Search results for: method of least square

Authors: Sheng-Gwo Chen, Wen-Haw Chen

Abstract:

It is an important problem to compute the geodesics on a surface in many fields. To find the geodesics in practice, however, the traditional discrete algorithms or numerical approaches can only find a list of discrete points. The first author proposed in 2010 a new, elegant and accurate method, the geodesic-like method, for approximating geodesics on a regular surface. This paper will present by use of this method a computation of the Bezier geodesic-like curves on spheres.

Keywords: Geodesics, Geodesic-like curve, Spheres, Bezier.

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Authors: Tao Zhao, Xin Wang

Abstract:

With the increasing complexity of engineering problems, the traditional, single-objective and deterministic optimization method can not meet people-s requirements. A multi-objective fuzzy optimization model of resource input is built for M chlor-alkali chemical eco-industrial park in this paper. First, the model is changed into the form that can be solved by genetic algorithm using fuzzy theory. And then, a fitness function is constructed for genetic algorithm. Finally, a numerical example is presented to show that the method compared with traditional single-objective optimization method is more practical and efficient.

Keywords: Fitness function, genetic algorithm, multi-objectivefuzzy optimization, satisfaction degree membership function.

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

Abstract:

Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.

Keywords: Adomian’s Decomposition Method, magneto-thermoelasticity, finite conductivity, iteration method, thermal load.

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Authors: P. Uthansakul, K. Attakitmongkol, N. Promsuvana, M. Uthansakul

Abstract:

It is well known that the channel capacity of Multiple- Input-Multiple-Output (MIMO) system increases as the number of antenna pairs between transmitter and receiver increases but it suffers from multiple expensive RF chains. To reduce the cost of RF chains, Antenna Selection (AS) method can offer a good tradeoff between expense and performance. In a transmitting AS system, Channel State Information (CSI) feedback is necessarily required to choose the best subset of antennas in which the effects of delays and errors occurred in feedback channels are the most dominant factors degrading the performance of the AS method. This paper presents the concept of AS method using CSI from channel reciprocity instead of feedback method. Reciprocity technique can easily archive CSI by utilizing a reverse channel where the forward and reverse channels are symmetrically considered in time, frequency and location. In this work, the capacity performance of MIMO system when using AS method at transmitter with reciprocity channels is investigated by own developing Testbed. The obtained results show that reciprocity technique offers capacity close to a system with a perfect CSI and gains a higher capacity than a system without AS method from 0.9 to 2.2 bps/Hz at SNR 10 dB.

Keywords: Antenna Selection, Capacity, Channel, Measurement, MIMO, Reciprocity.

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Authors: Monika Chuchro, Maciej Dwornik

Abstract:

The extraction of meaningful information from image could be an alternative method for time series analysis. In this paper, we propose a graphical analysis of time series grouped into table with adjusted colour scale for numerical values. The advantages of this method are also discussed. The proposed method is easy to understand and is flexible to implement the standard methods of pattern recognition and verification, especially for noisy environmental data.

Keywords: graphical analysis, time series, seasonality, noisy environmental data

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Authors: Mayowa Adeyeye

Abstract:

This study was conducted to investigate the psychological variables motivating sport participation and involvement among student-athletes of tertiary institutions in southwest Nigeria. One thousand three hundred and fifty (N-1350) studentathletes were randomly selected in all sports from nine tertiary institutions in south-west Nigeria. These tertiary institutions include University of Lagos, Lagos State University, Obafemi Awolowo University, Osun State University, University of Ibadan, University of Agriculture Abeokuta, Federal University of Technology Akungba, University of Ilorin, and Kwara State University. The descriptive survey research method was adopted while a self developed validated Likert type questionnaire named Sport Participation Scale (SPS) was used to elicit opinion from respondents. The test-retest reliability value obtained for the instrument, using Pearson Product Moment Correlation Co-efficient was 0.96. Out of the one thousand three hundred and fifty (N-1350) questionnaire administered, only one thousand two hundred and five (N-1286) were correctly filled, coded and analysed using inferential statistics of Chi-Square (X2) while all the tested hypotheses were set at. 05 alpha level. Based on the findings of this study, the result revealed that several psychological factors influence student athletes to continue participation in sport one which includes love for the game, famous athletes as role model and family support. However, the analysis further revealed that the stipends the student-athletes get from their universities have no influence on their participation and involvement in sport.

Keywords: Family support, peer, role model, sport participation, student-athletes.

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Authors: R. Saraçoğlu, N. Allahverdi

Abstract:

Searching similar documents and document management subjects have important place in text mining. One of the most important parts of similar document research studies is the process of classifying or clustering the documents. In this study, a similar document search approach that includes discussion of out the case of belonging to multiple categories (multiple categories problem) has been carried. The proposed method that based on Fuzzy Similarity Classification (FSC) has been compared with Rocchio algorithm and naive Bayes method which are widely used in text mining. Empirical results show that the proposed method is quite successful and can be applied effectively. For the second stage, multiple categories vector method based on information of categories regarding to frequency of being seen together has been used. Empirical results show that achievement is increased almost two times, when proposed method is compared with classical approach.

Keywords: Document similarity, Fuzzy classification, Multiple categories, Text mining.

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Authors: C. Ardil

Abstract:

Intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PyFS), Picture fuzzy sets (PFS), q-rung orthopair fuzzy sets (q-ROF), Spherical fuzzy sets (SFS), T-spherical FS, and Neutrosophic sets (NS) are reviewed as multidimensional extensions of fuzzy sets in order to more explicitly and informatively describe the opinions of decision-making experts under uncertainty. To handle operations with standard fuzzy sets (SFS), the necessary operators; weighted arithmetic mean (WAM), weighted geometric mean (WGM), and Minkowski distance function are defined. The algorithm of the proposed proximity measure method (PMM) is provided with a multiple criteria group decision making method (MCDM) for use in a standard fuzzy set environment. To demonstrate the feasibility of the proposed method, the problem of selecting the best drone for an Air Force procurement request is used. The proximity measure method (PMM) based multidimensional standard fuzzy sets (SFS) is introduced to demonstrate its use with an issue involving unmanned combat aircraft selection.

Keywords: standard fuzzy sets (SFS), unmanned combat aircraft selection, multiple criteria decision making (MCDM), proximity measure method (PMM).

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Authors: Adekitan I. Aderibigbe, Fakolujo A. Olaosebikan

Abstract:

The parameters of a two-layer soil can be determined by processing resistivity data obtained from resistivity measurements carried out on the soil of interest. The processing usually entails applying the resistivity data as inputs to an optimisation function. This paper proposes an algorithm which utilises the square error as an optimisation function. Resistivity data from previous works were applied to test the accuracy of the new algorithm developed and the result obtained conforms significantly to results from previous works.

 

Keywords: Algorithm, earthing, resistivity, two-layer soil-model.

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Authors: Kewei Xu, Jens Friedrich, Kevin Dwinger, Wei Fan, Xijin Zhang

Abstract:

Parallel Compressor Model (PCM) is a simplified approach to predict compressor performance with inlet distortions. In PCM calculation, it is assumed that the sub-compressors’ outlet static pressure is uniform and therefore simplifies PCM calculation procedure. However, if the compressor’s outlet duct is not long and straight, such assumption frequently induces error ranging from 10% to 15%. This paper provides a revised calculation method of PCM that can correct the error. The revised method employs energy equation, momentum equation and continuity equation to acquire needed parameters and replace the equal static pressure assumption. Based on the revised method, PCM is applied on two compression system with different blades types. The predictions of their performance in non-uniform inlet conditions are yielded through the revised calculation method and are employed to evaluate the method’s efficiency. Validating the results by experimental data, it is found that although little deviation occurs, calculated result agrees well with experiment data whose error ranges from 0.1% to 3%. Therefore, this proves the revised calculation method of PCM possesses great advantages in predicting the performance of the distorted compressor with limited exhaust duct.

Keywords: Parallel Compressor Model (PCM), Revised Calculation Method, Inlet Distortion, Outlet Unequal Pressure Distribution.

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Authors: Amir Farkhonde

Abstract:

The major objective of this study was to devise a method for solving mathematical problems. Three concepts including faculty of understanding, faculty of guess, and free mind or beginner's mind provided the foundation for this method. An explanatory approach along with a hermeneutic process was taken in this study to support the assumption that mathematical knowledge is constantly developing and it seems essential for students to solve math problems on their own using their faculty of understanding (interpretive dialogue) and faculty of guess. For doing so, a kind of movement from the mathematical problem to mathematical knowledge should be adopted for teaching students a new math topic. The research method of this paper is review, descriptive and conception development. This paper first reviews the research findings on the NRICH’S project (NRICH is part of the family of activities in the Millennium Mathematics Project) with the aim that these findings form the theoretical basis of the problem-solving method. Then, the curriculum, the conceptual structure of the new method, how to design the problem and an example of it are discussed. In this way, students are immersed in the story of discovering and understanding the problem formula, and interpretive dialogue with the text continues by following the questions posed by the problem and constantly reconstructing the answer to find a formula or solution to solve the problem.

Keywords: Interpretive dialogue, NRICH, inventing, a method of problem solving.

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Authors: Kei Fujii, Jun Okawa, Kaori Suigetsu

Abstract:

Concatenative speech synthesis is a method that can make speech sound which has naturalness and high-individuality of a speaker by introducing a large speech corpus. Based on this method, in this paper, we propose a voice conversion method whose conversion speech has high-individuality and naturalness. The authors also have two subjective evaluation experiments for evaluating individuality and sound quality of conversion speech. From the results, following three facts have be confirmed: (a) the proposal method can convert the individuality of speakers well, (b) employing the framework of unit selection (especially join cost) of concatenative speech synthesis into conventional voice conversion improves the sound quality of conversion speech, and (c) the proposal method is robust against the difference of genders between a source speaker and a target speaker.

Keywords: concatenative speech synthesis, join cost, speaker individuality, unit selection, voice conversion

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Authors: Liang Zhao, Jili Zhang, Kai Li

Abstract:

A microcontroller-based fan coil unit (FCU) fuzzy controller is designed and implemented in this paper. The controller employs the concept of duty ratio on the electric valve control, which could make full use of the cooling and dehumidifying capacity of the FCU when the valve is off. The traditional control method and its limitations are analyzed. The hardware and software design processes are introduced in detail. The experimental results show that the proposed method is more energy efficient compared to the traditional controlling strategy. Furthermore, a more comfortable room condition could be achieved by the proposed method. The proposed low-cost FCU fuzzy controller deserves to be widely used in engineering applications.

Keywords: Fan coil unit, duty ratio, fuzzy controller, experiment.

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Authors: K.Ramesh, A.Nirmalkumar, G.Gurusamy

Abstract:

In this paper, a new model order reduction phenomenon is introduced at the design stage of linear phase digital IIR filter. The complexity of a system can be reduced by adopting the model order reduction method in their design. In this paper a mixed method of model order reduction is proposed for linear IIR filter. The proposed method employs the advantages of factor division technique to derive the reduced order denominator polynomial and the reduced order numerator is obtained based on the resultant denominator polynomial. The order reduction technique is used to reduce the delay units at the design stage of IIR filter. The validity of the proposed method is illustrated with design example in frequency domain and stability is also examined with help of nyquist plot.

Keywords: Error index (J), Factor division method, IIR filter, Nyquist plot, Order reduction.

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Authors: A. R. Salimi, M. Esmaeili, B. Salehi

Abstract:

The development and extension of large cities induced a need for shallow tunnel in soft ground of building areas. Estimation of ground settlement caused by the tunnel excavation is important engineering point. In this paper, prediction of surface subsidence caused by tunneling in one section of seventh line of Tehran subway is considered. On the basis of studied geotechnical conditions of the region, tunnel with the length of 26.9km has been excavated applying a mechanized method using an EPB-TBM with a diameter of 9.14m. In this regard, settlement is estimated utilizing both analytical and numerical finite element method. The numerical method shows that the value of settlement in this section is 5cm. Besides, the analytical consequences (Bobet and Loganathan-Polous) are 5.29 and 12.36cm, respectively. According to results of this study, due tosaturation of this section, there are good agreement between Bobet and numerical methods. Therefore, tunneling processes in this section needs a special consolidation measurement and support system before the passage of tunnel boring machine.

Keywords: TBM, Subsidence, Numerical Method, Analytical Method.

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Authors: Jan Barák, Karel Fraňa, Jörg Stiller

Abstract:

This work presents results of moist air condensation in heat exchanger. It describes theoretical knowledge and definition of moist air. Model with geometry of square canal was created for better understanding and postprocessing of condensation phenomena. Different approaches were examined on this model to find suitable software and model. Obtained knowledge was applied to geometry of real heat exchanger and results from experiment were compared with numerical results. One of the goals is to solve this issue without creating any user defined function in the applied code. It also contains summary of knowledge and outlook for future work.

Keywords: Condensation, exchanger, experiment, validation.

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Authors: O. M. Bamigbola, A. A. Ibrahim

Abstract:

Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined apriori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss- Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss- Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

Keywords: Linear system of equations, Gauss-Seidel iteration, algebraic structure, convergence.

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Authors: Indar Chaerah Gunadin, Adi Soeprijanto, Ontoseno Penangsang

Abstract:

This paper will discuss about an active power generator scheduling method in order to increase the limit level of steady state systems. Some power generator optimization methods such as Langrange, PLN (Indonesian electricity company) Operation, and the proposed Z-Thevenin-based method will be studied and compared in respect of their steady state aspects. A method proposed in this paper is built upon the thevenin equivalent impedance values between each load respected to each generator. The steady state stability index obtained with the REI DIMO method. This research will review the 500kV-Jawa-Bali interconnection system. The simulation results show that the proposed method has the highest limit level of steady state stability compared to other optimization techniques such as Lagrange, and PLN operation. Thus, the proposed method can be used to create the steady state stability limit of the system especially in the peak load condition.

Keywords: generation scheduling, steady-state stability limit, REI Dimo, margin stability

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Authors: Yanli Qi, Ning Lv, Jing Li

Abstract:

Sub-Nyquist sampling jamming method (SNSJ) is a well known deception jamming method for inverse synthetic aperture radar (ISAR). However, the anti-decoy of the SNSJ method performs easier since the amplitude of the false-target images are weaker than the real-target image; the false-target images always lag behind the real-target image, and all targets are located in the same cross-range. In order to overcome the drawbacks mentioned above, a simple modulation based on SNSJ (M-SNSJ) is presented in this paper. The method first uses amplitude modulation factor to make the amplitude of the false-target images consistent with the real-target image, then uses the down-range modulation factor and cross-range modulation factor to make the false-target images move freely in down-range and cross-range, respectively, thus the capacity of deception is improved. Finally, the simulation results on the six available combinations of three modulation factors are given to illustrate our conclusion.

Keywords: Inverse synthetic aperture radar, ISAR, deceptive jamming, Sub-Nyquist sampling jamming method, SNSJ, modulation based on Sub-Nyquist sampling jamming method, M-SNSJ.

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Authors: Irakli V. Gugushvili, Nickolay M. Evstigneev

Abstract:

Numerical integration of initial boundary problem for advection equation in 3 ℜ is considered. The method used is  conditionally stable semi-Lagrangian advection scheme with high order interpolation on unstructured mesh. In order to increase time step integration the BFECC method with limiter TVD correction is used. The method is adopted on parallel graphic processor unit environment using NVIDIA CUDA and applied in Navier-Stokes solver. It is shown that the calculation on NVIDIA GeForce 8800  GPU is 184 times faster than on one processor AMDX2 4800+ CPU. The method is extended to the incompressible fluid dynamics solver. Flow over a Cylinder for 3D case is compared to the experimental data.

Keywords: Advection equations, CUDA technology, Flow overthe 3D Cylinder, Incompressible Pressure Projection Solver, Parallel computation.

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Authors: Saeed Sarabadan, Kamal Rashedi

Abstract:

This article presents a numerical method to find the heat flux in an inhomogeneous inverse heat conduction problem with linear boundary conditions and an extra specification at the terminal. The method is based upon applying the satisfier function along with the Ritz-Galerkin technique to reduce the approximate solution of the inverse problem to the solution of a system of algebraic equations. The instability of the problem is resolved by taking advantage of the Landweber’s iterations as an admissible regularization strategy. In computations, we find the stable and low-cost results which demonstrate the efficiency of the technique.

Keywords: Inverse problem, parabolic equations, heat equation, Ritz-Galerkin method, Landweber iterations.

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Authors: P. Jelodarian , E. Farshidi

Abstract:

In this paper, a new approach for design of a fully differential second order current mode continuous-time sigma-delta modulator is presented. For circuit implementation, square root domain (SRD) translinear loop based on floating-gate MOS transistors that operate in saturation region is employed. The modulator features, low supply voltage, low power consumption (8mW) and high dynamic range (55dB). Simulation results confirm that this design is suitable for data converters.

Keywords: Sigma-delta, current-mode, translinear loop, geometric mean, squarer/divider.

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Authors: Aymen Laadhari, Gábor Székely

Abstract:

This paper is concerned with the development of a fully implicit and purely Eulerian fluid-structure interaction method tailored for the modeling of the large deformations of elastic membranes in a surrounding Newtonian fluid. We consider a simplified model for the mechanical properties of the membrane, in which the surface strain energy depends on the membrane stretching. The fully Eulerian description is based on the advection of a modified surface tension tensor, and the deformations of the membrane are tracked using a level set strategy. The resulting nonlinear problem is solved by a Newton-Raphson method, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the presented method. We show that stability is maintained for significantly larger time steps.

Keywords: Fluid-membrane interaction, stretching, Eulerian, finite element method, Newton, implicit.

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Authors: Nasser Shamskia, Seyyed Habib Rahmati, Hassan Haleh , Seyyedeh Hoda Rahmati

Abstract:

The main criteria of designing in the most hydraulic constructions essentially are based on runoff or discharge of water. Two of those important criteria are runoff and return period. Mostly, these measures are calculated or estimated by stochastic data. Another feature in hydrological data is their impreciseness. Therefore, in order to deal with uncertainty and impreciseness, based on Buckley-s estimation method, a new fuzzy method of evaluating hydrological measures are developed. The method introduces triangular shape fuzzy numbers for different measures in which both of the uncertainty and impreciseness concepts are considered. Besides, since another important consideration in most of the hydrological studies is comparison of a measure during different months or years, a new fuzzy method which is consistent with special form of proposed fuzzy numbers, is also developed. Finally, to illustrate the methods more explicitly, the two algorithms are tested on one simple example and a real case study.

Keywords: Fuzzy Discharge, Fuzzy estimation, Fuzzy ranking method, Hydrological data

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Authors: A. Ashok, K.Satapathy, B. Prerana Nashine

Abstract:

The objective of this research work is to investigate for one dimensional transient radiative transfer equations with conduction using finite volume method. Within the infrastructure of finite-volume, we obtain the conservative discretization of the terms in order to preserve the overall conservative property of finitevolume schemes. Coupling of conductive and radiative equation resulting in fluxes is governed by the magnitude of emissivity, extinction coefficient, and temperature of the medium as well as geometry of the problem. The problem under consideration has been solved, for a slab dominating radiation coupled with transient conduction based on finite volume method. The boundary conditions are also chosen so as to give a good model of the discretized form of radiation transfer equation. The important feature of the present method is flexibility in specifying the control angles in the FVM, while keeping the simplicity in the solution procedure. Effects of various model parameters are examined on the distributions of temperature, radiative and conductive heat fluxes and incident radiation energy etc. The finite volume method is considered to effectively evaluate the propagation of radiation intensity through a participating medium.

Keywords: Radiative transfer equation, finite volume method, conduction, transient radiation.

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Authors: Masrour Dowlatabadi, Jalil Shirazi

Abstract:

In this paper, an improved edge detection algorithm based on fuzzy combination of mathematical morphology and wavelet transform is proposed. The combined method is proposed to overcome the limitation of wavelet based edge detection and mathematical morphology based edge detection in noisy images. Experimental results show superiority of the proposed method, as compared to the traditional Prewitt, wavelet based and morphology based edge detection methods. The proposed method is an effective edge detection method for noisy image and keeps clear and continuous edges.

Keywords: Edge detection, Wavelet transform, Mathematical morphology, Fuzzy logic.

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Authors: Kaewkarn Phuangsombat, Arthit Phuangsombat, Anupun Terdwongworakul

Abstract:

Hard seeds will not grow and can cause mold in sprouting process. Thus, the hard seeds need to be separated from the normal seeds. Near infrared hyperspectral imaging in a range of 900 to 1700 nm was implemented to develop a model by partial least squares discriminant analysis to discriminate the hard seeds from the normal seeds. The orientation of the seeds was also studied to compare the performance of the models. The model based on hilum-up orientation achieved the best result giving the coefficient of determination of 0.98, and root mean square error of prediction of 0.07 with classification accuracy was equal to 100%.

Keywords: Mung bean, near infrared, germinatability, hard seed.

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Authors: János Levendovszky, András Oláh

Abstract:

In this paper, novel statistical sampling based equalization techniques and CNN based detection are proposed to increase the spectral efficiency of multiuser communication systems over fading channels. Multiuser communication combined with selective fading can result in interferences which severely deteriorate the quality of service in wireless data transmission (e.g. CDMA in mobile communication). The paper introduces new equalization methods to combat interferences by minimizing the Bit Error Rate (BER) as a function of the equalizer coefficients. This provides higher performance than the traditional Minimum Mean Square Error equalization. Since the calculation of BER as a function of the equalizer coefficients is of exponential complexity, statistical sampling methods are proposed to approximate the gradient which yields fast equalization and superior performance to the traditional algorithms. Efficient estimation of the gradient is achieved by using stratified sampling and the Li-Silvester bounds. A simple mechanism is derived to identify the dominant samples in real-time, for the sake of efficient estimation. The equalizer weights are adapted recursively by minimizing the estimated BER. The near-optimal performance of the new algorithms is also demonstrated by extensive simulations. The paper has also developed a (Cellular Neural Network) CNN based approach to detection. In this case fast quadratic optimization has been carried out by t, whereas the task of equalizer is to ensure the required template structure (sparseness) for the CNN. The performance of the method has also been analyzed by simulations.

Keywords: Cellular Neural Network, channel equalization, communication over fading channels, multiuser communication, spectral efficiency, statistical sampling.

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Authors: M. Mahdi, N. Shariatmadari

Abstract:

An important aspect of planning for shallow tunneling under urban areas is the determination of likely surface movements and interaction with existing structures. Back analysis of built tunnels that their settlements magnitude is available, could aid the designers to have a more accuracy in future projects.

In this paper, one single Tehran Metro Tunnel (at west of Hor square, Jang University Street) was selected. At first, surface settlements of this tunnel were measured in situ. Then this tunnel was modeled using the commercial finite deference software FLAC-3D. Finally, Results of modeling and in situ measurements compared for verification.

Keywords: Shallow Tunnel, Back Analysis, Surface Movement, Numerical Modeling.

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Authors: Abdenour Bounsiar, Edith Grall, Pierre Beauseroy

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In this paper we are interested in classification problems with a performance constraint on error probability. In such problems if the constraint cannot be satisfied, then a rejection option is introduced. For binary labelled classification, a number of SVM based methods with rejection option have been proposed over the past few years. All of these methods use two thresholds on the SVM output. However, in previous works, we have shown on synthetic data that using thresholds on the output of the optimal SVM may lead to poor results for classification tasks with performance constraint. In this paper a new method for supervised classification with rejection option is proposed. It consists in two different classifiers jointly optimized to minimize the rejection probability subject to a given constraint on error rate. This method uses a new kernel based linear learning machine that we have recently presented. This learning machine is characterized by its simplicity and high training speed which makes the simultaneous optimization of the two classifiers computationally reasonable. The proposed classification method with rejection option is compared to a SVM based rejection method proposed in recent literature. Experiments show the superiority of the proposed method.

Keywords: rejection, Chow's rule, error-reject tradeoff, SupportVector Machine.

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