Search results for: Optimization method

Authors: Fadi Eleiwi, Taous Meriem Laleg-Kirati, Sofiane Khelladi, Farid Bakir

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This paper presents the use of a semi-classical signal analysis method that has been developed recently for the analysis of turbomachinery flow unsteadiness. We will focus on the correlation between theSemi-Classical Signal Analysis parameters and some physical parameters in relation with turbomachinery features. To demonstrate the potential of the proposed approach, a static pressure signal issued from a rotor/stator interaction of a centrifugal pump is studied. Several configurations of the pump are compared.

Keywords: Semi-classical signal analysis, turbomachines, newindices, physical parameters

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Authors: H. B. Kekre, Sudeep D. Thepade

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The automatic construction of large, high-resolution image vistas (mosaics) is an active area of research in the fields of photogrammetry [1,2], computer vision [1,4], medical image processing [4], computer graphics [3] and biometrics [8]. Image stitching is one of the possible options to get image mosaics. Vista Creation in image processing is used to construct an image with a large field of view than that could be obtained with a single photograph. It refers to transforming and stitching multiple images into a new aggregate image without any visible seam or distortion in the overlapping areas. Vista creation process aligns two partial images over each other and blends them together. Image mosaics allow one to compensate for differences in viewing geometry. Thus they can be used to simplify tasks by simulating the condition in which the scene is viewed from a fixed position with single camera. While obtaining partial images the geometric anomalies like rotation, scaling are bound to happen. To nullify effect of rotation of partial images on process of vista creation, we are proposing rotation invariant vista creation algorithm in this paper. Rotation of partial image parts in the proposed method of vista creation may introduce some missing region in the vista. To correct this error, that is to fill the missing region further we have used image inpainting method on the created vista. This missing view regeneration method also overcomes the problem of missing view [31] in vista due to cropping, irregular boundaries of partial image parts and errors in digitization [35]. The method of missing view regeneration generates the missing view of vista using the information present in vista itself.

Keywords: Vista, Overlap Estimation, Rotation Invariance, Missing View Regeneration.

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Authors: C. Senanayake, S. Veera Ragavan

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Warehousing is commonly used in factories for the storage of products until delivery of orders. As the amount of products stored increases it becomes tedious to be carried out manually. In recent years, the manual storing has converted into fully or partially computer controlled systems, also known as Automated Storage and Retrieval Systems (AS/RS). This paper discusses an ASRS system, which was designed such that the best storage location for the products is determined by utilizing a fuzzy control system. The design maintains the records of the products to be/already in store and the storage/retrieval times along with the availability status of the storage locations. This paper discusses on the maintenance of the above mentioned records and the utilization of the concept of fuzzy logic in order to determine the optimum storage location for the products. The paper will further discuss on the dynamic splitting and merging of the storage locations depending on the product sizes.

Keywords: ASRS, fuzzy control systems, MySQL database, dynamic splitting and merging.

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Authors: Hakan Işık, Esra Saraçoğlu

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In this study, a comparison of two control methods, Proportional Control (PC) and Fuzzy Logic Control (FLC), which have been used to develop an ideal thermoelectric renal hypothermia system in order to use in renal surgery, has been carried out. Since the most important issues in long-lasting parenchymatous renal surgery are to provide an operation medium free of blood and to prevent renal dysfunction in the postoperative period, control of the temperature has become very important in renal surgery. The final product is seriously affected from the changes in temperature, therefore, it is necessary to reach some desired temperature points quickly and avoid large overshoot. PIC16F877 microcontroller has been used as controller for both of these two methods. Each control method can simply ensure extra renal hypothermia in the targeted way. But investigation of advantages and disadvantages of every control method to each other is aimed and carried out by the experimental implementations. Shortly, investigation of the most appropriate method to use for development of system and that can be applied to people safely in the future, has been performed. In this sense, experimental results show that fuzzy logic control gives out more reliable responses and efficient performance.

Keywords: renal hypothermia, renal cooling, temperature control, proportional control fuzzy logic control

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Authors: Stelian Petrescu, Adina Frunzâ, Camelia Petrescu

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A method to determine experimentally the melting rate, rm, and the heat transfer coefficients, αv (W/(m3K)), at convective melting in a fixed bed of particles under adiabatic regime is established in this paper. The method lies in the determining of the melting rate by measuring the fixed bed height in time. Experimental values of rm, α and α v were determined using cylindrical particles of ice (d = 6.8 mm, h = 5.5 mm) and, as a melting agent, aqueous NaCl solution with a temperature of 283 K at different values of the liquid flow rate (11.63·10-6, 28.83·10-6, 38.83·10-6 m3/s). Our experimental results were compared with those existing in literature being noticed a good agreement for Re values higher than 50.

Keywords: Convective melting, fixed bed, packed bed, heat transfer, ice melting.

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Authors: Fei Long Wei, Hua Yang, Hai Tao Zhang, Zhou Ping Yin

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In this study, an local invariant generalized Houghtransform (LI-GHT) method is proposed for integrated circuit (IC) visual positioning. The original generalized Hough transform (GHT) is robust to external noise; however, it is not suitable for visual positioning of IC chips due to the four-dimensionality (4D) of parameter space which leads to the substantial storage requirement and high computational complexity. The proposed LI-GHT method can reduce the dimensionality of parameter space to 2D thanks to the rotational invariance of local invariant geometric feature and it can estimate the accuracy position and rotation angle of IC chips in real-time under noise and blur influence. The experiment results show that the proposed LI-GHT can estimate position and rotation angle of IC chips with high accuracy and fast speed. The proposed LI-GHT algorithm was implemented in IC visual positioning system of radio frequency identification (RFID) packaging equipment.

Keywords: Integrated Circuit Visual Positioning, Generalized Hough Transform, Local invariant Generalized Hough Transform, ICpacking equipment.

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Authors: T. Vigneswari, M. A. Maluk Mohamed

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Job Scheduling plays an important role for efficient utilization of grid resources available across different domains and geographical zones. Scheduling of jobs is challenging and NPcomplete. Evolutionary / Swarm Intelligence algorithms have been extensively used to address the NP problem in grid scheduling. Artificial Bee Colony (ABC) has been proposed for optimization problems based on foraging behaviour of bees. This work proposes a modified ABC algorithm, Cluster Heterogeneous Earliest First Min- Min Artificial Bee Colony (CHMM-ABC), to optimally schedule jobs for the available resources. The proposed model utilizes a novel Heterogeneous Earliest Finish Time (HEFT) Heuristic Algorithm along with Min-Min algorithm to identify the initial food source. Simulation results show the performance improvement of the proposed algorithm over other swarm intelligence techniques.

Keywords: Grid Computing, Grid Scheduling, Heterogeneous Earliest Finish Time (HEFT), Artificial Bee colony (ABC) Algorithm, Resource Management.

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Authors: Nada Mouchfiq, Ahmed Habbani, Chaimae Benjbara

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The security aspect of the IoT occupies a place of great importance especially after the evolution that has known this field lastly because it must take into account the transformations and the new applications .Blockchain is a new technology dedicated to the data sharing. However, this does not work the same way in the different systems with different operating principles. This article will discuss network security using the Blockchain to facilitate the sending of messages and information, enabling the use of new processes and enabling autonomous coordination of devices. To do this, we will discuss proposed solutions to ensure a high level of security in these networks in the work of other researchers. Finally, our article will propose a method of security more adapted to our needs as a team working in the ad hoc networks, this method is based on the principle of the Blockchain and that we named ”MPR Blockchain”.

Keywords: Ad hoc networks, blockchain, MPR, security.

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Authors: A. Kumar, G. K. Singh, R. S. Anand

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In this paper, various algorithms for designing quadrature mirror filter are reviewed and a new algorithm is presented for the design of near perfect reconstruction quadrature mirror filter bank. In the proposed algorithm, objective function is formulated using the perfect reconstruction condition or magnitude response condition of prototype filter at frequency (ω = 0.5π) in ideal condition. The cutoff frequency is iteratively changed to adjust the filters coefficients using optimization algorithm. The performances of the proposed algorithm are evaluated in term of computation time, reconstruction error and number of iterations. The design examples illustrate that the proposed algorithm is superior in term of peak reconstruction error, computation time, and number of iterations. The proposed algorithm is simple, easy to implement, and linear in nature.

Keywords: Aliasing cancellations filter bank, Filter banks, quadrature mirror filter (QMF), subband coding.

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Authors: Yan Lyu, Yiqun Pan, Zhizhong Huang

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In the design stage of a new building, the energy model of this building is often required for the analysis of the performance on energy efficiency. In practice, a certain degree of geometric simplification should be done in the establishment of building energy models, since the detailed geometric features of a real building are hard to be described perfectly in most energy simulation engine, such as ESP-r, eQuest or EnergyPlus. Actually, the detailed description is not necessary when the result with extremely high accuracy is not demanded. Therefore, this paper analyzed the relationship between the error of the simulation result from building energy models and the geometric simplification of the models. Finally, the following two parameters are selected as the indices to characterize the geometric feature of in building energy simulation: the southward projected area and total side surface area of the building. Based on the parameterization method, the simplification from an arbitrary column building to a typical shape (a cuboid) building can be made for energy modeling. The result in this study indicates that no more than 7% prediction error of annual cooling/heating load will be caused by the geometric simplification for those buildings with the ratio of southward projection length to total perimeter of the bottom of 0.25~0.35, which means this method is applicable for building performance simulation.

Keywords: building energy model, simulation, geometric simplification, design, regression

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Authors: R. Rama Kishore, Sunesh

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Nowadays, robust and secure watermarking algorithm and its optimization have been need of the hour. A watermarking algorithm is presented to achieve the copy right protection of the owner based on visual cryptography, histogram shape property and entropy. In this, both host image and watermark are preprocessed. Host image is preprocessed by using Butterworth filter, and watermark is with visual cryptography. Applying visual cryptography on water mark generates two shares. One share is used for embedding the watermark, and the other one is used for solving any dispute with the aid of trusted authority. Usage of histogram shape makes the process more robust against geometric and signal processing attacks. The combination of visual cryptography, Butterworth filter, histogram, and entropy can make the algorithm more robust, imperceptible, and copy right protection of the owner.

Keywords: Butterworth filter, digital watermarking, histogram, visual cryptography.

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Authors: B.S.Boyanov, M.P.Sandalski, K.I.Ivanov

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The production of glass, ceramic materials and many non-ferrous metals (Zn, Cu, Pb, etc.), ferrous metals (pig iron) and others is connected with the use of a considerable number of initial solid raw materials. Before carrying out the basic technological processes (oxidized roasting, melting, agglomeration, baking) it is necessary to mix and homogenize the raw materials that have different chemical and phase content, granulometry and humidity. For this purpose zinc sulfide concentrates differing in origin are studied for their more complete characteristics using chemical, X-ray diffraction analyses, DTA and TGA as well as Mössbauer spectroscopy. The phases established in most concentrates are: β-ZnS, mZnS.nFeS, FeS2, CuFeS2, PbS, SiO2 (α-quartz). With the help of the developed by us a Web-based information system for a continued period of time different mix proportions from zinc concentrates are calculated and used in practice (roasting in fluidized bed reactor), which have to conform to the technological requirements of the zinc hydrometallurgical technological scheme.

Keywords: fluidized bed reactor, roasting, Web-based information system, zinc concentrates.

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Authors: Khalid Al-Tahat, Khaled Zuhair Mahmoud, Ahmad Al-Mughrabi

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This paper proposes a novel methodology for enabling debugging and tracing of production web applications without affecting its normal flow and functionality. This method of debugging enables developers and maintenance engineers to replace a set of existing resources such as images, server side scripts, cascading style sheets with another set of resources per web session. The new resources will only be active in the debug session and other sessions will not be affected. This methodology will help developers in tracing defects, especially those that appear only in production environments and in exploring the behaviour of the system. A realization of the proposed methodology has been implemented in Java.

Keywords: Live debugging, web application, web resources, inconsistent bugs, tracing.

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Authors: B. Marungsri, W. Onchantuek, A. Oonsivilai, T. Kulworawanichpong

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This paper presents the simulation results of electric field and potential distributions along surface of silicone rubber polymer insulators under clean and various contamination conditions with/without water droplets. Straight sheds insulator having leakage distance 290 mm was used in this study. Two type of contaminants, playwood dust and cement dust, have been studied the effect of contamination on the insulator surface. The objective of this work is to comparison the effect of contamination on potential and electric field distributions along the insulator surface when water droplets exist on the insulator surface. Finite element method (FEM) is adopted for this work. The simulation results show that contaminations have no effect on potential distribution along the insulator surface while electric field distributions are obviously depended on contamination conditions.

Keywords: electric field distribution, potential distribution, silicone rubber polymer insulator, finite element method

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Authors: Nebi Gedik

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Electroencephalography (EEG) investigations of the brain computer interfaces are based on the electrical signals resulting from neural activities in the brain. In this paper, it is offered a method for classifying motor imagery EEG signals. The suggested method classifies EEG signals into two classes using the wave atom transform, and the transform coefficients are assessed, creating the feature set. Classification is done with SVM and k-NN algorithms with and without feature selection. For feature selection t-test approaches are utilized. A test of the approach is performed on the BCI competition III dataset IIIa.

Keywords: motor imagery, EEG, wave atom transform, SVM, k-NN, t-test

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Authors: D.Katherasan, Madana Sashikant, S.Sandeep Bhat, P.Sathiya

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Bead-on-plate welds were carried out on AISI 316L (N) austenitic stainless steel (ASS) using flux cored arc welding (FCAW) process. The bead on plates weld was conducted as per L25 orthogonal array. In this paper, the weld bead geometry such as depth of penetration (DOP), bead width (BW) and weld reinforcement (R) of AISI 316L (N) ASS are investigated. Taguchi approach is used as statistical design of experiment (DOE) technique for optimizing the selected welding input parameters. Grey relational analysis and desirability approach are applied to optimize the input parameters considering multiple output variables simultaneously. Confirmation experiment has also been conducted to validate the optimized parameters.

Keywords: bead-on-plate welding, bead profiles, desirability approach, grey relational analysis

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Authors: Yuichi Masukake, Yoshihisa Ishida

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In this paper, we proposed a method to design a model-following adaptive controller for linear/nonlinear plants. Radial basis function neural networks (RBF-NNs), which are known for their stable learning capability and fast training, are used to identify linear/nonlinear plants. Simulation results show that the proposed method is effective in controlling both linear and nonlinear plants with disturbance in the plant input.

Keywords: Linear/nonlinear plants, neural networks, radial basisfunction networks.

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Authors: Ilona I. Iatcheva, Rumena D. Stancheva, Mario Metodiev

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The paper deals with determination of electromagnetic and temperature field distribution of induction heating system used for pipe brazing. The problem is considered as coupled – time harmonic electromagnetic and transient thermal field. It has been solved using finite element method. The detailed maps of electromagnetic and thermal field distribution have been obtained. The good understanding of the processes in the considered system ensures possibilities for control, management and increasing the efficiency of the welding process.

Keywords: Electromagnetic field, temperature field, finiteelement method, induction heating, pipe brazing.

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Authors: Seyed Hossein Iranmanesh, Zahra Mokhtari

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Estimation time and cost of work completion in a project and follow up them during execution are contributors to success or fail of a project, and is very important for project management team. Delivering on time and within budgeted cost needs to well managing and controlling the projects. To dealing with complex task of controlling and modifying the baseline project schedule during execution, earned value management systems have been set up and widely used to measure and communicate the real physical progress of a project. But it often fails to predict the total duration of the project. In this paper data mining techniques is used predicting the total project duration in term of Time Estimate At Completion-EAC (t). For this purpose, we have used a project with 90 activities, it has updated day by day. Then, it is used regular indexes in literature and applied Earned Duration Method to calculate time estimate at completion and set these as input data for prediction and specifying the major parameters among them using Clem software. By using data mining, the effective parameters on EAC and the relationship between them could be extracted and it is very useful to manage a project with minimum delay risks. As we state, this could be a simple, safe and applicable method in prediction the completion time of a project during execution.

Keywords: Data Mining Techniques, Earned Duration Method, Earned Value, Estimate At Completion.

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Authors: Xiaoli Shen, Yuehui Chen

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Interactions among proteins are the basis of various life events. So, it is important to recognize and research protein interaction sites. A control set that contains 149 protein molecules were used here. Then 10 features were extracted and 4 sample sets that contained 9 sliding windows were made according to features. These 4 sample sets were calculated by Radial Basis Functional neutral networks which were optimized by Particle Swarm Optimization respectively. Then 4 groups of results were obtained. Finally, these 4 groups of results were integrated by decision fusion (DF) and Genetic Algorithm based Selected Ensemble (GASEN). A better accuracy was got by DF and GASEN. So, the integrated methods were proved to be effective.

Keywords: protein interaction sites, features, sliding windows, radial basis functional neutral networks, genetic algorithm basedselected ensemble.

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Authors: F. Barzegar, M. H. Sheikhi

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In the present work we model a Multiquantum Well structure Separate Absorption and Charge Multiplication Avalanche Photodiode (MQW-SACM-APD), while the Absorption region coincide with the MQW. We consider the nonuniformity of electric field using split-step method in active region. This model is based on the carrier rate equations in the different regions of the device. Using the model we obtain the photocurrent, and dark current. As an example, InGaAs/InP SACM-APD and MQW-SACM-APD are simulated. There is a good agreement between the simulation and experimental results.

Keywords: Avalanche Photodiode, Physical Model, MultiquantumWell, Split Step Method.

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Authors: Anita S. Gangal, P. K. Kalra, D. S. Chauhan

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The backpropagation algorithm in general employs quadratic error function. In fact, most of the problems that involve minimization employ the Quadratic error function. With alternative error functions the performance of the optimization scheme can be improved. The new error functions help in suppressing the ill-effects of the outliers and have shown good performance to noise. In this paper we have tried to evaluate and compare the relative performance of complex valued neural network using different error functions. During first simulation for complex XOR gate it is observed that some error functions like Absolute error, Cauchy error function can replace Quadratic error function. In the second simulation it is observed that for some error functions the performance of the complex valued neural network depends on the architecture of the network whereas with few other error functions convergence speed of the network is independent of architecture of the neural network.

Keywords: Complex backpropagation algorithm, complex errorfunctions, complex valued neural network, split activation function.

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Authors: Mehrnaz Najafi, Hassan Haghighi

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Morgan-s refinement calculus (MRC) is one of the well-known methods allowing the formality presented in the program specification to be continued all the way to code. On the other hand, Object-Z (OZ) is an extension of Z adding support for classes and objects. There are a number of methods for obtaining code from OZ specifications that can be categorized into refinement and animation methods. As far as we know, only one refinement method exists which refines OZ specifications into code. However, this method does not have fine-grained refinement rules and thus cannot be automated. On the other hand, existing animation methods do not present mapping rules formally and do not support the mapping of several important constructs of OZ, such as all cases of operation expressions and most of constructs in global paragraph. In this paper, with the aim of providing an automatic path from OZ specifications to code, we propose an approach to map OZ specifications into their counterparts in MRC in order to use fine-grained refinement rules of MRC. In this way, having counterparts of our specifications in MRC, we can refine them into code automatically using MRC tools such as RED. Other advantages of our work pertain to proposing mapping rules formally, supporting the mapping of all important constructs of Object-Z, and considering dynamic instantiation of objects while OZ itself does not cover this facility.

Keywords: Formal method, Formal specification, Formalprogram development, Morgan's Refinement Calculus, Object-Z

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Authors: Karim Kemih, Yacine Yaiche, Malek Benslama

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To establish optical communication between any two satellites, the transmitter satellite must track the beacon of the receiver satellite and point the information optical beam in its direction. Optical tracking and pointing systems for free space suffer during tracking from high-amplitude vibration because of background radiation from interstellar objects such as the Sun, Moon, Earth, and stars in the tracking field of view or the mechanical impact from satellite internal and external sources. The vibrations of beam pointing increase the bit error rate and jam communication between the two satellites. One way to overcome this problem is the use of very small transmitter beam divergence angles of too narrow divergence angle is that the transmitter beam may sometimes miss the receiver satellite, due to pointing vibrations. In this paper we propose the use of genetic algorithm to optimize the BER as function of transmitter optics aperture.

Keywords: Optical Satellite Communication, Genetic Algorithm, Transmitter Optics Aperture

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Authors: I. Lolic, P. Soric, M. Cizmesija

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Based on Business and Consumer Survey (BCS) data, the European Commission (EC) regularly publishes the monthly Economic Sentiment Indicator (ESI) for each EU member state. ESI is conceptualized as a leading indicator, aimed ad tracking the overall economic activity. In calculating ESI, the EC employs arbitrarily chosen weights on 15 BCS response balances. This paper raises the predictive quality of ESI by applying nonlinear programming to find such weights that maximize the correlation coefficient of ESI and year-on-year GDP growth. The obtained results show that the highest weights are assigned to the response balances of industrial sector questions, followed by questions from the retail trade sector. This comes as no surprise since the existing literature shows that the industrial production is a plausible proxy for the overall Croatian economic activity and since Croatian GDP is largely influenced by the aggregate personal consumption.

Keywords: Business and Consumer Survey, Economic Sentiment Indicator, Leading Indicator, Nonlinear Optimization with Constraints.

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Authors: Jonghyun Park, Toan Nguyen Dinh, Gueesang Lee

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In this paper, we present a novel approach to accurately detect text regions including shop name in signboard images with complex background for mobile system applications. The proposed method is based on the combination of text detection using edge profile and region segmentation using fuzzy c-means method. In the first step, we perform an elaborate canny edge operator to extract all possible object edges. Then, edge profile analysis with vertical and horizontal direction is performed on these edge pixels to detect potential text region existing shop name in a signboard. The edge profile and geometrical characteristics of each object contour are carefully examined to construct candidate text regions and classify the main text region from background. Finally, the fuzzy c-means algorithm is performed to segment and detected binarize text region. Experimental results show that our proposed method is robust in text detection with respect to different character size and color and can provide reliable text binarization result.

Keywords: Text detection, edge profile, signboard image, fuzzy clustering.

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Authors: Omid Jadidi, Fatemeh Firouzi, Enzo Bagliery

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Supplier selection, in real situation, is affected by several qualitative and quantitative factors and is one of the most important activities of purchasing department. Since at the time of evaluating suppliers against the criteria or factors, decision makers (DMS) do not have precise, exact and complete information, supplier selection becomes more difficult. In this case, Grey theory helps us to deal with this problem of uncertainty. Here, we apply Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to evaluate and select the best supplier by using interval fuzzy numbers. Through this article, we compare TOPSIS with some other approaches and afterward demonstrate that the concept of TOPSIS is very important for ranking and selecting right supplier.

Keywords: TOPSIS, fuzzy number, MADM, Supplier selection

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Authors: Apurv Kulkarni, Shreyas Badave, B. Rajiv

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Non-parametric reliability technique is useful for assessment of reliability of systems for which failure rates are not available. This is useful when detection of malfunctioning of any component is the key purpose during ongoing operation of the system. The main purpose of the Heat Exchanger Cycle discussed in this paper is to provide hot water at a constant temperature for longer periods of time. In such a cycle, certain components play a crucial role and this paper presents an effective way to predict the malfunctioning of the components by determination of system reliability. The method discussed in the paper is feasible and this is clarified with the help of various test cases.

Keywords: Heat exchanger cycle, K-statistics, PID controller, system reliability.

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Authors: Wenhui Tang, Daorong Wang, Xia Huang, Xianwen Ran

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Based on the thermodynamic theory, the dependence of sublimation energy of metal on temperature and pressure is discussed, and the results indicate that the sublimation energy decreases linearly with the increase of temperature and pressure. Combined with this result, the blow-off impulse of aluminum induced by pulsed X-ray is simulated by smoothed particle hydrodynamics (SPH) method. The numerical results show that, while the change of sublimation energy with temperature and pressure is considered, the blow-off impulse of aluminum is larger than the case that the sublimation energy is assumed to be a constant.

Keywords: sublimation energy, blow-off impulse, pulsed X-ray, SPH method.

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Authors: R. Haoui

Abstract:

The purpose of this work is to simulate the flow at the exit of Vulcan 1 engine of European launcher Ariane 5. The geometry of the propellant nozzle is already determined using the characteristics method. The pressure in the outlet section of the nozzle is less than atmospheric pressure on the ground, causing the existence of oblique and normal shock waves at the exit. During the rise of the launcher, the atmospheric pressure decreases and the shock wave disappears. The code allows the capture of shock wave at exit of nozzle. The numerical technique uses the Flux Vector Splitting method of Van Leer to ensure convergence and avoid the calculation instabilities. The Courant, Friedrichs and Lewy coefficient (CFL) and mesh size level are selected to ensure the numerical convergence. The nonlinear partial derivative equations system which governs this flow is solved by an explicit unsteady numerical scheme by the finite volume method. The accuracy of the solution depends on the size of the mesh and also the step of time used in the discretized equations. We have chosen in this study the mesh that gives us a stationary solution with good accuracy.

Keywords: Launchers, supersonic flow, finite volume, nozzles, shock wave.

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