbing system.

Keywords: Boneh Basht, Iran, pumping station.

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Authors: Marco Sernaglia, Augusto M. P. Carreira, Helena M. L. Carvalho, Pedro B. Água, Armindo Frias, Manuel Carrasqueira

Abstract:

The existence of mismatches between the qualification requirements of professionals in the maritime industry and existing higher education offers was verified within the scope of the European project MarLEM (Maritime Logistics Engineering and Management). Professionals in the maritime industry today and in the future face additional obstacles as a result of the sector's global nature as well as the sector's rapid technological and social evolution. As a result, they feel the need to update their skills and knowledge. A professional-oriented master's program was developed to fill this gap. The NOVA School of Science and Technology and the Portuguese Naval School co-developed this Master's program with the active participation of MarLEM project partners from academia and industry. In this work, the principles and approach used to design the master's program are presented. Its design and a concise synopsis of the courses' content are shown. In addition, other international courses covering the same topic are compared. As a result of this work, the teaching materials related to maritime logistics are improved and the assumptions and methodology that guided the creation of an international master's program in maritime logistics are disseminated.

Keywords: Education, maritime logistics, shipping, industrial engineering, management, soft skills.

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Authors: Carlos Gonzalez

Abstract:

This paper describes the use of the Internet as a feature to enhance the security of our software that is going to be distributed/sold to users potentially all over the world. By placing in a secure server some of the features of the secure software, we increase the security of such software. The communication between the protected software and the secure server is done by a double lock algorithm. This paper also includes an analysis of intruders and describes possible responses to detect threats.

Keywords: Internet, secure software, threats, cryptography process.

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Authors: R. Usubamatov, Z. A. Rashid

Abstract:

Simple design of a rotary valve system is capable of controlling intake and exhaust gases, which will eliminate the need of known complex mechanisms. The cost of material and production, maintenance, and noise level of the system can be further reduced. The new mechanism enables the elimination of the overlapping of valves work that reduces gas leakage. This paper examines theoretically the gas flow through the holes of a rotary valve design in a small engine. Preliminary results show that the new gas flow has many positive differences than a conventional poppet-valve system. New dependencies on the gas speed enable the finding of better solutions for the geometry of a rotary valve system that will result in a higher efficiency of an internal-combustion engine of the automotive industry.

Keywords: Gas arrangement, internal combustion engine.

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Authors: Siwar Fadhel, Imen Bahri, Man Zhang

Abstract:

The switched reluctance machine (SRM) has undeniable qualities in terms of low cost and mechanical robustness. However, its highly nonlinear character and its uncertain parameters justify the development of complicated controls. In this paper, authors present the design of a robust H-infinity current controller for an 8/6 SRM with taking into account the nonlinearity of the SRM and with rejection of disturbances. The electromagnetic torque is indirectly regulated through the current controller. To show the performances of this control, a robustness analysis is performed by comparing the H-infinity and PI controller simulation results. This comparison demonstrates better performances for the presented controller. The effectiveness and robustness of the presented controller are also demonstrated by experimental tests.

Keywords: Current regulation, experimentation, robust H-infinity control, switched reluctance machine.

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Authors: J. Barbarán, M. Díaz, I. Esteve, D. Garrido, L. Llopis, B. Rubio

Abstract:

Wireless Sensor and Actor Networks (WSANs) constitute an emerging and pervasive technology that is attracting increasing interest in the research community for a wide range of applications. WSANs have two important requirements: coordination interactions and real-time communication to perform correct and timely actions. This paper introduces a methodology to facilitate the task of the application programmer focusing on the coordination and real-time requirements of WSANs. The methodology proposed in this model uses a real-time component model, UM-RTCOM, which will help us to achieve the design and implementation of applications in WSAN by using the component oriented paradigm. This will help us to develop software components which offer some very interesting features, such as reusability and adaptability which are very suitable for WSANs as they are very dynamic environments with rapidly changing conditions. In addition, a high-level coordination model based on tuple channels (TC-WSAN) is integrated into the methodology by providing a component-based specification of this model in UM-RTCOM; this will allow us to satisfy both sensor-actor and actor-actor coordination requirements in WSANs. Finally, we present in this paper the design and implementation of an application which will help us to show how the methodology can be easily used in order to achieve the development of WSANs applications.

Keywords: Sensor networks, real time and embedded systems.

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Authors: Divyesh Patel, Tanuja Srivastava

Abstract:

This paper considers the NP-hard problem of reconstructing binary matrices satisfying exactly-1-4-adjacency constraint from its row and column projections. This problem is formulated into a maximization problem. The objective function gives a measure of adjacency constraint for the binary matrices. The maximization problem is solved by the simulated annealing algorithm and experimental results are presented.

Keywords: Discrete Tomography, exactly-1-4-adjacency, simulated annealing.

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Authors: J. Novak-Marcincin, J. Barna, M. Janak

Abstract:

Augmented Reality (AR) shows great promises for its usage as a tool for simulation and verification of design proposal of new technological systems. Main advantage of augmented reality application usage is possibility of creation and simulation of new technological unit before its realization. This may contribute to increasing of safety and ergonomics and decreasing of economical aspects of new proposed unit. Virtual model of proposed workcell could reveal hidden errors which elimination in later stage of new workcell creation should cause great difficulties. Paper describes process of such virtual model creation and possibilities of its simulation and verification by augmented reality tools.

Keywords: Augmented reality, simulation, workcell design.

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Authors: Shahryar Shaghaghi G., Mojtaba H. Ghoshouni, Bahareh S. Ghabel

Abstract:

The issue of scientific – technological parks has been proposed in several countries of the world especially in western countries since a few decades ago and its efficiency is under examination. In our county Iran, some scientific – technological parks have been established or are being established. This design would evaluate the urban role and method of architecture of these parks in order to criticize its efficiency and offer some suggestions, as much as possible to improve its building methods in Iran. The main problem of this design is that how much these parks in Iran do meet the international measurements. So for this reason, one scientific park in Iran and one from western countries would be studied and compared with each other.

Keywords: Applicability, Architectural pattern, Scientific _technological park , Urban role

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Authors: Hyen Ki Kim

Abstract:

This paper describes the design and implementation of cyber video consultation systems(CVCS) using hybrid P2P for video consultation between remote sites. The proposed system is based on client-server and P2P(Peer to Peer) architecture, where client-server is used for communication with the MCU(Multipoint Control Unit) and P2P is used for the cyber video consultation. The developed video consultation system decreases server traffic, and cuts down network expenses, as the multimedia data decentralizes to the client by hybrid P2P architecture. Also the developed system is tested by the group-type video consultation system using communication protocol and application software through Ethernet networks.

Keywords: Consultation, Cyber, Hybrid, Peer-to-Peer

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Authors: Nahid-Al-Masood, Rifat Mirza, Jubaer Ahmed, Amina Hasan Abedin, S.R. Deeba, Faeza Hafiz, Mahmuda Begum, A. Hasib Chowdhury

Abstract:

Bangladesh is a developing country with large population. Demand of electrical energy is increasing day by day because of increasing population and industrialization. But due to limited resources, people here are suffering from power crisis problem which is considered as a major obstacle to the economic development. In most of the cases, it is extremely difficult to extend high tension transmission lines to some of the places that are separated from the mainland. Renewable energy is considered to be the right choice for providing clean energy to these remote settlements. This paper proposes a cost effective design of off-grid wind-diesel hybrid power system using combined heat and power (CHP) technology in a grid isolated island, Sandwip, Bangladesh. Design and simulation of the wind-diesel hybrid power system is performed considering different factors for the island Sandwip. Detailed economic analysis and comparison with solar PV system clearly reveals that wind-diesel hybrid power system can be a cost effective solution for the isolated island like Sandwip.

Keywords: renewable energy, off-grid, wind-diesel hybrid system, CHP technology, economic analysis

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Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan

Abstract:

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Keywords: Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: Lara F. Horani, Shurong Tong

Abstract:

Identification of customer requirements and their preferences are the starting points in the process of product design. Most of design methodologies focus on traditional requirements. But in the previous decade, the green products and the environment requirements have increasingly attracted the attention with the constant increase in the level of consumer awareness towards environmental problems (such as green-house effect, global warming, pollution and energy crisis, and waste management). Determining the importance weights for the customer requirements is an essential and crucial process. This paper used the analytic hierarchy process (AHP) approach to evaluate and rate the customer requirements for green products. With respect to the ultimate goal of customer satisfaction, surveys are conducted using a five-point scale analysis. With the help of this scale, one can derive the weight vectors. This approach can improve the imprecise ranking of customer requirements inherited from studies based on the conventional AHP. Furthermore, the AHP with extent analysis is simple and easy to implement to prioritize customer requirements. The research is based on collected data through a questionnaire survey conducted over a sample of 160 people belonging to different age, marital status, education and income groups in order to identify the customer preferences for green product requirements.

Keywords: Analytic hierarchy process, green product, customer requirements for green design, importance weights for the customer requirements.

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Authors: Tsuyoshi Okita, Tatsuya Niwa

Abstract:

For a given specific problem an efficient algorithm has been the matter of study. However, an alternative approach orthogonal to this approach comes out, which is called a reduction. In general for a given specific problem this reduction approach studies how to convert an original problem into subproblems. This paper proposes a formal modeling language to support this reduction approach. We show three examples from the wide area of learning problems. The benefit is a fast prototyping of algorithms for a given new problem.

Keywords: Formal language, statistical inference problem, reduction.

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Authors: Sundus Ayyaz, Saad Rehman, Usman Qamar

Abstract:

Software Architecture is the basic structure of software that states the development and advancement of a software system. Software architecture is also considered as a significant tool for the construction of high quality software systems. A clean design leads to the control, value and beauty of software resulting in its longer life while a bad design is the cause of architectural erosion where a software evolution completely fails. This paper discusses the occurrence of software architecture erosion and presents a set of methods for the detection, declaration and prevention of architecture erosion. The causes and symptoms of architecture erosion are observed with the examples of prescriptive and descriptive architectures and the practices used to stop this erosion are also discussed by considering different types of software erosion and their affects. Consequently finding and devising the most suitable approach for fighting software architecture erosion and in some way reducing its affect is evaluated and tested on different scenarios.

Keywords: Software Architecture, Architecture Erosion, Prescriptive Architecture, Descriptive Architecture.

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Authors: M. Naserian, M. Jooshaki, M. Fotuhi-Firuzabad, M. Hossein Mohammadi Sanjani, A. Oraee

Abstract:

In recent years, the development of communication infrastructure and smart meters have facilitated the utilization of demand-side resources which can enhance stability and economic efficiency of power systems. Direct load control programs can play an important role in the utilization of demand-side resources in the residential sector. However, investments required for installing control equipment can be a limiting factor in the development of such demand response programs. Thus, selection of consumers with higher potentials is crucial to the success of a direct load control program. Heating, ventilation, and air conditioning (HVAC) systems, which due to the heat capacity of buildings feature relatively high flexibility, make up a major part of household consumption. Considering that the consumption of HVAC systems depends highly on the ambient temperature and bearing in mind the high investments required for control systems enabling direct load control demand response programs, in this paper, a solution is presented to uncover consumers with high air conditioner demand among a large number of consumers and to measure the demand response potential of such consumers. This can pave the way for estimating the investments needed for the implementation of direct load control programs for residential HVAC systems and for estimating the demand response potentials in a distribution system. In doing so, we first cluster consumers into several groups based on the correlation coefficients between hourly consumption data and hourly temperature data using K-means algorithm. Then, by applying a recent algorithm to the hourly consumption and temperature data, consumers with high air conditioner consumption are identified. Finally, demand response potential of such consumers is estimated based on the equivalent desired temperature setpoint changes.

Keywords: Data-driven analysis, demand response, direct load control, HVAC system.

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Authors: Maria S. Trimintziou, Michael G. Sakellariou, Prodromos N. Psarropoulos

Abstract:

The current study focuses on the seismic design of offshore pipelines against active faults. After an extensive literature review of the provisions of the seismic norms worldwide and of the available analytical methods, the study simulates numerically (through finite-element modeling and strain-based criteria) the distress of offshore pipelines subjected to PGDs induced by active normal and reverse seismic faults at the seabed. Factors, such as the geometrical properties of the fault, the mechanical properties of the ruptured soil formations, and the pipeline characteristics, are examined. After some interesting conclusions regarding the seismic vulnerability of offshore pipelines, potential cost-effective mitigation measures are proposed taking into account constructability issues.

Keywords: Active faults, Seismic design, offshore pipelines.

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Authors: Marcel Shirvanian, Wolfram Lippe

Abstract:

Although the usefulness of fuzzy databases has been pointed out in several works, they are not fully developed in numerous domains. A task that is mostly disregarded and which is the topic of this paper is the determination of suitable inequalities for fuzzy sets in fuzzy query languages. This paper examines which kinds of fuzzy inequalities exist at all. Afterwards, different procedures are presented that appear theoretically appropriate. By being applied to various examples, their strengths and weaknesses are revealed. Furthermore, an algorithm for an efficient computation of the selected fuzzy inequality is shown.

Keywords: Fuzzy Databases, Fuzzy Inequalities, Fuzzy QueryLanguages, Fuzzy Ranking.

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Authors: T. Taufik, R. Prasetyo, D. Dolan, D. Garinto

Abstract:

Today-s Voltage Regulator Modules (VRMs) face increasing design challenges as the number of transistors in microprocessors increases per Moore-s Law. These challenges have recently become even more demanding as microprocessors operate at sub voltage range at significantly high current. This paper presents a new multiphase topology with cell configuration for improved performance in low voltage and high current applications. A lab scale hardware prototype of the new topology was design and constructed. Laboratory tests were performed on the proposed converter and compared with a commercially available VRM. Results from the proposed topology exhibit improved performance compared to the commercially available counterpart.

Keywords: Voltage Regulator Modules, dc-dc converters, powerelectronics.

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Authors: Daniel M. Muntean, Viorel Ungureanu

Abstract:

More than half of the urban population in Romania lives today in residential buildings made out of large prefabricated reinforced concrete panels. Since their initial design was made in the 1960’s, these housing units are now being technically and morally outdated, consuming large amounts of energy for heating, cooling, ventilation and lighting, while failing to meet the needs of the contemporary life-style. Due to their widespread use, the design of a system that improves their energy efficiency would have a real impact, not only on the energy consumption of the residential sector, but also on the quality of life that it offers. Furthermore, with the transition of today’s existing power grid to a “smart grid”, buildings could become an active element for future electricity networks by contributing in micro-generation and energy storage. One of the most addressed issues today is to find locally adapted strategies that can be applied considering the 20-20-20 EU policy criteria and to offer sustainable and innovative solutions for the cost-optimal energy performance of buildings adapted on the existing local market. This paper presents a possible adaptive design scenario towards sustainable retrofitting of these housing units. The apartments are transformed in order to meet the current living requirements and additional extensions are placed on top of the building, replacing the unused roof space, acting not only as housing units, but as active solar energy collection systems. An adaptive building envelope is ensured in order to achieve overall air-tightness and an elevator system is introduced to facilitate access to the upper levels.

Keywords: Adaptive building, energy efficiency, retrofitting, residential buildings, smart grid.

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper examines the problem of designing a robust H8 state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H8 performance are derived. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard nonlinear two-time scale systems. A numerical example is provided to illustrate the design developed in this paper.

Keywords: TS fuzzy, Markovian jumps, LMI, two-time scale systems.

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