Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 170

Search results for: spline interpolation

170 Extended Cubic B-spline Interpolation Method Applied to Linear Two-Point Boundary Value Problems

Authors: Nur Nadiah Abd Hamid, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

Abstract:

Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method.

Keywords: two-point boundary value problem, B-spline, extendedcubic B-spline.

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169 Cubic Trigonometric B-Spline Applied to Linear Two-Point Boundary Value Problems of Order Two

Authors: Nur Nadiah Abd Hamid , Ahmad Abd. Majid, Ahmad Izani Md. Ismail

Abstract:

Linear two-point boundary value problems of order two are solved using cubic trigonometric B-spline interpolation method (CTBIM). Cubic trigonometric B-spline is a piecewise function consisting of trigonometric equations. This method is tested on some problems and the results are compared with cubic B-spline interpolation method (CBIM) from the literature. CTBIM is found to approximate the solution slightly more accurately than CBIM if the problems are trigonometric.

Keywords: trigonometric B-spline, two-point boundary valueproblem, spline interpolation, cubic spline

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168 A New Quadrature Rule Derived from Spline Interpolation with Error Analysis

Authors: Hadi Taghvafard

Abstract:

We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to Lp are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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167 Solving One-dimensional Hyperbolic Telegraph Equation Using Cubic B-spline Quasi-interpolation

Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

In this paper, the telegraph equation is solved numerically by cubic B-spline quasi-interpolation .We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions by calculating errors L2 and L∞ norms to confirm the good accuracy of the presented scheme.

Keywords: Cubic B-spline, quasi-interpolation, collocation method, second-order hyperbolic telegraph equation.

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166 Evaluating Sinusoidal Functions by a Low Complexity Cubic Spline Interpolator with Error Optimization

Authors: Abhijit Mitra, Harpreet Singh Dhillon

Abstract:

We present a novel scheme to evaluate sinusoidal functions with low complexity and high precision using cubic spline interpolation. To this end, two different approaches are proposed to find the interpolating polynomial of sin(x) within the range [- π , π]. The first one deals with only a single data point while the other with two to keep the realization cost as low as possible. An approximation error optimization technique for cubic spline interpolation is introduced next and is shown to increase the interpolator accuracy without increasing complexity of the associated hardware. The architectures for the proposed approaches are also developed, which exhibit flexibility of implementation with low power requirement.

Keywords: Arithmetic, spline interpolator, hardware design, erroranalysis, optimization methods.

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165 Visualization of Sediment Thickness Variation for Sea Bed Logging using Spline Interpolation

Authors: Hanita Daud, Noorhana Yahya, Vijanth Sagayan, Muizuddin Talib

Abstract:

This paper discusses on the use of Spline Interpolation and Mean Square Error (MSE) as tools to process data acquired from the developed simulator that shall replicate sea bed logging environment. Sea bed logging (SBL) is a new technique that uses marine controlled source electromagnetic (CSEM) sounding technique and is proven to be very successful in detecting and characterizing hydrocarbon reservoirs in deep water area by using resistivity contrasts. It uses very low frequency of 0.1Hz to 10 Hz to obtain greater wavelength. In this work the in house built simulator was used and was provided with predefined parameters and the transmitted frequency was varied for sediment thickness of 1000m to 4000m for environment with and without hydrocarbon. From series of simulations, synthetics data were generated. These data were interpolated using Spline interpolation technique (degree of three) and mean square error (MSE) were calculated between original data and interpolated data. Comparisons were made by studying the trends and relationship between frequency and sediment thickness based on the MSE calculated. It was found that the MSE was on increasing trends in the set up that has the presence of hydrocarbon in the setting than the one without. The MSE was also on decreasing trends as sediment thickness was increased and with higher transmitted frequency.

Keywords: Spline Interpolation, Mean Square Error, Sea Bed Logging, Controlled Source Electromagnetic

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164 Numerical Grid Generation of Oceanic Model for the Andaman Sea

Authors: Nitima Aschariyaphotha, Pratan Sakkaplangkul, Anirut Luadsong

Abstract:

The study of the Andaman Sea can be studied by using the oceanic model; therefore the grid covering the study area should be generated. This research aims to generate grid covering the Andaman Sea, situated between longitudes 90◦E to 101◦E and latitudes 1◦N to 18◦N. A horizontal grid is an orthogonal curvilinear with 87 × 217 grid points. The methods used in this study are cubic spline and bilinear interpolations. The boundary grid points are generated by spline interpolation while the interior grid points have to be specified by bilinear interpolation method. A vertical grid is sigma coordinate with 15 layers of water column.

Keywords: Sigma Coordinate, Curvilinear Coordinate, AndamanSea.

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163 Line Heating Forming: Methodology and Application Using Kriging and Fifth Order Spline Formulations

Authors: Henri Champliaud, Zhengkun Feng, Ngan Van Lê, Javad Gholipour

Abstract:

In this article, a method is presented to effectively estimate the deformed shape of a thick plate due to line heating. The method uses a fifth order spline interpolation, with up to C3 continuity at specific points to compute the shape of the deformed geometry. First and second order derivatives over a surface are the resulting parameters of a given heating line on a plate. These parameters are determined through experiments and/or finite element simulations. Very accurate kriging models are fitted to real or virtual surfaces to build-up a database of maps. Maps of first and second order derivatives are then applied on numerical plate models to evaluate their evolving shapes through a sequence of heating lines. Adding an optimization process to this approach would allow determining the trajectories of heating lines needed to shape complex geometries, such as Francis turbine blades.

Keywords: Deformation, kriging, fifth order spline interpolation, first, second and third order derivatives, C3 continuity, line heating, plate forming, thermal forming.

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162 Quartic Nonpolynomial Spline Solutions for Third Order Two-Point Boundary Value Problem

Authors: Talaat S. El-Danaf

Abstract:

In this paper, we develop quartic nonpolynomial spline method for the numerical solution of third order two point boundary value problems. It is shown that the new method gives approximations, which are better than those produced by other spline methods. Convergence analysis of the method is discussed through standard procedures. Two numerical examples are given to illustrate the applicability and efficiency of the novel method.

Keywords: Quartic nonpolynomial spline, Two-point boundary value problem.

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161 Application of Higher Order Splines for Boundary Value Problems

Authors: Pankaj Kumar Srivastava

Abstract:

Bringing forth a survey on recent higher order spline techniques for solving boundary value problems in ordinary differential equations. Here we have discussed the summary of the articles since 2000 till date based on higher order splines like Septic, Octic, Nonic, Tenth, Eleventh, Twelfth and Thirteenth Degree splines. Comparisons of methods with own critical comments as remarks have been included.

Keywords: Septic spline, Octic spline, Nonic spline, Tenth, Eleventh, Twelfth and Thirteenth Degree spline, parametric and non-parametric splines, thermal instability, astrophysics.

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160 Beta-spline Surface Fitting to Multi-slice Images

Authors: Normi Abdul Hadi, Arsmah Ibrahim, Fatimah Yahya, Jamaludin Md. Ali

Abstract:

Beta-spline is built on G2 continuity which guarantees smoothness of generated curves and surfaces using it. This curve is preferred to be used in object design rather than reconstruction. This study however, employs the Beta-spline in reconstructing a 3- dimensional G2 image of the Stanford Rabbit. The original data consists of multi-slice binary images of the rabbit. The result is then compared with related works using other techniques.

Keywords: Beta-spline, multi-slice image, rectangular surface, 3D reconstruction

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159 Cantor Interpolating Spline to Design Electronic Mail Boxes

Authors: Adil Al-Rammahi

Abstract:

Electronic mail is very important in present time. Many researchers work for designing, improving, securing, fasting, goodness and others fields in electronic mail. This paper introduced new algorithm to use Cantor sets and cubic spline interpolating function in the electronic mail design. Cantor sets used as the area (or domain) of the mail, while spline function used for designing formula. The roots of spline function versus Cantor sets used as the controller admin. The roots calculated by the numerical Newton – Raphson's method. The result of this algorithm was promised.

Keywords: Cantor sets, spline, electronic mail design, Newton – Raphson's method.

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158 A Comparison of the Nonparametric Regression Models using Smoothing Spline and Kernel Regression

Authors: Dursun Aydin

Abstract:

This paper study about using of nonparametric models for Gross National Product data in Turkey and Stanford heart transplant data. It is discussed two nonparametric techniques called smoothing spline and kernel regression. The main goal is to compare the techniques used for prediction of the nonparametric regression models. According to the results of numerical studies, it is concluded that smoothing spline regression estimators are better than those of the kernel regression.

Keywords: Kernel regression, Nonparametric models, Prediction, Smoothing spline.

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157 Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices

Authors: Khosrow Maleknejad, Yaser Rostami

Abstract:

In this paper, Semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions

Keywords: Integro-differential equations, Quartic B-spline wavelet, Operational matrices.

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156 Design of Compliant Mechanism Based Microgripper with Three Finger Using Topology Optimization

Authors: R. Bharanidaran, B. T. Ramesh

Abstract:

High precision in motion is required to manipulate the micro objects in precision industries for micro assembly, cell manipulation etc. Precision manipulation is achieved based on the appropriate mechanism design of micro devices such as microgrippers. Design of a compliant based mechanism is the better option to achieve a highly precised and controlled motion. This research article highlights the method of designing a compliant based three fingered microgripper suitable for holding asymmetric objects. Topological optimization technique, a systematic method is implemented in this research work to arrive a topologically optimized design of the mechanism needed to perform the required micro motion of the gripper. Optimization technique has a drawback of generating senseless regions such as node to node connectivity and staircase effect at the boundaries. Hence, it is required to have post processing of the design to make it manufacturable. To reduce the effect of post processing stage and to preserve the edges of the image, a cubic spline interpolation technique is introduced in the MATLAB program. Structural performance of the topologically developed mechanism design is tested using finite element method (FEM) software. Further the microgripper structure is examined to find its fatigue life and vibration characteristics.

Keywords: Compliant mechanism, Cubic spline interpolation, FEM, Topology optimization.

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155 Interpolation of Geofield Parameters

Authors: A. Pashayev, C. Ardil, R. Sadiqov

Abstract:

Various methods of geofield parameters restoration (by algebraic polynoms; filters; rational fractions; interpolation splines; geostatistical methods – kriging; search methods of nearest points – inverse distance, minimum curvature, local – polynomial interpolation; neural networks) have been analyzed and some possible mistakes arising during geofield surface modeling have been presented.

Keywords: interpolation methods, geofield parameters, neural networks.

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154 Application of Generalized NAUT B-Spline Curveon Circular Domain to Generate Circle Involute

Authors: Ashok Ganguly, Pranjali Arondekar

Abstract:

In the present paper, we use generalized B-Spline curve in trigonometric form on circular domain, to capture the transcendental nature of circle involute curve and uncertainty characteristic of design. The required involute curve get generated within the given tolerance limit and is useful in gear design.

Keywords: Bézier, Circle Involute, NAUT B-Spline, Spur Gear.

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153 Non-Polynomial Spline Method for the Solution of Problems in Calculus of Variations

Authors: M. Zarebnia, M. Hoshyar, M. Sedaghati

Abstract:

In this paper, a numerical solution based on nonpolynomial cubic spline functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.

Keywords: Calculus of variation; Non-polynomial spline functions; Numerical method

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152 GMDH Modeling Based on Polynomial Spline Estimation and Its Applications

Authors: LI qiu-min, TIAN yi-xiang, ZHANG gao-xun

Abstract:

GMDH algorithm can well describe the internal structure of objects. In the process of modeling, automatic screening of model structure and variables ensure the convergence rate.This paper studied a new GMDH model based on polynomial spline  stimation. The polynomial spline function was used to instead of the transfer function of GMDH to characterize the relationship between the input variables and output variables. It has proved that the algorithm has the optimal convergence rate under some conditions. The empirical results show that the algorithm can well forecast Consumer Price Index (CPI).

Keywords: spline, GMDH, nonparametric, bias, forecast.

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151 Spline Collocation for Solving System of Fredholm and Volterra Integral Equations

Authors: N. Ebrahimi, J. Rashidinia

Abstract:

In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.

Keywords: Convergence analysis, Cubic B-spline, Newton- Cotes formula, System of Fredholm and Volterra integral equations.

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150 Statistical Approach to Basis Function Truncation in Digital Interpolation Filters

Authors: F. Castillo, J. Arellano, S. Sánchez

Abstract:

In this paper an alternative analysis in the time domain is described and the results of the interpolation process are presented by means of functions that are based on the rule of conditional mathematical expectation and the covariance function. A comparison between the interpolation error caused by low order filters and the classic sinc(t) truncated function is also presented. When fewer samples are used, low-order filters have less error. If the number of samples increases, the sinc(t) type functions are a better alternative. Generally speaking there is an optimal filter for each input signal which depends on the filter length and covariance function of the signal. A novel scheme of work for adaptive interpolation filters is also presented.

Keywords: Interpolation, basis function, over-sampling.

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149 Better Perception of Low Resolution Images Using Wavelet Interpolation Techniques

Authors: Tarun Gulati, Kapil Gupta, Dushyant Gupta

Abstract:

High resolution images are always desired as they contain the more information and they can better represent the original data. So, to convert the low resolution image into high resolution interpolation is done. The quality of such high resolution image depends on the interpolation function and is assessed in terms of sharpness of image. This paper focuses on Wavelet based Interpolation Techniques in which an input image is divided into subbands. Each subband is processed separately and finally combined the processed subbandsto get the super resolution image. 

Keywords: SWT, DWTSR, DWTSWT, DWCWT.

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148 Quintic Spline Solution of Fourth-Order Parabolic Equations Arising in Beam Theory

Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: Fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis.

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147 The Estimation Method of Stress Distribution for Beam Structures Using the Terrestrial Laser Scanning

Authors: Sang Wook Park, Jun Su Park, Byung Kwan Oh, Yousok Kim, Hyo Seon Park

Abstract:

This study suggests the estimation method of stress distribution for the beam structures based on TLS (Terrestrial Laser Scanning). The main components of method are the creation of the lattices of raw data from TLS to satisfy the suitable condition and application of CSSI (Cubic Smoothing Spline Interpolation) for estimating stress distribution. Estimation of stress distribution for the structural member or the whole structure is one of the important factors for safety evaluation of the structure. Existing sensors which include ESG (Electric strain gauge) and LVDT (Linear Variable Differential Transformer) can be categorized as contact type sensor which should be installed on the structural members and also there are various limitations such as the need of separate space where the network cables are installed and the difficulty of access for sensor installation in real buildings. To overcome these problems inherent in the contact type sensors, TLS system of LiDAR (light detection and ranging), which can measure the displacement of a target in a long range without the influence of surrounding environment and also get the whole shape of the structure, has been applied to the field of structural health monitoring. The important characteristic of TLS measuring is a formation of point clouds which has many points including the local coordinate. Point clouds are not linear distribution but dispersed shape. Thus, to analyze point clouds, the interpolation is needed vitally. Through formation of averaged lattices and CSSI for the raw data, the method which can estimate the displacement of simple beam was developed. Also, the developed method can be extended to calculate the strain and finally applicable to estimate a stress distribution of a structural member. To verify the validity of the method, the loading test on a simple beam was conducted and TLS measured it. Through a comparison of the estimated stress and reference stress, the validity of the method is confirmed.

Keywords: Structural health monitoring, terrestrial laser scanning, estimation of stress distribution, coordinate transformation, cubic smoothing spline interpolation.

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146 A Conservative Multi-block Algorithm for Two-dimensional Numerical Model

Authors: Yaoxin Zhang, Yafei Jia, Sam S.Y. Wang

Abstract:

A multi-block algorithm and its implementation in two-dimensional finite element numerical model CCHE2D are presented. In addition to a conventional Lagrangian Interpolation Method (LIM), a novel interpolation method, called Consistent Interpolation Method (CIM), is proposed for more accurate information transfer across the interfaces. The consistent interpolation solves the governing equations over the auxiliary elements constructed around the interpolation nodes using the same numerical scheme used for the internal computational nodes. With the CIM, the momentum conservation can be maintained as well as the mass conservation. An imbalance correction scheme is used to enforce the conservation laws (mass and momentum) across the interfaces. Comparisons of the LIM and the CIM are made using several flow simulation examples. It is shown that the proposed CIM is physically more accurate and produces satisfactory results efficiently.

Keywords: Multi-block algorithm, conservation, interpolation, numerical model, flow simulation.

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145 Non-Polynomial Spline Solution of Fourth-Order Obstacle Boundary-Value Problems

Authors: Jalil Rashidinia, Reza Jalilian

Abstract:

In this paper we use quintic non-polynomial spline functions to develop numerical methods for approximation to the solution of a system of fourth-order boundaryvalue problems associated with obstacle, unilateral and contact problems. The convergence analysis of the methods has been discussed and shown that the given approximations are better than collocation and finite difference methods. Numerical examples are presented to illustrate the applications of these methods, and to compare the computed results with other known methods.

Keywords: Quintic non-polynomial spline, Boundary formula, Convergence, Obstacle problems.

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144 Cubic Trigonometric B-spline Approach to Numerical Solution of Wave Equation

Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

Abstract:

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: Collocation method, Cubic trigonometric B-spline, Finite difference, Wave equation.

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143 Strength Optimization of Induction Hardened Splined Shaft – Material and Geometric Aspects

Authors: I. Barsoum, F. Khan

Abstract:

the current study presents a modeling framework to determine the torsion strength of an induction hardened splined shaft by considering geometry and material aspects with the aim to optimize the static torsion strength by selection of spline geometry and hardness depth. Six different spline geometries and seven different hardness profiles including non-hardened and throughhardened shafts have been considered. The results reveal that the torque that causes initial yielding of the induction hardened splined shaft is strongly dependent on the hardness depth and the geometry of the spline teeth. Guidelines for selection of the appropriate hardness depth and spline geometry are given such that an optimum static torsion strength of the component can be achieved.

Keywords: Static strength, splined shaft, torsion, induction hardening, hardness profile, finite element, optimization, design.

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142 A Comparison of Some Splines-Based Methods for the One-dimensional Heat Equation

Authors: Joan Goh, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

Abstract:

In this paper, collocation based cubic B-spline and extended cubic uniform B-spline method are considered for solving one-dimensional heat equation with a nonlocal initial condition. Finite difference and θ-weighted scheme is used for time and space discretization respectively. The stability of the method is analyzed by the Von Neumann method. Accuracy of the methods is illustrated with an example. The numerical results are obtained and compared with the analytical solutions.

Keywords: Heat equation, Collocation based, Cubic Bspline, Extended cubic uniform B-spline.

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141 A Localized Interpolation Method Using Radial Basis Functions

Authors: Mehdi Tatari

Abstract:

Finding the interpolation function of a given set of nodes is an important problem in scientific computing. In this work a kind of localization is introduced using the radial basis functions which finds a sufficiently smooth solution without consuming large amount of time and computer memory. Some examples will be presented to show the efficiency of the new method.

Keywords: Radial basis functions, local interpolation method, closed form solution.

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