Search results for: truncated spline

Authors: Kornelius Ronald Demu, Dewi Retno Sari Saputro, Purnami Widyaningsih

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Human Development Index (HDI) is a standard measurement for a country's human development. Several factors may have influenced it, such as life expectancy, gross domestic product (GDP) based on the province's annual expenditure, the number of poor people, and the percentage of an illiterate people. The scatter plot between HDI and the influenced factors show that the plot does not follow a specific pattern or form. Therefore, the HDI's data in Indonesia can be applied with a nonparametric regression model. The estimation of the regression curve in the nonparametric regression model is flexible because it follows the shape of the data pattern. One of the nonparametric regression's method is a truncated spline. Truncated spline regression is one of the nonparametric approach, which is a modification of the segmented polynomial functions. The estimator of a truncated spline regression model was affected by the selection of the optimal knots point. Knot points is a focus point of spline truncated functions. The optimal knots point was determined by the minimum value of generalized cross validation (GCV). In this article were applied the data of Human Development Index with a truncated spline nonparametric regression model. The results of this research were obtained the best-truncated spline regression model to the HDI's data in Indonesia with the combination of optimal knots point 5-5-5-4. Life expectancy and the percentage of an illiterate people were the significant factors depend to the HDI in Indonesia. The coefficient of determination is 94.54%. This means the regression model is good enough to applied on the data of HDI in Indonesia.

Keywords: generalized cross validation (GCV), Human Development Index (HDI), knots point, nonparametric regression, truncated spline

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Authors: Maryam Khazaei Pool, Lori Lewis

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This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method, Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper, we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions, including Burgers equation, spline functions, and B-spline functions, are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided, and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ equation, Septic B-spline, modified cubic B-spline differential quadrature method, exponential cubic B-spline technique, B-spline Galerkin method, quintic B-spline Galerkin method

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Authors: Autcha Araveeporn

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This paper presents a study about a nonparametric regression model consisting of a smoothing spline method and a penalized spline regression method. We also compare the techniques used for estimation and prediction of nonparametric regression model. We tried both methods with crude oil prices in dollars per barrel and the Stock Exchange of Thailand (SET) index. According to the results, it is concluded that smoothing spline method performs better than that of penalized spline regression method.

Keywords: nonparametric regression model, penalized spline regression method, smoothing spline method, Stock Exchange of Thailand (SET)

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Authors: Sifriyani Sifriyani, I Nyoman Budiantara, Sri Haryatmi, Gunardi Gunardi

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East Java Province has a first rank as a province that has the most counties and cities in Indonesia and has the largest population. In 2015, the population reached 38.847.561 million, this figure showed a very high population growth. High population growth is feared to lead to increase the levels of unemployment. In this study, the researchers mapped and modeled the unemployment rate with 6 variables that were supposed to influence. Modeling was done by nonparametric geographically weighted regression methods with truncated spline approach. This method was chosen because spline method is a flexible method, these models tend to look for its own estimation. In this modeling, there were point knots, the point that showed the changes of data. The selection of the optimum point knots was done by selecting the most minimun value of Generalized Cross Validation (GCV). Based on the research, 6 variables were declared to affect the level of unemployment in eastern Java. They were the percentage of population that is educated above high school, the rate of economic growth, the population density, the investment ratio of total labor force, the regional minimum wage and the ratio of the number of big industry and medium scale industry from the work force. The nonparametric geographically weighted regression models with truncated spline approach had a coefficient of determination 98.95% and the value of MSE equal to 0.0047.

Keywords: East Java, nonparametric geographically weighted regression, spatial, spline approach, unemployed rate

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Authors: Ritu Rani

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In this paper, we apply minimalistically upheld linear semi-orthogonal B-spline wavelets, exceptionally developed for the limited interim to rough the obscure function present in the integral equations. Semi-orthogonal wavelets utilizing B-spline uniquely developed for the limited interim and these wavelets can be spoken to in a shut frame. This gives a minimized help. Semi-orthogonal wavelets frame the premise in the space L²(R). Utilizing this premise, an arbitrary function in L²(R) can be communicated as the wavelet arrangement. For the limited interim, the wavelet arrangement cannot be totally introduced by utilizing this premise. This is on the grounds that backings of some premise are truncated at the left or right end purposes of the interim. Subsequently, an uncommon premise must be brought into the wavelet development on the limited interim. These functions are alluded to as the limit scaling functions and limit wavelet functions. B-spline wavelet method has been connected to fathom linear and nonlinear integral equations and their systems. The above method diminishes the integral equations to systems of algebraic equations and afterward these systems can be illuminated by any standard numerical methods. Here, we have connected Newton's method with suitable starting speculation for solving these systems.

Keywords: semi-orthogonal, wavelet arrangement, integral equations, wavelet development

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Authors: Khosrow Maleknejad, Yaser Rostami

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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: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Liyana Zahid, Mohd Fareq Abd Malek, Ee Meng Cheng, Wei Wen Liu, Yeng Seng Lee, Muhammad Nadeem Iqbal, Fwen Hoon Wee

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One of the parameters that affect the performance of microwave absorbers is the shape of the absorbers. This paper shows the performance (reflection loss) of truncated pyramidal and truncated wedge microwave absorbers in the range frequency between 8.2 to 12.4 GHz (X-Band) in simulation. The material used is sugarcane bagasse (SCB) which is one of the new materials that used to fabricate the microwave absorber. The complex permittivity was measured using Agilent dielectric probe technique. The designs were simulated using CST Microwave Studio Software. The reflection losses between these two shapes were compared.

Keywords: microwave absorber, reflection loss, sugarcane bagasse (SCB), X-Band

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Authors: Reza Mohammadi, Mahdieh Sahebi

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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

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Authors: N. Sateesh, C. S. P. Rao, K. Satyanarayana, C. Rajashekar

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This paper proposes a development of a CAD/CAM system for complex profiles of various machine members using a synthetic curve i.e. B-spline. Conventional methods in designing and manufacturing of complex profiles are tedious and time consuming. Even programming those on a computer numerical control (CNC) machine can be a difficult job because of the complexity of the profiles. The system developed provides graphical and numerical representation B-spline profile for any given input. In this paper, the system is applicable to represent a cam profile with B-spline and attempt is made to improve the follower motion.

Keywords: plate-cams, cam profile, b-spline, computer numerical control (CNC), computer aided design and computer aided manufacturing (CAD/CAM), R-D-R-D (rise-dwell-return-dwell)

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Authors: M. Z. Kurian, M. V. Chidananda Murthy, H. S. Guruprasad

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An approach to super-resolve the low-resolution (LR) image is presented in this paper which is very useful in multimedia communication, medical image enhancement and satellite image enhancement to have a clear view of the information in the image. The proposed Advanced B-Spline method generates a high-resolution (HR) image from single LR image and tries to retain the higher frequency components such as edges in the image. This method uses B-Spline technique and Crispening. This work is evaluated qualitatively and quantitatively using Mean Square Error (MSE) and Peak Signal to Noise Ratio (PSNR). The method is also suitable for real-time applications. Different combinations of decimation and super-resolution algorithms in the presence of different noise and noise factors are tested.

Keywords: advanced b-spline, image super-resolution, mean square error (MSE), peak signal to noise ratio (PSNR), resolution down converter

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

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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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Authors: Reza Mohammadi, Mahdieh Sahebi

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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 proposed derived method. Numerical comparison with other existence methods shows the superiority of our presented scheme.

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

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Authors: Shunpu Zhang

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We propose a new multiple test called the minPOP test for testing multiple hypotheses simultaneously. Under the assumption that the test statistics are independent, we show that the minPOP test has higher global power than the existing multiple testing methods. We further propose a stepwise multiple-testing procedure based on the minPOP test and two of its modified versions (the Double Truncated and Left Truncated minPOP tests). We show that these multiple tests have strong control of the family-wise error rate (FWER). A method for finding the p-values of the proposed tests after adjusting for multiplicity is also developed. Simulation results show that the Double Truncated and Left Truncated minPOP tests, in general, have a higher number of rejections than the existing multiple testing procedures.

Keywords: multiple test, single-step procedure, stepwise procedure, p-value for multiple testing

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Authors: Bharti Gupta, V. K. Kukreja

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A comprehensive numerical study is presented for the solution of time-dependent advection diffusion problems by using cubic B-spline collocation method. The linear combination of cubic B-spline basis, taken as approximating function, is evaluated using the zeros of shifted Chebyshev polynomials as collocation points in each element to obtain the best approximation. A comparison, on the basis of efficiency and accuracy, with the previous techniques is made which confirms the superiority of the proposed method. An asymptotic convergence analysis of technique is also discussed, and the method is found to be of order two. The theoretical analysis is supported with suitable examples to show second order convergence of technique. Different numerical examples are simulated using MATLAB in which the 3-D graphical presentation has taken at different time steps as well as different domain of interest.

Keywords: cubic B-spline basis, spectral norms, shifted Chebyshev polynomials, collocation points, error estimates

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Authors: Rongli Gai, Zhiyuan Chang

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At this stage, in view of various situations in the interpolation process, most researchers use self-adaptation to adjust the interpolation process, which is also one of the current and future research hotspots in the field of CNC machining. In the interpolation process, according to the overview of the spline curve interpolation algorithm, the adaptive analysis is carried out from the factors affecting the interpolation process. The adaptive operation is reflected in various aspects, such as speed, parameters, errors, nodes, feed rates, random Period, sensitive point, step size, curvature, adaptive segmentation, adaptive optimization, etc. This paper will analyze and summarize the research of adaptive imputation in the direction of the above factors affecting imputation.

Keywords: adaptive algorithm, CNC machining, interpolation constraints, spline curve interpolation

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Authors: M. De Maaijer, Wenxuan Shi, , Dolores Pose, Ditmar, F. Barati

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Friction has several detrimental effects on Blind performance, Therefore Ziptak company as the leading company in the blind manufacturing sector, start investigating on how to conquer this problem in next generation of blinds. This problem is more sever in extremely sever condition. Although in these condition Ziptrak suggest not to use the blind, working on blind and its associated parts was the priority of Ziptrak company. The purpose of this article is to measure the effects of lubrication process on reducing friction force between spline and track especially at windy conditions Four different lubricants were implicated to measure their efficiency on reducing friction force.

Keywords: libricant, ziptrak, blind, spline

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Waheed Zahra, Mohamed El-Beltagy, Ashraf El Mhlawy, Reda Elkhadrawy

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In this paper, we consider singular perturbation reaction-diffusion boundary value problems, which contain a small uncertain perturbation parameter. To solve these problems, we propose a numerical method which is based on an exponential spline and Shishkin mesh discretization. While interval analysis principle is used to deal with the uncertain parameter, sensitivity analysis has been conducted using different methods. Numerical results are provided to show the applicability and efficiency of our method, which is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, shishkin mesh, two small parameters, exponential spline, interval analysis, sensitivity analysis

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Authors: B. Mahfoud, A. Bendjaghlouli

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Natural convection is simulated in a truncated cone filled with nanofluid. Inclined and top walls have constant temperature where the heat source is located on the bottom wall of the conical container which is thermally insulated. A finite volume approach is used to solve the governing equations using the SIMPLE algorithm for different parameters such as Rayleigh number, inclination angle of inclined walls of the enclosure and heat source length. The results showed an enhancement in cooling system by using a nanofluid, when conduction regime is assisted. The inclination angle of inclined sidewall and heat source length affect the heat transfer rate and the maximum temperature.

Keywords: heat source, truncated cone, nanofluid, natural convection

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Authors: Anastasiia Yu. Timofeeva

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Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.

Keywords: grade point average, orthogonal regression, penalized regression spline, locally weighted regression

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Authors: Reza Mohammadi

Abstract:

Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Aiman Alshare, Sahar Qaadan

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A curvature dependent force correction algorithm for planning force controlled grinding process with off-line programming flexibility is designed for ABB industrial robot, in order to avoid the manual interface during the process. The machining path utilizes a spline curve fit that is constructed from the CAD data of the workpiece. The fitted spline has a continuity of the second order to assure path smoothness. The implemented algorithm computes uniform forces normal to the grinding surface of the workpiece, by constructing a curvature path in the spatial coordinates using the spline method.

Keywords: ABB industrial robot, grinding process, offline programming, CAD data extraction, force correction algorithm

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Authors: Srinivasa Rao Gadde

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In this article, we considered a group acceptance sampling plans for exponentiated half logistic distribution when the life-test is truncated at a pre-specified time. It is assumed that the index parameter of the exponentiated half logistic distribution is known. The design parameters such as the number of groups and the acceptance number are obtained by satisfying the producer’s and consumer’s risks at the specified quality levels in terms of medians and 10th percentiles under the assumption that the termination time and the number of items in each group are pre-fixed. Finally, an example is given to illustration the methodology.

Keywords: group acceptance sampling plan, operating characteristic, consumer and producer’s risks, truncated life-test

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Authors: Saif Akram, E. Rathakrishnan

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The mixing promoting efficiency of two identical sharp and truncated vertex triangular tabs offering geometrical blockage of 2.5% each, placed at the exit of a Mach 1.5 elliptic nozzle was studied experimentally. The effectiveness of both the tabs in enhancing the mixing of jets with the ambient air are determined by measuring the Pitot pressure along the jet axis and the jet spread in both the minor and major axes of the elliptic nozzle, covering marginally overexpanded to moderately underexpanded levels at the nozzle exit. The results reveal that both the tabs enhance mixing characteristics of the uncontrolled elliptic jet when placed at minor axis. A core length reduction of 67% is achieved at NPR 3 which is the overexpanded state. Similarly, the core length is reduced by about 67%, 50% and 57% at NPRs of 4, 5 and 6 (underexpanded states) respectively. However, unlike the considerable increment in mixing promoting efficiency by the use of truncated vertex tabs for axisymmetric jets, the effect is not much pronounced for the case of supersonic elliptic jets. The CPD plots for both the cases almost overlap, especially when tabs are placed at minor axis, at all the pressure conditions. While, when the tabs are used at major axis, in the case of overexpanded condition, the sharp vertex triangular tabs act as a better mixing enhancer for the supersonic elliptic jets. For the jet controlled with truncated vertex triangular tabs, the core length reductions are of the same order as those for the sharp vertex triangular tabs. The jet mixing is hardly influenced by the tip effect in case of supersonic elliptic jet.

Keywords: elliptic jet, tabs, truncated, triangular

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Authors: Qijiao He, Lin Ye

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To evaluate the effect of the ribs on internal structure in film hole and the film cooling performance on outer surface, the numerical study investigates on the effects of rib configuration on the film cooling performance with ribbed cross-flow coolant channel. The base smooth case and three ribbed cases, including the continuous rib case and two cross-truncated rib cases with different arrangement, are studied. The distributions of adiabatic film cooling effectiveness and heat transfer coefficient are obtained under the blowing ratios with the value of 0.5 and 1.0, respectively. A commercial steady RANS (Reynolds-averaged Navier-Stokes) code with realizable k-ε turbulence model and enhanced wall treatment were performed for numerical simulations. The numerical model is validated against available experimental data. The two cross-truncated rib cases produce approximately identical cooling effectiveness compared with the smooth case under lower blowing ratio. The continuous rib case significantly outperforms the other cases. With the increase of blowing ratio, the cases with ribs are inferior to the smooth case, especially in the upstream region. The cross-truncated rib I case produces the highest cooling effectiveness among the studied the ribbed channel case. It is found that film cooling effectiveness deteriorates with the increase of spiral intensity of the cross-flow inside the film hole. Lower spiral intensity leads to a better film coverage and thus results in better cooling effectiveness. The distinct relative merits among the cases at different blowing ratios are explored based on the aforementioned dominant mechanism. With regard to the heat transfer coefficient, the smooth case has higher heat transfer intensity than the ribbed cases under the studied blowing ratios. The laterally-averaged heat transfer coefficient of the cross-truncated rib I case is higher than the cross-truncated rib II case.

Keywords: cross-flow, cross-truncated rib, film cooling, numerical simulation

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Authors: O. Anan, D. Böhning, A. Maruotti

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The purpose of the study is to estimate the elusive target population size under a truncated count model that accounts for heterogeneity. The purposed estimator is based on the generalized Poisson distribution (GPD), which extends the Poisson distribution by adding a dispersion parameter. Thus, it becomes an useful model for capture-recapture data where concurrent events are not homogeneous. In addition, it can account for over-dispersion and under-dispersion. The ratios of neighboring frequency counts are used as a tool for investigating the validity of whether generalized Poisson or Poisson distribution. Since capture-recapture approaches do not provide the zero counts, the estimated parameters can be achieved by modifying the EM-algorithm technique for the zero-truncated generalized Poisson distribution. The properties and the comparative performance of proposed estimator were investigated through simulation studies. Furthermore, some empirical examples are represented insights on the behavior of the estimators.

Keywords: capture, recapture methods, ratio plot, heterogeneous population, zero-truncated count

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Authors: A. D. Abdellatif, A. N. Ahmed, M. E. Abdelaziz

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The main purpose of this paper is to design a double acceptance sampling plan under the time truncated life test when the product lifetime follows an exponentiated transmuted Weibull distribution. Here, the motive is to meet both the consumer’s risk and producer’s risk simultaneously at the specified quality levels, while the termination time is specified. A comparison between the results of the double and single acceptance sampling plans is conducted. We demonstrate the applicability of our results to real data sets.

Keywords: double sampling plan, single sampling plan, producer’s risk, consumer’s risk, exponentiated transmuted weibull distribution, time truncated experiment, single, double, Marshal-Olkin

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Authors: Guesh Simretab Gebremedhin, Saumya Rajan Jena

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In this work, a septic B-spline scheme has been used to simplify the process of solving an approximate solution of the generalized Rosenau-regularized long-wave equation (GR-RLWE) with initial boundary conditions. The resulting system of first-order ODEs has dealt with Butcher’s fifth order Runge-Kutta (BFRK) approach without using finite difference techniques for discretizing the time-dependent variables at each time level. Here, no transformation or any kind of linearization technique is employed to tackle the nonlinearity of the equation. Two test problems have been selected for numerical justifications and comparisons with other researchers on the basis of efficiency, accuracy, and results of the two invariants Mᵢ (mass) and Eᵢ (energy) of some motion that has been used to test the conservative properties of the proposed scheme.

Keywords: septic B-spline scheme, Butcher's fifth order Runge-Kutta approach, error norms, generalized Rosenau-RLW equation

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

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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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Authors: Alberto Hananel

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The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: approximation, evolutionary PDE, Finite Element Method, temporomandibular disorders, variational spline

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