Search results for: discretization error

Authors: Bashar Albaalbaki, Roger E. Khayat

Abstract:

This work is a comparative study on the effect of Delaunay triangulation algorithms on discretization error for conduction-convection conservation problems. A structured triangulation and many unstructured Delaunay triangulations using three popular algorithms for node placement strategies are used. The numerical method employed is the vertex-centered finite volume method. It is found that when the computational domain can be meshed using a structured triangulation, the discretization error is lower for structured triangulations compared to unstructured ones for only low Peclet number values, i.e. when conduction is dominant. However, as the Peclet number is increased and convection becomes more significant, the unstructured triangulations reduce the discretization error. Also, no statistical correlation between triangulation angle extremums and the discretization error is found using 200 samples of randomly generated Delaunay and non-Delaunay triangulations. Thus, the angle extremums cannot be an indicator of the discretization error on their own and need to be combined with other triangulation quality measures, which is the subject of further studies.

Keywords: Conduction-convection problems, Delaunay triangulation, discretization error, finite volume method.

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Authors: Taimur Qureshi, Djamel A Zighed

Abstract:

Many supervised induction algorithms require discrete data, even while real data often comes in a discrete and continuous formats. Quality discretization of continuous attributes is an important problem that has effects on speed, accuracy and understandability of the induction models. Usually, discretization and other types of statistical processes are applied to subsets of the population as the entire population is practically inaccessible. For this reason we argue that the discretization performed on a sample of the population is only an estimate of the entire population. Most of the existing discretization methods, partition the attribute range into two or several intervals using a single or a set of cut points. In this paper, we introduce a technique by using resampling (such as bootstrap) to generate a set of candidate discretization points and thus, improving the discretization quality by providing a better estimation towards the entire population. Thus, the goal of this paper is to observe whether the resampling technique can lead to better discretization points, which opens up a new paradigm to construction of soft decision trees.

Keywords: Bootstrap, discretization, resampling, soft decision trees.

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Authors: Tirthankar Ghosh, Dilip Roy, Nimai Kumar Chandra

Abstract:

Sometime it is difficult to determine the exact reliability for complex systems in analytical procedures. Approximate solution of this problem can be provided through discretization of random variables. In this paper we describe the usefulness of discretization of a random variable using the reversed hazard rate function of its continuous version. Discretization of the exponential distribution has been demonstrated. Applications of this approach have also been cited. Numerical calculations indicate that the proposed approach gives very good approximation of reliability of complex systems under stress-strength set-up. The performance of the proposed approach is better than the existing discrete concentration method of discretization. This approach is conceptually simple, handles analytic intractability and reduces computational time. The approach can be applied in manufacturing industries for producing high-reliable items.

Keywords: Discretization, Reversed Hazard Rate, Exponential distribution, reliability approximation, engineering item.

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Authors: Chansopheak Seang, Afia David Kouadri, Eric Ragneau

Abstract:

Three dimensional analysis of thermal model in laser full penetration welding, Nd:YAG, by transparent mode DP600 alloy steel 1.25mm of thickness and gap of 0.1mm. Three models studied the influence of thermal dependent temperature properties, thermal independent temperature and the effect of peak value of specific heat at phase transformation temperature, AC1, on the transient temperature. Another seven models studied the influence of discretization, meshes on the temperature distribution in weld plate. It is shown that for the effects of thermal properties, the errors less 4% of maximum temperature in FZ and HAZ have identified. The minimum value of discretization are at least one third increment per radius for temporal discretization and the spatial discretization requires two elements per radius and four elements through thickness of the assembled plate, which therefore represent the minimum requirements of modeling for the laser welding in order to get minimum errors less than 5% compared to the fine mesh.

Keywords: FEA, welding, discretization, ABAQUS user subroutine DFLUX

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Authors: W. Y. Leng, S. M. Shamsuddin

Abstract:

Fingerprint based identification system; one of a well known biometric system in the area of pattern recognition and has always been under study through its important role in forensic science that could help government criminal justice community. In this paper, we proposed an identification framework of individuals by means of fingerprint. Different from the most conventional fingerprint identification frameworks the extracted Geometrical element features (GEFs) will go through a Discretization process. The intention of Discretization in this study is to attain individual unique features that could reflect the individual varianceness in order to discriminate one person from another. Previously, Discretization has been shown a particularly efficient identification on English handwriting with accuracy of 99.9% and on discrimination of twins- handwriting with accuracy of 98%. Due to its high discriminative power, this method is adopted into this framework as an independent based method to seek for the accuracy of fingerprint identification. Finally the experimental result shows that the accuracy rate of identification of the proposed system using Discretization is 100% for FVC2000, 93% for FVC2002 and 89.7% for FVC2004 which is much better than the conventional or the existing fingerprint identification system (72% for FVC2000, 26% for FVC2002 and 32.8% for FVC2004). The result indicates that Discretization approach manages to boost up the classification effectively, and therefore prove to be suitable for other biometric features besides handwriting and fingerprint.

Keywords: Discretization, fingerprint identification, geometrical features, pattern recognition

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Authors: Naveed Ahmed, Gunar Matthies

Abstract:

We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.

Keywords: Convection-diffusion-reaction equations, stabilized finite elements, discontinuous Galerkin, continuous Galerkin-Petrov.

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Authors: Mehmet Hacibeyoglu, Ahmet Arslan, Sirzat Kahramanli

Abstract:

This study analyzes the effect of discretization on classification of datasets including continuous valued features. Six datasets from UCI which containing continuous valued features are discretized with entropy-based discretization method. The performance improvement between the dataset with original features and the dataset with discretized features is compared with k-nearest neighbors, Naive Bayes, C4.5 and CN2 data mining classification algorithms. As the result the classification accuracies of the six datasets are improved averagely by 1.71% to 12.31%.

Keywords: Data mining classification algorithms, entropy-baseddiscretization method

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Authors: S. Sfarni, E. Bellenger, J. Fortin, M. Guessasma

Abstract:

The use of the mechanical simulation (in particular the finite element analysis) requires the management of assumptions in order to analyse a real complex system. In finite element analysis (FEA), two modeling steps require assumptions to be able to carry out the computations and to obtain some results: the building of the physical model and the building of the simulation model. The simplification assumptions made on the analysed system in these two steps can generate two kinds of errors: the physical modeling errors (mathematical model, domain simplifications, materials properties, boundary conditions and loads) and the mesh discretization errors. This paper proposes a mesh adaptive method based on the use of an h-adaptive scheme in combination with an error estimator in order to choose the mesh of the simulation model. This method allows us to choose the mesh of the simulation model in order to control the cost and the quality of the finite element analysis.

Keywords: Finite element, discretization errors, adaptivity.

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Authors: José Alberto García Fernández, Zhimin Du, Xinqiao Jin

Abstract:

Nowadays, data center industry faces strong challenges for increasing the speed and data processing capacities while at the same time is trying to keep their devices a suitable working temperature without penalizing that capacity. Consequently, the cooling systems of this kind of facilities use a large amount of energy to dissipate the heat generated inside the servers, and developing new cooling techniques or perfecting those already existing would be a great advance in this type of industry. The installation of a temperature sensor matrix distributed in the structure of each server would provide the necessary information for collecting the required data for obtaining a temperature profile instantly inside them. However, the number of temperature probes required to obtain the temperature profiles with sufficient accuracy is very high and expensive. Therefore, other less intrusive techniques are employed where each point that characterizes the server temperature profile is obtained by solving differential equations through simulation methods, simplifying data collection techniques but increasing the time to obtain results. In order to reduce these calculation times, complicated and slow computational fluid dynamics simulations are replaced by simpler and faster finite element method simulations which solve the Burgers‘ equations by backward, forward and central discretization techniques after simplifying the energy and enthalpy conservation differential equations. The discretization methods employed for solving the first and second order derivatives of the obtained Burgers‘ equation after these simplifications are the key for obtaining results with greater or lesser accuracy regardless of the characteristic truncation error.

Keywords: Burgers’ equations, CFD simulation, data center, discretization methods, FEM simulation, temperature profile.

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Authors: Yeonsoo Jang, Dongweon Yoon, Ki Ho Kwon, Jaeyoon Lee, Wooju Lee

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Phase error in communications systems degrades error performance. In this paper, we present a simple approximation for the average error probability of the binary phase shift keying (BPSK) in the presence of phase error having a uniform distribution on arbitrary intervals. For the simple approximation, we use symmetry and periodicity of a sinusoidal function. Approximate result for the average error probability is derived, and the performance is verified through comparison with simulation result.

Keywords: Average error probability, Phase shift keying, Phase error

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Authors: Shuting Ji, Yueming Zhang, Jing Zhao

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The output error of the globoidal cam mechanism can be considered as a relevant indicator of mechanism performance, because it determines kinematic and dynamical behavior of mechanical transmission. Based on the differential geometry and the rigid body transformations, the mathematical model of surface geometry of the globoidal cam is established. Then we present the analytical expression of the output error (including the transmission error and the displacement error along the output axis) by considering different manufacture and assembly errors. The effects of the center distance error, the perpendicular error between input and output axes and the rotational angle error of the globoidal cam on the output error are systematically analyzed. A globoidal cam mechanism which is widely used in automatic tool changer of CNC machines is applied for illustration. Our results show that the perpendicular error and the rotational angle error have little effects on the transmission error but have great effects on the displacement error along the output axis. This study plays an important role in the design, manufacture and assembly of the globoidal cam mechanism.

Keywords: Globoidal cam mechanism, manufacture error, transmission error, automatic tool changer.

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Authors: R. Fatehi, M.A. Fayazbakhsh, M.T. Manzari

Abstract:

Discretization of spatial derivatives is an important issue in meshfree methods especially when the derivative terms contain non-linear coefficients. In this paper, various methods used for discretization of second-order spatial derivatives are investigated in the context of Smoothed Particle Hydrodynamics. Three popular forms (i.e. "double summation", "second-order kernel derivation", and "difference scheme") are studied using one-dimensional unsteady heat conduction equation. To assess these schemes, transient response to a step function initial condition is considered. Due to parabolic nature of the heat equation, one can expect smooth and monotone solutions. It is shown, however in this paper, that regardless of the type of kernel function used and the size of smoothing radius, the double summation discretization form leads to non-physical oscillations which persist in the solution. Also, results show that when a second-order kernel derivative is used, a high-order kernel function shall be employed in such a way that the distance of inflection point from origin in the kernel function be less than the nearest particle distance. Otherwise, solutions may exhibit oscillations near discontinuities unlike the "difference scheme" which unconditionally produces monotone results.

Keywords: Heat conduction, Meshfree methods, Smoothed ParticleHydrodynamics (SPH), Second-order derivatives.

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

Abstract:

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: Jiming Yang

Abstract:

A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.

Keywords: Convergence analysis, green's function, singularly perturbed, equi-distribution, moving mesh.

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Authors: E. Arsuaga Uriarte, F. Díaz Martín

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The SOM has several beneficial features which make it a useful method for data mining. One of the most important features is the ability to preserve the topology in the projection. There are several measures that can be used to quantify the goodness of the map in order to obtain the optimal projection, including the average quantization error and many topological errors. Many researches have studied how the topology preservation should be measured. One option consists of using the topographic error which considers the ratio of data vectors for which the first and second best BMUs are not adjacent. In this work we present a study of the behaviour of the topographic error in different kinds of maps. We have found that this error devaluates the rectangular maps and we have studied the reasons why this happens. Finally, we suggest a new topological error to improve the deficiency of the topographic error.

Keywords: Map lattice, Self-Organizing Map, topographic error, topology preservation.

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Authors: Vinita V. Sondur, Vilas B. Sondur, Narasimha H. Ayachit

Abstract:

It is observed that the Weighted least-square (WLS) technique, including the modifications, results in equiripple error curve. The resultant error as a percent of the ideal value is highly non-uniformly distributed over the range of frequencies for which the differentiator is designed. The present paper proposes a modification to the technique so that the optimization procedure results in lower maximum relative error compared to the ideal values. Simulation results for first order as well as higher order differentiators are given to illustrate the excellent performance of the proposed method.

Keywords: Differentiator, equiripple, error distribution, relative error.

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Authors: Sang-Chul Kim, Sung-Il Chien

Abstract:

The error diffusion method generates worm artifacts, and weakens the edge of the halftone image when the continuous gray scale image is reproduced by a binary image. First, to enhance the edges, we propose the edge-enhancing filter by considering the quantization error information and gradient of the neighboring pixels. Furthermore, to remove worm artifacts often appearing in a halftone image, we add adaptively random noise into the weights of an error filter.

Keywords: Artifact suppression, Edge enhancement, Error diffusion method, Halftone image

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

Abstract:

In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results is in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes.

Keywords: Semi-Lagrangian method, Iteration free method, Nonlinear advection-diffusion equation.

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Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

Abstract:

This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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Authors: Yung-Yuan Hsu

Abstract:

The primary objective of this paper was to construct a “kinematic parameter-independent modeling of three-axis machine tools for geometric error measurement" technique. Improving the accuracy of the geometric error for three-axis machine tools is one of the machine tools- core techniques. This paper first applied the traditional method of HTM to deduce the geometric error model for three-axis machine tools. This geometric error model was related to the three-axis kinematic parameters where the overall errors was relative to the machine reference coordinate system. Given that the measurement of the linear axis in this model should be on the ideal motion axis, there were practical difficulties. Through a measurement method consolidating translational errors and rotational errors in the geometric error model, we simplified the three-axis geometric error model to a kinematic parameter-independent model. Finally, based on the new measurement method corresponding to this error model, we established a truly practical and more accurate error measuring technique for three-axis machine tools.

Keywords: Three-axis machine tool, Geometric error, HTM, Error measuring

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Authors: M. T. Anwar, P. K. Lala, P. Thenappan

Abstract:

This paper presents the decoder design for the single error correcting and double error detecting code proposed by the authors in an earlier paper. The speed of error detection and correction of a code is largely dependent upon the associated encoder and decoder circuits. The complexity and the speed of such circuits are determined by the number of 1?s in the parity check matrix (PCM). The number of 1?s in the parity check matrix for the code proposed by the authors are fewer than in any currently known single error correcting/double error detecting code. This results in simplified encoding and decoding circuitry for error detection and correction.

Keywords: Decoder, Hsiao code, Parity Check Matrix, Syndrome Pattern.

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Authors: Danni Cong, Meiping Wu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokuncai, Hao Qin

Abstract:

Gravity gradient instrument (GGI) is the core of the gravity gradiometer, so the structural error of the sensor has a great impact on the measurement results. In order not to affect the aimed measurement accuracy, limit error is required in the installation of the accelerometer. In this paper, based on the established measuring principle model, the radial installation limit error is calibrated, which is taken as an example to provide a method to calculate the other limit error of the installation under the premise of ensuring the accuracy of the measurement result. This method provides the idea for deriving the limit error of the geometry structure of the sensor, laying the foundation for the mechanical precision design and physical design.

Keywords: Gravity gradient sensor, radial installation limit error, accelerometer, uniaxial rotational modulation.

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Authors: O. P. Sharma, V. Janyani, S. Sancheti

Abstract:

Data rate, tolerable bit error rate or frame error rate and range & coverage are the key performance requirement of a communication link. In this paper performance of MFSK link is analyzed in terms of bit error rate, number of errors and total number of data processed. In the communication link model proposed, which is implemented using MATLAB block set, an improvement in BER is observed. Different parameters which effects and enables to keep BER low in M-ary communication system are also identified.

Keywords: Additive White Gaussian Noise (AWGN), Bit Error Rate (BER), Frequency Shift Keying (FSK), Orthogonal Signaling.

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Authors: Hae-Yeoun Lee

Abstract:

Reversible watermarking that not only protects the copyright but also preserve the original quality of the digital content have been intensively studied. In particular, the demand for reversible watermarking has increased. In this paper, we propose a reversible watermarking scheme based on interpolation-error shifting and error pre-compensation. The intensity of a pixel is interpolated from the intensities of neighboring pixels, and the difference histogram between the interpolated and the original intensities is obtained and modified to embed the watermark message. By restoring the difference histogram, the embedded watermark is extracted and the original image is recovered by compensating for the interpolation error. The overflow and underflow are prevented by error pre-compensation. To show the performance of the method, the proposed algorithm is compared with other methods using various test images.

Keywords: Reversible watermarking, High capacity, High quality, Interpolated error shifting, Error pre-compensation.

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Authors: Heesung Lee, Joonkyung Sung, Euntai Kim

Abstract:

This paper proposes a method which reduces power consumption in single-error correcting, double error-detecting checker circuits that perform memory error correction code. Power is minimized with little or no impact on area and delay, using the degrees of freedom in selecting the parity check matrix of the error correcting codes. The genetic algorithm is employed to solve the non linear power optimization problem. The method is applied to two commonly used SEC-DED codes: standard Hamming and odd column weight Hsiao codes. Experiments were performed to show the performance of the proposed method.

Keywords: Error correcting codes, genetic algorithm, non-linearpower optimization, Hamming code, Hsiao code.

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Authors: T. Hirner, J. Polec

Abstract:

This paper describes a new method of unequal error protection (UEP) for region of interest (ROI) with embedded zerotree wavelet algorithm (EZW). ROI technique is important in applications with different parts of importance. In ROI coding, a chosen ROI is encoded with higher quality than the background (BG). Unequal error protection of image is provided by different coding techniques. In our proposed method, image is divided into two parts (ROI, BG) that consist of more important bytes (MIB) and less important bytes (LIB). The experimental results verify effectiveness of the design. The results of our method demonstrate the comparison of the unequal error protection (UEP) of image transmission with defined ROI and the equal error protection (EEP) over multiple noisy channels.

Keywords: embedded zerotree wavelet (EZW), equal error protection (EEP), region of interest (ROI), RS code, unequal error protection (UEP)

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Authors: Yu-Sheng Lee, Qi An

Abstract:

Offset mismatch, gain mismatch, and time-skew error between time-interleaved channels limit the performance of time-interleaved analog-to-digital converters (TIADC). This paper focused on the time-skew error. A new technique for calibrating time-skew error in M-channels TIADC is described, and simulation results are also presented.

Keywords: Calibration, time-skew error, time-interleavedanalog-to-digital converters.

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Authors: Cuiran Li, Jianli Xie, Chengshu Li

Abstract:

In the paper, the performance of quasi-synchronous CDMA (QS-CDMA) system, which can allow an increased timing error in synchronized access, is discussed. Average BER performance of the system is analyzed in the condition of different access timing error and different asynchronous users by simulation in AWGN channel. The results show that QS-CDMA system is shown to have great performance gain over the asynchronous system when access timing error is within a few chips and asynchronous users is tolerable. However, with access timing error increasing and asynchronous users increasing, the performance of QS-CDMA will degrade. Also, we can determine the number of tolerable asynchronous users for different access timing error by simulation figures.

Keywords: Code-division multiple access, Quasi-SynchronousCDMA, Access timing error

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Authors: Rabiˆı DARITI, El Mamoun SOUIDI

Abstract:

Linear error-block codes are a natural generalization of linear error correcting codes. The purpose of this paper is to generalize some results on the packing and the covering radii to the error-block case. We study their properties when a code undergoes some specific modifications and combinations with another code. We give a few bounds on the packing and the covering radii of these codes.

Keywords: Linear error-block codes, π-distance, Correction capacity, Packing radius, Covering radius.

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Authors: Wenlong Feng, Zhenchun Du, Jianguo Yang

Abstract:

To decrease the grating scale thermal expansion error, a novel method which based on multiple temperature detection is proposed. Several temperature sensors are installed on the grating scale and the temperatures of these sensors are recorded. The temperatures of every point on the grating scale are calculated by interpolating between adjacent sensors. According to the thermal expansion principle, the grating scale thermal expansion error model can be established by doing the integral for the variations of position and temperature. A novel compensation method is proposed in this paper. By applying the established error model, the grating scale thermal expansion error is decreased by 90% compared with no compensation. The residual positioning error of the grating scale is less than 15μm/10m and the accuracy of the machine tool is significant improved.

Keywords: Thermal expansion error of grating scale, error compensation, machine tools, integral method.

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