Search results for: Short-Term Load Forecasting

Authors: Sang Hyun Kim

Abstract:

In this paper, a fast motion compensation algorithm is proposed that improves coding efficiency for video sequences with brightness variations. We also propose a cross entropy measure between histograms of two frames to detect brightness variations. The framewise brightness variation parameters, a multiplier and an offset field for image intensity, are estimated and compensated. Simulation results show that the proposed method yields a higher peak signal to noise ratio (PSNR) compared with the conventional method, with a greatly reduced computational load, when the video scene contains illumination changes.

Keywords: Motion estimation, Fast motion compensation, Brightness variation compensation, Brightness change detection, Cross entropy.

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Authors: M.H. Djavareshkian, A. Esmaeli

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A pressure-based implicit procedure to solve Navier- Stokes equations on a nonorthogonal mesh with collocated finite volume formulation is used to simulate flow around the smart and conventional flaps of spoiler under the ground effect. Cantilever beam with uniformly varying load with roller support at the free end is considered for smart flaps. The boundedness criteria for this procedure are determined from a Normalized Variable diagram (NVD) scheme. The procedure incorporates es the k -ε eddyviscosity turbulence model. The method is first validated against experimental data. Then, the algorithm is applied for turbulent aerodynamic flows around a spoiler section with smart and conventional flaps for different attack angle, flap angle and ground clearance where the results of two flaps are compared.

Keywords: Smart spoiler, Ground Effect, Flap, Aerodynamic coefficients, Race car.

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Authors: K. Nirmala Devi, V. Murali Bhaskaran

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Traditional document representation for classification follows Bag of Words (BoW) approach to represent the term weights. The conventional method uses the Vector Space Model (VSM) to exploit the statistical information of terms in the documents and they fail to address the semantic information as well as order of the terms present in the documents. Although, the phrase based approach follows the order of the terms present in the documents rather than semantics behind the word. Therefore, a semantic concept based approach is used in this paper for enhancing the semantics by incorporating the ontology information. In this paper a novel method is proposed to forecast the intraday stock market price directional movement based on the sentiments from Twitter and money control news articles. The stock market forecasting is a very difficult and highly complicated task because it is affected by many factors such as economic conditions, political events and investor’s sentiment etc. The stock market series are generally dynamic, nonparametric, noisy and chaotic by nature. The sentiment analysis along with wisdom of crowds can automatically compute the collective intelligence of future performance in many areas like stock market, box office sales and election outcomes. The proposed method utilizes collective sentiments for stock market to predict the stock price directional movements. The collective sentiments in the above social media have powerful prediction on the stock price directional movements as up/down by using Granger Causality test.

Keywords: Bag of Words, Collective Sentiments, Ontology, Semantic relations, Sentiments, Social media, Stock Prediction, Twitter, Vector Space Model and wisdom of crowds.

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Authors: K. -H. Yang

Abstract:

In the past, the quay crane operations have been well studied. There were a certain number of scheduling algorithms for quay crane operations, but without considering some nuisance factors that might disrupt the quay crane operations. For example, bad grapples make a crane unable to load or unload containers or a sudden strong breeze stops operations temporarily. Although these disruptive conditions randomly occur, they influence the efficiency of quay crane operations. The disruption is not considered in the operational procedures nor is evaluated in advance for its impacts. This study applies simulation and optimization approaches to develop structures of pre-analysis and post-analysis for the Quay Crane Scheduling Problem to deal with disruptive scenarios for quay crane operation. Numerical experiments are used for demonstrations for the validity of the developed approaches.

Keywords: Disruptive Quay Crane Scheduling, pre-analysis, post-analysis, disruption.

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Authors: Jin-Lung Guan, Jyh-Cherng Gu, Ming-Ta Yang, Hsin-Hung Chang, Chun-Wei Huang, Shao-Yu Huang

Abstract:

One of the most important power quality issues is voltage flicker. Nowadays this issue also impacts the power system all over the world. The fact of the matter is that the more and the larger capacity of wind generator has been installed. Under unstable wind power situation, the variation of output current and voltage have caused trouble to voltage flicker. Hence, the major purpose of this study is to analyze the impact of wind generator on voltage flicker of power system. First of all, digital simulation and analysis are carried out based on wind generator operating under various system short circuit capacity, impedance angle, loading, and power factor of load. The simulation results have been confirmed by field measurements.

Keywords: Wind Generator, Voltage Flicker

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Authors: M. H. Arslan, U. K. Sahin, H. Acikgoz-Tufan, I. Gocek, I. Erdem

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Various exterior factors have perpetual effects on textile materials during wear, use and laundering in everyday life. In accordance with their frequency of use, textile materials are required to be laundered at certain intervals. The medium in which the laundering process takes place have inevitable detrimental physical and chemical effects on textile materials caused by the unique parameters of the process inherently existing. Connatural structures of various textile materials result in many different physical, chemical and mechanical characteristics. Because of their specific structures, these materials have different behaviors against several exterior factors. By modeling the behavior of commercial and test textiles as group-wise against laundering process, it is possible to disclose the relation in between these two groups of materials, which will lead to better understanding of their behaviors in terms of similarities and differences against the washing parameters of the laundering. Thus, the goal of the current research is to examine the behavior of two groups of textile materials as commercial textiles and as test textiles towards the main washing machine parameters during laundering process such as temperature, load quantity, mechanical action and level of water amount by concentrating on shrinkage, pilling, sewing defects, collar abrasion, the other defects other than sewing, whitening and overall properties of textiles. In this study, cotton fabrics were preferred as commercial textiles due to the fact that garments made of cotton are the most demanded products in the market by the textile consumers in daily life. Full factorial experimental set-up was used to design the experimental procedure. All profiles always including all of the commercial and the test textiles were laundered for 20 cycles by commercial home laundering machine to investigate the effects of the chosen parameters. For the laundering process, a modified version of ‘‘IEC 60456 Test Method’’ was utilized. The amount of detergent was altered as 0.5% gram per liter depending on varying load quantity levels. Datacolor 650®, EMPA Photographic Standards for Pilling Test and visual examination were utilized to test and characterize the textiles. Furthermore, in the current study the relation in between commercial and test textiles in terms of their performance was deeply investigated by the help of statistical analysis performed by MINITAB® package program modeling their behavior against the parameters of the laundering process. In the experimental work, the behaviors of both groups of textiles towards washing machine parameters were visually and quantitatively assessed in dry state.

Keywords: Behavior against washing machine parameters, performance evaluation of textiles, statistical analysis, commercial and test textiles.

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Authors: M. R. Haboğlu, A. Kurşun, Ş. Aksoy, H. Aykul, N. B. Bektaş

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Athermal elastic stress analysis of steel fiber reinforced aluminum laminated composite plate is investigated. Four sides of the composite plate are clamped and subjected to a uniform temperature load. The analysis is performed both analytically and numerically. Laminated composite is manufactured via hot pressing method. The investigation of the effects of the orientation angle is provided. Different orientation angles are used such as [0°/90°]s, [30°/-30°]s, [45°/-45°]s, and [60/-60]s. The analytical solution is obtained via classical laminated composite theory and the numerical solution is obtained by applying finite element method via ANSYS.

Keywords: Laminated Composites, Thermo Elastic Stress, Finite Element Method.

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Authors: O. Arikan, C. Kocatepe, G. Ucar, Y. Hacialiefendioglu

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In this paper, influence of harmonics on medium voltage distribution system of Bogazici Electricity Distribution Inc. (BEDAS) which takes place at Istanbul/Turkey is investigated. A ring network consisting of residential loads is taken into account for this study. Real system parameters and measurement results are used for simulations. Also, probable working conditions of the system are analyzed for 50%, 75%, and 100% loading of transformers with similar harmonic contents. Results of the study are exhibited the influence of nonlinear loads on %THDV, P.F. and technical losses of the medium voltage distribution system.

Keywords: Distribution system, harmonic, technical losses, power factor (PF), total harmonic distortion (THD), residential load, medium voltage.

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Authors: E. Doğan, B. Kekezoğlu

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Voltage level must be raised in order to deliver the produced energy to the consumption zones with less loss and less cost. Power transformers used to raise or lower voltage are important parts of the energy transmission system. Power transformers used in switchgear and power generation plants stay in human's intensive habitat zones as a result of expanding cities. Accordingly, noise levels produced by power transformers have begun more and more important and they have established itself as one of the research field. In this research, the noise cause on transformers has been investigated, it's causes has been examined and noise measurement techniques have been introduced. Examples of transformer noise test results are submitted and precautions to be taken were discussed for the purpose of decreasing of the noise which will occurred by transformers.

Keywords: Power transformer, noise measurement, core noise, load noise, fan-pump noise.

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Authors: Haidy S. Ghali, Engy Serag, A. Samer Ezeldin

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Copper is an essential raw material used in the construction industry. During 2021 and the first half of 2022, the global market suffered from a significant fluctuation in copper raw material prices due to the aftermath of both the COVID-19 pandemic and the Russia-Ukraine war which exposed its consumers to an unexpected financial risk. Thereto, this paper aims to develop two hybrid price prediction models using artificial neural network and long short-term memory (ANN-LSTM), by Python, that can forecast the average monthly copper prices, traded in the London Metal Exchange; the first model is a multivariate model that forecasts the copper price of the next 1-month and the second is a univariate model that predicts the copper prices of the upcoming three months. Historical data of average monthly London Metal Exchange copper prices are collected from January 2009 till July 2022 and potential external factors are identified and employed in the multivariate model. These factors lie under three main categories: energy prices, and economic indicators of the three major exporting countries of copper depending on the data availability. Before developing the LSTM models, the collected external parameters are analyzed with respect to the copper prices using correlation, and multicollinearity tests in R software; then, the parameters are further screened to select the parameters that influence the copper prices. Then, the two LSTM models are developed, and the dataset is divided into training, validation, and testing sets. The results show that the performance of the 3-month prediction model is better than the 1-month prediction model; but still, both models can act as predicting tools for diverse economic situations.

Keywords: Copper prices, prediction model, neural network, time series forecasting.

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Authors: Bachir Belmadani, Rachid Taleb, Zinelaabidine Boudjema, Adil Yahdou

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Carrier-based methods have been used widely for switching of multilevel inverters due to their simplicity, flexibility and reduced computational requirements compared to space vector modulation (SVM). This paper focuses on Multicarrier Sinusoidal Pulse Width Modulation (MCSPWM) strategy for the three phase Five-Level Flying Capacitor Inverter (5LFCI). The inverter is simulated for Induction Motor (IM) load and Total Harmonic Distortion (THD) for output waveforms is observed for different controlling schemes.

Keywords: Flying capacitor inverter, multicarrier sinusoidal pulse width modulation, space vector modulation, total harmonic distortion, induction motor.

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Authors: George Cristian Gruia, Michal Kavan

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The article describes a case study on one of Czech Republic-s manufacturing middle size enterprises (ME), where due to the European financial crisis, production lines had to be redesigned and optimized in order to minimize the total costs of the production of goods. It is considered an optimization problem of minimizing the total cost of the work load, according to the costs of the possible locations of the workplaces, with an application of the Greedy algorithm and a partial analogy to a Set Packing Problem. The displacement of working tables in a company should be as a one-toone monotone increasing function in order for the total costs of production of the goods to be at minimum. We use a heuristic approach with greedy algorithm for solving this linear optimization problem, regardless the possible greediness which may appear and we apply it in a Czech ME.

Keywords: Czech, greedy algorithm, minimize, total costs.

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Authors: K. Kamalanand, P. Mannar Jawahar

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Methods of contemporary mathematical physics such as chaos theory are useful for analyzing and understanding the behavior of complex biological and physiological systems. The three dimensional model of HIV/AIDS is the basis of active research since it provides a complete characterization of disease dynamics and the interaction of HIV-1 with the immune system. In this work, the behavior of the HIV system is analyzed using the three dimensional HIV model and a chaotic measure known as the Hurst exponent. Results demonstrate that Hurst exponents of CD4, CD8 cells and viral load vary nonlinearly with respect to variations in system parameters. Further, it was observed that the three dimensional HIV model can accommodate both persistent (H>0.5) and anti-persistent (H<0.5) dynamics of HIV states. In this paper, the objectives of the study, methodology and significant observations are presented in detail.

Keywords: HIV/AIDS, mathematical model, chaos theory, Hurst exponent

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Authors: Bi-Huei Tsai

Abstract:

Prior research has not effectively investigated how the profitability of Chinese branches affect FDIs in China [1, 2], so this study for the first time incorporates realistic earnings information to systematically investigate effects of innovation, imitation, and profit factors of FDI diffusions from Taiwan to China. Our nonlinear least square (NLS) model, which incorporates earnings factors, forms a nonlinear ordinary differential equation (ODE) in numerical simulation programs. The model parameters are obtained through a genetic algorithms (GA) technique and then optimized with the collected data for the best accuracy. Particularly, Taiwanese regulatory FDI restrictions are also considered in our modified model to meet the realistic conditions. To validate the model-s effectiveness, this investigation compares the prediction accuracy of modified model with the conventional diffusion model, which does not take account of the profitability factors. The results clearly demonstrate the internal influence to be positive, as early FDI adopters- consistent praises of FDI attract potential firms to make the same move. The former erects a behavior model for the latter to imitate their foreign investment decision. Particularly, the results of modified diffusion models show that the earnings from Chinese branches are positively related to the internal influence. In general, the imitating tendency of potential consumers is substantially hindered by the losses in the Chinese branches, and these firms would invest less into China. The FDI inflow extension depends on earnings of Chinese branches, and companies will adjust their FDI strategies based on the returns. Since this research has proved that earning is an influential factor on FDI dynamics, our revised model explicitly performs superior in prediction ability than conventional diffusion model.

Keywords: diffusion model, genetic algorithms, nonlinear leastsquares (NLS) model, prediction error.

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Authors: Abdolamir Nekoubin

Abstract:

The line start permanent magnet motor (LSPMM) combines a permanent magnet rotor for a better motor efficiency during synchronous running with an induction motor squirrel cage rotor to permit the motor starting by direct coupling to power source. In this paper effect of the rotor structure on a line start synchronous permanent magnet motor (LSPMM) is analyzed. LSPMM motor with three different structures for rotor is designed by using RMxprt software; efficiency and line current of LSPMM motor for different structures in full-load condition have been presented. The results indicate that with correct choosing of rotor structure, maximum efficiency can be found.

Keywords: Permanent magnets, LSPMM motor, rotor.

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Authors: İsmail Aksoy, Hacı Bodur, Nihan Altıntas

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This paper introduces a boost converter with a new active snubber cell. In this circuit, all of the semiconductor components in the converter softly turns on and turns off with the help of the active snubber cell. Compared to the other converters, the proposed converter has advantages of size, number of components and cost. The main feature of proposed converter is that the extra voltage stresses do not occur on the main switches and main diodes. Also, the current stress on the main switch is acceptable level. Moreover, the proposed converter can operates under light load conditions and wide input line voltage. In this study, the operating principle of the proposed converter is presented and its operation is verified with the Proteus simulation software for a 1 kW and 100 kHz model.

Keywords: Active snubber cell, boost converter, zero current switching, zero voltage switching.

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Authors: Shao-Ku Kao

Abstract:

This paper presents an active rectifier with time-domain delay compensation to enhance the efficiency. A delay calibration circuit is designed to convert delay time to voltage and adaptive control on/off delay in variable input voltage. This circuit is designed in 0.18 mm CMOS process. The input voltage range is from 2 V to 3.6 V with the output voltage from 1.8 V to 3.4 V. The efficiency can maintain more than 85% when the load from 50 Ω ~ 1500 Ω for 3.6 V input voltage. The maximum efficiency is 92.4 % at output power to be 38.6 mW for 3.6 V input voltage.

Keywords: Wireless power transfer, active diode, delay compensation, time to voltage converter, PCE.

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Authors: Min Goo Lee, Yong Kuk Park, Kyung Kwon Jung, Jun Jae Yoo

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This paper describes the smart energy monitoring system with a wireless sensor network for monitoring of electrical usage in smart house. Proposed system is composed of wireless plugs and energy control wallpad server. The wireless plug integrates an AC power socket, a relay to switch the socket ON/OFF, a Hall effect sensor to sense current of load appliance and a Kmote. The Kmote is a wireless communication interface based on TinyOS. We evaluated wireless plug in a laboratory, analyzed and presented energy consumption data from electrical appliances for 3 months in home.

Keywords: smart house, energy monitoring, wireless plug, wireless sensor network, current consumption.

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Authors: H. Zengin, M. E. Turan, Y. Turen, H. Ahlatci, Y. Sun

Abstract:

This study aimed for improving wear resistance of AM60 magnesium alloy by Ti addition (0, 0.2, 0.5, 1wt%Ti). An electric resistance furnace was used to produce alloys. Pure Mg together with Al, Al-Ti and Al-Mn were melted at 750 ⁰C in a stainless steel crucible under controlled Ar gas atmosphere and then poured into a metal mould preheated at 250 ⁰C. Microstructure characterizations were performed by light optical (LOM) and scanning electron microscope (SEM) after the wear test. Wear rates and friction coefficients were measured with a pin-on-disk type UTS-10 Tribometer test device under a load of 20N. The results showed that Ti addition altered the morphology and the amount of b-Mg₁₇Al₁₂ phase in the microstructure of AM60 alloy. b-Mg₁₇Al₁₂ phases on the grain boundaries were refined with increasing amount of Ti. An improvement in wear resistance of AM60 alloy was observed due to the alteration in the microstructure by Ti addition.

Keywords: Magnesium alloy, titanium, SEM, wear.

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Authors: Antônio P. de Araújo Neto, Ruy D. A. da Silva Neto, Juliana R. de Souza, Salete K. P. de Medeiros, João T. N. de Medeiros

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The tribological test with Pin-On-Disc configuration measures friction and wear properties in dry or lubricated sliding surfaces of a variety of materials and coatings. Polymeric matrix composites loaded with mineral filler were used, 1%, 3%, 10%, 30%, and 50% mass percentage of filler, to reduce the material cost by using mineral tailings. Using a pin-on-disc tribometer to quantify coefficient of friction and wear resistance of the specimens. The parameters known to performing the test were 300 rpm rotation, normal load of 16N and duration of 33.5 minutes. The composite with 10% mineral filler performed better, considering that the wear resistance was good when compared to the other compositions and an average low coefficient of friction, in the order of μ ≤ 0.15.

Keywords: Microcomposites, microparticles tailings of scheelite, PTFE, tribology.

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Authors: D. B. Gohil

Abstract:

Closed die forging is a very complex process, and measurement of actual forces for real material is difficult and time consuming. Hence, the modelling technique has taken the advantage of carrying out the experimentation with the proper model material which needs lesser forces and relatively low temperature. The results of experiments on the model material then may be correlated with the actual material by using the theory of similarity. There are several methods available to resolve the complexity involved in the closed die forging process. Finite Element Method (FEM) and Finite Difference Method (FDM) are relatively difficult as compared to the slab method. The slab method is very popular and very widely used by the people working on shop floor because it is relatively easy to apply and reasonably accurate for most of the common forging load requirement computations.

Keywords: Experimentation, forging, process modeling, strain distribution.

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Authors: F. Gurkalo, K. Poutos

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Earthquakes produce some of the most violent loading situations that a structure can be subjected to and if a structure fails under these loads then inevitably human life is put at risk. One of the most common methods by which a structure fails under seismic loading is at the connection of structural elements. The research presented in this paper investigates the interlock systems as a novel method for building structures. The main objective of this experimental study wasto determine the dynamic characteristics and the seismic behaviour of the proposed structures compared to conventional structural systemsduring seismic motions. Results of this study indicate that the interlock mechanism of the panels influences the behaviour of lateral load-resisting systems of the structures during earthquakes, contributing to better structural flexibility and easier maintenance.

Keywords: Watertower, earthquake, seismic, interlocked panels

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Authors: M. Li, V. D. Thi, M. Khelifa, M. El Ganaoui

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This study presents an overview of the work carried out by the use of wood waste as coarse aggregate in mortar. The paper describes experimental and numerical investigations carried on pervious concrete made of wood chips and also sheds lights on the mechanical properties of this new product. The properties of pervious wood-concrete such as strength, elastic modulus, and failure modes are compared and evaluated. The characterization procedure of the mechanical properties of wood waste ash are presented and discussed. The numerical and tested load–deflection response results are compared. It was observed that the numerical results are in good agreement with the experimental results.

Keywords: Wood waste ash, characterization, mechanical properties, finite element analysis, flexural behavior, bending tests.

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Authors: Amjaad Alsalamah, Liyakathunsia Syed

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Transportation is an essential need for many people to go to their work, school, and home. In particular, the main common method inside many cities is to drive the car. Driving a car can be an easy job to reach the destination and load all stuff in a reasonable time. However, deciding to find a parking lot for a car can take a long time using the traditional system that can issue a paper ticket for each customer. The old system cannot guarantee a parking lot for all customers. Also, payment methods are not always available, and many customers struggled to find their car among a numerous number of cars. As a result, this research focuses on providing an online smart parking system in order to save time and budget. This system provides a flexible management system for both parking owner and customers by receiving all request via the online system and it gets an accurate result for all available parking and its location.

Keywords: Smart parking system, IoT, tracking system, process model, cost, time.

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Authors: D. H. Park, Y. H. Tak, H. H. Kwon, G. J. Kwon, H. G. Kim

Abstract:

The purpose of this study is to develop a forging process of automotive parts that satisfies the deformation characteristics. The analyses of temperature variation and deformation behavior of the material are important to obtain the optimal forging products. The hot compression test was carried out to know formability at high temperature. In order to define the optimum forging conditions including material temperature, strain and forging load, the commercial finite element analysis code was used to simulate the forging procedure of engine mounting parts. Experimental results were compared with the simulation results by finite element analysis. Test results were in good agreement with the simulations.

Keywords: Cold forging, hot forging, engine mounting, automotive parts, optimization.

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Authors: S. Al Dandachli, F. Perales, Y. Monerie, F. Jamin, M. S. El Youssoufi, C. Pelissou

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The goal of this research is to study the fracture process and mechanical behavior of concrete under I–II mixed-mode stress, which is essential for ensuring the safety of concrete structures. For this purpose, two-dimensional simulations of three-point bending tests under variable load and geometry on notched cement paste samples of composite samples (cement paste/siliceous aggregate) are modeled by employing Cohesive Zone Models (CZMs). As a result of experimental validation of these tests, the CZM model demonstrates its capacity to predict fracture propagation at the local scale.

Keywords: Concrete, cohesive zone model, microstructure, fracture, three-point flexural test bending.

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Authors: Ali Reza Pouladkhan, Jalil Emadi, Hamed Habibolahiyan

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This paper presents an exact solution and a finite element method (FEM) for a Piezoceramic Rod under static load. The cylindrical rod is made from polarized ceramics (piezoceramics) with axial poling. The lateral surface of the rod is traction-free and is unelectroded. The two end faces are under a uniform normal traction. Electrically, the two end faces are electroded with a circuit between the electrodes, which can be switched on or off. Two cases of open and shorted electrodes (short circuit and open circuit) will be considered. Finally, a finite element model will be used to compare the results with an exact solution. The study uses ABAQUS (v.6.7) software to derive the finite element model of the ceramic rod.

Keywords: Finite element method, Ceramic rod; Axial poling, Normal traction, Short circuit, Open circuit.

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Authors: T. Mathumathi, S. Ganesh, R. Gunabalan

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This work presents an approach for AC load flow based centralized model for congestion management in the forward markets. In this model, transaction maximizes its profit under the limits of transmission line capacities allocated by Independent System Operator (ISO). The voltage and reactive power impact of the system are also incorporated in this model. Genetic algorithm is used to solve centralized congestion management problem for multilateral transactions. Results obtained for centralized model using genetic algorithm is compared with Sequential Quadratic Programming (SQP) technique. The statistical performances of various algorithms such as best, worst, mean and standard deviations of social welfare are given. Simulation results clearly demonstrate the better performance of genetic algorithm over SQP.

Keywords: Congestion management, Genetic algorithm, Sequential quadratic programming.

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Authors: Jairo Aparecido Martins, Estaner Claro Romão

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This paper presents the static and cyclic stresses in combination with fatigue analysis resultant of loads applied on the friction discs usually utilized on industrial clutches. The material chosen to simulate the friction discs under load is aluminum. The numerical simulation was done by software COMSOL^TM Multiphysics. The results obtained for static loads showed enough stiffness for both geometries and the material utilized. On the other hand, in the fatigue standpoint, failure is clearly verified, what demonstrates the importance of both approaches, mainly dynamical analysis. The results and the conclusion are based on the stresses on disc, counted stress cycles, and fatigue usage factor.

Keywords: Aluminum, industrial clutch, static and dynamic loading, numerical simulation.

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Authors: J. B. V. Subrahmanyam, C. Radhakrishna

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This paper presents a simple three phase power flow method for solution of three-phase unbalanced radial distribution system (RDN) with voltage dependent loads. It solves a simple algebraic recursive expression of voltage magnitude, and all the data are stored in vector form. The algorithm uses basic principles of circuit theory and can be easily understood. Mutual coupling between the phases has been included in the mathematical model. The proposed algorithm has been tested with several unbalanced radial distribution networks and the results are presented in the article. 8- bus and IEEE 13 bus unbalanced radial distribution system results are in agreements with the literature and show that the proposed model is valid and reliable.

Keywords: radial distribution networks, load flow, circuitmodel, three-phase four-wire, unbalance.

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