Search results for: Optimization Model Reduction

Authors: N. Sefiani, L. Chraibi, K. Reklaoui, Y. Sefiani

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Currently, business environment is characterized by pressure caused by stiff competition, constant changes (e.g., product/ technological innovations, decreasing product lifecycles, and product proliferation), and a high level of market uncertainty band unpredictability. The agility of the Supply Chain Management (SCM) is clearly identified as a key factor for success and a strategic essential lever. This paper explores the impact of deploying competence management and Supply Chain Operations Reference (SCOR) model on firm performance. Our approach is based on a systemic view by considering the SCOR reference model as the heart of competence management system.

Keywords: Competence, competence management, performance, SCOR model and agility.

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Authors: Phruksaphanrat B.

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This research presents a fuzzy multi-objective model for a machine selection problem in a flexible manufacturing system of a tire company. Two main objectives are minimization of an average machine error and minimization of the total setup time. Conventionally, the working team uses trial and error in selecting a pressing machine for each task due to the complexity and constraints of the problem. So, both objectives may not satisfy. Moreover, trial and error takes a lot of time to get the final decision. Therefore, in this research preemptive fuzzy goal programming model is developed for solving this multi-objective problem. The proposed model can obtain the appropriate results that the Decision Making (DM) is satisfied for both objectives. Besides, alternative choice can be easily generated by varying the satisfaction level. Additionally, decision time can be reduced by using the model, which includes all constraints of the system to generate the solutions. A numerical example is also illustrated to show the effectiveness of the proposed model.

Keywords: Machine Selection, Preemptive Fuzzy Goal Programming, Mixed Integer Programming, Application of Tire Industry.

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Authors: Samson Okwakol Ariko, Venansius Baryamureeba

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Internet Access Technologies (IAT) provide a means through which Internet can be accessed. The choice of a suitable Internet technology is increasingly becoming an important issue to ISP clients. Currently, the choice of IAT is based on discretion and intuition of the concerned managers and the reliance on ISPs. In this paper we propose a model and designs algorithms that are used in the Internet access technology specification. In the proposed model, three ranking approaches are introduced; concurrent ranking, stepwise ranking and weighted ranking. The model ranks the IAT based on distance measures computed in ascending order while the global ranking system assigns weights to each IAT according to the position held in each ranking technique, determines the total weight of a particular IAT and ranks them in descending order. The final output is an objective ranking of IAT in descending order.

Keywords: Internet Access Technology (IAT).

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Authors: M.A. Ahmad

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This paper presents the use of anti-sway angle control approaches for a two-dimensional gantry crane with disturbances effect in the dynamic system. Delayed feedback signal (DFS) and proportional-derivative (PD)-type fuzzy logic controller are the techniques used in this investigation to actively control the sway angle of the rope of gantry crane system. A nonlinear overhead gantry crane system is considered and the dynamic model of the system is derived using the Euler-Lagrange formulation. A complete analysis of simulation results for each technique is presented in time domain and frequency domain respectively. Performances of both controllers are examined in terms of sway angle suppression and disturbances cancellation. Finally, a comparative assessment of the impact of each controller on the system performance is presented and discussed.

Keywords: Gantry crane, anti-sway control, DFS controller, PD-type Fuzzy Logic Controller.

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Authors: Shun Horikoshi, Tohru Kawabe

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This study presents performance analysis results of SMC (Sliding mode control) with changing the chattering functions applied to slip suppression problem of electric vehicles (EVs). In SMC, chattering phenomenon always occurs through high frequency switching of the control inputs. It is undesirable phenomenon and degrade the control performance, since it causes the oscillations of the control inputs. Several studies have been conducted on this problem by introducing some general saturation function. However, study about whether saturation function was really best and the performance analysis when using the other functions, weren’t being done so much. Therefore, in this paper, several candidate functions for SMC are selected and control performance of candidate functions is analyzed. In the analysis, evaluation function based on the trade-off between slip suppression performance and chattering reduction performance is proposed. The analyses are conducted in several numerical simulations of slip suppression problem of EVs. Then, we can see that there is no difference of employed candidate functions in chattering reduction performance. On the other hand, in slip suppression performance, the saturation function is excellent overall. So, we conclude the saturation function is most suitable for slip suppression sliding mode control.

Keywords: Sliding mode control, chattering function, electric vehicle, slip suppression, performance analysis.

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Authors: Mansoureh Naderipour, Susan Bastani, Mohammad Fazel Zarandi

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Predicting links that may occur in the future and missing links in social networks is an attractive problem in social network analysis. Granular computing can help us to model the relationships between human-based system and social sciences in this field. In this paper, we present a model based on granular computing approach and Type-2 fuzzy logic to predict links regarding nodes’ activity and the relationship between two nodes. Our model is tested on collaboration networks. It is found that the accuracy of prediction is significantly higher than the Type-1 fuzzy and crisp approach.

Keywords: Social Network, link prediction, granular computing, Type-2 fuzzy sets.

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Authors: B. Bahmani Firouzi, T. Niknam, M. Nayeripour

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With Power system movement toward restructuring along with factors such as life environment pollution, problems of transmission expansion and with advancement in construction technology of small generation units, it is expected that small units like wind turbines, fuel cells, photovoltaic, ... that most of the time connect to the distribution networks play a very essential role in electric power industry. With increase in developing usage of small generation units, management of distribution networks should be reviewed. The target of this paper is to present a new method for optimal management of active and reactive power in distribution networks with regard to costs pertaining to various types of dispersed generations, capacitors and cost of electric energy achieved from network. In other words, in this method it-s endeavored to select optimal sources of active and reactive power generation and controlling equipments such as dispersed generations, capacitors, under load tapchanger transformers and substations in a way that firstly costs in relation to them are minimized and secondly technical and physical constraints are regarded. Because the optimal management of distribution networks is an optimization problem with continuous and discrete variables, the new evolutionary method based on Ant Colony Algorithm has been applied. The simulation results of the method tested on two cases containing 23 and 34 buses exist and will be shown at later sections.

Keywords: Distributed Generation, Optimal Operation Management of distribution networks, Ant Colony Optimization(ACO).

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Authors: A.R. Rahmani, M.T. Samadi, R. Noroozi

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The present work was conducted for the synthesis of nano size zerovalent iron (nZVI) and hexavalent chromium (Cr(VI)) removal as a highly toxic pollutant by using this nanoparticles. Batch experiments were performed to investigate the effects of Cr(VI), nZVI concentration, pH of solution and contact time variation on the removal efficiency of Cr(VI). nZVI was synthesized by reduction of ferric chloride using sodium borohydrid. SEM and XRD examinations applied for determination of particle size and characterization of produced nanoparticles. The results showed that the removal efficiency decreased with Cr(VI) concentration and pH of solution and increased with adsorbent dosage and contact time. The Langmuir and Freundlich isotherm models were used for the adsorption equilibrium data and the Langmuir isotherm model was well fitted. Nanoparticle ZVI presented an outstanding ability to remove Cr(VI) due to high surface area, low particle size and high inherent activity.

Keywords: Adsorption, aqueous solution, Chromium, nZVI, removal.

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Authors: Magdy B. Eteiba, Essam A. Alzahab, Yomna O. Shaker

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In this paper, a thermal model of cast- resin dry type transformer is proposed. The proposed thermal model is solved by finite element technique to get the temperature at any location of the transformer. The basic modes of heat transfer such as conduction; convection and radiation are used to get the steady state temperature distribution of the transformer. The predicted temperatures are compared with experimental results reported in this paper and it is found a good agreement between them. The effects of various parameters such as width of air duct, ambient temperature and emissivity of the outer surface were also studied.

Keywords: Convection, dry type transformer, finite-elementtechnique, thermal model.

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Authors: Changyi Liu, Gui Wang, Matthew Dargusch

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Helical milling operations are used to generate or enlarge boreholes by means of a milling tool. The bore diameter can be adjusted through the diameter of the helical path. The kinematics of helical milling on a three axis machine tool is analysed firstly. The relationships between processing parameters, cutting tool geometry characters with machined hole feature are formulated. The feed motion of the cutting tool has been decomposed to plane circular feed and axial linear motion. In this paper, the time varying cutting forces acted on the side cutting edges and end cutting edges of the flat end cylinder miller is analysed using a discrete method separately. These two components then are combined to produce the cutting force model considering the complicated interaction between the cutters and workpiece. The time varying cutting force model describes the instantaneous cutting force during processing. This model could be used to predict cutting force, calculate statics deflection of cutter and workpiece, and also could be the foundation of dynamics model and predicting chatter limitation of the helical milling operations.

Keywords: Helical milling, Hole machining, Cutting force, Analytical model, Time domain

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Authors: Saif Ullah, Guan Zailin, Xu Xianhao, He Zongdong, Wang Baoxi

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Assembly line balancing problem is aimed to divide the tasks among the stations in assembly lines and optimize some objectives. In assembly lines the workload on stations is different from each other due to different tasks times and the difference in workloads between stations can cause blockage or starvation in some stations in assembly lines. Buffers are used to store the semi-finished parts between the stations and can help to smooth the assembly production. The assembly line balancing and buffer sizing problem can affect the throughput of the assembly lines. Assembly line balancing and buffer sizing problems have been studied separately in literature and due to their collective contribution in throughput rate of assembly lines, balancing and buffer sizing problem are desired to study simultaneously and therefore they are considered concurrently in current research. Current research is aimed to maximize throughput, minimize total size of buffers in assembly line and minimize workload variations in assembly line simultaneously. A multi objective optimization objective is designed which can give better Pareto solutions from the Pareto front and a simple example problem is solved for assembly line balancing and buffer sizing simultaneously. Current research is significant for assembly line balancing research and it can be significant to introduce optimization approaches which can optimize current multi objective problem in future.

Keywords: Assembly line balancing, Buffer sizing, Pareto solutions.

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Authors: Elison Eduardo Jardim Bierhals, Claudineia Brazil, Deivid Pires, Rafael Haag, Elton Gimenez Rossini

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This study evaluated the uncertainties involved in the solar radiation projections generated by the Brazilian Earth System Model (BESM) of the Weather and Climate Prediction Center (CPTEC) belonging to Coupled Model Intercomparison Phase 5 (CMIP5), with the aim of identifying efficiency in the projections for solar radiation of said model and in this way establish the viability of its use. Two different scenarios elaborated by Intergovernmental Panel on Climate Change (IPCC) were evaluated: RCP 4.5 (with more optimistic contour conditions) and 8.5 (with more pessimistic initial conditions). The method used to verify the accuracy of the present model was the Nash coefficient and the Statistical bias, as it better represents these atmospheric patterns. The BESM showed a tendency to overestimate the data ​​of solar radiation projections in most regions of the state of Rio Grande do Sul and through the validation methods adopted by this study, BESM did not present a satisfactory accuracy.

Keywords: Climate changes, projections, solar radiation, uncertainty.

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Authors: Jamalizadeh, M.R., Moghaddamnia, A., Piri, J., Arbabi, V., Homayounifar, M., Shahryari, A.

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Dust storms are one of the most costly and destructive events in many desert regions. They can cause massive damages both in natural environments and human lives. This paper is aimed at presenting a preliminary study on dust storms, as a major natural hazard in arid and semi-arid regions. As a case study, dust storm events occurred in Zabol city located in Sistan Region of Iran was analyzed to diagnose and predict dust storms. The identification and prediction of dust storm events could have significant impacts on damages reduction. Present models for this purpose are complicated and not appropriate for many areas with poor-data environments. The present study explores Gamma test for identifying inputs of ANNs model, for dust storm prediction. Results indicate that more attempts must be carried out concerning dust storms identification and segregate between various dust storm types.

Keywords: Dust Storm, Gamma Test, Prediction, ANNs, Zabol.

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Authors: Marina Franulovic, Robert Basan, Bozidar Krizan

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Constitutive modeling of material behavior is becoming increasingly important in prediction of possible failures in highly loaded engineering components, and consequently, optimization of their design. In order to account for large number of phenomena that occur in the material during operation, such as kinematic hardening effect in low cycle fatigue behavior of steels, complex nonlinear material models are used ever more frequently, despite of the complexity of determination of their parameters. As a method for the determination of these parameters, genetic algorithm is good choice because of its capability to provide very good approximation of the solution in systems with large number of unknown variables. For the application of genetic algorithm to parameter identification, inverse analysis must be primarily defined. It is used as a tool to fine-tune calculated stress-strain values with experimental ones. In order to choose proper objective function for inverse analysis among already existent and newly developed functions, the research is performed to investigate its influence on material behavior modeling.

Keywords: Genetic algorithm, kinematic hardening, material model, objective function

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Authors: Dinesh M., Kenny Mark V., Dharni Vasudhevan Venkatesan, Santhosh Kumar B., Sree Radesh R., V. R. Sanal Kumar

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Comprehensive numerical studies have been carried out to examine the best aerodynamic performance of subsonic aircraft at different winglet cant angles using a validated 3D k-ω SST model. In the parametric analytical studies NACA series of airfoils are selected. Basic design of the winglet is selected from the literature and flow features of the entire wing including the winglet tip effects have been examined with different cant angles varying from 150 to 600 at different angles of attack up to 140. We have observed, among the cases considered in this study that a case, with 150 cant angle the aerodynamics performance of the subsonic aircraft during takeoff was found better up to an angle of attack of 2.80 and further its performance got diminished at higher angles of attack. Analyses further revealed that increasing the winglet cant angle from 150 to 600 at higher angles of attack could negate the performance deterioration and additionally it could enhance the peak CL/CD on the order of 3.5%. The investigated concept of variable-cant-angle winglets appears to be a promising alternative for improving the aerodynamic efficiency of aircraft.

Keywords: Aerodynamic efficiency, Cant-angle, Drag reduction, Flexible Winglets.

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Authors: Norwati Mustapha, Manijeh Jalali, Abolghasem Bozorgniya, Mehrdad Jalali

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Web usage mining algorithms have been widely utilized for modeling user web navigation behavior. In this study we advance a model for mining of user-s navigation pattern. The model makes user model based on expectation-maximization (EM) algorithm.An EM algorithm is used in statistics for finding maximum likelihood estimates of parameters in probabilistic models, where the model depends on unobserved latent variables. The experimental results represent that by decreasing the number of clusters, the log likelihood converges toward lower values and probability of the largest cluster will be decreased while the number of the clusters increases in each treatment.

Keywords: Web Usage Mining, Expectation maximization, navigation pattern mining.

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Authors: R. Parameshwaran, R. Karunakaran, S. Iniyan, Anand A. Samuel

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The objective of this study is to present the test results of variable air volume (VAV) air conditioning system optimized by two objective genetic algorithm (GA). The objective functions are energy savings and thermal comfort. The optimal set points for fuzzy logic controller (FLC) are the supply air temperature (Ts), the supply duct static pressure (Ps), the chilled water temperature (Tw), and zone temperature (Tz) that is taken as the problem variables. Supply airflow rate and chilled water flow rate are considered to be the constraints. The optimal set point values are obtained from GA process and assigned into fuzzy logic controller (FLC) in order to conserve energy and maintain thermal comfort in real time VAV air conditioning system. A VAV air conditioning system with FLC installed in a software laboratory has been taken for the purpose of energy analysis. The total energy saving obtained in VAV GA optimization system with FLC compared with constant air volume (CAV) system is expected to achieve 31.5%. The optimal duct static pressure obtained through Genetic fuzzy methodology attributes to better air distribution by delivering the optimal quantity of supply air to the conditioned space. This combination enhanced the advantages of uniform air distribution, thermal comfort and improved energy savings potential.

Keywords: Energy savings, fuzzy logic, Genetic algorithm, Thermal Comfort

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Authors: M. Mordjaoui, B. Boudjema, M. Chabane, R. Daira

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In determining the electromagnetic properties of magnetic materials, hysteresis modeling is of high importance. Many models are available to investigate those characteristics but they tend to be complex and difficult to implement. In this paper a new qualitative hysteresis model for ferromagnetic core is presented, based on the function approximation capabilities of adaptive neuro fuzzy inference system (ANFIS). The proposed ANFIS model combined the neural network adaptive capabilities and the fuzzy logic qualitative approach can restored the hysteresis curve with a little RMS error. The model accuracy is good and can be easily adapted to the requirements of the application by extending or reducing the network training set and thus the required amount of measurement data.

Keywords: ANFIS modeling technique, magnetic hysteresis, Jiles-Atherton model, ferromagnetic core.

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Authors: Katsumi Wasaki, Naoki Iwasaki

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Model-checking tools such as Symbolic Model Verifier (SMV) and NuSMV are available for checking hardware designs. These tools can automatically check the formal legitimacy of a design. However, NuSMV is too low level for describing a complete hardware design. It is therefore necessary to translate the system definition, as designed in a language such as Verilog or VHDL, into a language such as NuSMV for validation. In this paper, we present a meta hardware description language, Melasy, that contains a code generator for existing hardware description languages (HDLs) and languages for model checking that solve this problem.

Keywords: meta description language, software/hardware codesign, co-verification, formal verification, hardware compiler, modelchecking.

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Authors: N. Barka, P. Bocher, A. Chebak, J. Brousseau, D. S. Ramdenee

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This paper presents the study of induced currents and temperature distribution in gear heated by induction process using 2D finite element (FE) model. The model is developed by coupling Maxwell and heat transfer equations into a multi-physics model. The obtained results allow comparing the medium frequency (MF) and high frequency (HF) cases and the effect of machine parameters on the evolution of induced currents and temperature during heating. The sensitivity study of the temperature profile is conducted and the case hardness is predicted using the final temperature profile. These results are validated using tests and give a good understanding of phenomena during heating process.

Keywords: 2D model, induction heating, spur gear, induced currents, experimental validation

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Authors: Sujit K. Basak

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The aim of this paper is to analyze the impact of literature review software on researchers. The aim of this study was achieved by analyzing models in terms of perceived usefulness, perceived ease of use, and acceptance level. Collected data were analyzed using WarpPLS 4.0 software. This study used two theoretical frameworks, namely, Technology Acceptance Model and the Training Needs Assessment Model. The study was experimental and was conducted at a public university in South Africa. The results of the study showed that acceptance level has a high impact on research productivity followed by perceived usefulness and perceived ease of use.

Keywords: Technology acceptance model, training needs assessment model, literature review software, research productivity.

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Authors: Bilal Saeed Raja, M. Ali Iqbal, Imran Ihsan

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Extracting and elaborating software requirements and transforming them into viable software architecture are still an intricate task. This paper defines a solution architecture which is based on the blurred amalgamation of problem space and solution space. The dependencies between domain constraints, requirements and architecture and their importance are described that are to be considered collectively while evolving from problem space to solution space. This paper proposes a revised version of Twin Peaks Model named Win Peaks Model that reconciles software requirements and architecture in more consistent and adaptable manner. Further the conflict between stakeholders- win-requirements is resolved by proposed Voting methodology that is simple adaptation of win-win requirements negotiation model and QARCC.

Keywords: Functional Requirements, Non Functional Requirements, Twin Peaks Model, QARCC.

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Authors: Yoshimoto Kurihara, Tad Gonsalves

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Currently, in the field of object posture estimation, there is research on estimating the position and angle of an object by storing a 3D model of the object to be estimated in advance in a computer and matching it with the model. However, in this research, we have succeeded in creating a module that is much simpler, smaller in scale, and faster in operation. Our 6D pose estimation model consists of two different networks – a classification network and a regression network. From a single RGB image, the trained model estimates the class of the object in the image, the coordinates of the object, and its rotation angle in 3D space. In addition, we compared the estimation accuracy of each camera position, i.e., the angle from which the object was captured. The highest accuracy was recorded when the camera position was 75°, the accuracy of the classification was about 87.3%, and that of regression was about 98.9%.

Keywords: AlexNet, Deep learning, image recognition, 6D posture estimation.

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Authors: Lely A. Luengas, Pedro R. Vizcaya, Giovanni Sánchez

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In this paper, a methodology is presented to obtain the Static Alignment Model for any transtibial amputee person. The proposed methodology starts from experimental data collected on the Hospital Militar Central, Bogotá, Colombia. The effects of transtibial prosthesis malalignment on amputees were measured in terms of joint angles, center of pressure (COP) and weight distribution. Some statistical tools are used to obtain the model parameters. Mathematical predictive models of prosthetic alignment were created. The proposed models are validated in amputees and finding promising results for the prosthesis Static Alignment. Static alignment process is unique to each subject; nevertheless the proposed methodology can be used in each transtibial amputee.

Keywords: Information theory, prediction model, prosthetic alignment, transtibial prosthesis.

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Authors: Camille A. Issa, Omar Masri

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In this study, the commercial finite element software ABAQUS was used to develop a three-dimensional nonlinear finite element model capable of simulating the pull-out test of reinforcing bars from underwater concrete. The results of thirty-two pull-out tests that have different parameters were implemented in the software to study the effect of the concrete cover, the bar size, the use of stirrups, and the compressive strength of concrete. The interaction properties used in the model provided accurate results in comparison with the experimental bond-slip results, thus the model has successfully simulated the pull-out test. The results of the finite element model are used to better understand and visualize the distribution of stresses in each component of the model, and to study the effect of the various parameters used in this study including the role of the stirrups in preventing the stress from reaching to the sides of the specimens.

Keywords: Bond strength, nonlinear finite element analysis, pull-out test, underwater concrete.

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Authors: R. Srinivasa Rao, S. V. L. Narasimham

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This paper presents a new and efficient approach for capacitor placement in radial distribution systems that determine the optimal locations and size of capacitor with an objective of improving the voltage profile and reduction of power loss. The solution methodology has two parts: in part one the loss sensitivity factors are used to select the candidate locations for the capacitor placement and in part two a new algorithm that employs Plant growth Simulation Algorithm (PGSA) is used to estimate the optimal size of capacitors at the optimal buses determined in part one. The main advantage of the proposed method is that it does not require any external control parameters. The other advantage is that it handles the objective function and the constraints separately, avoiding the trouble to determine the barrier factors. The proposed method is applied to 9, 34, and 85-bus radial distribution systems. The solutions obtained by the proposed method are compared with other methods. The proposed method has outperformed the other methods in terms of the quality of solution.

Keywords: Distribution systems, Capacitor placement, loss reduction, Loss sensitivity factors, PGSA.

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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: Sulata Maharana, B Biswas, Adity Ganguly, Ashok Kumar

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In this paper, the requirement for Coke quality prediction, its role in Blast furnaces, and the model output is explained. By applying method of Artificial Neural Networking (ANN) using back propagation (BP) algorithm, prediction model has been developed to predict CSR. Important blast furnace functions such as permeability, heat exchanging, melting, and reducing capacity are mostly connected to coke quality. Coke quality is further dependent upon coal characterization and coke making process parameters. The ANN model developed is a useful tool for process experts to adjust the control parameters in case of coke quality deviations. The model also makes it possible to predict CSR for new coal blends which are yet to be used in Coke Plant. Input data to the model was structured into 3 modules, for tenure of past 2 years and the incremental models thus developed assists in identifying the group causing the deviation of CSR.

Keywords: Artificial Neural Networks, backpropagation, CokeStrength after Reaction, Multilayer Perceptron.

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Authors: Nermin Ozgulbas, Ali Serhan Koyuncugil

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One of the biggest problems of SMEs is their tendencies to financial distress because of insufficient finance background. In this study, an Early Warning System (EWS) model based on data mining for financial risk detection is presented. CHAID algorithm has been used for development of the EWS. Developed EWS can be served like a tailor made financial advisor in decision making process of the firms with its automated nature to the ones who have inadequate financial background. Besides, an application of the model implemented which covered 7,853 SMEs based on Turkish Central Bank (TCB) 2007 data. By using EWS model, 31 risk profiles, 15 risk indicators, 2 early warning signals, and 4 financial road maps has been determined for financial risk mitigation.

Keywords: Early Warning Systems, Data Mining, Financial Risk, SMEs.

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Authors: W. D. Wan Rosli, Z. Zainuddin, R. Lanouette, S. Sathasivam

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This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of Pulping of Sugar Maple problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified problem where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

Keywords: Convergence, Modeling, Neural Networks, Preconditioned Conjugate Gradient.

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