Search results for: Flexible Manufacturing System

Authors: Lari Kela

Abstract:

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

Keywords: adaptive, damper, hydraulics, pressure, pulsating

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Authors: Marc Landry, Azeddine Kaddouri, Yassine Bouslimani, Mohsen Ghribi

Abstract:

In this paper, a new alignment method based on the particle swarm optimization (PSO) technique is presented. The PSO algorithm is used for locating the optimal coupling position with the highest optical power with three-degrees of freedom alignment. This algorithm gives an interesting results without a need to go thru the complex mathematical modeling of the alignment system. The proposed algorithm is validated considering practical tests considering the alignment of two Single Mode Fibers (SMF) and the alignment of SMF and PCF fibers.

Keywords: Particle-swarm optimization, optical fiber, automatic alignment.

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Authors: Li-Chung Su, Chia-Yu Chen, Tzu-Yuan Lai, Sheng-Jye Hwang

Abstract:

Mechanical design of the thin-film solar framed module and mounting system is important to enhance module reliability and to increase areas of applications. The stress induced by different mounting positions played a main role controlling the stability of the whole mechanical structure. From the finite element method, under the pressure from the back of module, the stress at Lc (center point of the Long frame) increased and the stresses at Center, Corner and Sc (center point of the Short frame) decreased while the mounting position was away from the center of the module. In addition, not only the stress of the glass but also the stress of the frame decreased. Accordingly it was safer to mount in the position away from the center of the module. The emphasis of designing frame system of the module was on the upper support of the Short frame. Strength of the overall structure and design of the corner were also important due to the complexity of the stress in the Long frame.

Keywords: Finite element method, Framed module, Mountingposition

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Authors: H. Ghanbari, H. Nikbakht, A. Zahedi, M. Ghanbari

Abstract:

This paper is focusing on designing a control system for wind turbine which can control the speed and output power according to arbitrary algorithm. Reference Tracking Method is used to control the turbine spinning speed in order to increase its output energy.

Keywords: Wind Turbine, Simulink, Reference Tracking Method.

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Authors: Luminiţa Duţică

Abstract:

For the music composer Myriam Marbe the musical time and memory represent 2 (complementary) phenomena with conclusive impact on the settlement of new musical ontologies. Summarizing the most important achievements of the contemporary techniques of composition, her vision on the microform presented in The Concert for Daniel Kientzy, saxophone and orchestra transcends the linear and unidirectional time in favour of a flexible, multivectorial speech with spiral developments, where the sound substance is auto(re)generated by analogy with the fundamental processes of the memory. The conceptual model is of an archetypal essence, the music composer being concerned with identifying the mechanisms of the creation process, especially of those specific to the collective creation (of oral tradition). Hence the spontaneity of expression, improvisation tint, free rhythm, micro-interval intonation, coloristictimbral universe dominated by multiphonics and unique sound effects, hence the atmosphere of ritual, however purged by the primary connotations and reprojected into a wonderful spectacular space. The Concert is a work of artistic maturity and enforces respect, among others, by the timbral diversity of the three species of saxophone required by the music composer (baritone, sopranino and alt), in Part III Daniel Kientzy shows the performance of playing two saxophones concomitantly. The score of the music composer Myriam Marbe contains a deeply spiritualized music, full or archetypal symbols, a music whose drama suggests a real cinematographic movement.

Keywords: Archetype, chronogenesis, concert, multiphonics.

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Authors: David M. Jenkins Jr.

Abstract:

Scale Time Offset Robust Modulation (STORM) [1]– [3] is a high bandwidth waveform design that adds time-scale to embedded reference modulations using only time-delay [4]. In an environment where each user has a specific delay and scale, identification of the user with the highest signal power and that user-s phase is facilitated by the STORM processor. Both of these parameters are required in an efficient multiuser detection algorithm. In this paper, the STORM modulation approach is evaluated with a direct sequence spread quadrature phase shift keying (DS-QPSK) system. A misconception of the STORM time scale modulation is that a fine temporal resolution is required at the receiver. STORM will be applied to a QPSK code division multiaccess (CDMA) system by modifying the spreading codes. Specifically, the in-phase code will use a typical spreading code, and the quadrature code will use a time-delayed and time-scaled version of the in-phase code. Subsequently, the same temporal resolution in the receiver is required before and after the application of STORM. In this paper, the bit error performance of STORM in a synchronous CDMA system is evaluated and compared to theory, and the bit error performance of STORM incorporated in a single user WCDMA downlink is presented to demonstrate the applicability of STORM in a modern communication system.

Keywords: Pseudonoise coded communication, Cyclic codes, Code division multiaccess

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Authors: Mehmet Savsar

Abstract:

This paper presents a model for an unreliable production line, which is operated according to demand with constant work-in-process (CONWIP). A simulation model is developed based on the discrete model and several case problems are analyzed using the model. The model is utilized to optimize storage space capacities at intermediate stages and the number of kanbans at the last stage, which is used to trigger the production at the first stage. Furthermore, effects of several line parameters on production rate are analyzed using design of experiments.

Keywords: Production line simulator, Push-pull system, JIT system, Constant WIP, Machine failures.

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Authors: M.G.A. Nassef, Linghan Li, C. Schenck, B. Kuhfuss

Abstract:

Design and modeling of nonlinear systems require the knowledge of all inside acting parameters and effects. An empirical alternative is to identify the system-s transfer function from input and output data as a black box model. This paper presents a procedure using least squares algorithm for the identification of a feed drive system coefficients in time domain using a reduced model based on windowed input and output data. The command and response of the axis are first measured in the first 4 ms, and then least squares are applied to predict the transfer function coefficients for this displacement segment. From the identified coefficients, the next command response segments are estimated. The obtained results reveal a considerable potential of least squares method to identify the system-s time-based coefficients and predict accurately the command response as compared to measurements.

Keywords: feed drive systems, least squares algorithm, onlineparameter identification, short time window

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Authors: B. Singh, A. Singh, R. C. Yadav

Abstract:

Utmost care of human related issues are essentially required for sustainable growth of micro, small and medium enterprises (MSMEs) of India, as these MSMEs are contributing enormously to socio-economic development of country. In this research, aspects related to human factors and functioning of MSMEs of India were studied. The investigation, based on a survey of 84 MSMEs of India cited that the enterprises are mostly employing unskilled labor whose wages are less with poor training. In spite of reported minor accidents, attention towards safety is poorly paid. To meet-out the production target, MSMEs generally employ over-time and payment towards this overtime is sometimes missing. Hence, honest and humanitarian attention for better human resources is needed to improve the performance and competitiveness of MSMEs of India.

Keywords: Human factors, Small and medium enterprises, Working culture.

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Authors: Hany Mahgoub

Abstract:

This paper presents a system for discovering association rules from collections of unstructured documents called EART (Extract Association Rules from Text). The EART system treats texts only not images or figures. EART discovers association rules amongst keywords labeling the collection of textual documents. The main characteristic of EART is that the system integrates XML technology (to transform unstructured documents into structured documents) with Information Retrieval scheme (TF-IDF) and Data Mining technique for association rules extraction. EART depends on word feature to extract association rules. It consists of four phases: structure phase, index phase, text mining phase and visualization phase. Our work depends on the analysis of the keywords in the extracted association rules through the co-occurrence of the keywords in one sentence in the original text and the existing of the keywords in one sentence without co-occurrence. Experiments applied on a collection of scientific documents selected from MEDLINE that are related to the outbreak of H5N1 avian influenza virus.

Keywords: Association rules, information retrieval, knowledgediscovery in text, text mining.

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Authors: Claudia L. Zuñiga, Andres F. Millan, Jose L. Abadia, Monica Lora, Andres Navarro, Juan C. Burguillo, Pedro S. Rodriguez

Abstract:

The increasing popularity of wireless technologies and mobile computing devices has enabled new application areas and research. One of these new areas is pervasive systems in urban environments, because urban environments are characterized by high concentration of these technologies and devices. In this paper we will show the process of pervasive system design in urban environments, using as use case a local zoo in Cali, Colombia. Based on an ethnographic studio, we present the design of a pervasive system for urban computing based on service oriented architecture to controlled environment of Cali Zoo. In this paper, the reader will find a methodological approach for the design of similar systems, using data collection methods, conceptual frameworks for urban environments and considerations of analysis and design of service oriented systems.

Keywords: Service Oriented Architecture, Urban Computing, Design of pervasive systems for urban environments, PSP Design Framework (Public Social Private), Cali Zoo.

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Authors: K. Prajindra Sankar, S.K. Tiong, S.P. Johnny Koh

Abstract:

This paper presents a tested research concept that implements a complex evolutionary algorithm, genetic algorithm (GA), in a multi-microcontroller environment. Parallel Distributed Genetic Algorithm (PDGA) is employed in adaptive beam forming technique to reduce power usage of adaptive antenna at WCDMA base station. Adaptive antenna has dynamic beam that requires more advanced beam forming algorithm such as genetic algorithm which requires heavy computation and memory space. Microcontrollers are low resource platforms that are normally not associated with GAs, which are typically resource intensive. The aim of this project was to design a cooperative multiprocessor system by expanding the role of small scale PIC microcontrollers to optimize WCDMA base station transmitter power. Implementation results have shown that PDGA multi-microcontroller system returned optimal transmitted power compared to conventional GA.

Keywords: Microcontroller, Genetic Algorithm, Adaptiveantenna, Power optimization.

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Authors: A. Bulatbayeva, A. Kusainov

Abstract:

In this article has been analyzed Kazakhstani experience in organizing the system after the institute of higher education, legislative-regulative assurance of master preparation, and statistic data in the republic. Have been the features of projecting the master programs, a condition of realization of studying credit system, have been analyzed the technologies of research teaching masters. In conclusion have been given some recommendation on creating personal-oriented environment of research teaching masters.

Keywords: Personal-oriented Environment, Research Teaching, Research Activity, the Technologies of Research Teaching

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Authors: Ali Beydoun, Van-Tam Nguyen, Patrick Loumeau

Abstract:

Time interleaved sigma-delta (TIΣΔ) architecture is a potential candidate for high bandwidth analog to digital converters (ADC) which remains a bottleneck for software and cognitive radio receivers. However, the performance of the TIΣΔ architecture is limited by the unavoidable gain and offset mismatches resulting from the manufacturing process. This paper presents a novel digital calibration method to compensate the gain and offset mismatch effect. The proposed method takes advantage of the reconstruction digital signal processing on each channel and requires only few logic components for implementation. The run time calibration is estimated to 10 and 15 clock cycles for offset cancellation and gain mismatch calibration respectively.

Keywords: sigma-delta, calibration, gain and offset mismatches, analog-to-digital conversion, time-interleaving.

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Authors: M. H. Hairi, H. Zainuddin, M.H.N. Talib, A. Khamis, J. Y. Lichun

Abstract:

Short circuit currents plays a vital role in influencing the design and operation of equipment and power system and could not be avoided despite careful planning and design, good maintenance and thorough operation of the system. This paper discusses the short circuit analysis conducted in KSO briefly comprising of its significances, methods and results. A result sample of the analysis based on a single transformer is detailed in this paper. Furthermore, the results of the analysis and its significances were also discussed and commented.

Keywords: Short circuit currents, Transformer fault current

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Authors: Masood Karamoozian, Zhang Hong

Abstract:

The necessity and complexity of the decision-making process and the interference of the various factors to make decisions and consider all the relevant factors in a problem are very obvious nowadays. Hence, researchers show their interest in multi-criteria decision-making methods. In this research, the Analytical Hierarchy Process (AHP), Simple Additive Weighting (SAW), and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods of multi-criteria decision-making have been used to solve the problem of optimal construction systems. Systems being evaluated in this problem include; Light Steel Frames (LSF), a case study of designs by Zhang Hong studio in the Southeast University of Nanjing, Insulating Concrete Form (ICF), Ordinary Construction System (OCS), and Precast Concrete System (PRCS) as another case study designs in Zhang Hong studio in the Southeast University of Nanjing. Crowdsourcing was done by using a questionnaire at the sample level (200 people). Questionnaires were distributed among experts in university centers and conferences. According to the results of the research, the use of different methods of decision-making led to relatively the same results. In this way, with the use of all three multi-criteria decision-making methods mentioned above, the PRCS was in the first rank, and the LSF system ranked second. Also, the PRCS, in terms of performance standards and economics, was ranked first, and the LSF system was allocated the first rank in terms of environmental standards.

Keywords: Multi-criteria decision making, AHP, SAW, TOPSIS.

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Authors: Huaiyu Zhang

Abstract:

The method of modeling is the key technology for digital mockup (DMU). Based upon the developing for mechanical product DMU, the theory, method and approach for virtual environment (VE) and virtual object (VO) were studied. This paper has expounded the design goal and architecture of DMU system, analyzed the method of DMU application, and researched the general process of physics modeling and behavior modeling.

Keywords: DMU, VR, virtual environment, virtual object, physics modeling, behavior modeling

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Authors: Mohamad Sukeri Khalid, Che Su Mustaffa, Mohd Najib Marzuki, Mohd Fo’ad Sakdan, Sapora Sipon, Mohd Taib Ariffin, Shazwani Shafiai

Abstract:

This paper describes the issues relating to the role of the flash flood early warning system provided by the Malaysian Government to the communities in Malaysia, specifically during the flash flood disaster in the Cameron Highlands, Malaysia. Normally, flash flood disasters can occur as a result of heavy rainfall in an area, and that water may possibly cause flooding via streams or narrow channels. The focus of this study is the flash flood disaster which occurred on 23 October 2013 in the Cameron Highlands, and as a result the Sungai Bertam overflowed after the release of water from the Sultan Abu Bakar Dam. This release of water from the dam caused flash flooding which led to damage to properties and also the death of residents and livestock in the area. Therefore, the effort of this study is to identify the perceptions of the flash flood victims on the role of the flash flood early warning system. For the purposes of this study, data were gathered through face-to-face interviews from those flood victims who were willing to participate in this study. This approach helped the researcher to glean in-depth information about their feelings and perceptions of the role of the flash flood early warning system offered by the government. The data were analysed descriptively and the findings show that the respondents of 22 flood victims believe strongly that the flash flood early warning system was confusing and dysfunctional, and communities had failed to response positively to it. Therefore, most of the communities were not well prepared for the releasing of water from the dam which caused property damage, and 3 people were killed in the Cameron Highland flash flood disaster.

Keywords: Communities affected, disaster management, early warning system, flash flood disaster.

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Authors: F.Agalianos, S.Patelis , P. Kyratsis, E. Maravelakis, E.Vasarmidis, A.Antoniadis

Abstract:

Laser engraving is a manufacturing method for those applications where previously Electrical Discharge Machining (EDM) was the only choice. Laser engraving technology removes material layer-by-layer and the thickness of layers is usually in the range of few microns. The aim of the present work is to investigate the influence of the process parameters on the surface quality when machined by laser engraving. The examined parameters were: the pulse frequency, the beam speed and the layer thickness. The surface quality was determined by the surface roughness for every set of parameters. Experimental results on Al7075 material showed that the surface roughness strictly depends on the process parameters used.

Keywords: Laser engraving, Al7075, Yb: YAG laser, laser process parameters, material roughness.

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Authors: Christian Mayr, Matthias Ehrlich, Stephan Henker, Karsten Wendt, René Schüffny

Abstract:

Traditionally, VLSI implementations of spiking neural nets have featured large neuron counts for fixed computations or small exploratory, configurable nets. This paper presents the system architecture of a large configurable neural net system employing a dedicated mapping algorithm for projecting the targeted biology-analog nets and dynamics onto the hardware with its attendant constraints.

Keywords: Large scale VLSI neural net, topology mapping, complex pulse communication.

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Authors: Mahboubeh Molaei

Abstract:

Transferring information developed by other peoples is an ordinary event that happens during daily conversations, for example when employees sea each other in the organization, or when they are having lunch together, or attending a meeting, they use to talk about their experience, and discuss about their current projects, and talk about their successes over some specific problems. Despite the potential value of leveraging organizational memory and expertise by using OMS and ER, still small organizations haven-t been able to capitalize on its promised value. Each organization has its internal knowledge management system, in some of organizations the system face the lack of expert people to save their experience in the repository and in another hand on some other organizations there are lots of expert people but the organization doesn-t have the maximum use of their knowledge.

Keywords: Knowledge, knowledge management.

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Authors: P.Varzakas

Abstract:

In this paper, an accurate theoretical analysis for the achievable average channel capacity (in the Shannon sense) per user of a hybrid cellular direct-sequence/fast frequency hopping code-division multiple-access (DS/FFH-CDMA) system operating in a Rayleigh fading environment is presented. The analysis covers the downlink operation and leads to the derivation of an exact mathematical expression between the normalized average channel capacity available to each system-s user, under simultaneous optimal power and rate adaptation and the system-s parameters, as the number of hops per bit, the processing gain applied, the number of users per cell and the received signal-tonoise power ratio over the signal bandwidth. Finally, numerical results are presented to illustrate the proposed mathematical analysis.

Keywords: Shannon capacity, adaptive systems, code-division multiple access, fading channels.

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Authors: Baseem Khan, Ganga Agnihotri

Abstract:

Restructuring of Electricity supply industry introduced many issues such as transmission pricing, transmission loss allocation and congestion management. Many methodologies and algorithms were proposed for addressing these issues. In this paper a power flow tracing based method is proposed which involves Matrices methodology for the transmission usage and loss allocation for generators and demands. This method provides loss allocation in a direct way because all the computation is previously done for usage allocation. The proposed method is simple and easy to implement in a large power system. Further it is less computational because it requires matrix inversion only a single time. After usage and loss allocation cooperative game theory is applied to results for finding efficient economic signals. Nucleolus and Shapely value approach is used for optimal allocation of results. Results are shown for the IEEE 6 bus system and IEEE 14 bus system.

Keywords: Modified Kirchhoff Matrix, Power flow tracing, Transmission Pricing, Transmission Loss Allocation.

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Authors: Kyung-Jung Lee, Young-Hun Ki, Hyun-Sik Ahn

Abstract:

In this paper, we propose a hardware and software design method for automotive Electronic Control Units (ECU) considering the functional safety. The proposed ECU is considered for the application to Electro-Mechanical Actuator systems and the validity of the design method is shown by the application to the Electro-Mechanical Brake (EMB) control system which is used as a brake actuator in Brake-By-Wire (BBW) systems. The importance of a functional safety-based design approach to EMB ECU design has been emphasized because of its safety-critical functions, which are executed with the aid of many electric actuators, sensors, and application software. Based on hazard analysis and risk assessment according to ISO26262, the EMB system should be ASIL-D-compliant, the highest ASIL level. To this end, an external signature watchdog and an Infineon 32-bit microcontroller TriCore are used to reduce risks considering common-cause hardware failure. Moreover, a software design method is introduced for implementing functional safety-oriented monitoring functions based on an asymmetric dual core architecture considering redundancy and diversity. The validity of the proposed ECU design approach is verified by using the EMB Hardware-In-the-Loop (HILS) system, which consists of the EMB assembly, actuator ECU, a host PC, and a few debugging devices. Furthermore, it is shown that the existing sensor fault tolerant control system can be used more effectively for mitigating the effects of hardware and software faults by applying the proposed ECU design method.

Keywords: BBW (Brake-By-wire), EMB (Electro-Mechanical Brake), Functional Safety, ISO26262.

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Authors: Hee Suk Seo, Tae Kyung Kim

Abstract:

Adapting wireless devices to communicate within grid networks empowers us by providing range of possibilities.. These devices create a mechanism for consumers and publishers to create modern networks with or without peer device utilization. Emerging mobile networks creates new challenges in the areas of reliability, security, and adaptability. In this paper, we propose a system encompassing mobility management using AAA context transfer for mobile grid networks. This system ultimately results in seamless task processing and reduced packet loss, communication delays, bandwidth, and errors.

Keywords: Mobile Grid, AAA, Mobility Management.

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Authors: Doaa M. Atia, Faten H. Fahmy, Ninet M. Ahmed, Hassen T. Dorrah

Abstract:

Fuel cells have become one of the major areas of research in the academia and the industry. The goal of most fish farmers is to maximize production and profits while holding labor and management efforts to the minimum. Risk of fish kills, disease outbreaks, poor water quality in most pond culture operations, aeration offers the most immediate and practical solution to water quality problems encountered at higher stocking and feeding rates. Many units of aeration system are electrical units so using a continuous, high reliability, affordable, and environmentally friendly power sources is necessary. Aeration of water by using PEM fuel cell power is not only a new application of the renewable energy, but also, it provides an affordable method to promote biodiversity in stagnant ponds and lakes. This paper presents a new design and control of PEM fuel cell powered a diffused air aeration system for a shrimp farm in Mersa Matruh in Egypt. Also Artificial intelligence (AI) techniques control is used to control the fuel cell output power by control input gases flow rate. Moreover the mathematical modeling and simulation of PEM fuel cell is introduced. A comparison study is applied between the performance of fuzzy logic control (FLC) and neural network control (NNC). The results show the effectiveness of NNC over FLC.

Keywords: PEM fuel cell, Diffused aeration system, Artificialintelligence (AI) techniques, neural network control, fuzzy logiccontrol

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Authors: Barenten Suciu

Abstract:

In this paper, effectiveness of a machine design process is evaluated on the basis of the specific output calculus. Concretely, a screw-worm gear mechanical transmission is designed by using the classical and the 3D-CAD methods. Strength analysis and drawing of the designed parts is substantially aided by employing the SolidWorks software. Quality of the design process is assessed by manufacturing (printing) the parts, and by computing the efficiency, specific load, as well as the specific output (work) of the mechanical transmission. Influence of the stroke, travelling velocity and load on the mechanical output, is emphasized. Optimal design of the mechanical transmission becomes possible by the appropriate usage of the acquired results.

Keywords: Mechanical transmission, design, screw, worm-gear, efficiency, specific output, 3D-printing.

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Authors: Yi Chao Huang, Yu Ling Liao, Chiu Shuang Lin

Abstract:

A data cutting and sorting method (DCSM) is proposed to optimize the performance of data mining. DCSM reduces the calculation time by getting rid of redundant data during the data mining process. In addition, DCSM minimizes the computational units by splitting the database and by sorting data with support counts. In the process of searching for the relationship between metabolic syndrome and lifestyles with the health examination database of an electronics manufacturing company, DCSM demonstrates higher search efficiency than the traditional Apriori algorithm in tests with different support counts.

Keywords: Data mining, Data cutting and sorting method, Apriori algorithm, Metabolic syndrome

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Authors: Zulaiha Ali Othman, Helmi Md Rais, Abdul Razak Hamdan

Abstract:

Ants are fascinating creatures that demonstrate the ability to find food and bring it back to their nest. Their ability as a colony, to find paths to food sources has inspired the development of algorithms known as Ant Colony Systems (ACS). The principle of cooperation forms the backbone of such algorithms, commonly used to find solutions to problems such as the Traveling Salesman Problem (TSP). Ants communicate to each other through chemical substances called pheromones. Modeling individual ants- ability to manipulate this substance can help an ACS find the best solution. This paper introduces a Dynamic Ant Colony System with threelevel updates (DACS3) that enhance an existing ACS. Experiments were conducted to observe single ant behavior in a colony of Malaysian House Red Ants. Such behavior was incorporated into the DACS3 algorithm. We benchmark the performance of DACS3 versus DACS on TSP instances ranging from 14 to 100 cities. The result shows that the DACS3 algorithm can achieve shorter distance in most cases and also performs considerably faster than DACS.

Keywords: Dynamic Ant Colony System (DACS), TravelingSalesmen Problem (TSP), Optimization, Swarm Intelligent.

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Authors: Mahesh K. Chudasama, Harit K. Raval

Abstract:

3-roller conical bending process is widely used in the industries for manufacturing of conical sections and shells. It involves static as well dynamic bending stages. Analytical models for prediction of bending force during static as well as dynamic bending stage are available in the literature. In this paper bending forces required for static bending stage and dynamic bending stages have been compared using the analytical models. It is concluded that force required for dynamic bending is very less as compared to the bending force required during the static bending stage.

Keywords: Analytical modeling, cone frustum, dynamic bending, static bending.

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