Schwarz and multilevel methods for quadratic spline collocation
Christara, C.C.; Smith, B.
1994-12-31
Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.
Tensorial Basis Spline Collocation Method for Poisson's Equation
NASA Astrophysics Data System (ADS)
Plagne, Laurent; Berthou, Jean-Yves
2000-01-01
This paper aims to describe the tensorial basis spline collocation method applied to Poisson's equation. In the case of a localized 3D charge distribution in vacuum, this direct method based on a tensorial decomposition of the differential operator is shown to be competitive with both iterative BSCM and FFT-based methods. We emphasize the O(h4) and O(h6) convergence of TBSCM for cubic and quintic splines, respectively. We describe the implementation of this method on a distributed memory parallel machine. Performance measurements on a Cray T3E are reported. Our code exhibits high performance and good scalability: As an example, a 27 Gflops performance is obtained when solving Poisson's equation on a 2563 non-uniform 3D Cartesian mesh by using 128 T3E-750 processors. This represents 215 Mflops per processors.
Domain identification in impedance computed tomography by spline collocation method
NASA Technical Reports Server (NTRS)
Kojima, Fumio
1990-01-01
A method for estimating an unknown domain in elliptic boundary value problems is considered. The problem is formulated as an inverse problem of integral equations of the second kind. A computational method is developed using a splice collocation scheme. The results can be applied to the inverse problem of impedance computed tomography (ICT) for image reconstruction.
Preconditioning cubic spline collocation method by FEM and FDM for elliptic equations
Kim, Sang Dong
1996-12-31
In this talk we discuss the finite element and finite difference technique for the cubic spline collocation method. For this purpose, we consider the uniformly elliptic operator A defined by Au := -{Delta}u + a{sub 1}u{sub x} + a{sub 2}u{sub y} + a{sub 0}u in {Omega} (the unit square) with Dirichlet or Neumann boundary conditions and its discretization based on Hermite cubic spline spaces and collocation at the Gauss points. Using an interpolatory basis with support on the Gauss points one obtains the matrix A{sub N} (h = 1/N).
Quadratic spline collocation and parareal deferred correction method for parabolic PDEs
NASA Astrophysics Data System (ADS)
Liu, Jun; Wang, Yan; Li, Rongjian
2016-06-01
In this paper, we consider a linear parabolic PDE, and use optimal quadratic spline collocation (QSC) methods for the space discretization, proceed the parareal technique on the time domain. Meanwhile, deferred correction technique is used to improve the accuracy during the iterations. The error estimation is presented and the stability is analyzed. Numerical experiments, which is carried out on a parallel computer with 40 CPUs, are attached to exhibit the effectiveness of the hybrid algorithm.
NASA Astrophysics Data System (ADS)
Li, Xinxiu
2012-10-01
Physical processes with memory and hereditary properties can be best described by fractional differential equations due to the memory effect of fractional derivatives. For that reason reliable and efficient techniques for the solution of fractional differential equations are needed. Our aim is to generalize the wavelet collocation method to fractional differential equations using cubic B-spline wavelet. Analytical expressions of fractional derivatives in Caputo sense for cubic B-spline functions are presented. The main characteristic of the approach is that it converts such problems into a system of algebraic equations which is suitable for computer programming. It not only simplifies the problem but also speeds up the computation. Numerical results demonstrate the validity and applicability of the method to solve fractional differential equation.
NASA Astrophysics Data System (ADS)
Fernandes, Ryan I.; Fairweather, Graeme
2012-08-01
An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only O(N) operations where N is the number of unknowns. Moreover, it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties.
Castillo, V M
2005-01-12
A collocation method using cubic splines is developed and applied to simulate steady and time-dependent, including turbulent, thermally convecting flows for two-dimensional compressible fluids. The state variables and the fluxes of the conserved quantities are approximated by cubic splines in both space direction. This method is shown to be numerically conservative and to have a local truncation error proportional to the fourth power of the grid spacing. A ''dual-staggered'' Cartesian grid, where energy and momentum are updated on one grid and mass density on the other, is used to discretize the flux form of the compressible Navier-Stokes equations. Each grid-line is staggered so that the fluxes, in each direction, are calculated at the grid midpoints. This numerical method is validated by simulating thermally convecting flows, from steady to turbulent, reproducing known results. Once validated, the method is used to investigate many aspects of thermal convection with high numerical accuracy. Simulations demonstrate that multiple steady solutions can coexist at the same Rayleigh number for compressible convection. As a system is driven further from equilibrium, a drop in the time-averaged dimensionless heat flux (and the dimensionless internal entropy production rate) occurs at the transition from laminar-periodic to chaotic flow. This observation is consistent with experiments of real convecting fluids. Near this transition, both harmonic and chaotic solutions may exist for the same Rayleigh number. The chaotic flow loses phase-space information at a greater rate, while the periodic flow transports heat (produces entropy) more effectively. A linear sum of the dimensionless forms of these rates connects the two flow morphologies over the entire range for which they coexist. For simulations of systems with higher Rayleigh numbers, a scaling relation exists relating the dimensionless heat flux to the two-seventh's power of the Rayleigh number, suggesting the
Quartic B-spline collocation method applied to Korteweg de Vries equation
NASA Astrophysics Data System (ADS)
Zin, Shazalina Mat; Majid, Ahmad Abd; Ismail, Ahmad Izani Md
2014-07-01
The Korteweg de Vries (KdV) equation is known as a mathematical model of shallow water waves. The general form of this equation is ut+ɛuux+μuxxx = 0 where u(x,t) describes the elongation of the wave at displacement x and time t. In this work, one-soliton solution for KdV equation has been obtained numerically using quartic B-spline collocation method for displacement x and using finite difference approach for time t. Two problems have been identified to be solved. Approximate solutions and errors for these two test problems were obtained for different values of t. In order to look into accuracy of the method, L2-norm and L∞-norm have been calculated. Mass, energy and momentum of KdV equation have also been calculated. The results obtained show the present method can approximate the solution very well, but as time increases, L2-norm and L∞-norm are also increase.
The basis spline method and associated techniques
Bottcher, C.; Strayer, M.R.
1989-01-01
We outline the Basis Spline and Collocation methods for the solution of Partial Differential Equations. Particular attention is paid to the theory of errors, and the handling of non-self-adjoint problems which are generated by the collocation method. We discuss applications to Poisson's equation, the Dirac equation, and the calculation of bound and continuum states of atomic and nuclear systems. 12 refs., 6 figs.
NASA Astrophysics Data System (ADS)
Ersoy, Ozlem; Dag, Idris
2015-12-01
The solutions of the reaction-diffusion system are given by method of collocation based on the exponential B-splines. Thus the reaction-diffusion systemturns into an iterative banded algebraic matrix equation. Solution of the matrix equation is carried out byway of Thomas algorithm. The present methods test on both linear and nonlinear problems. The results are documented to compare with some earlier studies by use of L∞ and relative error norm for problems respectively.
A fourth order spline collocation approach for a business cycle model
NASA Astrophysics Data System (ADS)
Sayfy, A.; Khoury, S.; Ibdah, H.
2013-10-01
A collocation approach, based on a fourth order cubic B-splines is presented for the numerical solution of a Kaleckian business cycle model formulated by a nonlinear delay differential equation. The equation is approximated and the nonlinearity is handled by employing an iterative scheme arising from Newton's method. It is shown that the model exhibits a conditionally dynamical stable cycle. The fourth-order rate of convergence of the scheme is verified numerically for different special cases.
NASA Astrophysics Data System (ADS)
Khoury, S.; Ibdah, H.; Sayfy, A.
2013-10-01
A mixed approach, based on cubic B-spline collocation and asymptotic boundary conditions (ABCs), is presented for the numerical solution of an extended class of two-point linear boundary value problems (BVPs) over an infinite interval as well as a system of BVPs. The condition at infinity is reduced to an asymptotic boundary condition that approaches the required value at infinity over a large finite interval. The resulting problem is handled using an adaptive spline collocation approach constructed over uniform meshes. The rate of convergence is verified numerically to be of fourth-order. The efficiency and applicability of the method are demonstrated by applying the strategy to a number of examples. The numerical solutions are compared with existing analytical solutions.
Collocation and Galerkin Time-Stepping Methods
NASA Technical Reports Server (NTRS)
Huynh, H. T.
2011-01-01
We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods.
A multilevel stochastic collocation method for SPDEs
Gunzburger, Max; Jantsch, Peter; Teckentrup, Aretha; Webster, Clayton
2015-03-10
We present a multilevel stochastic collocation method that, as do multilevel Monte Carlo methods, uses a hierarchy of spatial approximations to reduce the overall computational complexity when solving partial differential equations with random inputs. For approximation in parameter space, a hierarchy of multi-dimensional interpolants of increasing fidelity are used. Rigorous convergence and computational cost estimates for the new multilevel stochastic collocation method are derived and used to demonstrate its advantages compared to standard single-level stochastic collocation approximations as well as multilevel Monte Carlo methods.
B-spline Method in Fluid Dynamics
NASA Technical Reports Server (NTRS)
Botella, Olivier; Shariff, Karim; Mansour, Nagi N. (Technical Monitor)
2001-01-01
B-spline functions are bases for piecewise polynomials that possess attractive properties for complex flow simulations : they have compact support, provide a straightforward handling of boundary conditions and grid nonuniformities, and yield numerical schemes with high resolving power, where the order of accuracy is a mere input parameter. This paper reviews the progress made on the development and application of B-spline numerical methods to computational fluid dynamics problems. Basic B-spline approximation properties is investigated, and their relationship with conventional numerical methods is reviewed. Some fundamental developments towards efficient complex geometry spline methods are covered, such as local interpolation methods, fast solution algorithms on cartesian grid, non-conformal block-structured discretization, formulation of spline bases of higher continuity over triangulation, and treatment of pressure oscillations in Navier-Stokes equations. Application of some of these techniques to the computation of viscous incompressible flows is presented.
Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models
NASA Astrophysics Data System (ADS)
Gomez, Hector; Reali, Alessandro; Sangalli, Giancarlo
2014-04-01
We propose new collocation methods for phase-field models. Our algorithms are based on isogeometric analysis, a new technology that makes use of functions from computational geometry, such as, for example, Non-Uniform Rational B-Splines (NURBS). NURBS exhibit excellent approximability and controllable global smoothness, and can represent exactly most geometries encapsulated in Computer Aided Design (CAD) models. These attributes permitted us to derive accurate, efficient, and geometrically flexible collocation methods for phase-field models. The performance of our method is demonstrated by several numerical examples of phase separation modeled by the Cahn-Hilliard equation. We feel that our method successfully combines the geometrical flexibility of finite elements with the accuracy and simplicity of pseudo-spectral collocation methods, and is a viable alternative to classical collocation methods.
Multivariate spline methods in surface fitting
NASA Technical Reports Server (NTRS)
Guseman, L. F., Jr. (Principal Investigator); Schumaker, L. L.
1984-01-01
The use of spline functions in the development of classification algorithms is examined. In particular, a method is formulated for producing spline approximations to bivariate density functions where the density function is decribed by a histogram of measurements. The resulting approximations are then incorporated into a Bayesiaan classification procedure for which the Bayes decision regions and the probability of misclassification is readily computed. Some preliminary numerical results are presented to illustrate the method.
A Collocation Method for Volterra Integral Equations
NASA Astrophysics Data System (ADS)
Kolk, Marek
2010-09-01
We propose a piecewise polynomial collocation method for solving linear Volterra integral equations of the second kind with logarithmic kernels which, in addition to a diagonal singularity, may have a singularity at the initial point of the interval of integration. An attainable order of the convergence of the method is studied. We illustrate our results with a numerical example.
A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics
M. D. Landon; R. W. Johnson
1999-07-01
The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve complex curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.
A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics
Johnson, Richard Wayne; Landon, Mark Dee
1999-07-01
The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.
Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's
NASA Technical Reports Server (NTRS)
Cai, Wei; Wang, Jian-Zhong
1993-01-01
We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.
Stochastic Collocation Method for Three-dimensional Groundwater Flow
NASA Astrophysics Data System (ADS)
Shi, L.; Zhang, D.
2008-12-01
The stochastic collocation method (SCM) has recently gained extensive attention in several disciplines. The numerical implementation of SCM only requires repetitive runs of an existing deterministic solver or code as in the Monte Carlo simulation. But it is generally much more efficient than the Monte Carlo method. In this paper, the stochastic collocation method is used to efficiently qualify uncertainty of three-dimensional groundwater flow. We introduce the basic principles of common collocation methods, i.e., the tensor product collocation method (TPCM), Smolyak collocation method (SmCM), Stround-2 collocation method (StCM), and probability collocation method (PCM). Their accuracy, computational cost, and limitation are discussed. Illustrative examples reveal that the seamless combination of collocation techniques and existing simulators makes the new framework possible to efficiently handle complex stochastic problems.
Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations
NASA Astrophysics Data System (ADS)
Buffa, A.; Sangalli, G.; Vázquez, R.
2014-01-01
In this paper we introduce methods for electromagnetic wave propagation, based on splines and on T-splines. We define spline spaces which form a De Rham complex and following the isogeometric paradigm, we map them on domains which are (piecewise) spline or NURBS geometries. We analyze their geometric and topological structure, as related to the connectivity of the underlying mesh, and we present degrees of freedom together with their physical interpretation. The theory is then extended to the case of meshes with T-junctions, leveraging on the recent theory of T-splines. The use of T-splines enhance our spline methods with local refinement capability and numerical tests show the efficiency and the accuracy of the techniques we propose.
Aerodynamic influence coefficient method using singularity splines.
NASA Technical Reports Server (NTRS)
Mercer, J. E.; Weber, J. A.; Lesferd, E. P.
1973-01-01
A new numerical formulation with computed results, is presented. This formulation combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of the loading function methods. The formulation employs a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfies all of the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise (termed 'spline'). Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral.
Aerodynamic influence coefficient method using singularity splines
NASA Technical Reports Server (NTRS)
Mercer, J. E.; Weber, J. A.; Lesferd, E. P.
1974-01-01
A numerical lifting surface formulation, including computed results for planar wing cases is presented. This formulation, referred to as the vortex spline scheme, combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of loading function methods. The formulation employes a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfied all the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise. Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral. The current formulation uses the elementary horseshoe vortex as the basic singularity and is therefore restricted to linearized potential flow. As part of the study, a non planar development was considered, but the numerical evaluation of the lifting surface concept was restricted to planar configurations. Also, a second order sideslip analysis based on an asymptotic expansion was investigated using the singularity spline formulation.
Parallel adaptive wavelet collocation method for PDEs
Nejadmalayeri, Alireza; Vezolainen, Alexei; Brown-Dymkoski, Eric; Vasilyev, Oleg V.
2015-10-01
A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 2048{sup 3} using as many as 2048 CPU cores.
Collocation method for fractional quantum mechanics
Amore, Paolo; Hofmann, Christoph P.; Saenz, Ricardo A.; Fernandez, Francisco M.
2010-12-15
We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on little sinc functions, which discretizes the Schroedinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a Wentzel-Kramers-Brillouin analysis is performed.
Collocation Method for Numerical Solution of Coupled Nonlinear Schroedinger Equation
Ismail, M. S.
2010-09-30
The coupled nonlinear Schroedinger equation models several interesting physical phenomena presents a model equation for optical fiber with linear birefringence. In this paper we use collocation method to solve this equation, we test this method for stability and accuracy. Numerical tests using single soliton and interaction of three solitons are used to test the resulting scheme.
Comparison of Implicit Collocation Methods for the Heat Equation
NASA Technical Reports Server (NTRS)
Kouatchou, Jules; Jezequel, Fabienne; Zukor, Dorothy (Technical Monitor)
2001-01-01
We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.
Coding of images by methods of a spline interpolation
NASA Astrophysics Data System (ADS)
Kozhemyako, Vladimir P.; Maidanuik, V. P.; Etokov, I. A.; Zhukov, Konstantin M.; Jorban, Saleh R.
2000-06-01
In the case of image coding are containing interpolation methods, a linear methods of component forming usually used. However, taking in account the huge speed increasing of a computer and hardware integration power, of special interest was more complicated interpolation methods, in particular spline interpolation. A spline interpolation is known to be a approximation that performed by spline, which consist of polynomial bounds, where a cub parabola usually used. At this article is to perform image analysis by 5 X 5 aperture, result in count rejection of low-frequence component of image: an one base count per 5 X 5 size fragment. The passed source counts were restoring by spline interpolation methods, then formed counts of high-frequence image component, by subtract from counts of initial image a low-frequence component and their quantization. At the final stage Huffman coding performed to divert of statistical redundancy. Spacious set of experiments with various images showed that source compression factor may be founded into limits of 10 - 70, which for majority test images are superlative source compression factor by JPEG standard applications at the same image quality. Investigated research show that spline approximation allow to improve restored image quality and compression factor to compare with linear interpolation. Encoding program modules has work out for BMP-format files, on the Windows and MS-DOS platforms.
NASA Astrophysics Data System (ADS)
Gotovac, Hrvoje; Srzic, Veljko
2014-05-01
Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different Eulerian, Lagrangian and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present Eulerian Lagrangian Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large
Collocation and Least Residuals Method and Its Applications
NASA Astrophysics Data System (ADS)
Shapeev, Vasily
2016-02-01
The collocation and least residuals (CLR) method combines the methods of collocations (CM) and least residuals. Unlike the CM, in the CLR method an approximate solution of the problem is found from an overdetermined system of linear algebraic equations (SLAE). The solution of this system is sought under the requirement of minimizing a functional involving the residuals of all its equations. On the one hand, this added complication of the numerical algorithm expands the capabilities of the CM for solving boundary value problems with singularities. On the other hand, the CLR method inherits to a considerable extent some convenient features of the CM. In the present paper, the CLR capabilities are illustrated on benchmark problems for 2D and 3D Navier-Stokes equations, the modeling of the laser welding of metal plates of similar and different metals, problems investigating strength of loaded parts made of composite materials, boundary-value problems for hyperbolic equations.
Higher-order numerical solutions using cubic splines
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1976-01-01
A cubic spline collocation procedure was developed for the numerical solution of partial differential equations. This spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy of a nonuniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, are presented for several model problems.
Domain decomposition preconditioners for the spectral collocation method
NASA Technical Reports Server (NTRS)
Quarteroni, Alfio; Sacchilandriani, Giovanni
1988-01-01
Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate which does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor systems due to their high degree of parallelism.
Collocation methods for distillation design. 2: Applications for distillation
Huss, R.S.; Westerberg, A.W.
1996-05-01
The authors present applications for a collocation method for modeling distillation columns that they developed in a companion paper. They discuss implementation of the model, including discussion of the ASCEND (Advanced System for Computations in ENgineering Design) system, which enables one to create complex models with simple building blocks and interactively learn to solve them. They first investigate applying the model to compute minimum reflux for a given separation task, exactly solving nonsharp and approximately solving sharp split minimum reflux problems. They next illustrate the use of the collocation model to optimize the design a single column capable of carrying out a prescribed set of separation tasks. The optimization picks the best column diameter and total number of trays. It also picks the feed tray for each of the prescribed separations.
Pseudospectral collocation methods for fourth order differential equations
NASA Technical Reports Server (NTRS)
Malek, Alaeddin; Phillips, Timothy N.
1994-01-01
Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.
Simplex-stochastic collocation method with improved scalability
NASA Astrophysics Data System (ADS)
Edeling, W. N.; Dwight, R. P.; Cinnella, P.
2016-04-01
The Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code. However, it becomes prohibitively expensive for problems with dimensions higher than 5. The main purpose of this paper is to identify bottlenecks, and to improve upon this bad scalability. In order to do so, we propose an alternative interpolation stencil technique based upon the Set-Covering problem, and we integrate the SSC method in the High-Dimensional Model-Reduction framework. In addition, we address the issue of ill-conditioned sample matrices, and we present an analytical map to facilitate uniformly-distributed simplex sampling.
Collocation method for chatter avoidance of general turning operations
NASA Astrophysics Data System (ADS)
Urbicain, G.; Olvera, D.; Fernández, A.; Rodríguez, A.; López de Lacalle, L. N.
2012-04-01
An accurate prediction of the dynamic stability of a cutting system involves the implementation of tool geometry and cutting conditions on any model used for such purpose. This study presents a dynamic cutting force model based on the collocation method by Chebyshev polynomials taking advantage from its ability to consider tool geometry and cutting parameters. In the paper, a simple 1DOF model is used to forecast chatter vibrations due to the workpiece and tool, which are distinguished in separate sections. The proposed model is verified positively against experimental dynamic tests.
NASA Technical Reports Server (NTRS)
Zhang, Zhimin; Tomlinson, John; Martin, Clyde
1994-01-01
In this work, the relationship between splines and the control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as trigonometric splines and the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations.
Spacecraft Orbit Determination with The B-spline Approximation Method
NASA Astrophysics Data System (ADS)
Song, Ye-zhi; Huang, Yong; Hu, Xiao-gong; Li, Pei-jia; Cao, Jian-feng
2014-04-01
It is known that the dynamical orbit determination is the most common way to get the precise orbits of spacecraft. However, it is hard to build up the precise dynamical model of spacecraft sometimes. In order to solve this problem, the technique of the orbit determination with the B-spline approximation method based on the theory of function approximation is presented in this article. In order to verify the effectiveness of this method, simulative orbit determinations in the cases of LEO (Low Earth Orbit), MEO (Medium Earth Orbit), and HEO (Highly Eccentric Orbit) satellites are performed, and it is shown that this method has a reliable accuracy and stable solution. The approach can be performed in both the conventional celestial coordinate system and the conventional terrestrial coordinate system. The spacecraft's position and velocity can be calculated directly with the B-spline approximation method, it needs not to integrate the dynamical equations, nor to calculate the state transfer matrix, thus the burden of calculations in the orbit determination is reduced substantially relative to the dynamical orbit determination method. The technique not only has a certain theoretical significance, but also can serve as a conventional algorithm in the spacecraft orbit determination.
Adaptive wavelet collocation method simulations of Rayleigh-Taylor instability
NASA Astrophysics Data System (ADS)
Reckinger, S. J.; Livescu, D.; Vasilyev, O. V.
2010-12-01
Numerical simulations of single-mode, compressible Rayleigh-Taylor instability are performed using the adaptive wavelet collocation method (AWCM), which utilizes wavelets for dynamic grid adaptation. Due to the physics-based adaptivity and direct error control of the method, AWCM is ideal for resolving the wide range of scales present in the development of the instability. The problem is initialized consistent with the solutions from linear stability theory. Non-reflecting boundary conditions are applied to prevent the contamination of the instability growth by pressure waves created at the interface. AWCM is used to perform direct numerical simulations that match the early-time linear growth, the terminal bubble velocity and a reacceleration region.
Spacecraft Orbit Determination with B Spline Approximation Method
NASA Astrophysics Data System (ADS)
Song, Y. Z.; Huang, Y.; Hu, X. G.; Li, P. J.; Cao, J. F.
2013-07-01
It is known that the dynamical orbit determination is the most common way to get the precise orbit of spacecraft. However, it is hard to describe the precise orbit of spacecraft sometimes. In order to solve this problem, the technique of the orbit determination with the B spline approximation method based on the theory of function approximation is presented in this article. Several simulation cases of the orbit determination including LEO (Low Earth Orbit), MEO (Medium Earth Orbit), and HEO (Highly Eccentric Orbit) satellites are performed, and it is shown that the accuracy of this method is reliable and stable.The approach can be performed in the conventional celestial coordinate system and conventional terrestrial coordinate system.The spacecraft's position and velocity can be calculated directly with the B spline approximation method, which means that it is unnecessary to integrate the dynamics equations and variational equations. In that case, it makes the calculation amount of orbit determination reduce substantially relative to the dynamical orbit determination method. The technique not only has a certain theoretical significance, but also can be as a conventional algorithm in the spacecraft orbit determination.
An analytic reconstruction method for PET based on cubic splines
NASA Astrophysics Data System (ADS)
Kastis, George A.; Kyriakopoulou, Dimitra; Fokas, Athanasios S.
2014-03-01
PET imaging is an important nuclear medicine modality that measures in vivo distribution of imaging agents labeled with positron-emitting radionuclides. Image reconstruction is an essential component in tomographic medical imaging. In this study, we present the mathematical formulation and an improved numerical implementation of an analytic, 2D, reconstruction method called SRT, Spline Reconstruction Technique. This technique is based on the numerical evaluation of the Hilbert transform of the sinogram via an approximation in terms of 'custom made' cubic splines. It also imposes sinogram thresholding which restricts reconstruction only within object pixels. Furthermore, by utilizing certain symmetries it achieves a reconstruction time similar to that of FBP. We have implemented SRT in the software library called STIR and have evaluated this method using simulated PET data. We present reconstructed images from several phantoms. Sinograms have been generated at various Poison noise levels and 20 realizations of noise have been created at each level. In addition to visual comparisons of the reconstructed images, the contrast has been determined as a function of noise level. Further analysis includes the creation of line profiles when necessary, to determine resolution. Numerical simulations suggest that the SRT algorithm produces fast and accurate reconstructions at realistic noise levels. The contrast is over 95% in all phantoms examined and is independent of noise level.
Ren, K
1990-07-01
A new numerical method of determining potentiometric titration end-points is presented. It consists in calculating the coefficients of approximative spline functions describing the experimental data (e.m.f., volume of titrant added). The end-point (the inflection point of the curve) is determined by calculating zero points of the second derivative of the approximative spline function. This spline function, unlike rational spline functions, is free from oscillations and its course is largely independent of random errors in e.m.f. measurements. The proposed method is useful for direct analysis of titration data and especially as a basis for construction of microcomputer-controlled automatic titrators. PMID:18964999
Multi-element probabilistic collocation method in high dimensions
Foo, Jasmine; Karniadakis, George Em
2010-03-01
We combine multi-element polynomial chaos with analysis of variance (ANOVA) functional decomposition to enhance the convergence rate of polynomial chaos in high dimensions and in problems with low stochastic regularity. Specifically, we employ the multi-element probabilistic collocation method MEPCM and so we refer to the new method as MEPCM-A. We investigate the dependence of the convergence of MEPCM-A on two decomposition parameters, the polynomial order {mu} and the effective dimension {nu}, with {nu}<
Efficient Combustion Simulation via the Adaptive Wavelet Collocation Method
NASA Astrophysics Data System (ADS)
Lung, Kevin; Brown-Dymkoski, Eric; Guerrero, Victor; Doran, Eric; Museth, Ken; Balme, Jo; Urberger, Bob; Kessler, Andre; Jones, Stephen; Moses, Billy; Crognale, Anthony
Rocket engine development continues to be driven by the intuition and experience of designers, progressing through extensive trial-and-error test campaigns. Extreme temperatures and pressures frustrate direct observation, while high-fidelity simulation can be impractically expensive owing to the inherent muti-scale, multi-physics nature of the problem. To address this cost, an adaptive multi-resolution PDE solver has been designed which targets the high performance, many-core architecture of GPUs. The adaptive wavelet collocation method is used to maintain a sparse-data representation of the high resolution simulation, greatly reducing the memory footprint while tightly controlling physical fidelity. The tensorial, stencil topology of wavelet-based grids lends itself to highly vectorized algorithms which are necessary to exploit the performance of GPUs. This approach permits efficient implementation of direct finite-rate kinetics, and improved resolution of steep thermodynamic gradients and the smaller mixing scales that drive combustion dynamics. Resolving these scales is crucial for accurate chemical kinetics, which are typically degraded or lost in statistical modeling approaches.
Spline interpolation on unbounded domains
NASA Astrophysics Data System (ADS)
Skeel, Robert D.
2016-06-01
Spline interpolation is a splendid tool for multiscale approximation on unbounded domains. In particular, it is well suited for use by the multilevel summation method (MSM) for calculating a sum of pairwise interactions for a large set of particles in linear time. Outlined here is an algorithm for spline interpolation on unbounded domains that is efficient and elegant though not so simple. Further gains in efficiency are possible via quasi-interpolation, which compromises collocation but with minimal loss of accuracy. The MSM, which may also be of value for continuum models, embodies most of the best features of both hierarchical clustering methods (tree methods, fast multipole methods, hierarchical matrix methods) and FFT-based 2-level methods (particle-particle particle-mesh methods, particle-mesh Ewald methods).
Ninth order block hybrid collocation method for second order ordinary differential equations
NASA Astrophysics Data System (ADS)
Yap, Lee Ken; Ismail, Fudziah
2016-02-01
A ninth order block hybrid collocation method is proposed for solving general second order ordinary differential equations directly. The derivation involves interpolation and collocation of basic polynomial that generates the main and additional methods. These methods are applied simultaneously to provide approximate solutions at five main points and three off-step points. The stability properties of the block method are discussed. Some illustrative examples are given to demonstrate the efficiency of the method.
NASA Astrophysics Data System (ADS)
Tu, Lianghui; Yuan, Jianping; Luo, Jianjun; Ning, Xin; Zhou, Ruiwu
2007-11-01
Direct collocation method has been widely used for trajectory optimization. In this paper, the application of direct optimization method (direct collocation method & nonlinear programming (NLP)) to lunar probe soft-landing trajectory optimization is introduced. Firstly, the model of trajectory optimization control problem to lunar probe soft landing trajectory is established and the equations of motion are simplified respectively based on some reasonable hypotheses. Performance is selected to minimize the fuel consumption. The control variables are thrust attack angle and thrust of engine. Terminal state variable constraints are velocity and altitude constraints. Then, the optimal control problem is transformed into nonlinear programming problem using direct collocation method. The state variables and control variables are selected as optimal parameters at all nodes and collocation nodes. Parameter optimization problem is solved using the SNOPT software package. The simulation results demonstrate that the direct collocation method is not sensitive to lunar soft landing initial conditions; they also show that the optimal solutions of trajectory optimization problem are fairly good in real-time. Therefore, the direct collocation method is a viable approach to lunar probe soft landing trajectory optimization problem.
Extension of spline wavelets element method to membrane vibration analysis
NASA Astrophysics Data System (ADS)
Wu, C. W.; Chen, W.-H.
1996-05-01
The B-spline wavelets element technique developed by Chen and Wu (1995a) is extended to the membrane vibration analysis. The tensor product of the finite splines and spline wavelets expansions in different resolutions is applied in the development of a curved quadrilateral element. Unlike the process of direct wavelets adding in the previous work, the elemental displacement field represented by the coefficients of wavelets expansions is transformed into edges and internal modes via elemental geometric conditions and “two-scale relations”. The “multiple stages two-scale sequence” of quadratic B-spline function is provided to accelerate the sequential transformations between different resolution levels of wavelets. The hierarchical property of wavelets basis approximation is also reserved in this extension. For membrane vibration problems where variations lack regularity at certain lower vibration modes, the present element can still effectively provide accurate results through a multi-level solving procedure. Some numerical examples are studied to demonstrate the proposed element.
Liu, Yi-Xin Zhang, Hong-Dong
2014-06-14
We present a fast and accurate numerical method for the self-consistent field theory calculations of confined polymer systems. It introduces an exponential time differencing method (ETDRK4) based on Chebyshev collocation, which exhibits fourth-order accuracy in temporal domain and spectral accuracy in spatial domain, to solve the modified diffusion equations. Similar to the approach proposed by Hur et al. [Macromolecules 45, 2905 (2012)], non-periodic boundary conditions are adopted to model the confining walls with or without preferential interactions with polymer species, avoiding the use of surface field terms and the mask technique in a conventional approach. The performance of ETDRK4 is examined in comparison with the operator splitting methods with either Fourier collocation or Chebyshev collocation. Numerical experiments show that our exponential time differencing method is more efficient than the operator splitting methods in high accuracy calculations. This method has been applied to diblock copolymers confined by two parallel flat surfaces.
The double exponential sinc collocation method for singular Sturm-Liouville problems
NASA Astrophysics Data System (ADS)
Gaudreau, P.; Slevinsky, R.; Safouhi, H.
2016-04-01
Sturm-Liouville problems are abundant in the numerical treatment of scientific and engineering problems. In the present contribution, we present an efficient and highly accurate method for computing eigenvalues of singular Sturm-Liouville boundary value problems. The proposed method uses the double exponential formula coupled with sinc collocation method. This method produces a symmetric positive-definite generalized eigenvalue system and has exponential convergence rate. Numerical examples are presented and comparisons with single exponential sinc collocation method clearly illustrate the advantage of using the double exponential formula.
Webster, Clayton G; Tran, Hoang A; Trenchea, Catalin S
2013-01-01
n this paper we show how stochastic collocation method (SCM) could fail to con- verge for nonlinear differential equations with random coefficients. First, we consider Navier-Stokes equation with uncertain viscosity and derive error estimates for stochastic collocation discretization. Our analysis gives some indicators on how the nonlinearity negatively affects the accuracy of the method. The stochastic collocation method is then applied to noisy Lorenz system. Simulation re- sults demonstrate that the solution of a nonlinear equation could be highly irregular on the random data and in such cases, stochastic collocation method cannot capture the correct solution.
On the collocation methods for singular integral equations with Hilbert kernel
NASA Astrophysics Data System (ADS)
Du, Jinyuan
2009-06-01
In the present paper, we introduce some singular integral operators, singular quadrature operators and discretization matrices of singular integral equations with Hilbert kernel. These results both improve the classical theory of singular integral equations and develop the theory of singular quadrature with Hilbert kernel. Then by using them a unified framework for various collocation methods of numerical solutions of singular integral equations with Hilbert kernel is given. Under the framework, it is very simple and obvious to obtain the coincidence theorem of collocation methods, then the existence and convergence for constructing approximate solutions are also given based on the coincidence theorem.
Uncertainty quantification for unsaturated flow in porous media: a stochastic collocation method
NASA Astrophysics Data System (ADS)
Barajas-Solano, D. A.; Tartakovsky, D. M.
2011-12-01
We present a stochastic collocation (SC) method to quantify epistemic uncertainty in predictions of unsaturated flow in porous media. SC provides a non-intrusive framework for uncertainty propagation in models based on the non-linear Richards' equation with arbitrary constitutive laws describing soil properties (relative conductivity and retention curve). To illustrate the approach, we use the Richards' equation with the van Genutchen-Mualem model for water retention and relative conductivity to describe infiltration into an initially dry soil whose uncertain parameters are treated as random fields. These parameters are represented using a truncated Karhunen-Loève expansion; Smolyak algorithm is used to construct a structured set of collocation points from univariate Gauss quadrature rules. A resulting deterministic problem is solved for each collocation point, and together with the collocation weights, the statistics of hydraulic head and infiltration rate are computed. The results are in agreement with Monte Carlo simulations. We demonstrate that highly heterogeneous soils (large variances of hydraulic parameters) require cubature formulas of high degree of exactness, while their short correlation lengths increase the dimensionality of the problem. Both effects increase the number of collocation points and thus of deterministic problems to solve, affecting the overall computational cost of uncertainty quantification.
Hill, G.R.
1987-11-10
A power transmission member is described comprising a radially-extending end wall and a cylindrical axially-extending sleeve connected to the end wall and terminating remote from the end wall in an open end. The sleeve has pressure formed internal and external axially-extending splines formed therein by intermeshing of teeth of a mandrel on which the sleeve is mounted and teeth of a pair of racks slidable therepast. The splines terminate short of the open sleeve end in an unsplined cylindrical ring-shaped lip portion which reduced bellmouth of the splines to within about 0.010 inch along their length.
NOKIN1D: one-dimensional neutron kinetics based on a nodal collocation method
NASA Astrophysics Data System (ADS)
Verdú, G.; Ginestar, D.; Miró, R.; Jambrina, A.; Barrachina, T.; Soler, Amparo; Concejal, Alberto
2014-06-01
The TRAC-BF1 one-dimensional kinetic model is a formulation of the neutron diffusion equation in the two energy groups' approximation, based on the analytical nodal method (ANM). The advantage compared with a zero-dimensional kinetic model is that the axial power profile may vary with time due to thermal-hydraulic parameter changes and/or actions of the control systems but at has the disadvantages that in unusual situations it fails to converge. The nodal collocation method developed for the neutron diffusion equation and applied to the kinetics resolution of TRAC-BF1 thermal-hydraulics, is an adaptation of the traditional collocation methods for the discretization of partial differential equations, based on the development of the solution as a linear combination of analytical functions. It has chosen to use a nodal collocation method based on a development of Legendre polynomials of neutron fluxes in each cell. The qualification is carried out by the analysis of the turbine trip transient from the NEA benchmark in Peach Bottom NPP using both the original 1D kinetics implemented in TRAC-BF1 and the 1D nodal collocation method.
A Collocation Method for Volterra Integral Equations with Diagonal and Boundary Singularities
NASA Astrophysics Data System (ADS)
Kolk, Marek; Pedas, Arvet; Vainikko, Gennadi
2009-08-01
We propose a smoothing technique associated with piecewise polynomial collocation methods for solving linear weakly singular Volterra integral equations of the second kind with kernels which, in addition to a diagonal singularity, may have a singularity at the initial point of the interval of integration.
Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation
NASA Technical Reports Server (NTRS)
Kouatchou, Jules; Halem, Milton (Technical Monitor)
2000-01-01
We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.
NASA Astrophysics Data System (ADS)
Parand, K.; Khaleqi, S.
2016-02-01
The Lane-Emden equation has been used to model several phenomena in theoretical physics, mathematical physics and astrophysics such as the theory of stellar structure. This study is an attempt to utilize the collocation method with the rational Chebyshev function of Second kind (RCS) to solve the Lane-Emden equation over the semi-infinite interval [0,+∞[ . According to well-known results and comparing with previous methods, it can be said that this method is efficient and applicable.
Higher-order numerical solutions using cubic splines. [for partial differential equations
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1975-01-01
A cubic spline collocation procedure has recently been developed for the numerical solution of partial differential equations. In the present paper, this spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a non-uniform mesh and overall fourth-order accuracy for a uniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, will be presented for several model problems.-
Domain decomposition methods for systems of conservation laws: Spectral collocation approximations
NASA Technical Reports Server (NTRS)
Quarteroni, Alfio
1989-01-01
Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.
NASA Astrophysics Data System (ADS)
Sweilam, N. H.; Abou Hasan, M. M.
2016-08-01
This paper reports a new spectral algorithm for obtaining an approximate solution for the Lévy-Feller diffusion equation depending on Legendre polynomials and Chebyshev collocation points. The Lévy-Feller diffusion equation is obtained from the standard diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative. A new formula expressing explicitly any fractional-order derivatives, in the sense of Riesz-Feller operator, of Legendre polynomials of any degree in terms of Jacobi polynomials is proved. Moreover, the Chebyshev-Legendre collocation method together with the implicit Euler method are used to reduce these types of differential equations to a system of algebraic equations which can be solved numerically. Numerical results with comparisons are given to confirm the reliability of the proposed method for the Lévy-Feller diffusion equation.
A novel stochastic collocation method for uncertainty propagation in complex mechanical systems
NASA Astrophysics Data System (ADS)
Qi, WuChao; Tian, SuMei; Qiu, ZhiPing
2015-02-01
This paper presents a novel stochastic collocation method based on the equivalent weak form of multivariate function integral to quantify and manage uncertainties in complex mechanical systems. The proposed method, which combines the advantages of the response surface method and the traditional stochastic collocation method, only sets integral points at the guide lines of the response surface. The statistics, in an engineering problem with many uncertain parameters, are then transformed into a linear combination of simple functions' statistics. Furthermore, the issue of determining a simple method to solve the weight-factor sets is discussed in detail. The weight-factor sets of two commonly used probabilistic distribution types are given in table form. Studies on the computational accuracy and efforts show that a good balance in computer capacity is achieved at present. It should be noted that it's a non-gradient and non-intrusive algorithm with strong portability. For the sake of validating the procedure, three numerical examples concerning a mathematical function with analytical expression, structural design of a straight wing, and flutter analysis of a composite wing are used to show the effectiveness of the guided stochastic collocation method.
Global collocation methods for approximation and the solution of partial differential equations
NASA Technical Reports Server (NTRS)
Solomonoff, A.; Turkel, E.
1986-01-01
Polynomial interpolation methods are applied both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations. The derivative matrix for a general sequence of the collocation points is constructed. The approximate derivative is then found by a matrix times vector multiply. The effects of several factors on the performance of these methods including the effect of different collocation points are then explored. The resolution of the schemes for both smooth functions and functions with steep gradients or discontinuities in some derivative are also studied. The accuracy when the gradients occur both near the center of the region and in the vicinity of the boundary is investigated. The importance of the aliasing limit on the resolution of the approximation is investigated in detail. Also examined is the effect of boundary treatment on the stability and accuracy of the scheme.
Spurious Modes in Spectral Collocation Methods with Two Non-Periodic Directions
NASA Technical Reports Server (NTRS)
Balachandar, S.; Madabhushi, Ravi K.
1992-01-01
Collocation implementation of the Kleiser-Schumann's method in geometries with two non-periodic directions is shown to suffer from three spurious modes - line, column and checkerboard - contaminating the computed pressure field. The corner spurious modes are also present but they do not affect evaluation of pressure related quantities. A simple methodology in the inversion of the influence matrix will efficiently filter out these spurious modes.
NASA Astrophysics Data System (ADS)
Vasilyev, Oleg V.; Gazzola, Mattia; Koumoutsakos, Petros
2009-11-01
In this talk we discuss preliminary results for the use of hybrid wavelet collocation - Brinkman penalization approach for shape and topology optimization of fluid flows. Adaptive wavelet collocation method tackles the problem of efficiently resolving a fluid flow on a dynamically adaptive computational grid in complex geometries (where grid resolution varies both in space and time time), while Brinkman volume penalization allows easy variation of flow geometry without using body-fitted meshes by simply changing the shape of the penalization region. The use of Brinkman volume penalization approach allow seamless transition from shape to topology optimization by combining it with level set approach and increasing the size of the optimization space. The approach is demonstrated for shape optimization of a variety of fluid flows by optimizing single cost function (time averaged Drag coefficient) using covariance matrix adaptation (CMA) evolutionary algorithm.
Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method
NASA Technical Reports Server (NTRS)
Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.
1997-01-01
A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.
Spatially-Anisotropic Parallel Adaptive Wavelet Collocation Method
NASA Astrophysics Data System (ADS)
Vasilyev, Oleg V.; Brown-Dymkoski, Eric
2015-11-01
Despite latest advancements in development of robust wavelet-based adaptive numerical methodologies to solve partial differential equations, they all suffer from two major ``curses'': 1) the reliance on rectangular domain and 2) the ``curse of anisotropy'' (i.e. homogeneous wavelet refinement and inability to have spatially varying aspect ratio of the mesh elements). The new method addresses both of these challenges by utilizing an adaptive anisotropic wavelet transform on curvilinear meshes that can be either algebraically prescribed or calculated on the fly using PDE-based mesh generation. In order to ensure accurate representation of spatial operators in physical space, an additional adaptation on spatial physical coordinates is also performed. It is important to note that when new nodes are added in computational space, the physical coordinates can be approximated by interpolation of the existing solution and additional local iterations to ensure that the solution of coordinate mapping PDEs is converged on the new mesh. In contrast to traditional mesh generation approaches, the cost of adding additional nodes is minimal, mainly due to localized nature of iterative mesh generation PDE solver requiring local iterations in the vicinity of newly introduced points. This work was supported by ONR MURI under grant N00014-11-1-069.
A Fourier collocation time domain method for numerically solving Maxwell's equations
NASA Technical Reports Server (NTRS)
Shebalin, John V.
1991-01-01
A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.
A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation
NASA Technical Reports Server (NTRS)
Jones, Brandon A.; Anderson, Rodney L.
2012-01-01
Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.
Webster, Clayton G; Zhang, Guannan; Gunzburger, Max D
2012-10-01
Accurate predictive simulations of complex real world applications require numerical approximations to first, oppose the curse of dimensionality and second, converge quickly in the presence of steep gradients, sharp transitions, bifurcations or finite discontinuities in high-dimensional parameter spaces. In this paper we present a novel multi-dimensional multi-resolution adaptive (MdMrA) sparse grid stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from interpolating wavelets. The basis for our non-intrusive method forms a stable multiscale splitting and thus, optimal adaptation is achieved. Error estimates and numerical examples will used to compare the efficiency of the method with several other techniques.
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
Foo, Jasmine; Wan Xiaoliang; Karniadakis, George Em
2008-11-20
Stochastic spectral methods are numerical techniques for approximating solutions to partial differential equations with random parameters. In this work, we present and examine the multi-element probabilistic collocation method (ME-PCM), which is a generalized form of the probabilistic collocation method. In the ME-PCM, the parametric space is discretized and a collocation/cubature grid is prescribed on each element. Both full and sparse tensor product grids based on Gauss and Clenshaw-Curtis quadrature rules are considered. We prove analytically and observe in numerical tests that as the parameter space mesh is refined, the convergence rate of the solution depends on the quadrature rule of each element only through its degree of exactness. In addition, the L{sup 2} error of the tensor product interpolant is examined and an adaptivity algorithm is provided. Numerical examples demonstrating adaptive ME-PCM are shown, including low-regularity problems and long-time integration. We test the ME-PCM on two-dimensional Navier-Stokes examples and a stochastic diffusion problem with various random input distributions and up to 50 dimensions. While the convergence rate of ME-PCM deteriorates in 50 dimensions, the error in the mean and variance is two orders of magnitude lower than the error obtained with the Monte Carlo method using only a small number of samples (e.g., 100). The computational cost of ME-PCM is found to be favorable when compared to the cost of other methods including stochastic Galerkin, Monte Carlo and quasi-random sequence methods.
Two-dimensional mesh embedding for Galerkin B-spline methods
NASA Technical Reports Server (NTRS)
Shariff, Karim; Moser, Robert D.
1995-01-01
A number of advantages result from using B-splines as basis functions in a Galerkin method for solving partial differential equations. Among them are arbitrary order of accuracy and high resolution similar to that of compact schemes but without the aliasing error. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. Both integer and non-integer refinement ratios are allowed. The report begins by developing an algorithm for choosing basis functions that yield the desired mesh resolution. These functions are suitable products of one-dimensional B-splines. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented. The scheme is conservative and has uniformly high order of accuracy throughout the domain.
Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation
NASA Technical Reports Server (NTRS)
Kouatchou, Jules
1999-01-01
In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.
Legendre spectral-collocation method for solving some types of fractional optimal control problems.
Sweilam, Nasser H; Al-Ajami, Tamer M
2015-05-01
In this paper, the Legendre spectral-collocation method was applied to obtain approximate solutions for some types of fractional optimal control problems (FOCPs). The fractional derivative was described in the Caputo sense. Two different approaches were presented, in the first approach, necessary optimality conditions in terms of the associated Hamiltonian were approximated. In the second approach, the state equation was discretized first using the trapezoidal rule for the numerical integration followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Illustrative examples were included to demonstrate the validity and applicability of the proposed techniques. PMID:26257937
Numerical Algorithm Based on Haar-Sinc Collocation Method for Solving the Hyperbolic PDEs
Javadi, H. H. S.; Navidi, H. R.
2014-01-01
The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. To analyze the efficiency, precision, and performance of the proposed method, we presented four examples through which our claim was confirmed. PMID:25485295
NASA Astrophysics Data System (ADS)
Tirani, M. Dadkhah; Sohrabi, F.; Almasieh, H.; Kajani, M. Tavassoli
2015-10-01
In this paper, a collocation method based on Taylor polynomials is developed for solving systems linear differential-difference equations with variable coefficients defined in large intervals. By using Taylor polynomials and their properties in obtaining operational matrices, the solution of the differential-difference equation system with given conditions is reduced to the solution of a system of linear algebraic equations. We first divide the large interval into M equal subintervals and then Taylor polynomials solutions are obtained in each interval, separately. Some numerical examples are given and results are compared with analytical solutions and other techniques in the literature to demonstrate the validity and applicability of the proposed method.
NASA Astrophysics Data System (ADS)
Zheng, Hui; Zhang, Chuanzeng; Wang, Yuesheng; Sladek, Jan; Sladek, Vladimir
2016-01-01
In this paper, a meshfree or meshless local radial basis function (RBF) collocation method is proposed to calculate the band structures of two-dimensional (2D) anti-plane transverse elastic waves in phononic crystals. Three new techniques are developed for calculating the normal derivative of the field quantity required by the treatment of the boundary conditions, which improve the stability of the local RBF collocation method significantly. The general form of the local RBF collocation method for a unit-cell with periodic boundary conditions is proposed, where the continuity conditions on the interface between the matrix and the scatterer are taken into account. The band structures or dispersion relations can be obtained by solving the eigenvalue problem and sweeping the boundary of the irreducible first Brillouin zone. The proposed local RBF collocation method is verified by using the corresponding results obtained with the finite element method. For different acoustic impedance ratios, various scatterer shapes, scatterer arrangements (lattice forms) and material properties, numerical examples are presented and discussed to show the performance and the efficiency of the developed local RBF collocation method compared to the FEM for computing the band structures of 2D phononic crystals.
NASA Astrophysics Data System (ADS)
Blakely, Christopher D.
This dissertation thesis has three main goals: (1) To explore the anatomy of meshless collocation approximation methods that have recently gained attention in the numerical analysis community; (2) Numerically demonstrate why the meshless collocation method should clearly become an attractive alternative to standard finite-element methods due to the simplicity of its implementation and its high-order convergence properties; (3) Propose a meshless collocation method for large scale computational geophysical fluid dynamics models. We provide numerical verification and validation of the meshless collocation scheme applied to the rotational shallow-water equations on the sphere and demonstrate computationally that the proposed model can compete with existing high performance methods for approximating the shallow-water equations such as the SEAM (spectral-element atmospheric model) developed at NCAR. A detailed analysis of the parallel implementation of the model, along with the introduction of parallel algorithmic routines for the high-performance simulation of the model will be given. We analyze the programming and computational aspects of the model using Fortran 90 and the message passing interface (mpi) library along with software and hardware specifications and performance tests. Details from many aspects of the implementation in regards to performance, optimization, and stabilization will be given. In order to verify the mathematical correctness of the algorithms presented and to validate the performance of the meshless collocation shallow-water model, we conclude the thesis with numerical experiments on some standardized test cases for the shallow-water equations on the sphere using the proposed method.
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252
Motsa, S. S.; Magagula, V. M.; Sibanda, P.
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252
Simulating the focusing of light onto 1D nanostructures with a B-spline modal method
NASA Astrophysics Data System (ADS)
Bouchon, P.; Chevalier, P.; Héron, S.; Pardo, F.; Pelouard, J.-L.; Haïdar, R.
2015-03-01
Focusing the light onto nanostructures thanks to spherical lenses is a first step to enhance the field, and is widely used in applications, in particular for enhancing non-linear effects like the second harmonic generation. Nonetheless, the electromagnetic response of such nanostructures, which have subwavelength patterns, to a focused beam can not be described by the simple ray tracing formalism. Here, we present a method to compute the response to a focused beam, based on the B-spline modal method. The simulation of a gaussian focused beam is obtained thanks to a truncated decomposition on plane waves computed on a single period, which limits the computation burden.
NASA Technical Reports Server (NTRS)
Mier Muth, A. M.; Willsky, A. S.
1978-01-01
In this paper we describe a method for approximating a waveform by a spline. The method is quite efficient, as the data are processed sequentially. The basis of the approach is to view the approximation problem as a question of estimation of a polynomial in noise, with the possibility of abrupt changes in the highest derivative. This allows us to bring several powerful statistical signal processing tools into play. We also present some initial results on the application of our technique to the processing of electrocardiograms, where the knot locations themselves may be some of the most important pieces of diagnostic information.
A Haar wavelet collocation method for coupled nonlinear Schrödinger-KdV equations
NASA Astrophysics Data System (ADS)
Oruç, Ömer; Esen, Alaattin; Bulut, Fatih
2016-04-01
In this paper, to obtain accurate numerical solutions of coupled nonlinear Schrödinger-Korteweg-de Vries (KdV) equations a Haar wavelet collocation method is proposed. An explicit time stepping scheme is used for discretization of time derivatives and nonlinear terms that appeared in the equations are linearized by a linearization technique and space derivatives are discretized by Haar wavelets. In order to test the accuracy and reliability of the proposed method L2, L∞ error norms and conserved quantities are used. Also obtained results are compared with previous ones obtained by finite element method, Crank-Nicolson method and radial basis function meshless methods. Error analysis of Haar wavelets is also given.
MULTILEVEL ACCELERATION OF STOCHASTIC COLLOCATION METHODS FOR PDE WITH RANDOM INPUT DATA
Webster, Clayton G; Jantsch, Peter A; Teckentrup, Aretha L; Gunzburger, Max D
2013-01-01
Stochastic Collocation (SC) methods for stochastic partial differential equa- tions (SPDEs) suffer from the curse of dimensionality, whereby increases in the stochastic dimension cause an explosion of computational effort. To combat these challenges, multilevel approximation methods seek to decrease computational complexity by balancing spatial and stochastic discretization errors. As a form of variance reduction, multilevel techniques have been successfully applied to Monte Carlo (MC) methods, but may be extended to accelerate other methods for SPDEs in which the stochastic and spatial degrees of freedom are de- coupled. This article presents general convergence and computational complexity analysis of a multilevel method for SPDEs, demonstrating its advantages with regard to standard, single level approximation. The numerical results will highlight conditions under which multilevel sparse grid SC is preferable to the more traditional MC and SC approaches.
NASA Technical Reports Server (NTRS)
Zhang, Yiqiang; Alexander, J. I. D.; Ouazzani, J.
1994-01-01
Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and name propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectra collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.
An iterative finite-element collocation method for parabolic problems using domain decomposition
Curran, M.C.
1992-01-01
Advection-dominated flows occur widely in the transport of groundwater contaminants, the movements of fluids in enhanced oil recovery projects, and many other contexts. In numerical models of such flows, adaptive local grid refinement is a conceptually attractive approach for resolving the sharp fronts or layers that tend to characterize the solutions. However, this approach can be difficult to implement in practice. A domain decomposition method developed by Bramble, Ewing, Pasciak, and Schatz, known as the BEPS method, overcomes many of the difficulties. We demonstrate the applicability of the iterative BEPS ideas to finite-element collocation on trial spaces of piecewise Hermite bicubics. The resulting scheme allows one to refine selected parts of a spatial grid without destroying algebraic efficiencies associated with the original coarse grid. We apply the method to two dimensional time-dependent advection-diffusion problems.
An iterative finite-element collocation method for parabolic problems using domain decomposition
Curran, M.C.
1992-11-01
Advection-dominated flows occur widely in the transport of groundwater contaminants, the movements of fluids in enhanced oil recovery projects, and many other contexts. In numerical models of such flows, adaptive local grid refinement is a conceptually attractive approach for resolving the sharp fronts or layers that tend to characterize the solutions. However, this approach can be difficult to implement in practice. A domain decomposition method developed by Bramble, Ewing, Pasciak, and Schatz, known as the BEPS method, overcomes many of the difficulties. We demonstrate the applicability of the iterative BEPS ideas to finite-element collocation on trial spaces of piecewise Hermite bicubics. The resulting scheme allows one to refine selected parts of a spatial grid without destroying algebraic efficiencies associated with the original coarse grid. We apply the method to two dimensional time-dependent advection-diffusion problems.
Sankaran, Sethuraman; Audet, Charles; Marsden, Alison L.
2010-06-20
Recent advances in coupling novel optimization methods to large-scale computing problems have opened the door to tackling a diverse set of physically realistic engineering design problems. A large computational overhead is associated with computing the cost function for most practical problems involving complex physical phenomena. Such problems are also plagued with uncertainties in a diverse set of parameters. We present a novel stochastic derivative-free optimization approach for tackling such problems. Our method extends the previously developed surrogate management framework (SMF) to allow for uncertainties in both simulation parameters and design variables. The stochastic collocation scheme is employed for stochastic variables whereas Kriging based surrogate functions are employed for the cost function. This approach is tested on four numerical optimization problems and is shown to have significant improvement in efficiency over traditional Monte-Carlo schemes. Problems with multiple probabilistic constraints are also discussed.
NASA Astrophysics Data System (ADS)
Xu, ShengYong; Wu, JuanJuan; Zhu, Li; Li, WeiHao; Wang, YiTian; Wang, Na
2015-12-01
Visual navigation is a fundamental technique of intelligent cotton-picking robot. There are many components and cover in the cotton field, which make difficulties of furrow recognition and trajectory extraction. In this paper, a new field navigation path extraction method is presented. Firstly, the color image in RGB color space is pre-processed by the OTSU threshold algorithm and noise filtering. Secondly, the binary image is divided into numerous horizontally spline areas. In each area connected regions of neighboring images' vertical center line are calculated by the Two-Pass algorithm. The center points of the connected regions are candidate points for navigation path. Thirdly, a series of navigation points are determined iteratively on the principle of the nearest distance between two candidate points in neighboring splines. Finally, the navigation path equation is fitted by the navigation points using the least squares method. Experiments prove that this method is accurate and effective. It is suitable for visual navigation in the complex environment of cotton field in different phases.
Extended cubic B-spline method for solving a linear system of second-order boundary value problems.
Heilat, Ahmed Salem; Hamid, Nur Nadiah Abd; Ismail, Ahmad Izani Md
2016-01-01
A method based on extended cubic B-spline is proposed to solve a linear system of second-order boundary value problems. In this method, two free parameters, [Formula: see text] and [Formula: see text], play an important role in producing accurate results. Optimization of these parameters are carried out and the truncation error is calculated. This method is tested on three examples. The examples suggest that this method produces comparable or more accurate results than cubic B-spline and some other methods. PMID:27547688
NASA Astrophysics Data System (ADS)
Yi, Longtao; Liu, Zhiguo; Wang, Kai; Chen, Man; Peng, Shiqi; Zhao, Weigang; He, Jialin; Zhao, Guangcui
2015-03-01
A new method is presented to subtract the background from the energy dispersive X-ray fluorescence (EDXRF) spectrum using a cubic spline interpolation. To accurately obtain interpolation nodes, a smooth fitting and a set of discriminant formulations were adopted. From these interpolation nodes, the background is estimated by a calculated cubic spline function. The method has been tested on spectra measured from a coin and an oil painting using a confocal MXRF setup. In addition, the method has been tested on an existing sample spectrum. The result confirms that the method can properly subtract the background.
Ren, K; Ren-Kurc, A
1986-08-01
A new numerical method of determining the position of the inflection point of a potentiometric titration curve is presented. It consists of describing the experimental data (emf, volume data-points) by means of a rational spline function. The co-ordinates of the titration end-point are determined by analysis of the first and second derivatives of the spline function formed. The method also allows analysis of distorted titration curves which cannot be interpreted by Gran's or other computational methods. PMID:18964159
An Automatic Method for Nucleus Boundary Segmentation Based on a Closed Cubic Spline
Feng, Zhao; Li, Anan; Gong, Hui; Luo, Qingming
2016-01-01
The recognition of brain nuclei is the basis for localizing brain functions. Traditional histological research, represented by atlas illustration, achieves the goal of nucleus boundary recognition by manual delineation, but it has become increasingly difficult to extend this handmade method to delineating brain regions and nuclei from large datasets acquired by the recently developed single-cell-resolution imaging techniques for the whole brain. Here, we propose a method based on a closed cubic spline (CCS), which can automatically segment the boundaries of nuclei that differ to a relatively high degree in cell density from the surrounding areas and has been validated on model images and Nissl-stained microimages of mouse brain. It may even be extended to the segmentation of target outlines on MRI or CT images. The proposed method for the automatic extraction of nucleus boundaries would greatly accelerate the illustration of high-resolution brain atlases. PMID:27378903
NASA Astrophysics Data System (ADS)
Soghrati, Soheil; Mai, Weijie; Liang, Bowen; Buchheit, Rudolph G.
2015-01-01
A new meshfree method based on a discrete transformation of Green's basis functions is introduced to simulate Poisson problems with complex morphologies. The proposed Green's Discrete Transformation Method (GDTM) uses source points that are located along a virtual boundary outside the problem domain to construct the basis functions needed to approximate the field. The optimal number of Green's functions source points and their relative distances with respect to the problem boundaries are evaluated to obtain the best approximation of the partition of unity condition. A discrete transformation technique together with the boundary point collocation method is employed to evaluate the unknown coefficients of the solution series via satisfying the problem boundary conditions. A comprehensive convergence study is presented to investigate the accuracy and convergence rate of the GDTM. We will also demonstrate the application of this meshfree method for simulating the conductive heat transfer in a heterogeneous materials system and the dissolved aluminum ions concentration in the electrolyte solution formed near a passive corrosion pit.
Chebyshev collocation spectral lattice Boltzmann method for simulation of low-speed flows.
Hejranfar, Kazem; Hajihassanpour, Mahya
2015-01-01
In this study, the Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low-speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation with the Bhatnagar-Gross-Krook approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the lattice Boltzmann equation is made by the fourth-order Runge-Kutta scheme. To achieve numerical stability and accuracy, physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used. An iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows. The main advantage of using the CCSLBM over other high-order accurate lattice Boltzmann method (LBM)-based flow solvers is the decay of the error at exponential rather than at polynomial rates. Note also that the CCSLBM applied does not need any numerical dissipation or filtering for the solution to be stable, leading to highly accurate solutions. Three two-dimensional (2D) test cases are simulated herein that are a regularized cavity, the Taylor vortex problem, and doubly periodic shear layers. The results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement. The computational efficiency of the proposed solution methodology based on the CCSLBM is also examined by comparison with those of the standard streaming-collision (classical) LBM and two finite-difference LBM solvers. The study indicates that the CCSLBM provides more accurate and efficient solutions than these LBM solvers in terms of CPU and memory usage and an exponential
NASA Astrophysics Data System (ADS)
Ma, Xiang; Zabaras, Nicholas
2009-03-01
A new approach to modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adaptive hierarchical sparse grid collocation (ASGC) method is used for constructing an interpolant to the solution of the forward model in this prior space which is large enough to capture all the variability/uncertainty in the posterior distribution of the unknown parameters. This solution can be considered as a function of the random unknowns and serves as a stochastic surrogate model for the likelihood calculation. Hierarchical Bayesian formulation is used to derive the posterior probability density function (PPDF). The spatial model is represented as a convolution of a smooth kernel and a Markov random field. The state space of the PPDF is explored using Markov chain Monte Carlo algorithms to obtain statistics of the unknowns. The likelihood calculation is performed by directly sampling the approximate stochastic solution obtained through the ASGC method. The technique is assessed on two nonlinear inverse problems: source inversion and permeability estimation in flow through porous media.
Estimation of river pollution source using the space-time radial basis collocation method
NASA Astrophysics Data System (ADS)
Li, Zi; Mao, Xian-Zhong; Li, Tak Sing; Zhang, Shiyan
2016-02-01
River contaminant source identification problems can be formulated as an inverse model to estimate the missing source release history from the observed contaminant plume. In this study, the identification of pollution sources in rivers, where strong advection is dominant, is solved by the global space-time radial basis collocation method (RBCM). To search for the optimal shape parameter and scaling factor which strongly determine the accuracy of the RBCM method, a new cost function based on the residual errors of not only the observed data but also the specified governing equation, the initial and boundary conditions, was constructed for the k-fold cross-validation technique. The performance of three global radial basis functions, Hardy's multiquadric, inverse multiquadric and Gaussian, were also compared in the test cases. The numerical results illustrate that the new cost function is a good indicator to search for near-optimal solutions. Application to a real polluted river shows that the source release history is reasonably recovered, demonstrating that the RBCM with the k-fold cross-validation is a powerful tool for source identification problems in advection-dominated rivers.
Webster, Clayton; Tempone, Raul; Nobile, Fabio
2007-12-01
This work describes the convergence analysis of a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms (input data of the model). To compute solution statistics, the sparse grid stochastic collocation method uses approximate solutions, produced here by finite elements, corresponding to a deterministic set of points in the random input space. This naturally requires solving uncoupled deterministic problems and, as such, the derived strong error estimates for the fully discrete solution are used to compare the computational efficiency of the proposed method with the Monte Carlo method. Numerical examples illustrate the theoretical results and are used to compare this approach with several others, including the standard Monte Carlo.
Splines for Diffeomorphic Image Regression
Singh, Nikhil; Niethammer, Marc
2016-01-01
This paper develops a method for splines on diffeomorphisms for image regression. In contrast to previously proposed methods to capture image changes over time, such as geodesic regression, the method can capture more complex spatio-temporal deformations. In particular, it is a first step towards capturing periodic motions for example of the heart or the lung. Starting from a variational formulation of splines the proposed approach allows for the use of temporal control points to control spline behavior. This necessitates the development of a shooting formulation for splines. Experimental results are shown for synthetic and real data. The performance of the method is compared to geodesic regression. PMID:25485370
High-order numerical solutions using cubic splines
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1975-01-01
The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.
NASA Astrophysics Data System (ADS)
Cherry, M. R.; Knopp, J. S.; Blodgett, M. P.
2012-05-01
In order to quantify the reliability of NDE systems, large numbers of experiments are performed to develop a probability of detection (POD) curve for the system. These POD studies require a substantial amount of experimentation which can sometimes be cost prohibitive. To expedite the process of developing these curves, highly precise numerical models are used in conjunction with NDE sensors to understand the uncertainties associated with the inspections. Numerical models are also used in stochastic inversion methods such as Bayesian inversion, which provide a means of characterizing system properties with uncertainties. A strong basis has been developed in the modeling and simulation community for deterministic forward models in NDE, but to fully incorporate these models in model-assisted probability of detection (MAPOD) studies or stochastic inversion schemes, the models must be treated in a stochastic sense. A method of taking random inputs to a "black box" forward model and developing the full probability distribution function (PDF) of the response has been proposed. This method, called the probabilistic collocation method (PCM), takes random inputs to a forward model and uses orthogonal polynomials to construct a surrogate model in the area of the expected values of the inputs which is solved much quicker than the original forward model. In the NDE community, this method has only been used with inputs of known, named distributions. In this work, inputs of arbitrary distribution were used and the orthogonal polynomials for these inputs were developed with a recursion relationship that has been shown to produce orthogonal polynomials with respect to a given, continuous function. A concise code was written to make testing the method and incorporating it into MAPOD studies and inversion schemes relatively easy. The routine was tested with academic problems as well as eddy current problems.
NASA Astrophysics Data System (ADS)
Vu, Q. H.; Brenner, R.; Castelnau, O.; Moulinec, H.; Suquet, P.
2012-03-01
The correspondence principle is customarily used with the Laplace-Carson transform technique to tackle the homogenization of linear viscoelastic heterogeneous media. The main drawback of this method lies in the fact that the whole stress and strain histories have to be considered to compute the mechanical response of the material during a given macroscopic loading. Following a remark of Mandel (1966 Mécanique des Milieux Continus(Paris, France: Gauthier-Villars)), Ricaud and Masson (2009 Int. J. Solids Struct. 46 1599-1606) have shown the equivalence between the collocation method used to invert Laplace-Carson transforms and an internal variables formulation. In this paper, this new method is developed for the case of polycrystalline materials with general anisotropic properties for local and macroscopic behavior. Applications are provided for the case of constitutive relations accounting for glide of dislocations on particular slip systems. It is shown that the method yields accurate results that perfectly match the standard collocation method and reference full-field results obtained with a FFT numerical scheme. The formulation is then extended to the case of time- and strain-dependent viscous properties, leading to the incremental collocation method (ICM) that can be solved efficiently by a step-by-step procedure. Specifically, the introduction of isotropic and kinematic hardening at the slip system scale is considered.
Accuracy of the collocated transfer standard method for wind instrument auditing
NASA Astrophysics Data System (ADS)
Lockhart, Thomas J.
1989-08-01
The application of collocated data collection for the purpose of estimating the accuracy of an operating wind instrument requires some baseline demonstrating the best agreement which can be expected. A series of data were carefully taken in 1982 from six different collocated wind instruments. The published reports of these data suggest that the best agreement from averaged wind-speed measurements will be between 0.3 and 0.5 m/s, and for wind direction it will be 4 to 6 degrees. A new analysis of the same data reduces the best expected agreement to about 0.2 m/s and 2 degrees. The several reasons for claiming the better potential accuracy for collocated measurement (auditing) with calibrated transfer standard instruments are discussed.
NASA Astrophysics Data System (ADS)
Shukla, H. S.; Tamsir, Mohammad; Srivastava, Vineet K.; Rashidi, Mohammad Mehdi
2016-04-01
In this paper, we propose a modified cubic B-spline differential quadrature method (MCB-DQM) to solve three-dimensional (3D) coupled viscous Burger equation with appropriate initial and boundary conditions. In this method, modified cubic B-spline is treated as a basis function in the differential quadrature method (DQM) to compute the weighting coefficients. In this way, the Burger equation is reduced into a system of ordinary differential equations. An optimal strong stability-preserving Runge-Kutta (SSP-RK) method is employed to solve the resulting system of ordinary differential equations. In order to illustrate the accuracy and efficiency of the proposed method, a numerical problem is considered. From the numerical experiment, it is found that the computed result is in good agreement with the exact solution. Stability analysis of the method is also carried out using the matrix stability analysis method and found to be unconditionally stable.
B-spline methods and zonal grids for numerical simulations of turbulent flows
NASA Astrophysics Data System (ADS)
Kravchenko, Arthur Grigorievich
1998-12-01
A novel numerical technique is developed for simulations of complex turbulent flows on zonal embedded grids. This technique is based on the Galerkin method with basis functions constructed using B-splines. The technique permits fine meshes to be embedded in physically significant flow regions without placing a large number of grid points in the rest of the computational domain. The numerical technique has been tested successfully in simulations of a fully developed turbulent channel flow. Large eddy simulations of turbulent channel flow at Reynolds numbers up to Rec = 110,000 (based on centerline velocity and channel half-width) show good agreement with the existing experimental data. These tests indicate that the method provides an efficient information transfer between zones without accumulation of errors in the regions of sudden grid changes. The numerical solutions on multi-zone grids are of the same accuracy as those on a single-zone grid but require less computer resources. The performance of the numerical method in a generalized coordinate system is assessed in simulations of laminar flows over a circular cylinder at low Reynolds numbers and three-dimensional simulations at ReD = 300 (based on free-stream velocity and cylinder diameter). The drag coefficients, the size of the recirculation region, and the vortex shedding frequency all agree well with the experimental data and previous simulations of these flows. Large eddy simulations of a flow over a circular cylinder at a sub-critical Reynolds number, ReD = 3900, are performed and compared with previous upwind-biased and central finite-difference computations. In the very near-wake, all three simulations are in agreement with each other and agree fairly well with the PIV experimental data of Lourenco & Shih (1993). Farther downstream, the results of the B- spline computations are in better agreement with the hot- wire experiment of Ong & Wallace (1996) than those obtained in finite-difference simulations
NASA Astrophysics Data System (ADS)
Khani, F.; Darvishi, M. T.; Gorla, R. S.. R.; Gireesha, B. J.
2016-05-01
Heat transfer with natural convection and radiation effect on a fully wet porous radial fin is considered. The radial velocity of the buoyancy driven flow at any radial location is obtained by applying Darcy's law. The obtained non-dimensionalized ordinary differential equation involving three highly nonlinear terms is solved numerically with the spectral collocation method. In this approach, the dimensionless temperature is approximated by Chebyshev polynomials and discretized by Chebyshev-Gausse-Lobatto collocation points. A particular algorithm is used to reduce the nonlinearity of the conservation of energy equation. The present analysis characterizes the effect of ambient temperature in different ways and it provides a better picture regarding the effect of ambient temperature on the thermal performance of the fin. The profiles for temperature distributions and dimensionless base heat flow are obtained for different parameters which influence the heat transfer rate.
NASA Astrophysics Data System (ADS)
Karkar, Sami; Cochelin, Bruno; Vergez, Christophe
2014-06-01
The high-order purely frequency-based harmonic balance method (HBM) presented by Cochelin and Vergez (2009) [1] and extended by Karkar et al. (2013) [2] now allows to follow the periodic solutions of regularized non-smooth systems (stiff systems). This paper compares its convergence property to a reference method in applied mathematics: orthogonal collocation with piecewise polynomials. A first test is conducted on a nonlinear smooth 2 degree-of-freedom spring mass system, showing better convergence of the HBM. The second test is conducted on a one degree-of-freedom vibro-impact system with a very stiff regularization of the impact law. The HBM continuation of the nonlinear mode was found to be very robust, even with a very large number of harmonics. Surprisingly, the HBM was found to have a better convergence than the collocation method for this vibro-impact system. absolute threshold on the norm of the residue for the Newton-Raphson corrector: εNR=10-9 (the residue norm is checked at the end of each step, and correction is carried out only if necessary), ANM series threshold used for step length estimation: εANM=10-12, ANM series order: Nseries=20. The choice of a small correction threshold ensures that the accuracy of a solution is mainly dependent on the accuracy of the discretization method, and not on that of the solver of the quadratic problem. Similarly, the choice of an even smaller ANM threshold ensures that the approximation at the end of each step is accurate enough so that no correction is usually needed at the beginning of the next step. Finally, the choice of the series order is arbitrary and mainly influences the step length.
NASA Astrophysics Data System (ADS)
Vasilyev, Oleg V.; Gazzola, Mattia; Koumoutsakos, Petros
2010-11-01
In this talk we discuss preliminary results for the use of hybrid wavelet collocation - Brinkman penalization approach for shape optimization for drag reduction in flows past linked bodies. This optimization relies on Adaptive Wavelet Collocation Method along with the Brinkman penalization technique and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Adaptive wavelet collocation method tackles the problem of efficiently resolving a fluid flow on a dynamically adaptive computational grid, while a level set approach is used to describe the body shape and the Brinkman volume penalization allows for an easy variation of flow geometry without requiring body-fitted meshes. We perform 2D simulations of linked bodies in order to investigate whether flat geometries are optimal for drag reduction. In order to accelerate the costly cost function evaluations we exploit the inherent parallelism of ES and we extend the CMA-ES implementation to a multi-host framework. This framework allows for an easy distribution of the cost function evaluations across several parallel architectures and it is not limited to only one computing facility. The resulting optimal shapes are geometrically consistent with the shapes that have been obtained in the pioneering wind tunnel experiments for drag reduction using Evolution Strategies by Ingo Rechenberg.
NASA Astrophysics Data System (ADS)
Shukla, H. S.; Tamsir, Mohammad; Srivastava, Vineet K.; Kumar, Jai
2014-11-01
In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge-Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation.
Swenson, Darrell J.; Geneser, Sarah E.; Stinstra, Jeroen G.; Kirby, Robert M.; MacLeod, Rob S.
2012-01-01
The electrocardiogram (ECG) is ubiquitously employed as a diagnostic and monitoring tool for patients experiencing cardiac distress and/or disease. It is widely known that changes in heart position resulting from, for example, posture of the patient (sitting, standing, lying) and respiration significantly affect the body-surface potentials; however, few studies have quantitatively and systematically evaluated the effects of heart displacement on the ECG. The goal of this study was to evaluate the impact of positional changes of the heart on the ECG in the specific clinical setting of myocardial ischemia. To carry out the necessary comprehensive sensitivity analysis, we applied a relatively novel and highly efficient statistical approach, the generalized polynomial chaos-stochastic collocation method, to a boundary element formulation of the electrocardiographic forward problem, and we drove these simulations with measured epicardial potentials from whole-heart experiments. Results of the analysis identified regions on the body-surface where the potentials were especially sensitive to realistic heart motion. The standard deviation (STD) of ST-segment voltage changes caused by the apex of a normal heart, swinging forward and backward or side-to-side was approximately 0.2 mV. Variations were even larger, 0.3 mV, for a heart exhibiting elevated ischemic potentials. These variations could be large enough to mask or to mimic signs of ischemia in the ECG. Our results suggest possible modifications to ECG protocols that could reduce the diagnostic error related to postural changes in patients possibly suffering from myocardial ischemia. PMID:21909818
NASA Astrophysics Data System (ADS)
Senses, Begum
A state-defect constraint pairing graph coarsening method is described for improving computational efficiency during the numerical factorization of large sparse Karush-Kuhn-Tucker matrices that arise from the discretization of optimal control problems via a Legendre-Gauss-Radau orthogonal collocation method. The method takes advantage of the particular sparse structure of the Karush-Kuhn-Tucker matrix that arises from the orthogonal collocation method. The state-defect constraint pairing graph coarsening method pairs each component of the state with its corresponding defect constraint and forces paired rows to be adjacent in the reordered Karush-Kuhn-Tucker matrix. Aggregate state-defect constraint pairing results are presented using a wide variety of benchmark optimal control problems where it is found that the proposed state-defect constraint pairing graph coarsening method significantly reduces both the number of delayed pivots and the number of floating point operations and increases the computational efficiency by performing more floating point operations per unit time. It is then shown that the state-defect constraint pairing graph coarsening method is less effective on Karush-Kuhn-Tucker matrices arising from Legendre-Gauss-Radau collocation when the optimal control problem contains state and control equality path constraints because such matrices may have delayed pivots that correspond to both defect and path constraints. An unweighted alternate graph coarsening method that employs maximal matching and a weighted alternate graph coarsening method that employs Hungarian algorithm on a weighting matrix are then used to attempt to further reduce the number of delayed pivots. It is found, however, that these alternate graph coarsening methods provide no further advantage over the state-defect constraint pairing graph coarsening method.
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1986-01-01
Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator-theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are used to argue convergence and establish rates of convergence. An example and numerical results are discussed.
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1985-01-01
Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are useed to argue convergence and establish rates of convergence. An example and numerical results are discussed.
Ray-tracing method for creeping waves on arbitrarily shaped nonuniform rational B-splines surfaces.
Chen, Xi; He, Si-Yuan; Yu, Ding-Feng; Yin, Hong-Cheng; Hu, Wei-Dong; Zhu, Guo-Qiang
2013-04-01
An accurate creeping ray-tracing algorithm is presented in this paper to determine the tracks of creeping waves (or creeping rays) on arbitrarily shaped free-form parametric surfaces [nonuniform rational B-splines (NURBS) surfaces]. The main challenge in calculating the surface diffracted fields on NURBS surfaces is due to the difficulty in determining the geodesic paths along which the creeping rays propagate. On one single parametric surface patch, the geodesic paths need to be computed by solving the geodesic equations numerically. Furthermore, realistic objects are generally modeled as the union of several connected NURBS patches. Due to the discontinuity of the parameter between the patches, it is more complicated to compute geodesic paths on several connected patches than on one single patch. Thus, a creeping ray-tracing algorithm is presented in this paper to compute the geodesic paths of creeping rays on the complex objects that are modeled as the combination of several NURBS surface patches. In the algorithm, the creeping ray tracing on each surface patch is performed by solving the geodesic equations with a Runge-Kutta method. When the creeping ray propagates from one patch to another, a transition method is developed to handle the transition of the creeping ray tracing across the border between the patches. This creeping ray-tracing algorithm can meet practical requirements because it can be applied to the objects with complex shapes. The algorithm can also extend the applicability of NURBS for electromagnetic and optical applications. The validity and usefulness of the algorithm can be verified from the numerical results. PMID:23595326
Algebraic grid adaptation method using non-uniform rational B-spline surface modeling
NASA Technical Reports Server (NTRS)
Yang, Jiann-Cherng; Soni, B. K.
1992-01-01
An algebraic adaptive grid system based on equidistribution law and utilized by the Non-Uniform Rational B-Spline (NURBS) surface for redistribution is presented. A weight function, utilizing a properly weighted boolean sum of various flow field characteristics is developed. Computational examples are presented to demonstrate the success of this technique.
Bahşı, Ayşe Kurt; Yalçınbaş, Salih
2016-01-01
In this study, the Fibonacci collocation method based on the Fibonacci polynomials are presented to solve for the fractional diffusion equations with variable coefficients. The fractional derivatives are described in the Caputo sense. This method is derived by expanding the approximate solution with Fibonacci polynomials. Using this method of the fractional derivative this equation can be reduced to a set of linear algebraic equations. Also, an error estimation algorithm which is based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation algorithm. If the exact solution of the problem is not known, the absolute error function of the problems can be approximately computed by using the Fibonacci polynomial solution. By using this error estimation function, we can find improved solutions which are more efficient than direct numerical solutions. Numerical examples, figures, tables are comparisons have been presented to show efficiency and usable of proposed method. PMID:27610294
Interchangeable spline reference guide
Dolin, R.M.
1994-05-01
The WX-Division Integrated Software Tools (WIST) Team evolved from two previous committees, First was the W78 Solid Modeling Pilot Project`s Spline Subcommittee, which later evolved into the Vv`X-Division Spline Committee. The mission of the WIST team is to investigate current CAE engineering processes relating to complex geometry and to develop methods for improving those processes. Specifically, the WIST team is developing technology that allows the Division to use multiple spline representations. We are also updating the contour system (CONSYS) data base to take full advantage of the Division`s expanding electronic engineering process. Both of these efforts involve developing interfaces to commercial CAE systems and writing new software. The WIST team is comprised of members from V;X-11, -12 and 13. This {open_quotes}cross-functional{close_quotes} approach to software development is somewhat new in the Division so an effort is being made to formalize our processes and assure quality at each phase of development. Chapter one represents a theory manual and is one phase of the formal process. The theory manual is followed by a software requirements document, specification document, software verification and validation documents. The purpose of this guide is to present the theory underlying the interchangeable spline technology and application. Verification and validation test results are also presented for proof of principal.
NASA Technical Reports Server (NTRS)
Vranish, John M. (Inventor)
1993-01-01
A split spline screw type payload fastener assembly, including three identical male and female type split spline sections, is discussed. The male spline sections are formed on the head of a male type spline driver. Each of the split male type spline sections has an outwardly projecting load baring segment including a convex upper surface which is adapted to engage a complementary concave surface of a female spline receptor in the form of a hollow bolt head. Additionally, the male spline section also includes a horizontal spline releasing segment and a spline tightening segment below each load bearing segment. The spline tightening segment consists of a vertical web of constant thickness. The web has at least one flat vertical wall surface which is designed to contact a generally flat vertically extending wall surface tab of the bolt head. Mutual interlocking and unlocking of the male and female splines results upon clockwise and counter clockwise turning of the driver element.
A Stochastic Collocation Algorithm for Uncertainty Analysis
NASA Technical Reports Server (NTRS)
Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)
2003-01-01
This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.
NASA Astrophysics Data System (ADS)
Zhu, W.; Sommar, J.; Lin, C.-J.; Feng, X.
2015-01-01
Reliable quantification of air-biosphere exchange flux of elemental mercury vapor (Hg0) is crucial for understanding the global biogeochemical cycle of mercury. However, there has not been a standard analytical protocol for flux quantification, and little attention has been devoted to characterize the temporal variability and comparability of fluxes measured by different methods. In this study, we deployed a collocated set of micrometeorological (MM) and dynamic flux chamber (DFC) measurement systems to quantify Hg0 flux over bare soil and low standing crop in an agricultural field. The techniques include relaxed eddy accumulation (REA), modified Bowen ratio (MBR), aerodynamic gradient (AGM) as well as dynamic flux chambers of traditional (TDFC) and novel (NDFC) designs. The five systems and their measured fluxes were cross-examined with respect to magnitude, temporal trend and correlation with environmental variables. Fluxes measured by the MM and DFC methods showed distinct temporal trends. The former exhibited a highly dynamic temporal variability while the latter had much more gradual temporal features. The diurnal characteristics reflected the difference in the fundamental processes driving the measurements. The correlations between NDFC and TDFC fluxes and between MBR and AGM fluxes were significant (R>0.8, p<0.05), but the correlation between DFC and MM fluxes were from weak to moderate (R=0.1-0.5). Statistical analysis indicated that the median of turbulent fluxes estimated by the three independent MM techniques were not significantly different. Cumulative flux measured by TDFC is considerably lower (42% of AGM and 31% of MBR fluxes) while those measured by NDFC, AGM and MBR were similar (<10% difference). This suggests that incorporating an atmospheric turbulence property such as friction velocity for correcting the DFC-measured flux effectively bridged the gap between the Hg0 fluxes measured by enclosure and MM techniques. Cumulated flux measured by REA
Chevalier, Paul; Bouchon, Patrick; Pardo, Fabrice; Haïdar, Riad
2014-08-01
Focusing light onto nanostructures thanks to spherical lenses is a first step in enhancing the field and is widely used in applications. Nonetheless, the electromagnetic response of such nanostructures, which have subwavelength patterns, to a focused beam cannot be described by the simple ray tracing formalism. Here, we present a method for computing the response to a focused beam, based on the B-spline modal method adapted to nanostructures in conical mounting. The eigenmodes are computed in each layer for both polarizations and are then combined for the computation of scattering matrices. The simulation of a Gaussian focused beam is obtained thanks to a truncated decomposition into plane waves computed on a single period, which limits the computation burden. PMID:25121523
NASA Astrophysics Data System (ADS)
Tanaka, Satoyuki; Okada, Hiroshi; Okazawa, Shigenobu
2012-07-01
This study develops a wavelet Galerkin method (WGM) that uses B-spline wavelet bases for application to solid mechanics problems. A fictitious domain is often adopted to treat general boundaries in WGMs. In the analysis, the body is extended to its exterior but very low stiffness is applied to the exterior region. The stiffness matrix in the WGM becomes singular without the use of a fictitious domain. The problem arises from the lack of linear independence of the basis functions. A technique to remove basis functions that can be represented by the superposition of the other basis functions is proposed. The basis functions are automatically eliminated in the pre conditioning step. An adaptive strategy is developed using the proposed technique. The solution is refined by superposing finer wavelet functions. Numerical examples of solid mechanics problems are presented to demonstrate the multiresolution properties of the WGM.
Banihani, Suleiman; De, Suvranu
2009-01-01
In this paper we develop the Point Collocation-based Method of Finite Spheres (PCMFS) to simulate the viscoelastic response of soft biological tissues and evaluate the effectiveness of model order reduction methods such as modal truncation, Hankel optimal model and truncated balanced realization techniques for PCMFS. The PCMFS was developed in [1] as a physics-based technique for real time simulation of surgical procedures. It is a meshfree numerical method in which discretization is performed using a set of nodal points with approximation functions compactly supported on spherical subdomains centered at the nodes. The point collocation method is used as the weighted residual technique where the governing differential equations are directly applied at the nodal points. Since computational speed has a significant role in simulation of surgical procedures, model order reduction methods have been compared for relative gains in efficiency and computational accuracy. Of these methods, truncated balanced realization results in the highest accuracy while modal truncation results in the highest efficiency. PMID:20300494
NASA Astrophysics Data System (ADS)
Tirani, M. D.; Maleki, M.; Kajani, M. T.
2014-11-01
A numerical method for solving the Lane-Emden equations of the polytropic index α when 4.75 ≤ α ≤ 5 is introduced. The method is based upon nonclassical Gauss-Radau collocation points and Freud type weights. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced and are utilized in the interval [0,1]. A smooth, strictly monotonic transformation is used to map the infinite domain x ∈ [0,∞) onto a half-open interval t ∈ [0,1). The resulting problem on the finite interval is then transcribed to a system of nonlinear algebraic equations using collocation. The method is easy to implement and yields very accurate results.
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method
NASA Astrophysics Data System (ADS)
Schillinger, Dominik; Ruess, Martin; Zander, Nils; Bazilevs, Yuri; Düster, Alexander; Rank, Ernst
2012-10-01
The Finite Cell Method (FCM) is an embedded domain method, which combines the fictitious domain approach with high-order finite elements, adaptive integration, and weak imposition of unfitted Dirichlet boundary conditions. For smooth problems, FCM has been shown to achieve exponential rates of convergence in energy norm, while its structured cell grid guarantees simple mesh generation irrespective of the geometric complexity involved. The present contribution first unhinges the FCM concept from a special high-order basis. Several benchmarks of linear elasticity and a complex proximal femur bone with inhomogeneous material demonstrate that for small deformation analysis, FCM works equally well with basis functions of the p-version of the finite element method or high-order B-splines. Turning to large deformation analysis, it is then illustrated that a straightforward geometrically nonlinear FCM formulation leads to the loss of uniqueness of the deformation map in the fictitious domain. Therefore, a modified FCM formulation is introduced, based on repeated deformation resetting, which assumes for the fictitious domain the deformation-free reference configuration after each Newton iteration. Numerical experiments show that this intervention allows for stable nonlinear FCM analysis, preserving the full range of advantages of linear elastic FCM, in particular exponential rates of convergence. Finally, the weak imposition of unfitted Dirichlet boundary conditions via the penalty method, the robustness of FCM under severe mesh distortion, and the large deformation analysis of a complex voxel-based metal foam are addressed.
Archibald, Richard K; Deiterding, Ralf; Hauck, Cory D; Jakeman, John D; Xiu, Dongbin
2012-01-01
We have develop a fast method that can capture piecewise smooth functions in high dimensions with high order and low computational cost. This method can be used for both approximation and error estimation of stochastic simulations where the computations can either be guided or come from a legacy database.
Wu, Hulin; Xue, Hongqi; Kumar, Arun
2012-06-01
Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. PMID:22376200
Incidental Learning of Collocation
ERIC Educational Resources Information Center
Webb, Stuart; Newton, Jonathan; Chang, Anna
2013-01-01
This study investigated the effects of repetition on the learning of collocation. Taiwanese university students learning English as a foreign language simultaneously read and listened to one of four versions of a modified graded reader that included different numbers of encounters (1, 5, 10, and 15 encounters) with a set of 18 target collocations.…
Zhang, Guannan; Webster, Clayton G; Gunzburger, Max D
2012-09-01
Although Bayesian analysis has become vital to the quantification of prediction uncertainty in groundwater modeling, its application has been hindered due to the computational cost associated with numerous model executions needed for exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, we utilize a compactly supported higher-order hierar- chical basis to construct the surrogate system, resulting in a significant reduction in the number of computational simulations required. In addition, we use hierarchical surplus as an error indi- cator to determine adaptive sparse grids. This allows local refinement in the uncertain domain and/or anisotropic detection with respect to the random model parameters, which further improves computational efficiency. Finally, we incorporate a global optimization technique and propose an iterative algorithm for building the surrogate system for the PPDF with multiple significant modes. Once the surrogate system is determined, the PPDF can be evaluated by sampling the surrogate system directly with very little computational cost. The developed method is evaluated first using a simple analytical density function with multiple modes and then using two synthetic groundwater reactive transport models. The groundwater models represent different levels of complexity; the first example involves coupled linear reactions and the second example simulates nonlinear ura- nium surface complexation. The results show that the aSG-hSC is an effective and efficient tool for Bayesian inference in groundwater modeling in comparison with conventional
NASA Technical Reports Server (NTRS)
Karageorghis, Andreas; Phillips, Timothy N.
1990-01-01
The numerical simulation of steady planar two-dimensional, laminar flow of an incompressible fluid through an abruptly contracting channel using spectral domain decomposition methods is described. The key features of the method are the decomposition of the flow region into a number of rectangular subregions and spectral approximations which are pointwise C(1) continuous across subregion interfaces. Spectral approximations to the solution are obtained for Reynolds numbers in the range 0 to 500. The size of the salient corner vortex decreases as the Reynolds number increases from 0 to around 45. As the Reynolds number is increased further the vortex grows slowly. A vortex is detected downstream of the contraction at a Reynolds number of around 175 that continues to grow as the Reynolds number is increased further.
NASA Astrophysics Data System (ADS)
Walsh, Raymond P.; Alam, Jahrul M.
2016-09-01
The fundamental interaction between tropical cyclones was investigated through a series of water tank experiements by Fujiwhara [20, 21, 22]. However, a complete understanding of tropical cyclones remains an open research challenge although there have been numerous investigations through measurments with aircrafts/satellites, as well as with numerical simulations. This article presents a computational model for simulating the interaction between cyclones. The proposed numerical method is presented briefly, where the time integration is performed by projecting the discrete system onto a Krylov subspace. The method filters the large scale fluid dynamics using a multiresolution approximation, and the unresolved dynamics is modeled with a Smagorinsky type subgrid scale parameterization scheme. Numerical experiments with Fujiwhara interactions are considered to verify modeling accuracy. An excellent agreement between the present simulation and a reference simulation at Re = 5000 has been demonstrated. At Re = 37440, the kinetic energy of cyclones is seen consolidated into larger scales with concurrent enstrophy cascade, suggesting a steady increase of energy containing scales, a phenomena that is typical in two-dimensional turbulence theory. The primary results of this article suggest a novel avenue for addressing some of the computational challenges of mesoscale atmospheric circulations.
2013-08-29
An analytical model is developed to evaluate the design of a spline coupling. For a given torque and shaft misalignment, the model calculates the number of teeth in contact, tooth loads, stiffnesses, stresses, and safety factors. The analytic model provides essential spline coupling design and modeling information and could be easily integrated into gearbox design and simulation tools.
Detection of defects on apple using B-spline lighting correction method
NASA Astrophysics Data System (ADS)
Li, Jiangbo; Huang, Wenqian; Guo, Zhiming
To effectively extract defective areas in fruits, the uneven intensity distribution that was produced by the lighting system or by part of the vision system in the image must be corrected. A methodology was used to convert non-uniform intensity distribution on spherical objects into a uniform intensity distribution. A basically plane image with the defective area having a lower gray level than this plane was obtained by using proposed algorithms. Then, the defective areas can be easily extracted by a global threshold value. The experimental results with a 94.0% classification rate based on 100 apple images showed that the proposed algorithm was simple and effective. This proposed method can be applied to other spherical fruits.
NASA Technical Reports Server (NTRS)
Kojima, Fumio
1989-01-01
The geometrical structure of the boundary shape for a two-dimensional boundary value problem is identified. The output least square identification method is considered for estimating partially unknown boundary shapes. A numerical parameter estimation technique using the spline collocation method is proposed.
Number systems, α-splines and refinement
NASA Astrophysics Data System (ADS)
Zube, Severinas
2004-12-01
This paper is concerned with the smooth refinable function on a plane relative with complex scaling factor . Characteristic functions of certain self-affine tiles related to a given scaling factor are the simplest examples of such refinable function. We study the smooth refinable functions obtained by a convolution power of such charactericstic functions. Dahlke, Dahmen, and Latour obtained some explicit estimates for the smoothness of the resulting convolution products. In the case α=1+i, we prove better results. We introduce α-splines in two variables which are the linear combination of shifted basic functions. We derive basic properties of α-splines and proceed with a detailed presentation of refinement methods. We illustrate the application of α-splines to subdivision with several examples. It turns out that α-splines produce well-known subdivision algorithms which are based on box splines: Doo-Sabin, Catmull-Clark, Loop, Midedge and some -subdivision schemes with good continuity. The main geometric ingredient in the definition of α-splines is the fundamental domain (a fractal set or a self-affine tile). The properties of the fractal obtained in number theory are important and necessary in order to determine two basic properties of α-splines: partition of unity and the refinement equation.
Li, Xin; Miller, Eric L.; Rappaport, Carey; Silevich, Michael
2000-04-11
and delete redundant knots based on the estimation of a weight associated with each basis vector. The overall algorithm iterates by inserting and deleting knots and end up with much fewer knots than pixels to represent the object, while the estimation error is within a certain tolerance. Thus, an efficient reconstruction can be obtained which significantly reduces the complexity of the problem. In this thesis, the adaptive B-Spline method is applied to a cross-well tomography problem. The problem comes from the application of finding underground pollution plumes. Cross-well tomography method is applied by placing arrays of electromagnetic transmitters and receivers along the boundaries of the interested region. By utilizing inverse scattering method, a linear inverse model is set up and furthermore the adaptive B-Spline method described above is applied. The simulation results show that the B-Spline method reduces the dimensional complexity by 90%, compared with that o f a pixel-based method, and decreases time complexity by 50% without significantly degrading the estimation.
Lin, Guang; Tartakovsky, Alexandre M.
2009-05-01
In this study, a probabilistic collocation method (PCM) on sparse grids was used to solve stochastic equations describing flow and transport in three-dimensional in saturated, randomly heterogeneous porous media. Karhunen-Lo\\`{e}ve (KL) decomposition was used to represent the three-dimensional log hydraulic conductivity $Y=\\ln K_s$. The hydraulic head $h$ and average pore-velocity $\\bf v$ were obtained by solving the three-dimensional continuity equation coupled with Darcy's law with random hydraulic conductivity field. The concentration was computed by solving a three-dimensional stochastic advection-dispersion equation with stochastic average pore-velocity $\\bf v$ computed from Darcy's law. PCM is an extension of the generalized polynomial chaos (gPC) that couples gPC with probabilistic collocation. By using the sparse grid points, PCM can handle a random process with large number of random dimensions, with relatively lower computational cost, compared to full tensor products. Monte Carlo (MC) simulations have also been conducted to verify accuracy of the PCM. By comparing the MC and PCM results for mean and standard deviation of concentration, it is evident that the PCM approach is computational more efficient than Monte Carlo simulations. Unlike the conventional moment-equation approach, there is no limitation on the amplitude of random perturbation in PCM. Furthermore, PCM on sparse grids can efficiently simulate solute transport in randomly heterogeneous porous media with large variances.
Lin, Guang; Elizondo, Marcelo A.; Lu, Shuai; Wan, Xiaoliang
2014-01-01
This paper proposes a probabilistic collocation method (PCM) to quantify the uncertainties with dynamic simulations in power systems. The appraoch was tested on a single-machine-infinite-bus system and the over 15,000 -bus Western Electricity Coordinating Council (WECC) system. Comparing to classic Monte-Carlo (MC) method, the proposed PCM applies the Smolyak algorithm to reduce the number of simulations that have to be performed. Therefore, the computational cost can be greatly reduced using PCM. The algorithm and procedures are described in the paper. Comparison was made with MC method on the single machine as well as the WECC system. The simulation results shows that using PCM only a small number of sparse grid points need to be sampled even when dealing with systems with a relatively large number of uncertain parameters. PCM is, therefore, computationally more efficient than MC method.
NASA Astrophysics Data System (ADS)
Laksâ, Arne
2015-11-01
B-splines are the de facto industrial standard for surface modelling in Computer Aided design. It is comparable to bend flexible rods of wood or metal. A flexible rod minimize the energy when bending, a third degree polynomial spline curve minimize the second derivatives. B-spline is a nice way of representing polynomial splines, it connect polynomial splines to corner cutting techniques, which induces many nice and useful properties. However, the B-spline representation can be expanded to something we can call general B-splines, i.e. both polynomial and non-polynomial splines. We will show how this expansion can be done, and the properties it induces, and examples of non-polynomial B-spline.
Multivariate Spline Algorithms for CAGD
NASA Technical Reports Server (NTRS)
Boehm, W.
1985-01-01
Two special polyhedra present themselves for the definition of B-splines: a simplex S and a box or parallelepiped B, where the edges of S project into an irregular grid, while the edges of B project into the edges of a regular grid. More general splines may be found by forming linear combinations of these B-splines, where the three-dimensional coefficients are called the spline control points. Univariate splines are simplex splines, where s = 1, whereas splines over a regular triangular grid are box splines, where s = 2. Two simple facts render the development of the construction of B-splines: (1) any face of a simplex or a box is again a simplex or box but of lower dimension; and (2) any simplex or box can be easily subdivided into smaller simplices or boxes. The first fact gives a geometric approach to Mansfield-like recursion formulas that express a B-spline in B-splines of lower order, where the coefficients depend on x. By repeated recursion, the B-spline will be expressed as B-splines of order 1; i.e., piecewise constants. In the case of a simplex spline, the second fact gives a so-called insertion algorithm that constructs the new control points if an additional knot is inserted.
NASA Technical Reports Server (NTRS)
Schiess, J. R.
1994-01-01
Scientific data often contains random errors that make plotting and curve-fitting difficult. The Rational-Spline Approximation with Automatic Tension Adjustment algorithm lead to a flexible, smooth representation of experimental data. The user sets the conditions for each consecutive pair of knots:(knots are user-defined divisions in the data set) to apply no tension; to apply fixed tension; or to determine tension with a tension adjustment algorithm. The user also selects the number of knots, the knot abscissas, and the allowed maximum deviations from line segments. The selection of these quantities depends on the actual data and on the requirements of a particular application. This program differs from the usual spline under tension in that it allows the user to specify different tension values between each adjacent pair of knots rather than a constant tension over the entire data range. The subroutines use an automatic adjustment scheme that varies the tension parameter for each interval until the maximum deviation of the spline from the line joining the knots is less than or equal to a user-specified amount. This procedure frees the user from the drudgery of adjusting individual tension parameters while still giving control over the local behavior of the spline The Rational Spline program was written completely in FORTRAN for implementation on a CYBER 850 operating under NOS. It has a central memory requirement of approximately 1500 words. The program was released in 1988.
NASA Astrophysics Data System (ADS)
M Ali, M. K.; Ruslan, M. H.; Muthuvalu, M. S.; Wong, J.; Sulaiman, J.; Yasir, S. Md.
2014-06-01
The solar drying experiment of seaweed using Green V-Roof Hybrid Solar Drier (GVRHSD) was conducted in Semporna, Sabah under the metrological condition in Malaysia. Drying of sample seaweed in GVRHSD reduced the moisture content from about 93.4% to 8.2% in 4 days at average solar radiation of about 600W/m2 and mass flow rate about 0.5 kg/s. Generally the plots of drying rate need more smoothing compared moisture content data. Special cares is needed at low drying rates and moisture contents. It is shown the cubic spline (CS) have been found to be effective for moisture-time curves. The idea of this method consists of an approximation of data by a CS regression having first and second derivatives. The analytical differentiation of the spline regression permits the determination of instantaneous rate. The method of minimization of the functional of average risk was used successfully to solve the problem. This method permits to obtain the instantaneous rate to be obtained directly from the experimental data. The drying kinetics was fitted with six published exponential thin layer drying models. The models were fitted using the coefficient of determination (R2), and root mean square error (RMSE). The modeling of models using raw data tested with the possible of exponential drying method. The result showed that the model from Two Term was found to be the best models describe the drying behavior. Besides that, the drying rate smoothed using CS shows to be effective method for moisture-time curves good estimators as well as for the missing moisture content data of seaweed Kappaphycus Striatum Variety Durian in Solar Dryer under the condition tested.
M Ali, M. K. E-mail: eutoco@gmail.com; Ruslan, M. H. E-mail: eutoco@gmail.com; Muthuvalu, M. S. E-mail: jumat@ums.edu.my; Wong, J. E-mail: jumat@ums.edu.my; Sulaiman, J. E-mail: hafidzruslan@eng.ukm.my; Yasir, S. Md. E-mail: hafidzruslan@eng.ukm.my
2014-06-19
The solar drying experiment of seaweed using Green V-Roof Hybrid Solar Drier (GVRHSD) was conducted in Semporna, Sabah under the metrological condition in Malaysia. Drying of sample seaweed in GVRHSD reduced the moisture content from about 93.4% to 8.2% in 4 days at average solar radiation of about 600W/m{sup 2} and mass flow rate about 0.5 kg/s. Generally the plots of drying rate need more smoothing compared moisture content data. Special cares is needed at low drying rates and moisture contents. It is shown the cubic spline (CS) have been found to be effective for moisture-time curves. The idea of this method consists of an approximation of data by a CS regression having first and second derivatives. The analytical differentiation of the spline regression permits the determination of instantaneous rate. The method of minimization of the functional of average risk was used successfully to solve the problem. This method permits to obtain the instantaneous rate to be obtained directly from the experimental data. The drying kinetics was fitted with six published exponential thin layer drying models. The models were fitted using the coefficient of determination (R{sup 2}), and root mean square error (RMSE). The modeling of models using raw data tested with the possible of exponential drying method. The result showed that the model from Two Term was found to be the best models describe the drying behavior. Besides that, the drying rate smoothed using CS shows to be effective method for moisture-time curves good estimators as well as for the missing moisture content data of seaweed Kappaphycus Striatum Variety Durian in Solar Dryer under the condition tested.
NASA Astrophysics Data System (ADS)
Zhu, W.; Sommar, J.; Lin, C.-J.; Feng, X.
2014-09-01
Reliable quantification of air-biosphere exchange flux of elemental mercury vapor (Hg0) is crucial for understanding global biogeochemical cycle of mercury. However, there has not been a standard analytical protocol for flux quantification, and little attention has been devoted to characterize the temporal variability and comparability of fluxes measured by different methods. In this study, we deployed a collocated set of micro-meteorological (MM) and enclosure measurement systems to quantify Hg0 flux over bare soil and low standing crop in an agricultural field. The techniques include relaxed eddy accumulation (REA), modified Bowen-ratio (MBR), aerodynamic gradient (AGM) as well as dynamic flux chambers of traditional (TDFC) and novel (NDFC) designs. The five systems and their measured fluxes were cross-examined with respect to magnitude, temporal trend and sensitivity to environmental variables. Fluxes measured by the MM and DFC methods showed distinct temporal trends. The former exhibited a highly dynamic temporal variability while the latter had much gradual temporal features. The diurnal characteristics reflected the difference in the fundamental processes driving the measurements. The correlations between NDFC and TDFC fluxes and between MBR and AGM fluxes were significant (R > 0.8, p < 0.05), but the correlation between DFC and MM instantaneous fluxes were from weak to moderate (R = 0.1-0.5). Statistical analysis indicated that the median of turbulent fluxes estimated by the three independent MM-techniques were not significantly different. Cumulative flux measured by TDFC is considerably lower (42% of AGM and 31% of MBR fluxes) while those measured by NDFC, AGM and MBR were similar (< 10% difference). This implicates that the NDFC technique, which accounts for internal friction velocity, effectively bridged the gap in measured Hg0 flux compared to MM techniques. Cumulated flux measured by REA was ~60% higher than the gradient-based fluxes. Environmental
Kananenka, Alexei A; Welden, Alicia Rae; Lan, Tran Nguyen; Gull, Emanuel; Zgid, Dominika
2016-05-10
The popular, stable, robust, and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate modifications the temperature dependence can be preserved while the Green's function grid size can be reduced by about 2 orders of magnitude by replacing the standard Matsubara frequency grid with a sparser grid and a set of interpolation coefficients. We benchmarked the accuracy of our algorithm as a function of a single parameter sensitive to the shape of the Green's function. Through numerous examples, we confirmed that our algorithm can be utilized in a systematically improvable, controlled, and black-box manner and highly accurate one- and two-body energies and one-particle density matrices can be obtained using only around 5% of the original grid points. Additionally, we established that to improve accuracy by an order of magnitude, the number of grid points needs to be doubled, whereas for the Matsubara frequency grid, an order of magnitude more grid points must be used. This suggests that realistic calculations with large basis sets that were previously out of reach because they required enormous grid sizes may now become feasible. PMID:27049642
Siefert, Andrew W.; Icenogle, David A.; Rabbah, Jean-Pierre; Saikrishnan, Neelakantan; Rossignac, Jarek; Lerakis, Stamatios; Yoganathan, Ajit P.
2013-01-01
Patient-specific models of the heart’s mitral valve (MV) exhibit potential for surgical planning. While advances in 3D echocardiography (3DE) have provided adequate resolution to extract MV leaflet geometry, no study has quantitatively assessed the accuracy of their modeled leaflets versus a ground-truth standard for temporal frames beyond systolic closure or for differing valvular dysfunctions. The accuracy of a 3DE-based segmentation methodology based on J-splines was assessed for porcine MVs with known 4D leaflet coordinates within a pulsatile simulator during closure, peak closure, and opening for a control, prolapsed, and billowing MV model. For all time points, the mean distance error between the segmented models and ground-truth data were 0.40±0.32 mm, 0.52±0.51 mm, and 0.74±0.69 mm for the control, flail, and billowing models. For all models and temporal frames, 95% of the distance errors were below 1.64 mm. When applied to a patient data set, segmentation was able to confirm a regurgitant orifice and post-operative improvements in coaptation. This study provides an experimental platform for assessing the accuracy of an MV segmentation methodology at phases beyond systolic closure and for differing MV dysfunctions. Results demonstrate the accuracy of a MV segmentation methodology for the development of future surgical planning tools. PMID:23460042
NASA Astrophysics Data System (ADS)
Owusu-Banson, Derek
In recent times, a variety of industries, applications and numerical methods including the meshless method have enjoyed a great deal of success by utilizing the graphical processing unit (GPU) as a parallel coprocessor. These benefits often include performance improvement over the previous implementations. Furthermore, applications running on graphics processors enjoy superior performance per dollar and performance per watt than implementations built exclusively on traditional central processing technologies. The GPU was originally designed for graphics acceleration but the modern GPU, known as the General Purpose Graphical Processing Unit (GPGPU) can be used for scientific and engineering calculations. The GPGPU consists of massively parallel array of integer and floating point processors. There are typically hundreds of processors per graphics card with dedicated high-speed memory. This work describes an application written by the author, titled GaussianRBF to show the implementation and results of a novel meshless method that in-cooperates the collocation of the Gaussian radial basis function by utilizing the GPU as a parallel co-processor. Key phases of the proposed meshless method have been executed on the GPU using the NVIDIA CUDA software development kit. Especially, the matrix fill and solution phases have been carried out on the GPU, along with some post processing. This approach resulted in a decreased processing time compared to similar algorithm implemented on the CPU while maintaining the same accuracy.
A smoothing algorithm using cubic spline functions
NASA Technical Reports Server (NTRS)
Smith, R. E., Jr.; Price, J. M.; Howser, L. M.
1974-01-01
Two algorithms are presented for smoothing arbitrary sets of data. They are the explicit variable algorithm and the parametric variable algorithm. The former would be used where large gradients are not encountered because of the smaller amount of calculation required. The latter would be used if the data being smoothed were double valued or experienced large gradients. Both algorithms use a least-squares technique to obtain a cubic spline fit to the data. The advantage of the spline fit is that the first and second derivatives are continuous. This method is best used in an interactive graphics environment so that the junction values for the spline curve can be manipulated to improve the fit.
General spline filters for discontinuous Galerkin solutions
Peters, Jörg
2015-01-01
The discontinuous Galerkin (dG) method outputs a sequence of polynomial pieces. Post-processing the sequence by Smoothness-Increasing Accuracy-Conserving (SIAC) convolution not only increases the smoothness of the sequence but can also improve its accuracy and yield superconvergence. SIAC convolution is considered optimal if the SIAC kernels, in the form of a linear combination of B-splines of degree d, reproduce polynomials of degree 2d. This paper derives simple formulas for computing the optimal SIAC spline coefficients for the general case including non-uniform knots. PMID:26594090
Spline screw payload fastening system
NASA Astrophysics Data System (ADS)
Vranish, John M.
1993-09-01
A system for coupling an orbital replacement unit (ORU) to a space station structure via the actions of a robot and/or astronaut is described. This system provides mechanical and electrical connections both between the ORU and the space station structure and between the ORU and the ORU and the robot/astronaut hand tool. Alignment and timing features ensure safe, sure handling and precision coupling. This includes a first female type spline connector selectively located on the space station structure, a male type spline connector positioned on the orbital replacement unit so as to mate with and connect to the first female type spline connector, and a second female type spline connector located on the orbital replacement unit. A compliant drive rod interconnects the second female type spline connector and the male type spline connector. A robotic special end effector is used for mating with and driving the second female type spline connector. Also included are alignment tabs exteriorally located on the orbital replacement unit for berthing with the space station structure. The first and second female type spline connectors each include a threaded bolt member having a captured nut member located thereon which can translate up and down the bolt but are constrained from rotation thereabout, the nut member having a mounting surface with at least one first type electrical connector located on the mounting surface for translating with the nut member. At least one complementary second type electrical connector on the orbital replacement unit mates with at least one first type electrical connector on the mounting surface of the nut member. When the driver on the robotic end effector mates with the second female type spline connector and rotates, the male type spline connector and the first female type spline connector lock together, the driver and the second female type spline connector lock together, and the nut members translate up the threaded bolt members carrying the
Spline screw payload fastening system
NASA Astrophysics Data System (ADS)
Vranish, John M.
1992-09-01
A system for coupling an orbital replacement unit (ORU) to a space station structure via the actions of a robot and/or astronaut is described. This system provides mechanical and electrical connections both between the ORU and the space station structure and between the ORU and the ORU and the robot/astronaut hand tool. Alignment and timing features ensure safe, sure handling and precision coupling. This includes a first female type spline connector selectively located on the space station structure, a male type spline connector positioned on the orbital replacement unit so as to mate with and connect to the first female type spline connector, and a second female type spline connector located on the orbital replacement unit. A compliant drive rod interconnects the second female type spline connector and the male type spline connector. A robotic special end effector is used for mating with and driving the second female type spline connector. Also included are alignment tabs exteriorally located on the orbital replacement unit for berthing with the space station structure. The first and second female type spline connectors each include a threaded bolt member having a captured nut member located thereon which can translate up and down the bolt but are constrained from rotation thereabout, the nut member having a mounting surface with at least one first type electrical connector located on the mounting surface for translating with the nut member. At least one complementary second type electrical connector on the orbital replacement unit mates with at least one first type electrical connector on the mounting surface of the nut member. When the driver on the robotic end effector mates with the second female type spline connector and rotates, the male type spline connector and the first female type spline connector lock together, the driver and the second female type spline connector lock together, and the nut members translate up the threaded bolt members carrying the
Spline screw payload fastening system
NASA Technical Reports Server (NTRS)
Vranish, John M. (Inventor)
1993-01-01
A system for coupling an orbital replacement unit (ORU) to a space station structure via the actions of a robot and/or astronaut is described. This system provides mechanical and electrical connections both between the ORU and the space station structure and between the ORU and the ORU and the robot/astronaut hand tool. Alignment and timing features ensure safe, sure handling and precision coupling. This includes a first female type spline connector selectively located on the space station structure, a male type spline connector positioned on the orbital replacement unit so as to mate with and connect to the first female type spline connector, and a second female type spline connector located on the orbital replacement unit. A compliant drive rod interconnects the second female type spline connector and the male type spline connector. A robotic special end effector is used for mating with and driving the second female type spline connector. Also included are alignment tabs exteriorally located on the orbital replacement unit for berthing with the space station structure. The first and second female type spline connectors each include a threaded bolt member having a captured nut member located thereon which can translate up and down the bolt but are constrained from rotation thereabout, the nut member having a mounting surface with at least one first type electrical connector located on the mounting surface for translating with the nut member. At least one complementary second type electrical connector on the orbital replacement unit mates with at least one first type electrical connector on the mounting surface of the nut member. When the driver on the robotic end effector mates with the second female type spline connector and rotates, the male type spline connector and the first female type spline connector lock together, the driver and the second female type spline connector lock together, and the nut members translate up the threaded bolt members carrying the
Clinical Trials: Spline Modeling is Wonderful for Nonlinear Effects.
Cleophas, Ton J
2016-01-01
Traditionally, nonlinear relationships like the smooth shapes of airplanes, boats, and motor cars were constructed from scale models using stretched thin wooden strips, otherwise called splines. In the past decades, mechanical spline methods have been replaced with their mathematical counterparts. The objective of the study was to study whether spline modeling can adequately assess the relationships between exposure and outcome variables in a clinical trial and also to study whether it can detect patterns in a trial that are relevant but go unobserved with simpler regression models. A clinical trial assessing the effect of quantity of care on quality of care was used as an example. Spline curves consistent of 4 or 5 cubic functions were applied. SPSS statistical software was used for analysis. The spline curves of our data outperformed the traditional curves because (1) unlike the traditional curves, they did not miss the top quality of care given in either subgroup, (2) unlike the traditional curves, they, rightly, did not produce sinusoidal patterns, and (3) unlike the traditional curves, they provided a virtually 100% match of the original values. We conclude that (1) spline modeling can adequately assess the relationships between exposure and outcome variables in a clinical trial; (2) spline modeling can detect patterns in a trial that are relevant but may go unobserved with simpler regression models; (3) in clinical research, spline modeling has great potential given the presence of many nonlinear effects in this field of research and given its sophisticated mathematical refinement to fit any nonlinear effect in the mostly accurate way; and (4) spline modeling should enable to improve making predictions from clinical research for the benefit of health decisions and health care. We hope that this brief introduction to spline modeling will stimulate clinical investigators to start using this wonderful method. PMID:23689089
NASA Astrophysics Data System (ADS)
Joshi, Sumedh M.; Thomsen, Greg N.; Diamessis, Peter J.
2016-05-01
A combination of block-Jacobi and deflation preconditioning is used to solve a high-order discontinuous element-based collocation discretization of the Schur complement of the Poisson-Neumann system as arises in the operator splitting of the incompressible Navier-Stokes equations. The preconditioners and deflation vectors are chosen to mitigate the effects of ill-conditioning due to highly-elongated domains typical of simulations of strongly non-hydrostatic environmental flows, and to achieve Generalized Minimum RESidual method (GMRES) convergence independent of the size of the number of elements in the long direction. The ill-posedness of the Poisson-Neumann system manifests as an inconsistency of the Schur complement problem, but it is shown that this can be accounted for with appropriate projections out of the null space of the Schur complement matrix without affecting the accuracy of the solution. The block-Jacobi preconditioner is shown to yield GMRES convergence independent of the polynomial order and only weakly dependent on the number of elements within a subdomain in the decomposition. The combined deflation and block-Jacobi preconditioning is compared with two-level non-overlapping block-Jacobi preconditioning of the Schur problem, and while both methods achieve convergence independent of the grid size, deflation is shown to require half as many GMRES iterations and 25% less wall-clock time for a variety of grid sizes and domain aspect ratios. The deflation methods shown to be effective for the two-dimensional Poisson-Neumann problem are extensible to the three-dimensional problem assuming a Fourier discretization in the third dimension. A Fourier discretization results in a two-dimensional Helmholtz problem for each Fourier component that is solved using deflated block-Jacobi preconditioning on its Schur complement. Here again deflation is shown to be superior to two-level non-overlapping block-Jacobi preconditioning, requiring about half as many GMRES
Mathematical research on spline functions
NASA Technical Reports Server (NTRS)
Horner, J. M.
1973-01-01
One approach in spline functions is to grossly estimate the integrand in J and exactly solve the resulting problem. If the integrand in J is approximated by Y" squared, the resulting problem lends itself to exact solution, the familiar cubic spline. Another approach is to investigate various approximations to the integrand in J and attempt to solve the resulting problems. The results are described.
NASA Astrophysics Data System (ADS)
Zhu, W.; Sommar, J.; Lin, C.-J.; Feng, X.
2015-05-01
Dynamic flux chambers (DFCs) and micrometeorological (MM) methods are extensively deployed for gauging air-surface Hg0 gas exchange. However, a systematic evaluation of the precision of the contemporary Hg0 flux quantification methods is not available. In this study, the uncertainty in Hg0 flux measured by the relaxed eddy accumulation (REA) method, the aerodynamic gradient method (AGM), the modified Bowen ratio (MBR) method, as well as DFC of traditional (TDFC) and novel (NDFC) designs, are assessed using a robust data set from two field intercomparison campaigns. The absolute precision in Hg0 concentration difference (ΔC) measurements is estimated at 0.064 ng m-3 for the gradient-based MBR and AGM systems. For the REA system, the parameter is Hg0 concentration (C) dependent at 0.069 + 0.022C. During the campaigns, 57 and 62 % of the individual vertical gradient measurements are found to be significantly different from 0, while for the REA technique, the percentage of significant observations is lower. For the chambers, non-significant fluxes are confined to a few night-time periods with varying ambient Hg0 concentrations. Relative bias for DFC-derived fluxes is estimated to be ~ ±10, and ~ 85% of the flux bias is within ±2 ng m-2 h-1 in absolute terms. The DFC flux bias follows a diurnal cycle, which is largely affected by the forced temperature and irradiation bias in the chambers. Due to contrasting prevailing micrometeorological conditions, the relative uncertainty (median) in turbulent exchange parameters differs by nearly a factor of 2 between the campaigns, while that in ΔC measurement is fairly consistent. The estimated flux uncertainties for the triad of MM techniques are 16-27, 12-23 and 19-31% (interquartile range) for the AGM, MBR and REA methods, respectively. This study indicates that flux-gradient-based techniques (MBR and AGM) are preferable to REA in quantifying Hg0 flux over ecosystems with low vegetation height. A limitation of all Hg0 flux
NASA Astrophysics Data System (ADS)
Zhu, W.; Sommar, J.; Lin, C.-J.; Feng, X.
2015-02-01
Dynamic flux chambers (DFCs) and micrometeorological (MM) methods are extensively deployed for gauging air-surface Hg0 gas exchange. However, a systematic evaluation of the precision of the contemporary Hg0 flux quantification methods is not available. In this study, the uncertainty in Hg0 flux measured by relaxed eddy accumulation (REA) method, aerodynamic gradient method (AGM), modified Bowen-ratio (MBR) method, as well as DFC of traditional (TDFC) and novel (NDFC) designs is assessed using a robust data-set from two field intercomparison campaigns. The absolute precision in Hg0 concentration difference (Δ C) measurements is estimated at 0.064 ng m-3 for the gradient-based MBR and AGM system. For the REA system, the parameter is Hg0 concentration (C) dependent at 0.069+0.022C. 57 and 62% of the individual vertical gradient measurements were found to be significantly different from zero during the campaigns, while for the REA-technique the percentage of significant observations was lower. For the chambers, non-significant fluxes are confined to a few nighttime periods with varying ambient Hg0 concentration. Relative bias for DFC-derived fluxes is estimated to be ~ ±10%, and ~ 85% of the flux bias are within ±2 ng m-2 h-1 in absolute term. The DFC flux bias follows a diurnal cycle, which is largely dictated by temperature controls on the enclosed volume. Due to contrasting prevailing micrometeorological conditions, the relative uncertainty (median) in turbulent exchange parameters differs by nearly a factor of two between the campaigns, while that in Δ C measurements is fairly stable. The estimated flux uncertainties for the triad of MM-techniques are 16-27, 12-23 and 19-31% (interquartile range) for the AGM, MBR and REA method, respectively. This study indicates that flux-gradient based techniques (MBR and AGM) are preferable to REA in quantifying Hg0 flux over ecosystems with low vegetation height. A limitation of all Hg0 flux measurement systems investigated
NASA Astrophysics Data System (ADS)
Khalilov, E. H.
2016-07-01
The surface integral equation for a spatial mixed boundary value problem for the Helmholtz equation is considered. At a set of chosen points, the equation is replaced with a system of algebraic equations, and the existence and uniqueness of the solution of this system is established. The convergence of the solutions of this system to the exact solution of the integral equation is proven, and the convergence rate of the method is determined.
Theory, computation, and application of exponential splines
NASA Technical Reports Server (NTRS)
Mccartin, B. J.
1981-01-01
A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.
Fitting multidimensional splines using statistical variable selection techniques
NASA Technical Reports Server (NTRS)
Smith, P. L.
1982-01-01
This report demonstrates the successful application of statistical variable selection techniques to fit splines. Major emphasis is given to knot selection, but order determination is also discussed. Two FORTRAN backward elimination programs using the B-spline basis were developed, and the one for knot elimination is compared in detail with two other spline-fitting methods and several statistical software packages. An example is also given for the two-variable case using a tensor product basis, with a theoretical discussion of the difficulties of their use.
Monotonicity preserving using GC1 rational quartic spline
NASA Astrophysics Data System (ADS)
Karim, Samsul Ariffin Abdul; Pang, Kong Voon
2012-09-01
This paper proposed GC1 rational quartic spline (quartic numerator and linear denominator) with two parameters to preserve the shape of the monotone data. Simple data dependent constraints will be derived on one of the parameters while the other is free to modify and refine the resultant shape of the data. Both parameters are independent to each other. The method under consideration here, avoid the modification of the derivative when the sufficient condition for the monotonicity are violated as can be noticed in the original construction of C1 rational quartic spline with linear denominator. Numerical comparison between the proposed scheme and C1 rational quartic spline will be given.
NASA Technical Reports Server (NTRS)
Fang, Ming; Bowin, Carl
1992-01-01
To construct Venus' gravity disturbance field (or gravity anomaly) with the spacecraft-observer line of site (LOS) acceleration perturbation data, both a global and a local approach can be used. The global approach, e.g., spherical harmonic coefficients, and the local approach, e.g., the integral operator method, based on geodetic techniques are generally not the same, so that they must be used separately for mapping long wavelength features and short wavelength features. Harmonic spline, as an interpolation and extrapolation technique, is intrinsically flexible to both global and local mapping of a potential field. Theoretically, it preserves the information of the potential field up to the bound by sampling theorem regardless of whether it is global or local mapping, and is never bothered with truncation errors. The improvement of harmonic spline methodology for global mapping is reported. New basis functions, a singular value decomposition (SVD) based modification to Parker & Shure's numerical procedure, and preliminary results are presented.
NASA Astrophysics Data System (ADS)
Yasui, Takashi; Hasegawa, Koji; Hirayama, Koichi
2016-07-01
The finite-difference time-domain (FD-TD) method using a staggered grid with the collocated grid points of velocities (SGCV) was formulated for elastic waves propagating in anisotropic solids and for a rectangular SGCV. Resonant frequency analysis of Lamé-mode resonators on a quartz plate was carried out to confirm the accuracy and validity of the proposed method. The resonant frequencies for the fundamental and higher-order Lamé-modes calculated by the proposed method agreed very well with their theoretical values.
C1 Hermite shape preserving polynomial splines in R3
NASA Astrophysics Data System (ADS)
Gabrielides, Nikolaos C.
2012-06-01
The C 2 variable degree splines1-3 have been proven to be an efficient tool for solving the curve shape-preserving interpolation problem in two and three dimensions. Based on this representation, the current paper proposes a Hermite interpolation scheme, to construct C 1 shape-preserving splines of variable degree. After this, a slight modification of the method leads to a C 1 shape-preserving Hermite cubic spline. Both methods can easily be developed within a CAD system, since they compute directly (without iterations) the B-spline control polygon. They have been implemented and tested within the DNV Software CAD/CAE system GeniE. [Figure not available: see fulltext.
Surface deformation over flexible joints using spline blending techniques
NASA Astrophysics Data System (ADS)
Haavardsholm, Birgitte; Bratlie, Jostein; Dalmo, Rune
2014-12-01
Skinning over a skeleton joint is the process of skin deformation based on joint transformation. Popular geometric skinning techniques include implicit linear blending and dual quaternions. Generalized expo-rational B-splines (GERBS) is a blending type spline construction where local functions at each knot are blended by Ck-smooth basis functions. A smooth skinning surface can be constructed over a transformable skeleton joint by combining various types of local surface constructions and applying local Hermite interpolation. Compared to traditional spline methods, increased flexibility and local control with respect to surface deformation can be achieved using the GERBS blending construction. We present a method using a blending-type spline surface for skinning over a flexible joint, where local geometry is individually adapted to achieve natural skin deformation based on skeleton transformations..
Parameter Choices for Approximation by Harmonic Splines
NASA Astrophysics Data System (ADS)
Gutting, Martin
2016-04-01
The approximation by harmonic trial functions allows the construction of the solution of boundary value problems in geoscience, e.g., in terms of harmonic splines. Due to their localizing properties regional modeling or the improvement of a global model in a part of the Earth's surface is possible with splines. Fast multipole methods have been developed for some cases of the occurring kernels to obtain a fast matrix-vector multiplication. The main idea of the fast multipole algorithm consists of a hierarchical decomposition of the computational domain into cubes and a kernel approximation for the more distant points. This reduces the numerical effort of the matrix-vector multiplication from quadratic to linear in reference to the number of points for a prescribed accuracy of the kernel approximation. The application of the fast multipole method to spline approximation which also allows the treatment of noisy data requires the choice of a smoothing parameter. We investigate different methods to (ideally automatically) choose this parameter with and without prior knowledge of the noise level. Thereby, the performance of these methods is considered for different types of noise in a large simulation study. Applications to gravitational field modeling are presented as well as the extension to boundary value problems where the boundary is the known surface of the Earth itself.
Using parametric {ital B} splines to fit specular reflectivities
Berk, N.F.; Majkrzak, C.F.
1995-05-01
Parametric {ital B}-spline curves offer a flexible and appropriate mathematical description of scattering length density profiles in specular reflectivity analysis. Profiles combining smooth and sharp features can be defined in low dimensional representations using control points in the density-depth plane which provide graded local influence on profile shape. These profiles exist in vector spaces defined by {ital B}-spline order and parameter knot set, which can be systematically densified during analysis. Such profiles can easily be rendered as adaptive histograms for reflectivity computation. {ital B}-spline order can be chosen to accommodate the asymptotic (large-{ital Q}) behavior indicated by reflectivity data. We describe an interactive fitting strategy in which the Nelder and Mead simplex method is used in the {ital B}-spline control point space to guide the discovery of profiles that can produce given reflectivity data. Examples using actual and simulated spectra are discussed.
Wavelets based on Hermite cubic splines
NASA Astrophysics Data System (ADS)
Cvejnová, Daniela; Černá, Dana; Finěk, Václav
2016-06-01
In 2000, W. Dahmen et al. designed biorthogonal multi-wavelets adapted to the interval [0,1] on the basis of Hermite cubic splines. In recent years, several more simple constructions of wavelet bases based on Hermite cubic splines were proposed. We focus here on wavelet bases with respect to which both the mass and stiffness matrices are sparse in the sense that the number of nonzero elements in any column is bounded by a constant. Then, a matrix-vector multiplication in adaptive wavelet methods can be performed exactly with linear complexity for any second order differential equation with constant coefficients. In this contribution, we shortly review these constructions and propose a new wavelet which leads to improved Riesz constants. Wavelets have four vanishing wavelet moments.
ERIC Educational Resources Information Center
Webb, Stuart; Kagimoto, Eve
2011-01-01
This study investigated the effects of three factors (the number of collocates per node word, the position of the node word, synonymy) on learning collocations. Japanese students studying English as a foreign language learned five sets of 12 target collocations. Each collocation was presented in a single glossed sentence. The number of collocates…
Interlanguage Development and Collocational Clash
ERIC Educational Resources Information Center
Shahheidaripour, Gholamabbass
2000-01-01
Background: Persian English learners committed mistakes and errors which were due to insufficient knowledge of different senses of the words and collocational structures they formed. Purpose: The study reported here was conducted for a thesis submitted in partial fulfillment of the requirements for The Master of Arts degree, School of Graduate…
Multi-quadric collocation model of horizontal crustal movement
NASA Astrophysics Data System (ADS)
Chen, G.; Zeng, A. M.; Ming, F.; Jing, Y. F.
2015-11-01
To establish the horizontal crustal movement velocity field of the Chinese mainland, a Hardy multi-quadric fitting model and collocation are usually used, but the kernel function, nodes, and smoothing factor are difficult to determine in the Hardy function interpolation, and in the collocation model the covariance function of the stochastic signal must be carefully constructed. In this paper, a new combined estimation method for establishing the velocity field, based on collocation and multi-quadric equation interpolation, is presented. The crustal movement estimation simultaneously takes into consideration an Euler vector as the crustal movement trend and the local distortions as the stochastic signals, and a kernel function of the multi-quadric fitting model substitutes for the covariance function of collocation. The velocities of a set of 1070 reference stations were obtained from the Crustal Movement Observation Network of China (CMONOC), and the corresponding velocity field established using the new combined estimation method. A total of 85 reference stations were used as check points, and the precision in the north and east directions was 1.25 and 0.80 mm yr-1, respectively. The result obtained by the new method corresponds with the collocation method and multi-quadric interpolation without requiring the covariance equation for the signals.
Analysis of chromatograph systems using orthogonal collocation
NASA Technical Reports Server (NTRS)
Woodrow, P. T.
1974-01-01
Research is generating fundamental engineering design techniques and concepts for the chromatographic separator of a chemical analysis system for an unmanned, Martian roving vehicle. A chromatograph model is developed which incorporates previously neglected transport mechanisms. The numerical technique of orthogonal collocation is studied. To establish the utility of the method, three models of increasing complexity are considered, the latter two being limiting cases of the derived model: (1) a simple, diffusion-convection model; (2) a rate of adsorption limited, inter-intraparticle model; and (3) an inter-intraparticle model with negligible mass transfer resistance.
Design Evaluation of Wind Turbine Spline Couplings Using an Analytical Model: Preprint
Guo, Y.; Keller, J.; Wallen, R.; Errichello, R.; Halse, C.; Lambert, S.
2015-02-01
Articulated splines are commonly used in the planetary stage of wind turbine gearboxes for transmitting the driving torque and improving load sharing. Direct measurement of spline loads and performance is extremely challenging because of limited accessibility. This paper presents an analytical model for the analysis of articulated spline coupling designs. For a given torque and shaft misalignment, this analytical model quickly yields insights into relationships between the spline design parameters and resulting loads; bending, contact, and shear stresses; and safety factors considering various heat treatment methods. Comparisons of this analytical model against previously published computational approaches are also presented.
Triple collocation: beyond three estimates and separation of structural/non-structural errors
Technology Transfer Automated Retrieval System (TEKTRAN)
This study extends the popular triple collocation method for error assessment from three source estimates to an arbitrary number of source estimates, i.e., to solve the “multiple” collocation problem. The error assessment problem is solved through Pythagorean constraints in Hilbert space, which is s...
Collocating satellite-based radar and radiometer measurements - methodology and usage examples
NASA Astrophysics Data System (ADS)
Holl, G.; Buehler, S. A.; Rydberg, B.; Jiménez, C.
2010-02-01
Collocations between two satellite sensors are occasions where both sensors observe the same place at roughly the same time. We study collocations between the Microwave Humidity Sounder (MHS) onboard NOAA-18 and the Cloud Profiling Radar (CPR) onboard the CloudSat CPR. First, a simple method is presented to obtain those collocations and this method is compared with a more complicated approach found in literature. We present the statistical properties of the collocations, with particular attention to the effects of the differences in footprint size. For 2007, we find approximately two and a half million MHS measurements with CPR pixels close to their centrepoints. Most of those collocations contain at least ten CloudSat pixels and image relatively homogeneous scenes. In the second part, we present three possible applications for the collocations. Firstly, we use the collocations to validate an operational Ice Water Path (IWP) product from MHS measurements, produced by the National Environment Satellite, Data and Information System (NESDIS) in the Microwave Surface and Precipitation Products System (MSPPS). IWP values from the CloudSat CPR are found to be significantly larger than those from the MSPPS. Secondly, we compare the relation between IWP and MHS channel 5 (190.311 GHz) brightness temperature for two datasets: the collocated dataset, and an artificial dataset. We find a larger variability in the collocated dataset. Finally, we use the collocations to train an Artificial Neural Network and describe how we can use it to develop a new MHS-based IWP product. We also study the effect of adding measurements from the High Resolution Infrared Radiation Sounder (HIRS), channels 8 (11.11 μm) and 11 (8.33 μm). This shows a small improvement in the retrieval quality. The collocations described in the article are available for public use.
Collocating satellite-based radar and radiometer measurements - methodology and usage examples
NASA Astrophysics Data System (ADS)
Holl, G.; Buehler, S. A.; Rydberg, B.; Jiménez, C.
2010-06-01
Collocations between two satellite sensors are occasions where both sensors observe the same place at roughly the same time. We study collocations between the Microwave Humidity Sounder (MHS) on-board NOAA-18 and the Cloud Profiling Radar (CPR) on-board CloudSat. First, a simple method is presented to obtain those collocations and this method is compared with a more complicated approach found in literature. We present the statistical properties of the collocations, with particular attention to the effects of the differences in footprint size. For 2007, we find approximately two and a half million MHS measurements with CPR pixels close to their centrepoints. Most of those collocations contain at least ten CloudSat pixels and image relatively homogeneous scenes. In the second part, we present three possible applications for the collocations. Firstly, we use the collocations to validate an operational Ice Water Path (IWP) product from MHS measurements, produced by the National Environment Satellite, Data and Information System (NESDIS) in the Microwave Surface and Precipitation Products System (MSPPS). IWP values from the CloudSat CPR are found to be significantly larger than those from the MSPPS. Secondly, we compare the relation between IWP and MHS channel 5 (190.311 GHz) brightness temperature for two datasets: the collocated dataset, and an artificial dataset. We find a larger variability in the collocated dataset. Finally, we use the collocations to train an Artificial Neural Network and describe how we can use it to develop a new MHS-based IWP product. We also study the effect of adding measurements from the High Resolution Infrared Radiation Sounder (HIRS), channels 8 (11.11 μm) and 11 (8.33 μm). This shows a small improvement in the retrieval quality. The collocations described in the article are available for public use.
Recent advances in (soil moisture) triple collocation analysis
Technology Transfer Automated Retrieval System (TEKTRAN)
To date, triple collocation (TC) analysis is one of the most important methods for the global scale evaluation of remotely sensed soil moisture data sets. In this study we review existing implementations of soil moisture TC analysis as well as investigations of the assumptions underlying the method....
Polynominal Interpolation Methods for Viscous Flow Calculations
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1976-01-01
Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different developments are discussed. The governing systems apply for both uniform and variable meshes. Hybrid schemes resulting from two different polynomial approximations for the first and second derivatives lead to a nonuniform mesh extension of the so-called compact or Pad? difference technique (Hermite 4). A variety of fourth-order methods are described and the Hermitian approach is extended to sixth-order (Hermite 6). The appropriate spline boundary conditions are derived for all procedures. For central finite differences, this leads to a two-point, second-order accurate generalization of the commonly used three-point end-difference formula. Solutions with several spline and Hermite procedures are presented for the boundary layer equations, with and without mass transfer, and for the incompressible viscous flow in a driven cavity. Divergence and nondivergence equations are considered for the cavity. Among the fourth-order techniques, it is shown that spline 4 has the smallest truncation error. The spline 4 procedure generally requires one-quarter the number of mesh points in a given coordinate direction as a central finite-difference calculation of equal accuracy. The Hermite 6 procedure leads to remarkably accurate boundary layer solutions.
Collocating satellite-based radar and radiometer measurements - methodology and usage examples.
NASA Astrophysics Data System (ADS)
Holl, G.; Buehler, S. A.; Rydberg, B.; Jiménez, C.
2010-05-01
Collocations between two satellite sensors are occasions where both sensors observe the same place at roughly the same time. We study collocations between the Microwave Humidity Sounder (MHS) onboard NOAA-18 and the Cloud Profiling Radar (CPR) onboard the CloudSat. First, a simple method is presented to obtain those collocations. We present the statistical properties of the collocations, with particular attention to the effects of the differences in footprint size. For 2007, we find approximately two and a half million MHS measurements with CPR pixels close to its centrepoint. Most of those collocations contain at least ten CloudSat pixels and image relatively homogeneous scenes. In the second part, we present three possible applications for the collocations. Firstly, we use the collocations to validate an operational Ice Water Path (IWP) product from MHS measurements, produced by the National Environment Satellite, Data and Information System (NESDIS) in the Microwave Surface and Precipitation Products System (MSPPS). IWP values from the CloudSat CPR are found to be significantly larger than those from the MSPPS. Secondly, we compare the relationship between IWP and MHS channel 5 (190.311 GHz) brightness temperature for two datasets: the collocated dataset, and an artificial dataset. We find a larger variability in the collocated dataset. Finally, we use the collocations to train an Artificial Neural Network and describe how we can use it to develop a new MHS-based IWP product. We also study the effect of adding measurements from the High Resolution Infrared Radiation Sounder (HIRS), channels 8 (11.11 μm) and 11 (8.33 μm). This shows a small improvement in the retrieval quality. The collocations are available for public use.
NASA Astrophysics Data System (ADS)
Nikolopoulos, L. A. A.
2003-02-01
A package is presented for the fully ab-initio calculation of one- and two-photon ionization cross sections for two-electron atomic systems (H -, He, Mg, Ca, …) under strong laser fields, within lowest-order perturbation theory (LOPT) and in the dipole approximation. The atomic structure is obtained through configuration interaction (CI) of antisymmetrized two-electron states expanded in a B-spline finite basis. The formulation of the theory and the relevant codes presented here represent the accumulation of work over the last ten years [1-11,13-15]. Extensions to more than two-photon ionization is straightforward. Calculation is possible for both the length and velocity form of the laser-atom interaction operator. The package is mainly, written in standard FORTRAN language and uses the publicly available libraries SLATEC, LAPACK and BLAS.
ERIC Educational Resources Information Center
Miyakoshi, Tomoko
2009-01-01
Although it is widely acknowledged that collocations play an important part in second language learning, especially at intermediate-advanced levels, learners' difficulties with collocations have not been investigated in much detail so far. The present study examines ESL learners' use of verb-noun collocations, such as "take notes," "place an…
Evaluation of assumptions in soil moisture triple collocation analysis
Technology Transfer Automated Retrieval System (TEKTRAN)
Triple collocation analysis (TCA) enables estimation of error variances for three or more products that retrieve or estimate the same geophysical variable using mutually-independent methods. Several statistical assumptions regarding the statistical nature of errors (e.g., mutual independence and ort...
NASA Astrophysics Data System (ADS)
Pan, M.; Zhan, W.; Fisher, C. K.; Crow, W. T.; Wood, E. F.
2014-12-01
This study extends the popular triple collocation method for error assessment from three source estimates to an arbitrary number of source estimates, i.e., to solve the multiple collocation problem. The error assessment problem is solved through Pythagorean constraints in Hilbert space, which is slightly different from the original inner product solution but easier to extend to multiple collocation cases. The Pythagorean solution is fully equivalent to the original inner product solution for the triple collocation case. The multiple collocation turns out to be an over-constrained problem and a least squared solution is presented. As the most critical assumption of uncorrelated errors will almost for sure fail in multiple collocation problems, we propose to divide the source estimates into structural categories and treat the structural and non-structural errors separately. Such error separation allows the source estimates to have their structural errors fully correlated within the same structural category, which is much more realistic than the original assumption. A new error assessment procedure is developed which performs the collocation twice, each for one type of errors, and then sums up the two types of errors. The new procedure is also fully backward compatible with the original triple collocation. Error assessment experiments are carried out for surface soil moisture data from multiple remote sensing models, land surface models, and in situ measurements.
ERIC Educational Resources Information Center
Woods, Carol M.; Thissen, David
2006-01-01
The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the…
Spline screw multiple rotations mechanism
NASA Technical Reports Server (NTRS)
Vranish, John M. (Inventor)
1993-01-01
A system for coupling two bodies together and for transmitting torque from one body to another with mechanical timing and sequencing is reported. The mechanical timing and sequencing is handled so that the following criteria are met: (1) the bodies are handled in a safe manner and nothing floats loose in space, (2) electrical connectors are engaged as long as possible so that the internal processes can be monitored throughout by sensors, and (3) electrical and mechanical power and signals are coupled. The first body has a splined driver for providing the input torque. The second body has a threaded drive member capable of rotation and limited translation. The embedded drive member will mate with and fasten to the splined driver. The second body has an embedded bevel gear member capable of rotation and limited translation. This bevel gear member is coaxial with the threaded drive member. A compression spring provides a preload on the rotating threaded member, and a thrust bearing is used for limiting the translation of the bevel gear member so that when the bevel gear member reaches the upward limit of its translation the two bodies are fully coupled and the bevel gear member then rotates due to the input torque transmitted from the splined driver through the threaded drive member to the bevel gear member. An output bevel gear with an attached output drive shaft is embedded in the second body and meshes with the threaded rotating bevel gear member to transmit the input torque to the output drive shaft.
Spline screw multiple rotations mechanism
NASA Astrophysics Data System (ADS)
Vranish, John M.
1993-12-01
A system for coupling two bodies together and for transmitting torque from one body to another with mechanical timing and sequencing is reported. The mechanical timing and sequencing is handled so that the following criteria are met: (1) the bodies are handled in a safe manner and nothing floats loose in space, (2) electrical connectors are engaged as long as possible so that the internal processes can be monitored throughout by sensors, and (3) electrical and mechanical power and signals are coupled. The first body has a splined driver for providing the input torque. The second body has a threaded drive member capable of rotation and limited translation. The embedded drive member will mate with and fasten to the splined driver. The second body has an embedded bevel gear member capable of rotation and limited translation. This bevel gear member is coaxial with the threaded drive member. A compression spring provides a preload on the rotating threaded member, and a thrust bearing is used for limiting the translation of the bevel gear member so that when the bevel gear member reaches the upward limit of its translation the two bodies are fully coupled and the bevel gear member then rotates due to the input torque transmitted from the splined driver through the threaded drive member to the bevel gear member. An output bevel gear with an attached output drive shaft is embedded in the second body and meshes with the threaded rotating bevel gear member to transmit the input torque to the output drive shaft.
Upsilon-quaternion splines for the smooth interpolation of orientations.
Nielson, Gregory M
2004-01-01
We present a new method for smoothly interpolating orientation matrices. It is based upon quaternions and a particular construction of upsilon-spline curves. The new method has tension parameters and variable knot (time) spacing which both prove to be effective in designing and controlling key frame animations. PMID:15384647
Spline Approximation of Thin Shell Dynamics
NASA Technical Reports Server (NTRS)
delRosario, R. C. H.; Smith, R. C.
1996-01-01
A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell-Mushtari thin shell equations, it can be easily extended to the Byrne-Flugge-Lur'ye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include accuracy, flexibility and efficiency in smart material applications. To accomplish this, the method was designed to be flexible with regard to boundary conditions, material nonhomogeneities due to sensors and actuators, and inputs from smart material actuators such as piezoceramic patches. The accuracy of the method was also of primary concern, both to guarantee full resolution of structural dynamics and to facilitate the development of PDE-based controllers which ultimately require real-time implementation. Several numerical examples provide initial evidence demonstrating the efficacy of the method.
Bidirectional Elastic Image Registration Using B-Spline Affine Transformation
Gu, Suicheng; Meng, Xin; Sciurba, Frank C.; Wang, Chen; Kaminski, Naftali; Pu, Jiantao
2014-01-01
A registration scheme termed as B-spline affine transformation (BSAT) is presented in this study to elastically align two images. We define an affine transformation instead of the traditional translation at each control point. Mathematically, BSAT is a generalized form of the affine transformation and the traditional B-Spline transformation (BST). In order to improve the performance of the iterative closest point (ICP) method in registering two homologous shapes but with large deformation, a bi-directional instead of the traditional unidirectional objective / cost function is proposed. In implementation, the objective function is formulated as a sparse linear equation problem, and a sub-division strategy is used to achieve a reasonable efficiency in registration. The performance of the developed scheme was assessed using both two-dimensional (2D) synthesized dataset and three-dimensional (3D) volumetric computed tomography (CT) data. Our experiments showed that the proposed B-spline affine model could obtain reasonable registration accuracy. PMID:24530210
Bidirectional elastic image registration using B-spline affine transformation.
Gu, Suicheng; Meng, Xin; Sciurba, Frank C; Ma, Hongxia; Leader, Joseph; Kaminski, Naftali; Gur, David; Pu, Jiantao
2014-06-01
A registration scheme termed as B-spline affine transformation (BSAT) is presented in this study to elastically align two images. We define an affine transformation instead of the traditional translation at each control point. Mathematically, BSAT is a generalized form of the affine transformation and the traditional B-spline transformation (BST). In order to improve the performance of the iterative closest point (ICP) method in registering two homologous shapes but with large deformation, a bidirectional instead of the traditional unidirectional objective/cost function is proposed. In implementation, the objective function is formulated as a sparse linear equation problem, and a sub-division strategy is used to achieve a reasonable efficiency in registration. The performance of the developed scheme was assessed using both two-dimensional (2D) synthesized dataset and three-dimensional (3D) volumetric computed tomography (CT) data. Our experiments showed that the proposed B-spline affine model could obtain reasonable registration accuracy. PMID:24530210
Covariance modeling in geodetic applications of collocation
NASA Astrophysics Data System (ADS)
Barzaghi, Riccardo; Cazzaniga, Noemi; De Gaetani, Carlo; Reguzzoni, Mirko
2014-05-01
Collocation method is widely applied in geodesy for estimating/interpolating gravity related functionals. The crucial problem of this approach is the correct modeling of the empirical covariance functions of the observations. Different methods for getting reliable covariance models have been proposed in the past by many authors. However, there are still problems in fitting the empirical values, particularly when different functionals of T are used and combined. Through suitable linear combinations of positive degree variances a model function that properly fits the empirical values can be obtained. This kind of condition is commonly handled by solver algorithms in linear programming problems. In this work the problem of modeling covariance functions has been dealt with an innovative method based on the simplex algorithm. This requires the definition of an objective function to be minimized (or maximized) where the unknown variables or their linear combinations are subject to some constraints. The non-standard use of the simplex method consists in defining constraints on model covariance function in order to obtain the best fit on the corresponding empirical values. Further constraints are applied so to have coherence with model degree variances to prevent possible solutions with no physical meaning. The fitting procedure is iterative and, in each iteration, constraints are strengthened until the best possible fit between model and empirical functions is reached. The results obtained during the test phase of this new methodology show remarkable improvements with respect to the software packages available until now. Numerical tests are also presented to check for the impact that improved covariance modeling has on the collocation estimate.
Collocation and Technicality in EAP Engineering
ERIC Educational Resources Information Center
Ward, Jeremy
2007-01-01
This article explores how collocation relates to lexical technicality, and how the relationship can be exploited for teaching EAP to second-year engineering students. First, corpus data are presented to show that complex noun phrase formation is a ubiquitous feature of engineering text, and that these phrases (or collocations) are highly…
Supporting Collocation Learning with a Digital Library
ERIC Educational Resources Information Center
Wu, Shaoqun; Franken, Margaret; Witten, Ian H.
2010-01-01
Extensive knowledge of collocations is a key factor that distinguishes learners from fluent native speakers. Such knowledge is difficult to acquire simply because there is so much of it. This paper describes a system that exploits the facilities offered by digital libraries to provide a rich collocation-learning environment. The design is based on…
Stochastic dynamic models and Chebyshev splines
Fan, Ruzong; Zhu, Bin; Wang, Yuedong
2015-01-01
In this article, we establish a connection between a stochastic dynamic model (SDM) driven by a linear stochastic differential equation (SDE) and a Chebyshev spline, which enables researchers to borrow strength across fields both theoretically and numerically. We construct a differential operator for the penalty function and develop a reproducing kernel Hilbert space (RKHS) induced by the SDM and the Chebyshev spline. The general form of the linear SDE allows us to extend the well-known connection between an integrated Brownian motion and a polynomial spline to a connection between more complex diffusion processes and Chebyshev splines. One interesting special case is connection between an integrated Ornstein–Uhlenbeck process and an exponential spline. We use two real data sets to illustrate the integrated Ornstein–Uhlenbeck process model and exponential spline model and show their estimates are almost identical. PMID:26045632
Approximation and modeling with ambient B-splines
NASA Astrophysics Data System (ADS)
Lehmann, N.; Maier, L.-B.; Odathuparambil, S.; Reif, U.
2016-06-01
We present a novel technique for solving approximation problems on manifolds in terms of standard tensor product B-splines. This method is easy to implement and provides optimal approximation order. Applications include the representation of smooth surfaces of arbitrary genus.
Computation Of An Optimal Laser Cavity Using Splines
NASA Astrophysics Data System (ADS)
Pantelic, Dejan V.; Janevski, Zoran D.
1989-03-01
As an attempt to improve the efficiency of a solid state laser cavity, a non-elliptical cavity is proposed. Efficiency was calculated by the ray trace method and the cavity was simulated using a novel approach with splines. Computation shows that substantial gain in efficiency can be achieved for a close coupled configuration.
NASA Astrophysics Data System (ADS)
Kuczyński, Paweł; Białecki, Ryszard
2014-06-01
The paper deals with a solution of radiation heat transfer problems in enclosures filled with nonparticipating medium using ray tracing on hierarchical ortho-Cartesian meshes. The idea behind the approach is that radiative heat transfer problems can be solved on much coarser grids than their counterparts from computational fluid dynamics (CFD). The resulting code is designed as an add-on to OpenFOAM, an open-source CFD program. Ortho-Cartesian mesh involving boundary elements is created based upon CFD mesh. Parametric non-uniform rational basis spline (NURBS) surfaces are used to define boundaries of the enclosure, allowing for dealing with domains of complex shapes. Algorithm for determining random, uniformly distributed locations of rays leaving NURBS surfaces is described. The paper presents results of test cases assuming gray diffusive walls. In the current version of the model the radiation is not absorbed within gases. However, the ultimate aim of the work is to upgrade the functionality of the model, to problems in absorbing, emitting and scattering medium projecting iteratively the results of radiative analysis on CFD mesh and CFD solution on radiative mesh.
Quintic nonpolynomial spline solutions for fourth order two-point boundary value problem
NASA Astrophysics Data System (ADS)
Ramadan, M. A.; Lashien, I. F.; Zahra, W. K.
2009-04-01
In this paper, we develop quintic nonpolynomial spline methods for the numerical solution of fourth order two-point boundary value problems. Using this spline function a few consistency relations are derived for computing approximations to the solution of the problem. The present approach gives better approximations and generalizes all the existing polynomial spline methods up to order four. This approach has less computational cost. Convergence analysis of these methods is discussed. Two numerical examples are included to illustrate the practical usefulness of our methods.
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.
2013-01-01
Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.
Implicit B-spline surface reconstruction.
Rouhani, Mohammad; Sappa, Angel D; Boyer, Edmond
2015-01-01
This paper presents a fast and flexible curve, and surface reconstruction technique based on implicit B-spline. This representation does not require any parameterization and it is locally supported. This fact has been exploited in this paper to propose a reconstruction technique through solving a sparse system of equations. This method is further accelerated to reduce the dimension to the active control lattice. Moreover, the surface smoothness and user interaction are allowed for controlling the surface. Finally, a novel weighting technique has been introduced in order to blend small patches and smooth them in the overlapping regions. The whole framework is very fast and efficient and can handle large cloud of points with very low computational cost. The experimental results show the flexibility and accuracy of the proposed algorithm to describe objects with complex topologies. Comparisons with other fitting methods highlight the superiority of the proposed approach in the presence of noise and missing data. PMID:25373084
Spline Curves, Wire Frames and Bvalue
NASA Technical Reports Server (NTRS)
Smith, L.; Munchmeyer, F.
1985-01-01
The methods that were developed for wire-frame design are described. The principal tools for control of a curve during interactive design are mathematical ducks. The simplest of these devices is an analog of the draftsman's lead weight that he uses to control a mechanical spline also create Ducks for controlling differential and integral properties of curves were created. Other methods presented include: constructing the end of a Bezier polygon to gain quick and reasonably confident control of the end tangent vector, end curvature and end torsion; keeping the magnitude of unwanted curvature oscillations within tolerance; constructing the railroad curves that appear in many engineering design problems; and controlling the frame to minimize errors at mesh points and to optimize the shapes of the curve elements.
Radial spline assembly for antifriction bearings
NASA Technical Reports Server (NTRS)
Moore, Jerry H. (Inventor)
1993-01-01
An outer race carrier is constructed for receiving an outer race of an antifriction bearing assembly. The carrier in turn is slidably fitted in an opening of a support wall to accommodate slight axial movements of a shaft. A plurality of longitudinal splines on the carrier are disposed to be fitted into matching slots in the opening. A deadband gap is provided between sides of the splines and slots, with a radial gap at ends of the splines and slots and a gap between the splines and slots sized larger than the deadband gap. With this construction, operational distortions (slope) of the support wall are accommodated by the larger radial gaps while the deadband gaps maintain a relatively high springrate of the housing. Additionally, side loads applied to the shaft are distributed between sides of the splines and slots, distributing such loads over a larger surface area than a race carrier of the prior art.
Daly, Don S.; Anderson, Kevin K.; White, Amanda M.; Gonzalez, Rachel M.; Varnum, Susan M.; Zangar, Richard C.
2008-07-14
Background: A microarray of enzyme-linked immunosorbent assays, or ELISA microarray, predicts simultaneously the concentrations of numerous proteins in a small sample. These predictions, however, are uncertain due to processing error and biological variability. Making sound biological inferences as well as improving the ELISA microarray process require require both concentration predictions and creditable estimates of their errors. Methods: We present a statistical method based on monotonic spline statistical models, penalized constrained least squares fitting (PCLS) and Monte Carlo simulation (MC) to predict concentrations and estimate prediction errors in ELISA microarray. PCLS restrains the flexible spline to a fit of assay intensity that is a monotone function of protein concentration. With MC, both modeling and measurement errors are combined to estimate prediction error. The spline/PCLS/MC method is compared to a common method using simulated and real ELISA microarray data sets. Results: In contrast to the rigid logistic model, the flexible spline model gave credible fits in almost all test cases including troublesome cases with left and/or right censoring, or other asymmetries. For the real data sets, 61% of the spline predictions were more accurate than their comparable logistic predictions; especially the spline predictions at the extremes of the prediction curve. The relative errors of 50% of comparable spline and logistic predictions differed by less than 20%. Monte Carlo simulation rendered acceptable asymmetric prediction intervals for both spline and logistic models while propagation of error produced symmetric intervals that diverged unrealistically as the standard curves approached horizontal asymptotes. Conclusions: The spline/PCLS/MC method is a flexible, robust alternative to a logistic/NLS/propagation-of-error method to reliably predict protein concentrations and estimate their errors. The spline method simplifies model selection and fitting
Modelling Childhood Growth Using Fractional Polynomials and Linear Splines
Tilling, Kate; Macdonald-Wallis, Corrie; Lawlor, Debbie A.; Hughes, Rachael A.; Howe, Laura D.
2014-01-01
Background There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines). Methods We related parental social class to height from birth to 10 years of age in 5,588 girls from the Avon Longitudinal Study of Parents and Children (ALSPAC). Multilevel fractional polynomial modelling identified the best-fitting model as being of degree 2 with powers of the square root of age, and the square root of age multiplied by the log of age. The multilevel linear spline model identified knot points at 3, 12 and 36 months of age. Results Both the fractional polynomial and linear spline models show an initially fast rate of growth, which slowed over time. Both models also showed that there was a disparity in length between manual and non-manual social class infants at birth, which decreased in magnitude until approximately 1 year of age and then increased. Conclusions Multilevel fractional polynomials give a more realistic smooth function, and linear spline models are easily interpretable. Each can be used to summarise individual growth trajectories and their relationships with individual-level exposures. PMID:25413651
NASA Astrophysics Data System (ADS)
Mitra, Jhimli; Marti, Robert; Oliver, Arnau; Llado, Xavier; Vilanova, Joan C.; Meriaudeau, Fabrice
2011-03-01
This paper provides a comparison of spline-based registration methods applied to register interventional Trans Rectal Ultrasound (TRUS) and pre-acquired Magnetic Resonance (MR) prostate images for needle guided prostate biopsy. B-splines and Thin-plate Splines (TPS) are the most prevalent spline-based approaches to achieve deformable registration. Pertaining to the strategic selection of correspondences for the TPS registration, we use an automatic method already proposed in our previous work to generate correspondences in the MR and US prostate images. The method exploits the prostate geometry with the principal components of the segmented prostate as the underlying framework and involves a triangulation approach. The correspondences are generated with successive refinements and Normalized Mutual Information (NMI) is employed to determine the optimal number of correspondences required to achieve TPS registration. B-spline registration with successive grid refinements are consecutively applied for a significant comparison of the impact of the strategically chosen correspondences on the TPS registration against the uniform B-spline control grids. The experimental results are validated on 4 patient datasets. Dice Similarity Coefficient (DSC) is used as a measure of the registration accuracy. Average DSC values of 0.97+/-0.01 and 0.95+/-0.03 are achieved for the TPS and B-spline registrations respectively. B-spline registration is observed to be more computationally expensive than the TPS registration with average execution times of 128.09 +/- 21.7 seconds and 62.83 +/- 32.77 seconds respectively for images with maximum width of 264 pixels and a maximum height of 211 pixels.
NASA Astrophysics Data System (ADS)
Rounaghi, Mohammad Mahdi; Abbaszadeh, Mohammad Reza; Arashi, Mohammad
2015-11-01
One of the most important topics of interest to investors is stock price changes. Investors whose goals are long term are sensitive to stock price and its changes and react to them. In this regard, we used multivariate adaptive regression splines (MARS) model and semi-parametric splines technique for predicting stock price in this study. The MARS model as a nonparametric method is an adaptive method for regression and it fits for problems with high dimensions and several variables. semi-parametric splines technique was used in this study. Smoothing splines is a nonparametric regression method. In this study, we used 40 variables (30 accounting variables and 10 economic variables) for predicting stock price using the MARS model and using semi-parametric splines technique. After investigating the models, we select 4 accounting variables (book value per share, predicted earnings per share, P/E ratio and risk) as influencing variables on predicting stock price using the MARS model. After fitting the semi-parametric splines technique, only 4 accounting variables (dividends, net EPS, EPS Forecast and P/E Ratio) were selected as variables effective in forecasting stock prices.
ERIC Educational Resources Information Center
Goudarzi, Zahra; Moini, M. Raouf
2012-01-01
Collocation is one of the most problematic areas in second language learning and it seems that if one wants to improve his or her communication in another language should improve his or her collocation competence. This study attempts to determine the effect of applying three different kinds of collocation on collocation learning and retention of…
An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics
NASA Astrophysics Data System (ADS)
Nguyen-Thanh, N.; Muthu, J.; Zhuang, X.; Rabczuk, T.
2014-02-01
An adaptive three-dimensional isogeometric formulation based on rational splines over hierarchical T-meshes (RHT-splines) for problems in elasto-statics and elasto-dynamics is presented. RHT-splines avoid some short-comings of NURBS-based formulations; in particular they allow for adaptive h-refinement with ease. In order to drive the adaptive refinement, we present a recovery-based error estimator for RHT-splines. The method is applied to several problems in elasto-statics and elasto-dynamics including three-dimensional modeling of thin structures. The results are compared to analytical solutions and results of NURBS based isogeometric formulations.
Technology Transfer Automated Retrieval System (TEKTRAN)
Advanced mathematical models have the potential to capture the complex metabolic and physiological processes that result in heat production, or energy expenditure (EE). Multivariate adaptive regression splines (MARS), is a nonparametric method that estimates complex nonlinear relationships by a seri...
Curve fitting and modeling with splines using statistical variable selection techniques
NASA Technical Reports Server (NTRS)
Smith, P. L.
1982-01-01
The successful application of statistical variable selection techniques to fit splines is demonstrated. Major emphasis is given to knot selection, but order determination is also discussed. Two FORTRAN backward elimination programs, using the B-spline basis, were developed. The program for knot elimination is compared in detail with two other spline-fitting methods and several statistical software packages. An example is also given for the two-variable case using a tensor product basis, with a theoretical discussion of the difficulties of their use.
A Two-Timescale Discretization Scheme for Collocation
NASA Technical Reports Server (NTRS)
Desai, Prasun; Conway, Bruce A.
2004-01-01
The development of a two-timescale discretization scheme for collocation is presented. This scheme allows a larger discretization to be utilized for smoothly varying state variables and a second finer discretization to be utilized for state variables having higher frequency dynamics. As such. the discretization scheme can be tailored to the dynamics of the particular state variables. In so doing. the size of the overall Nonlinear Programming (NLP) problem can be reduced significantly. Two two-timescale discretization architecture schemes are described. Comparison of results between the two-timescale method and conventional collocation show very good agreement. Differences of less than 0.5 percent are observed. Consequently. a significant reduction (by two-thirds) in the number of NLP parameters and iterations required for convergence can be achieved without sacrificing solution accuracy.
Locating CVBEM collocation points for steady state heat transfer problems
Hromadka, T.V., II
1985-01-01
The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the approximation depends upon the nodal point distribution specified by the numerical analyst. In order to develop subsequent, refined approximation functions, four techniques for selecting additional collocation points are presented. The techniques are compared as to the governing theory, representation of the error of approximation on the problem boundary, the computational costs, and the ease of use by the numerical analyst. ?? 1985.
The Impact of Corpus-Based Collocation Instruction on Iranian EFL Learners' Collocation Learning
ERIC Educational Resources Information Center
Ashouri, Shabnam; Arjmandi, Masoume; Rahimi, Ramin
2014-01-01
Over the past decades, studies of EFL/ESL vocabulary acquisition have identified the significance of collocations in language learning. Due to the fact that collocations have been regarded as one of the major concerns of both EFL teachers and learners for many years, the present study attempts to shed light on the impact of corpus-based…
ERIC Educational Resources Information Center
Wolter, Brent; Gyllstad, Henrik
2013-01-01
This study investigated the influence of frequency effects on the processing of congruent (i.e., having an equivalent first language [L1] construction) collocations and incongruent (i.e., not having an equivalent L1 construction) collocations in a second language (L2). An acceptability judgment task was administered to native and advanced…
47 CFR 51.323 - Standards for physical collocation and virtual collocation.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 3 2011-10-01 2011-10-01 false Standards for physical collocation and virtual collocation. 51.323 Section 51.323 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Additional Obligations of Incumbent Local Exchange Carriers § 51.323 Standards for...
47 CFR 51.323 - Standards for physical collocation and virtual collocation.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 3 2012-10-01 2012-10-01 false Standards for physical collocation and virtual collocation. 51.323 Section 51.323 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Additional Obligations of Incumbent Local Exchange Carriers § 51.323 Standards for...
NASA Astrophysics Data System (ADS)
Fatah, Abd.; Rozaimi
2015-12-01
In this paper, we will discuss about the construction of fuzzy tuning B-spline curve based on fuzzy set theory. The concept of fuzzy tuning in designing this B-spline curve is based on the uncertain knots values which has to be defined first and then the result will be blended together with B-spline function which exists in users presumption in deciding the best knots value of tuning. Therefore, fuzzy set theory especially fuzzy number concepts are used to define the uncertain knots values and then it will be become fuzzy knots values. The Result by using different values of fuzzy knots for constructing a fuzzy tuning of B-spline curves will be illustrated.
NASA Astrophysics Data System (ADS)
Stevens, D.; Power, H.; Meng, C. Y.; Howard, D.; Cliffe, K. A.
2013-12-01
This work proposes an alternative decomposition for local scalable meshless RBF collocation. The proposed method operates on a dataset of scattered nodes that are placed within the solution domain and on the solution boundary, forming a small RBF collocation system around each internal node. Unlike other meshless local RBF formulations that are based on a generalised finite difference (RBF-FD) principle, in the proposed "finite collocation" method the solution of the PDE is driven entirely by collocation of PDE governing and boundary operators within the local systems. A sparse global collocation system is obtained not by enforcing the PDE governing operator, but by assembling the value of the field variable in terms of the field value at neighbouring nodes. In analogy to full-domain RBF collocation systems, communication between stencils occurs only over the stencil periphery, allowing the PDE governing operator to be collocated in an uninterrupted manner within the stencil interior. The local collocation of the PDE governing operator allows the method to operate on centred stencils in the presence of strong convective fields; the reconstruction weights assigned to nodes in the stencils being automatically adjusted to represent the flow of information as dictated by the problem physics. This "implicit upwinding" effect mitigates the need for ad-hoc upwinding stencils in convective dominant problems. Boundary conditions are also enforced within the local collocation systems, allowing arbitrary boundary operators to be imposed naturally within the solution construction. The performance of the method is assessed using a large number of numerical examples with two steady PDEs; the convection-diffusion equation, and the Lamé-Navier equations for linear elasticity. The method exhibits high-order convergence in each case tested (greater than sixth order), and the use of centred stencils is demonstrated for convective-dominant problems. In the case of linear elasticity
Registration of sliding objects using direction dependent B-splines decomposition
NASA Astrophysics Data System (ADS)
Delmon, V.; Rit, S.; Pinho, R.; Sarrut, D.
2013-03-01
Sliding motion is a challenge for deformable image registration because it leads to discontinuities in the sought deformation. In this paper, we present a method to handle sliding motion using multiple B-spline transforms. The proposed method decomposes the sought deformation into sliding regions to allow discontinuities at their interfaces, but prevents unrealistic solutions by forcing those interfaces to match. The method was evaluated on 16 lung cancer patients against a single B-spline transform approach and a multi B-spline transforms approach without the sliding constraint at the interface. The target registration error (TRE) was significantly lower with the proposed method (TRE = 1.5 mm) than with the single B-spline approach (TRE = 3.7 mm) and was comparable to the multi B-spline approach without the sliding constraint (TRE = 1.4 mm). The proposed method was also more accurate along region interfaces, with 37% less gaps and overlaps when compared to the multi B-spline transforms without the sliding constraint. This work was presented in part at the 4th International Workshop on Pulmonary Image Analysis during the Medical Image Computing and Computer Assisted Intervention (MICCAI) in Toronto, Canada (2011).
An algorithm for natural spline interpolation
NASA Astrophysics Data System (ADS)
Traversoni, Leonardo
1993-01-01
Based on the work of Robin Sibson concerning Natural Neighbor Interpolant, this paper is devoted to incorporate this concept in Spline theory. To do this, first a new concept, the "Covering Spheres", is presented, which is then linked with Sibson's interpolant. Finally, the interpolant is reformulated to present it as a Bernstein polynomial in local coordinates instead of the usual presentation as rational quartics. As a corollary, the whole idea is presented as modified Vertex Splines.
Data approximation using a blending type spline construction
Dalmo, Rune; Bratlie, Jostein
2014-11-18
Generalized expo-rational B-splines (GERBS) is a blending type spline construction where local functions at each knot are blended together by C{sup k}-smooth basis functions. One way of approximating discrete regular data using GERBS is by partitioning the data set into subsets and fit a local function to each subset. Partitioning and fitting strategies can be devised such that important or interesting data points are interpolated in order to preserve certain features. We present a method for fitting discrete data using a tensor product GERBS construction. The method is based on detection of feature points using differential geometry. Derivatives, which are necessary for feature point detection and used to construct local surface patches, are approximated from the discrete data using finite differences.
Mars Mission Optimization Based on Collocation of Resources
NASA Technical Reports Server (NTRS)
Chamitoff, G. E.; James, G. H.; Barker, D. C.; Dershowitz, A. L.
2003-01-01
This paper presents a powerful approach for analyzing Martian data and for optimizing mission site selection based on resource collocation. This approach is implemented in a program called PROMT (Planetary Resource Optimization and Mapping Tool), which provides a wide range of analysis and display functions that can be applied to raw data or imagery. Thresholds, contours, custom algorithms, and graphical editing are some of the various methods that can be used to process data. Output maps can be created to identify surface regions on Mars that meet any specific criteria. The use of this tool for analyzing data, generating maps, and collocating features is demonstrated using data from the Mars Global Surveyor and the Odyssey spacecraft. The overall mission design objective is to maximize a combination of scientific return and self-sufficiency based on utilization of local materials. Landing site optimization involves maximizing accessibility to collocated science and resource features within a given mission radius. Mission types are categorized according to duration, energy resources, and in-situ resource utilization. Optimization results are shown for a number of mission scenarios.
Results of laser ranging collocations during 1983
NASA Technical Reports Server (NTRS)
Kolenkiewicz, R.
1984-01-01
The objective of laser ranging collocations is to compare the ability of two satellite laser ranging systems, located in the vicinity of one another, to measure the distance to an artificial Earth satellite in orbit over the sites. The similar measurement of this distance is essential before a new or modified laser system is deployed to worldwide locations in order to gather the data necessary to meet the scientific goals of the Crustal Dynamics Project. In order to be certain the laser systems are operating properly, they are periodically compared with each other. These comparisons or collocations are performed by locating the lasers side by side when they track the same satellite during the same time or pass. The data is then compared to make sure the lasers are giving essentially the same range results. Results of the three collocations performed during 1983 are given.
Technology Transfer Automated Retrieval System (TEKTRAN)
In the US, regional air quality compliance with national ambient air quality standards (NAAQS) for PM10 is based on concentration measurements taken by federal reference method (FRM) PM10 samplers. The EPA specifies the performance characteristics of the FRM PM10 sampler by defining ranges for the p...
Gauging the Effects of Exercises on Verb-Noun Collocations
ERIC Educational Resources Information Center
Boers, Frank; Demecheleer, Murielle; Coxhead, Averil; Webb, Stuart
2014-01-01
Many contemporary textbooks for English as a foreign language (EFL) and books for vocabulary study contain exercises with a focus on collocations, with verb-noun collocations (e.g. "make a mistake") being particularly popular as targets for collocation learning. Common exercise formats used in textbooks and other pedagogic materials…
Corpus-Based versus Traditional Learning of Collocations
ERIC Educational Resources Information Center
Daskalovska, Nina
2015-01-01
One of the aspects of knowing a word is the knowledge of which words it is usually used with. Since knowledge of collocations is essential for appropriate and fluent use of language, learning collocations should have a central place in the study of vocabulary. There are different opinions about the best ways of learning collocations. This study…
Is "Absorb Knowledge" an Improper Collocation?
ERIC Educational Resources Information Center
Su, Yujie
2010-01-01
Collocation is practically very tough to Chinese English learners. The main reason lies in the fact that English and Chinese belong to two distinct language systems. And the deep reason is that learners tend to develop different metaphorical concept in accordance with distinct ways of thinking in Chinese. The paper, taking "absorb…
Penalized Spline: a General Robust Trajectory Model for ZIYUAN-3 Satellite
NASA Astrophysics Data System (ADS)
Pan, H.; Zou, Z.
2016-06-01
Owing to the dynamic imaging system, the trajectory model plays a very important role in the geometric processing of high resolution satellite imagery. However, establishing a trajectory model is difficult when only discrete and noisy data are available. In this manuscript, we proposed a general robust trajectory model, the penalized spline model, which could fit trajectory data well and smooth noise. The penalized parameter λ controlling the smooth and fitting accuracy could be estimated by generalized cross-validation. Five other trajectory models, including third-order polynomials, Chebyshev polynomials, linear interpolation, Lagrange interpolation and cubic spline, are compared with the penalized spline model. Both the sophisticated ephemeris and on-board ephemeris are used to compare the orbit models. The penalized spline model could smooth part of noise, and accuracy would decrease as the orbit length increases. The band-to-band misregistration of ZiYuan-3 Dengfeng and Faizabad multispectral images is used to evaluate the proposed method. With the Dengfeng dataset, the third-order polynomials and Chebyshev approximation could not model the oscillation, and introduce misregistration of 0.57 pixels misregistration in across-track direction and 0.33 pixels in along-track direction. With the Faizabad dataset, the linear interpolation, Lagrange interpolation and cubic spline model suffer from noise, introducing larger misregistration than the approximation models. Experimental results suggest the penalized spline model could model the oscillation and smooth noise.
Exact sampling of the unobserved covariates in Bayesian spline models for measurement error problems
Carroll, Raymond J.
2015-01-01
In truncated polynomial spline or B-spline models where the covariates are measured with error, a fully Bayesian approach to model fitting requires the covariates and model parameters to be sampled at every Markov chain Monte Carlo iteration. Sampling the unobserved covariates poses a major computational problem and usually Gibbs sampling is not possible. This forces the practitioner to use a Metropolis–Hastings step which might suffer from unacceptable performance due to poor mixing and might require careful tuning. In this article we show for the cases of truncated polynomial spline or B-spline models of degree equal to one, the complete conditional distribution of the covariates measured with error is available explicitly as a mixture of double-truncated normals, thereby enabling a Gibbs sampling scheme. We demonstrate via a simulation study that our technique performs favorably in terms of computational efficiency and statistical performance. Our results indicate up to 62 and 54 % increase in mean integrated squared error efficiency when compared to existing alternatives while using truncated polynomial splines and B-splines respectively. Furthermore, there is evidence that the gain in efficiency increases with the measurement error variance, indicating the proposed method is a particularly valuable tool for challenging applications that present high measurement error. We conclude with a demonstration on a nutritional epidemiology data set from the NIH-AARP study and by pointing out some possible extensions of the current work. PMID:27418743
NASA Astrophysics Data System (ADS)
Bhrawy, A. H.
2016-01-01
This paper reports a new spectral collocation technique for solving time-space modified anomalous subdiffusion equation with a nonlinear source term subject to Dirichlet and Neumann boundary conditions. This model equation governs the evolution for the probability density function that describes anomalously diffusing particles. Anomalous diffusion is ubiquitous in physical and biological systems where trapping and binding of particles can occur. A space-time Jacobi collocation scheme is investigated for solving such problem. The main advantage of the proposed scheme is that, the shifted Jacobi Gauss-Lobatto collocation and shifted Jacobi Gauss-Radau collocation approximations are employed for spatial and temporal discretizations, respectively. Thereby, the problem is successfully reduced to a system of algebraic equations. The numerical results obtained by this algorithm have been compared with various numerical methods in order to demonstrate the high accuracy and efficiency of the proposed method. Indeed, for relatively limited number of Gauss-Lobatto and Gauss-Radau collocation nodes imposed, the absolute error in our numerical solutions is sufficiently small. The results have been compared with other techniques in order to demonstrate the high accuracy and efficiency of the proposed method.
Spline-Screw Multiple-Rotation Mechanism
NASA Technical Reports Server (NTRS)
Vranish, John M.
1994-01-01
Mechanism functions like combined robotic gripper and nut runner. Spline-screw multiple-rotation mechanism related to spline-screw payload-fastening system described in (GSC-13454). Incorporated as subsystem in alternative version of system. Mechanism functions like combination of robotic gripper and nut runner; provides both secure grip and rotary actuation of other parts of system. Used in system in which no need to make or break electrical connections to payload during robotic installation or removal of payload. More complicated version needed to make and break electrical connections. Mechanism mounted in payload.
NASA Astrophysics Data System (ADS)
Benda, Jakub; Houfek, Karel
2016-07-01
We provide an updated version of the program hex-ecs originally presented in Comput. Phys. Commun. 185 (2014) 2903-2912. The original version used an iterative method preconditioned by the incomplete LU factorization (ILU), which-though very stable and predictable-requires a large amount of working memory. In the new version we implemented a "separated electrons" (or "Kronecker product approximation", KPA) preconditioner as suggested by Bar-On et al., Appl. Num. Math. 33 (2000) 95-104. This preconditioner has much lower memory requirements, though in return it requires more iterations to reach converged results. By careful choice between ILU and KPA preconditioners one is able to extend the computational feasibility to larger calculations. Secondly, we added the option to run the KPA preconditioner on an OpenCL device (e.g. GPU). GPUs have generally better memory access times, which speeds up particularly the sparse matrix multiplication.
Achieving high data reduction with integral cubic B-splines
NASA Technical Reports Server (NTRS)
Chou, Jin J.
1993-01-01
During geometry processing, tangent directions at the data points are frequently readily available from the computation process that generates the points. It is desirable to utilize this information to improve the accuracy of curve fitting and to improve data reduction. This paper presents a curve fitting method which utilizes both position and tangent direction data. This method produces G(exp 1) non-rational B-spline curves. From the examples, the method demonstrates very good data reduction rates while maintaining high accuracy in both position and tangent direction.
Six-Degree-of-Freedom Trajectory Optimization Utilizing a Two-Timescale Collocation Architecture
NASA Technical Reports Server (NTRS)
Desai, Prasun N.; Conway, Bruce A.
2005-01-01
Six-degree-of-freedom (6DOF) trajectory optimization of a reentry vehicle is solved using a two-timescale collocation methodology. This class of 6DOF trajectory problems are characterized by two distinct timescales in their governing equations, where a subset of the states have high-frequency dynamics (the rotational equations of motion) while the remaining states (the translational equations of motion) vary comparatively slowly. With conventional collocation methods, the 6DOF problem size becomes extraordinarily large and difficult to solve. Utilizing the two-timescale collocation architecture, the problem size is reduced significantly. The converged solution shows a realistic landing profile and captures the appropriate high-frequency rotational dynamics. A large reduction in the overall problem size (by 55%) is attained with the two-timescale architecture as compared to the conventional single-timescale collocation method. Consequently, optimum 6DOF trajectory problems can now be solved efficiently using collocation, which was not previously possible for a system with two distinct timescales in the governing states.
Accuracy and speed in computing the Chebyshev collocation derivative
NASA Technical Reports Server (NTRS)
Don, Wai-Sun; Solomonoff, Alex
1991-01-01
We studied several algorithms for computing the Chebyshev spectral derivative and compare their roundoff error. For a large number of collocation points, the elements of the Chebyshev differentiation matrix, if constructed in the usual way, are not computed accurately. A subtle cause is is found to account for the poor accuracy when computing the derivative by the matrix-vector multiplication method. Methods for accurately computing the elements of the matrix are presented, and we find that if the entities of the matrix are computed accurately, the roundoff error of the matrix-vector multiplication is as small as that of the transform-recursion algorithm. Results of CPU time usage are shown for several different algorithms for computing the derivative by the Chebyshev collocation method for a wide variety of two-dimensional grid sizes on both an IBM and a Cray 2 computer. We found that which algorithm is fastest on a particular machine depends not only on the grid size, but also on small details of the computer hardware as well. For most practical grid sizes used in computation, the even-odd decomposition algorithm is found to be faster than the transform-recursion method.
Shaft Coupler With Friction and Spline Clutches
NASA Technical Reports Server (NTRS)
Thebert, Glenn W.
1987-01-01
Coupling, developed for rotor of lift/cruise aircraft, employs two clutches for smooth transmission of power from gas-turbine engine to rotor. Prior to ascent, coupling applies friction-type transition clutch that accelerates rotor shaft to speeds matching those of engine shaft. Once shafts synchronized, spline coupling engaged and friction clutch released to provide positive mechanical drive.
Spline smoothing of histograms by linear programming
NASA Technical Reports Server (NTRS)
Bennett, J. O.
1972-01-01
An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.
A Spline Regression Model for Latent Variables
ERIC Educational Resources Information Center
Harring, Jeffrey R.
2014-01-01
Spline (or piecewise) regression models have been used in the past to account for patterns in observed data that exhibit distinct phases. The changepoint or knot marking the shift from one phase to the other, in many applications, is an unknown parameter to be estimated. As an extension of this framework, this research considers modeling the…
NASA Technical Reports Server (NTRS)
Rogers, David
1991-01-01
G/SPLINES are a hybrid of Friedman's Multivariable Adaptive Regression Splines (MARS) algorithm with Holland's Genetic Algorithm. In this hybrid, the incremental search is replaced by a genetic search. The G/SPLINE algorithm exhibits performance comparable to that of the MARS algorithm, requires fewer least squares computations, and allows significantly larger problems to be considered.
An algorithm for surface smoothing with rational splines
NASA Technical Reports Server (NTRS)
Schiess, James R.
1987-01-01
Discussed is an algorithm for smoothing surfaces with spline functions containing tension parameters. The bivariate spline functions used are tensor products of univariate rational-spline functions. A distinct tension parameter corresponds to each rectangular strip defined by a pair of consecutive spline knots along either axis. Equations are derived for writing the bivariate rational spline in terms of functions and derivatives at the knots. Estimates of these values are obtained via weighted least squares subject to continuity constraints at the knots. The algorithm is illustrated on a set of terrain elevation data.
Trigonometric quadratic B-spline subdomain Galerkin algorithm for the Burgers' equation
NASA Astrophysics Data System (ADS)
Ay, Buket; Dag, Idris; Gorgulu, Melis Zorsahin
2015-12-01
A variant of the subdomain Galerkin method has been set up to find numerical solutions of the Burgers' equation. Approximate function consists of the combination of the trigonometric B-splines. Integration of Burgers' equation has been achived by aid of the subdomain Galerkin method based on the trigonometric B-splines as an approximate functions. The resulting first order ordinary differential system has been converted into an iterative algebraic equation by use of the Crank-Nicolson method at successive two time levels. The suggested algorithm is tested on somewell-known problems for the Burgers' equation.
NASA Astrophysics Data System (ADS)
Gutierrez, Ronald R.; Abad, Jorge D.; Parsons, Daniel R.; Best, James L.
2013-09-01
There is no standard nomenclature and procedure to systematically identify the scale and magnitude of bed forms such as bars, dunes, and ripples that are commonly present in many sedimentary environments. This paper proposes a standardization of the nomenclature and symbolic representation of bed forms and details the combined application of robust spline filters and continuous wavelet transforms to discriminate these morphodynamic features, allowing the quantitative recognition of bed form hierarchies. Herein the proposed methodology for bed form discrimination is first applied to synthetic bed form profiles, which are sampled at a Nyquist ratio interval of 2.5-50 and a signal-to-noise ratio interval of 1-20 and subsequently applied to a detailed 3-D bed topography from the Río Paraná, Argentina, which exhibits large-scale dunes with superimposed, smaller bed forms. After discriminating the synthetic bed form signals into three-bed form hierarchies that represent bars, dunes, and ripples, the accuracy of the methodology is quantified by estimating the reproducibility, the cross correlation, and the standard deviation ratio of the actual and retrieved signals. For the case of the field measurements, the proposed method is used to discriminate small and large dunes and subsequently obtain and statistically analyze the common morphological descriptors such as wavelength, slope, and amplitude of both stoss and lee sides of these different size bed forms. Analysis of the synthetic signals demonstrates that the Morlet wavelet function is the most efficient in retrieving smaller periodicities such as ripples and smaller dunes and that the proposed methodology effectively discriminates waves of different periods for Nyquist ratios higher than 25 and signal-to-noise ratios higher than 5. The analysis of bed forms in the Río Paraná reveals that, in most cases, a Gamma probability distribution, with a positive skewness, best describes the dimensionless wavelength and
Pierson, Jeffery L; Small, Scott R; Rodriguez, Jose A; Kang, Michael N; Glassman, Andrew H
2015-07-01
Design parameters affecting initial mechanical stability of tapered, splined modular titanium stems (TSMTSs) are not well understood. Furthermore, there is considerable variability in contemporary designs. We asked if spline geometry and stem taper angle could be optimized in TSMTS to improve mechanical stability to resist axial subsidence and increase torsional stability. Initial stability was quantified with stems of varied taper angle and spline geometry implanted in a foam model replicating 2cm diaphyseal engagement. Increased taper angle and a broad spline geometry exhibited significantly greater axial stability (+21%-269%) than other design combinations. Neither taper angle nor spline geometry significantly altered initial torsional stability. PMID:25754255
Error Estimates Derived from the Data for Least-Squares Spline Fitting
Jerome Blair
2007-06-25
The use of least-squares fitting by cubic splines for the purpose of noise reduction in measured data is studied. Splines with variable mesh size are considered. The error, the difference between the input signal and its estimate, is divided into two sources: the R-error, which depends only on the noise and increases with decreasing mesh size, and the Ferror, which depends only on the signal and decreases with decreasing mesh size. The estimation of both errors as a function of time is demonstrated. The R-error estimation requires knowledge of the statistics of the noise and uses well-known methods. The primary contribution of the paper is a method for estimating the F-error that requires no prior knowledge of the signal except that it has four derivatives. It is calculated from the difference between two different spline fits to the data and is illustrated with Monte Carlo simulations and with an example.
NASA Astrophysics Data System (ADS)
Korshunov, Andrei; Shershnev, Vladimir; Korshunova, Ksenia
2015-08-01
Methods of designing blades grids of power machines, such as equal thickness shape built on middle-line arc, or methods based on target stress spreading were invented long time ago, well described and still in use. Science and technology has moved far from that time and laboriousness of experimental research, which were involving unique equipment, requires development of new robust and flexible methods of design, which will determine the optimal geometry of flow passage.This investigation provides simple and universal method of designing blades, which, in comparison to the currently used methods, requires significantly less input data but still provides accurate results. The described method is purely analytical for both concave and convex sides of the blade, and therefore lets to describe the curve behavior down the flow path at any point. Compared with the blade grid designs currently used in industry, geometric parameters of the designs constructed with this method show the maximum deviation below 0.4%.
Semisupervised feature selection via spline regression for video semantic recognition.
Han, Yahong; Yang, Yi; Yan, Yan; Ma, Zhigang; Sebe, Nicu; Zhou, Xiaofang
2015-02-01
To improve both the efficiency and accuracy of video semantic recognition, we can perform feature selection on the extracted video features to select a subset of features from the high-dimensional feature set for a compact and accurate video data representation. Provided the number of labeled videos is small, supervised feature selection could fail to identify the relevant features that are discriminative to target classes. In many applications, abundant unlabeled videos are easily accessible. This motivates us to develop semisupervised feature selection algorithms to better identify the relevant video features, which are discriminative to target classes by effectively exploiting the information underlying the huge amount of unlabeled video data. In this paper, we propose a framework of video semantic recognition by semisupervised feature selection via spline regression (S(2)FS(2)R) . Two scatter matrices are combined to capture both the discriminative information and the local geometry structure of labeled and unlabeled training videos: A within-class scatter matrix encoding discriminative information of labeled training videos and a spline scatter output from a local spline regression encoding data distribution. An l2,1 -norm is imposed as a regularization term on the transformation matrix to ensure it is sparse in rows, making it particularly suitable for feature selection. To efficiently solve S(2)FS(2)R , we develop an iterative algorithm and prove its convergency. In the experiments, three typical tasks of video semantic recognition, such as video concept detection, video classification, and human action recognition, are used to demonstrate that the proposed S(2)FS(2)R achieves better performance compared with the state-of-the-art methods. PMID:25608288
Spline-Screw Payload-Fastening System
NASA Technical Reports Server (NTRS)
Vranish, John M.
1994-01-01
Payload handed off securely between robot and vehicle or structure. Spline-screw payload-fastening system includes mating female and male connector mechanisms. Clockwise (or counter-clockwise) rotation of splined male driver on robotic end effector causes connection between robot and payload to tighten (or loosen) and simultaneously causes connection between payload and structure to loosen (or tighten). Includes mechanisms like those described in "Tool-Changing Mechanism for Robot" (GSC-13435) and "Self-Aligning Mechanical and Electrical Coupling" (GSC-13430). Designed for use in outer space, also useful on Earth in applications needed for secure handling and secure mounting of equipment modules during storage, transport, and/or operation. Particularly useful in machine or robotic applications.
ERIC Educational Resources Information Center
Chatpunnarangsee, Kwanjira
2013-01-01
The purpose of this study is to explore ways of incorporating web-based concordancers for the purpose of teaching English collocations. A mixed-methods design utilizing a case study strategy was employed to uncover four specific dimensions of corpus use by twenty-four students in two classroom sections of a writing course at a university in…
A natural spline interpolation and exponential parameterization
NASA Astrophysics Data System (ADS)
Kozera, R.; Wilkołazka, M.
2016-06-01
We consider here a natural spline interpolation based on reduced data and the so-called exponential parameterization (depending on parameter λ ∈ [0, 1]). In particular, the latter is studied in the context of the trajectory approximation in arbitrary euclidean space. The term reduced data refers to an ordered collection of interpolation points without provision of the corresponding knots. The numerical verification of the intrinsic asymptotics α(λ) in γ approximation by natural spline γ^3'N is conducted here for regular and sufficiently smooth curve γ sampled more-or-less uniformly. We select in this paper the substitutes for the missing knots according to the exponential parameterization. The outcomes of the numerical tests manifest sharp linear convergence orders α(λ) = 1, for all λ ∈ [0, 1). In addition, the latter results in unexpected left-hand side dis-continuity at λ = 1, since as shown again here a sharp quadratic order α(1) = 2 prevails. Remarkably, the case of α(1)=2 (derived for reduced data) coincides with the well-known asymptotics established for a natural spline to fit non-reduced data determined by the sequence of interpolation points supplemented with the corresponding knots (see e.g. [1]).
A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation
NASA Astrophysics Data System (ADS)
Doha, Eid; Bhrawy, Ali; Abdelkawy, Mohamed; Hafez, Ramy
2014-02-01
This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.
Smoothing two-dimensional Malaysian mortality data using P-splines indexed by age and year
NASA Astrophysics Data System (ADS)
Kamaruddin, Halim Shukri; Ismail, Noriszura
2014-06-01
Nonparametric regression implements data to derive the best coefficient of a model from a large class of flexible functions. Eilers and Marx (1996) introduced P-splines as a method of smoothing in generalized linear models, GLMs, in which the ordinary B-splines with a difference roughness penalty on coefficients is being used in a single dimensional mortality data. Modeling and forecasting mortality rate is a problem of fundamental importance in insurance company calculation in which accuracy of models and forecasts are the main concern of the industry. The original idea of P-splines is extended to two dimensional mortality data. The data indexed by age of death and year of death, in which the large set of data will be supplied by Department of Statistics Malaysia. The extension of this idea constructs the best fitted surface and provides sensible prediction of the underlying mortality rate in Malaysia mortality case.
N-dimensional B-spline surface estimated by lofting for locally improving IRI
NASA Astrophysics Data System (ADS)
Koch, K.; Schmidt, M.
2011-03-01
N-dimensional surfaces are defined by the tensor product of B-spline basis functions. To estimate the unknown control points of these B-spline surfaces, the lofting method also called skinning method by cross-sectional curve fits is applied. It is shown by an analytical proof and numerically confirmed by the example of a four-dimensional surface that the results of the lofting method agree with the ones of the simultaneous estimation of the unknown control points. The numerical complexity for estimating
Optimization of Low-Thrust Spiral Trajectories by Collocation
NASA Technical Reports Server (NTRS)
Falck, Robert D.; Dankanich, John W.
2012-01-01
As NASA examines potential missions in the post space shuttle era, there has been a renewed interest in low-thrust electric propulsion for both crewed and uncrewed missions. While much progress has been made in the field of software for the optimization of low-thrust trajectories, many of the tools utilize higher-fidelity methods which, while excellent, result in extremely high run-times and poor convergence when dealing with planetocentric spiraling trajectories deep within a gravity well. Conversely, faster tools like SEPSPOT provide a reasonable solution but typically fail to account for other forces such as third-body gravitation, aerodynamic drag, solar radiation pressure. SEPSPOT is further constrained by its solution method, which may require a very good guess to yield a converged optimal solution. Here the authors have developed an approach using collocation intended to provide solution times comparable to those given by SEPSPOT while allowing for greater robustness and extensible force models.
Profiling the Collocation Use in ELT Textbooks and Learner Writing
ERIC Educational Resources Information Center
Tsai, Kuei-Ju
2015-01-01
The present study investigates the collocational profiles of (1) three series of graded textbooks for English as a foreign language (EFL) commonly used in Taiwan, (2) the written productions of EFL learners, and (3) the written productions of native speakers (NS) of English. These texts were examined against a purpose-built collocation list. Based…
The Repetition of Collocations in EFL Textbooks: A Corpus Study
ERIC Educational Resources Information Center
Wang, Jui-hsin Teresa; Good, Robert L.
2007-01-01
The importance of repetition in the acquisition of lexical items has been widely acknowledged in single-word vocabulary research but has been relatively neglected in collocation studies. Since collocations are considered one key to achieving language fluency, and because learners spend a great amount of time interacting with their textbooks, the…
The Effect of Grouping and Presenting Collocations on Retention
ERIC Educational Resources Information Center
Akpinar, Kadriye Dilek; Bardakçi, Mehmet
2015-01-01
The aim of this study is two-fold. Firstly, it attempts to determine the role of presenting collocations by organizing them based on (i) the keyword, (ii) topic related and (iii) grammatical aspect on retention of collocations. Secondly, it investigates the relationship between participants' general English proficiency and the presentation types…
Collocations of High Frequency Noun Keywords in Prescribed Science Textbooks
ERIC Educational Resources Information Center
Menon, Sujatha; Mukundan, Jayakaran
2012-01-01
This paper analyses the discourse of science through the study of collocational patterns of high frequency noun keywords in science textbooks used by upper secondary students in Malaysia. Research has shown that one of the areas of difficulty in science discourse concerns lexis, especially that of collocations. This paper describes a corpus-based…
Development and flight tests of vortex-attenuating splines
NASA Technical Reports Server (NTRS)
Hastings, E. C., Jr.; Patterson, J. C., Jr.; Shanks, R. E.; Champine, R. A.; Copeland, W. L.; Young, D. C.
1975-01-01
The ground tests and full-scale flight tests conducted during development of the vortex-attenuating spline are described. The flight tests were conducted using a vortex generating aircraft with and without splines; a second aircraft was used to probe the vortices generated in both cases. The results showed that splines significantly reduced the vortex effects, but resulted in some noise and climb performance penalties on the generating aircraft.
On the spline-based wavelet differentiation matrix
NASA Technical Reports Server (NTRS)
Jameson, Leland
1993-01-01
The differentiation matrix for a spline-based wavelet basis is constructed. Given an n-th order spline basis it is proved that the differentiation matrix is accurate of order 2n + 2 when periodic boundary conditions are assumed. This high accuracy, or superconvergence, is lost when the boundary conditions are no longer periodic. Furthermore, it is shown that spline-based bases generate a class of compact finite difference schemes.
Gridding heterogeneous bathymetric data sets with stacked continuous curvature splines in tension
NASA Astrophysics Data System (ADS)
Hell, Benjamin; Jakobsson, Martin
2011-12-01
Gridding heterogeneous bathymetric data sets for the compilation of Digital bathymetric models (DBMs), poses specific problems when there are extreme variations in source data density. This requires gridding routines capable of subsampling high-resolution source data while preserving as much as possible of the small details, at the same time as interpolating in areas with sparse data without generating gridding artifacts. A frequently used gridding method generalizes bicubic spline interpolation and is known as continuous curvature splines in tension. This method is further enhanced in this article in order to specifically handle heterogeneous bathymetric source data. Our method constructs the final grid through stacking several surfaces of different resolutions, each generated using the splines in tension algorithm. With this approach, the gridding resolution is locally adjusted to the density of the source data set: Areas with high-resolution data are gridded at higher resolution than areas with sparse source data. In comparison with some of the most widely used gridding methods, our approach yields superior DBMs based on heterogeneous bathymetric data sets with regard to preserving small bathymetric details in the high-resolution source data, while minimizing interpolation artifacts in the sparsely data constrained regions. Common problems such as artifacts from ship tracklines are suppressed. Even if our stacked continuous curvature splines in tension gridding algorithm has been specifically designed to construct DBMs from heterogeneous bathymetric source data, it may be used to compile regular grids from other geoscientific measurements.
NASA Astrophysics Data System (ADS)
Zhang, X.; Liang, S.; Wang, G.
2015-12-01
Incident solar radiation (ISR) over the Earth's surface plays an important role in determining the Earth's climate and environment. Generally, can be obtained from direct measurements, remotely sensed data, or reanalysis and general circulation models (GCMs) data. Each type of product has advantages and limitations: the surface direct measurements provide accurate but sparse spatial coverage, whereas other global products may have large uncertainties. Ground measurements have been normally used for validation and occasionally calibration, but transforming their "true values" spatially to improve the satellite products is still a new and challenging topic. In this study, an improved thin-plate smoothing spline approach is presented to locally "calibrate" the Global LAnd Surface Satellite (GLASS) ISR product using the reconstructed ISR data from surface meteorological measurements. The influences of surface elevation on ISR estimation was also considered in the proposed method. The point-based surface reconstructed ISR was used as the response variable, and the GLASS ISR product and the surface elevation data at the corresponding locations as explanatory variables to train the thin plate spline model. We evaluated the performance of the approach using the cross-validation method at both daily and monthly time scales over China. We also evaluated estimated ISR based on the thin-plate spline method using independent ground measurements at 10 sites from the Coordinated Enhanced Observation Network (CEON). These validation results indicated that the thin plate smoothing spline method can be effectively used for calibrating satellite derived ISR products using ground measurements to achieve better accuracy.
Fatigue crack growth monitoring of idealized gearbox spline component using acoustic emission
NASA Astrophysics Data System (ADS)
Zhang, Lu; Ozevin, Didem; Hardman, William; Kessler, Seth; Timmons, Alan
2016-04-01
The spline component of gearbox structure is a non-redundant element that requires early detection of flaws for preventing catastrophic failures. The acoustic emission (AE) method is a direct way of detecting active flaws; however, the method suffers from the influence of background noise and location/sensor based pattern recognition method. It is important to identify the source mechanism and adapt it to different test conditions and sensors. In this paper, the fatigue crack growth of a notched and flattened gearbox spline component is monitored using the AE method in a laboratory environment. The test sample has the major details of the spline component on a flattened geometry. The AE data is continuously collected together with strain gauges strategically positions on the structure. The fatigue test characteristics are 4 Hz frequency and 0.1 as the ratio of minimum to maximum loading in tensile regime. It is observed that there are significant amount of continuous emissions released from the notch tip due to the formation of plastic deformation and slow crack growth. The frequency spectra of continuous emissions and burst emissions are compared to understand the difference of sudden crack growth and gradual crack growth. The predicted crack growth rate is compared with the AE data using the cumulative AE events at the notch tip. The source mechanism of sudden crack growth is obtained solving the inverse mathematical problem from output signal to input signal. The spline component of gearbox structure is a non-redundant element that requires early detection of flaws for preventing catastrophic failures. In this paper, the fatigue crack growth of a notched and flattened gearbox spline component is monitored using the AE method The AE data is continuously collected together with strain gauges. There are significant amount of continuous emissions released from the notch tip due to the formation of plastic deformation and slow crack growth. The source mechanism of
An Algebraic Spline Model of Molecular Surfaces for Energetic Computations
Zhao, Wenqi; Bajaj, Chandrajit; Xu, Guoliang
2009-01-01
In this paper, we describe a new method to generate a smooth algebraic spline (AS) approximation of the molecular surface (MS) based on an initial coarse triangulation derived from the atomic coordinate information of the biomolecule, resident in the PDB (Protein data bank). Our method first constructs a triangular prism scaffold covering the PDB structure, and then generates a piecewise polynomial F on the Bernstein-Bezier (BB) basis within the scaffold. An ASMS model of the molecular surface is extracted as the zero contours of F which is nearly C1 and has dual implicit and parametric representations. The dual representations allow us easily do the point sampling on the ASMS model and apply it to the accurate estimation of the integrals involved in the electrostatic solvation energy computations. Meanwhile comparing with the trivial piecewise linear surface model, fewer number of sampling points are needed for the ASMS, which effectively reduces the complexity of the energy estimation. PMID:21519111
Color management with a hammer: the B-spline fitter
NASA Astrophysics Data System (ADS)
Bell, Ian E.; Liu, Bonny H. P.
2003-01-01
To paraphrase Abraham Maslow: If the only tool you have is a hammer, every problem looks like a nail. We have a B-spline fitter customized for 3D color data, and many problems in color management can be solved with this tool. Whereas color devices were once modeled with extensive measurement, look-up tables and trilinear interpolation, recent improvements in hardware have made B-spline models an affordable alternative. Such device characterizations require fewer color measurements than piecewise linear models, and have uses beyond simple interpolation. A B-spline fitter, for example, can act as a filter to remove noise from measurements, leaving a model with guaranteed smoothness. Inversion of the device model can then be carried out consistently and efficiently, as the spline model is well behaved and its derivatives easily computed. Spline-based algorithms also exist for gamut mapping, the composition of maps, and the extrapolation of a gamut. Trilinear interpolation---a degree-one spline---can still be used after nonlinear spline smoothing for high-speed evaluation with robust convergence. Using data from several color devices, this paper examines the use of B-splines as a generic tool for modeling devices and mapping one gamut to another, and concludes with applications to high-dimensional and spectral data.
Direct optimization method for reentry trajectory design
NASA Astrophysics Data System (ADS)
Jallade, S.; Huber, P.; Potti, J.; Dutruel-Lecohier, G.
The software package called `Reentry and Atmospheric Transfer Trajectory' (RATT) was developed under ESA contract for the design of atmospheric trajectories. It includes four software TOP (Trajectory OPtimization) programs, which optimize reentry and aeroassisted transfer trajectories. 6FD and 3FD (6 and 3 degrees of freedom Flight Dynamic) are devoted to the simulation of the trajectory. SCA (Sensitivity and Covariance Analysis) performs covariance analysis on a given trajectory with respect to different uncertainties and error sources. TOP provides the optimum guidance law of a three degree of freedom reentry of aeroassisted transfer (AAOT) trajectories. Deorbit and reorbit impulses (if necessary) can be taken into account in the optimization. A wide choice of cost function is available to the user such as the integrated heat flux, or the sum of the velocity impulses, or a linear combination of both of them for trajectory and vehicle design. The crossrange and the downrange can be maximized during reentry trajectory. Path constraints are available on the load factor, the heat flux and the dynamic pressure. Results on these proposed options are presented. TOPPHY is the part of the TOP software corresponding to the definition and the computation of the optimization problemphysics. TOPPHY can interface with several optimizes with dynamic solvers: TOPOP and TROPIC using direct collocation methods and PROMIS using direct multiple shooting method. TOPOP was developed in the frame of this contract, it uses Hermite polynomials for the collocation method and the NPSOL optimizer from the NAG library. Both TROPIC and PROMIS were developed by the DLR (Deutsche Forschungsanstalt fuer Luft und Raumfahrt) and use the SLSQP optimizer. For the dynamic equation resolution, TROPIC uses a collocation method with Splines and PROMIS uses a multiple shooting method with finite differences. The three different optimizers including dynamics were tested on the reentry trajectory of the
Analysis of the boundary conditions of the spline filter
NASA Astrophysics Data System (ADS)
Tong, Mingsi; Zhang, Hao; Ott, Daniel; Zhao, Xuezeng; Song, John
2015-09-01
The spline filter is a standard linear profile filter recommended by ISO/TS 16610-22 (2006). The main advantage of the spline filter is that no end-effects occur as a result of the filter. The ISO standard also provides the tension parameter β =0.625 24 to make the transmission characteristic of the spline filter approximately similar to the Gaussian filter. However, when the tension parameter β is not zero, end-effects appear. To resolve this problem, we analyze 14 different combinations of boundary conditions of the spline filter and propose a set of new boundary conditions in this paper. The new boundary conditions can provide satisfactory end portions of the output form without end-effects for the spline filter while still maintaining the value of β =0.625 24 .
Verdu, G.; Capilla, M.; Talavera, C. F.; Ginestar, D.
2012-07-01
PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)
Metal flowing of involute spline cold roll-beating forming
NASA Astrophysics Data System (ADS)
Cui, Fengkui; Wang, Xiaoqiang; Zhang, Fengshou; Xu, Hongyu; Quan, Jianhui; Li, Yan
2013-09-01
The present research on involute spline cold roll-beating forming is mainly about the principles and motion relations of cold roll-beating, the theory of roller design, and the stress and strain field analysis of cold roll-beating, etc. However, the research on law of metal flow in the forming process of involute spline cold roll-beating is rare. According to the principle of involute spline cold roll-beating, the contact model between the rollers and the spline shaft blank in the process of cold roll-beating forming is established, and the theoretical analysis of metal flow in the cold roll-beating deforming region is proceeded. A finite element model of the spline cold roll-beating process is established, the formation mechanism of the involute spline tooth profile in cold roll-beating forming process is studied, and the node flow tracks of the deformation area are analyzed. The experimental research on the metal flow of cold roll-beating spline is conducted, and the metallographic structure variation, grain characteristics and metal flow line of the different tooth profile area are analyzed. The experimental results show that the particle flow directions of the deformable bodies in cold roll-beating deformation area are determined by the minimum moving resistance. There are five types of metal flow rules of the deforming region in the process of cold roll-beating forming. The characteristics of involute spline cold roll-beating forming are given, and the forming mechanism of involute spline cold roll-beating is revealed. This paper researches the law of metal flow in the forming process of involute spline cold roll-beating, which provides theoretical supports for solving the tooth profile forming quality problem.
Locally Refined Splines Representation for Geospatial Big Data
NASA Astrophysics Data System (ADS)
Dokken, T.; Skytt, V.; Barrowclough, O.
2015-08-01
When viewed from distance, large parts of the topography of landmasses and the bathymetry of the sea and ocean floor can be regarded as a smooth background with local features. Consequently a digital elevation model combining a compact smooth representation of the background with locally added features has the potential of providing a compact and accurate representation for topography and bathymetry. The recent introduction of Locally Refined B-Splines (LR B-splines) allows the granularity of spline representations to be locally adapted to the complexity of the smooth shape approximated. This allows few degrees of freedom to be used in areas with little variation, while adding extra degrees of freedom in areas in need of more modelling flexibility. In the EU fp7 Integrating Project IQmulus we exploit LR B-splines for approximating large point clouds representing bathymetry of the smooth sea and ocean floor. A drastic reduction is demonstrated in the bulk of the data representation compared to the size of input point clouds. The representation is very well suited for exploiting the power of GPUs for visualization as the spline format is transferred to the GPU and the triangulation needed for the visualization is generated on the GPU according to the viewing parameters. The LR B-splines are interoperable with other elevation model representations such as LIDAR data, raster representations and triangulated irregular networks as these can be used as input to the LR B-spline approximation algorithms. Output to these formats can be generated from the LR B-spline applications according to the resolution criteria required. The spline models are well suited for change detection as new sensor data can efficiently be compared to the compact LR B-spline representation.
Quantitative analysis of dynamic contrast-enhanced MR images based on Bayesian P-splines.
Schmid, Volker J; Whitcher, Brandon; Padhani, Anwar R; Yang, Guang-Zhong
2009-06-01
Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is an important tool for detecting subtle kinetic changes in cancerous tissue. Quantitative analysis of DCE-MRI typically involves the convolution of an arterial input function (AIF) with a nonlinear pharmacokinetic model of the contrast agent concentration. Parameters of the kinetic model are biologically meaningful, but the optimization of the nonlinear model has significant computational issues. In practice, convergence of the optimization algorithm is not guaranteed and the accuracy of the model fitting may be compromised. To overcome these problems, this paper proposes a semi-parametric penalized spline smoothing approach, where the AIF is convolved with a set of B-splines to produce a design matrix using locally adaptive smoothing parameters based on Bayesian penalized spline models (P-splines). It has been shown that kinetic parameter estimation can be obtained from the resulting deconvolved response function, which also includes the onset of contrast enhancement. Detailed validation of the method, both with simulated and in vivo data, is provided. PMID:19272996
Cardiac motion tracking with multilevel B-splines and SinMod from tagged MRI
NASA Astrophysics Data System (ADS)
Wang, Hui; Amini, Amir A.
2011-03-01
Cardiac motion analysis can play an important role in cardiac disease diagnosis. Tagged magnetic resonance imaging (MRI) has the ability to directly and non-invasively alter tissue magnetization and produce tags on the deforming tissue. This paper proposes an approach to analysis of tagged MR images using a multilevel B-splines fitting model incorporating phase information. The novelty of the proposed technique is that phase information is extracted from SinMod.1 By using real tag intersections extracted directly from tagged MR image data and virtual tag intersections extracted from phase information, both considered to be scattered data, multilevel B-spline fitting can result in accurate displacement motion fields. The B-spline approximation which also serves to remove noise in the displacement measurements is performed without specifying control point locations explicitly and is very fast. Dense virtual tag intersections based on SinMod were created and incorporated into the multilevel B-spline fitting process. Experimental results on simulated data from the 13- parameter kinematic model of Arts et al.2 and in vivo canine data demonstrate further improvement in accuracy and effectiveness of the proposed method.
High-order boundary layer analysis using B-splines on hybrid unstructured meshes
NASA Astrophysics Data System (ADS)
Zhang, Alvin; Sahni, Onkar
2015-11-01
Boundary layer flows are present in many engineering applications. In such flows, boundary layers span only a fraction of the characteristic length of the problem near the walls and possess large velocity gradients in the wall normal direction. This mandates use of a layered and graded mesh with a dense anisotropic h-resolution near the walls in order to accurately resolve the boundary layer. To account for complex geometries, a hybrid unstructured mesh approach is adopted. In this approach, the mesh is decomposed into wall normal and wall parallel directions. An alternative to an anisotropic h-resolution is to use a similar setting for both h- and p-resolution possibly with greater smoothness. For this purpose a mixed B-spline basis becomes attractive, where B-splines are used in the wall-normal direction and a C0 basis in the wall-parallel directions as well as the fully unstructured region of the mesh. A mixed B-spline basis offers several advantages over the traditional C0 basis utilized in finite element methods, which include greater accuracy per degree-of-freedom, ease of p-refinement as well as potential for k-refinement. In this study we demonstrate that the mixed B-spline basis, defined for the hybrid unstructured mesh, accurately models the boundary layer behavior.
A mixed basis density functional approach for low dimensional systems with B-splines
NASA Astrophysics Data System (ADS)
Ren, Chung-Yuan; Hsue, Chen-Shiung; Chang, Yia-Chung
2015-03-01
A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction. B-splines have the following advantages: (1) the associated matrix elements are sparse, (2) B-splines possess a superior treatment of derivatives, (3) B-splines are not associated with atomic positions when the geometry structure is optimized, making the geometry optimization easy to implement. With this mixed basis set we can directly calculate the total energy of the system instead of using the conventional supercell model with a slab sandwiched between vacuum regions. A generalized Lanczos-Krylov iterative method is implemented for the diagonalization of the Hamiltonian matrix. To demonstrate the present approach, we apply it to study the C(001)-(2×1) surface with the norm-conserving pseudopotential, the n-type δ-doped graphene, and graphene nanoribbon with Vanderbilt's ultra-soft pseudopotentials. All the resulting electronic structures were found to be in good agreement with those obtained by the VASP code, but with a reduced number of basis.
Efficient Shape Priors for Spline-Based Snakes.
Delgado-Gonzalo, Ricard; Schmitter, Daniel; Uhlmann, Virginie; Unser, Michael
2015-11-01
Parametric active contours are an attractive approach for image segmentation, thanks to their computational efficiency. They are driven by application-dependent energies that reflect the prior knowledge on the object to be segmented. We propose an energy involving shape priors acting in a regularization-like manner. Thereby, the shape of the snake is orthogonally projected onto the space that spans the affine transformations of a given shape prior. The formulation of the curves is continuous, which provides computational benefits when compared with landmark-based (discrete) methods. We show that this approach improves the robustness and quality of spline-based segmentation algorithms, while its computational overhead is negligible. An interactive and ready-to-use implementation of the proposed algorithm is available and was successfully tested on real data in order to segment Drosophila flies and yeast cells in microscopic images. PMID:26353353
Developing and Evaluating a Web-Based Collocation Retrieval Tool for EFL Students and Teachers
ERIC Educational Resources Information Center
Chen, Hao-Jan Howard
2011-01-01
The development of adequate collocational knowledge is important for foreign language learners; nonetheless, learners often have difficulties in producing proper collocations in the target language. Among the various ways of learning collocations, the DDL (data-driven learning) approach encourages independent learning of collocations and allows…
The Use of Verb Noun Collocations in Writing Stories among Iranian EFL Learners
ERIC Educational Resources Information Center
Bazzaz, Fatemeh Ebrahimi; Samad, Arshad Abd
2011-01-01
An important aspect of native speakers' communicative competence is collocational competence which involves knowing which words usually come together and which do not. This paper investigates the possible relationship between knowledge of collocations and the use of verb noun collocation in writing stories because collocational knowledge…
Developing and Evaluating a Chinese Collocation Retrieval Tool for CFL Students and Teachers
ERIC Educational Resources Information Center
Chen, Howard Hao-Jan; Wu, Jian-Cheng; Yang, Christine Ting-Yu; Pan, Iting
2016-01-01
The development of collocational knowledge is important for foreign language learners; unfortunately, learners often have difficulties producing proper collocations in the target language. Among the various ways of collocation learning, the DDL (data-driven learning) approach encourages the independent learning of collocations and allows learners…
The Learning Burden of Collocations: The Role of Interlexical and Intralexical Factors
ERIC Educational Resources Information Center
Peters, Elke
2016-01-01
This study investigates whether congruency (+/- literal translation equivalent), collocate-node relationship (adjective-noun, verb-noun, phrasal-verb-noun collocations), and word length influence the learning burden of EFL learners' learning collocations at the initial stage of form-meaning mapping. Eighteen collocations were selected on the basis…
A space-time spectral collocation algorithm for the variable order fractional wave equation.
Bhrawy, A H; Doha, E H; Alzaidy, J F; Abdelkawy, M A
2016-01-01
The variable order wave equation plays a major role in acoustics, electromagnetics, and fluid dynamics. In this paper, we consider the space-time variable order fractional wave equation with variable coefficients. We propose an effective numerical method for solving the aforementioned problem in a bounded domain. The shifted Jacobi polynomials are used as basis functions, and the variable-order fractional derivative is described in the Caputo sense. The proposed method is a combination of shifted Jacobi-Gauss-Lobatto collocation scheme for the spatial discretization and the shifted Jacobi-Gauss-Radau collocation scheme for temporal discretization. The aforementioned problem is then reduced to a problem consists of a system of easily solvable algebraic equations. Finally, numerical examples are presented to show the effectiveness of the proposed numerical method. PMID:27536504
Nonlinear registration using B-spline feature approximation and image similarity
NASA Astrophysics Data System (ADS)
Kim, June-Sic; Kim, Jae Seok; Kim, In Young; Kim, Sun Il
2001-07-01
The warping methods are broadly classified into the image-matching method based on similar pixel intensity distribution and the feature-matching method using distinct anatomical feature. Feature based methods may fail to match local variation of two images. However, the method globally matches features well. False matches corresponding to local minima of the underlying energy functions can be obtained through the similarity based methods. To avoid local minima problem, we proposes non-linear deformable registration method utilizing global information of feature matching and the local information of image matching. To define the feature, gray matter and white matter of brain tissue are segmented by Fuzzy C-Mean (FCM) algorithm. B-spline approximation technique is used for feature matching. We use a multi-resolution B-spline approximation method which modifies multilevel B-spline interpolation method. It locally changes the resolution of the control lattice in proportion to the distance between features of two images. Mutual information is used for similarity measure. The deformation fields are locally refined until maximize the similarity. In two 3D T1 weighted MRI test, this method maintained the accuracy by conventional image matching methods without the local minimum problem.
Usability Study of Two Collocated Prototype System Displays
NASA Technical Reports Server (NTRS)
Trujillo, Anna C.
2007-01-01
Currently, most of the displays in control rooms can be categorized as status screens, alerts/procedures screens (or paper), or control screens (where the state of a component is changed by the operator). The primary focus of this line of research is to determine which pieces of information (status, alerts/procedures, and control) should be collocated. Two collocated displays were tested for ease of understanding in an automated desktop survey. This usability study was conducted as a prelude to a larger human-in-the-loop experiment in order to verify that the 2 new collocated displays were easy to learn and usable. The results indicate that while the DC display was preferred and yielded better performance than the MDO display, both collocated displays can be easily learned and used.
Spline-Locking Screw Fastening Strategy (SLSFS)
NASA Technical Reports Server (NTRS)
Vranish, John M.
1991-01-01
A fastener was developed by NASA Goddard for efficiently performing assembly, maintenance, and equipment replacement functions in space using either robotic or astronaut means. This fastener, the 'Spline Locking Screw' (SLS) would also have significant commercial value in advanced manufacturing. Commercial (or DoD) products could be manufactured in such a way that their prime subassemblies would be assembled using SLS fasteners. This would permit machines and robots to disconnect and replace these modules/parts with ease, greatly reducing life cycle costs of the products and greatly enhancing the quality, timeliness, and consistency of repairs, upgrades, and remanufacturing. The operation of the basic SLS fastener is detailed, including hardware and test results. Its extension into a comprehensive fastening strategy for NASA use in space is also outlined. Following this, the discussion turns toward potential commercial and government applications and the potential market significance of same.
Spline-locking screw fastening strategy
NASA Technical Reports Server (NTRS)
Vranish, John M.
1992-01-01
A fastener was developed by NASA Goddard for efficiently performing assembly, maintenance, and equipment replacement functions in space using either robotics or astronaut means. This fastener, the 'Spline Locking Screw' (SLS) would also have significant commercial value in advanced space manufacturing. Commercial (or DoD) products could be manufactured in such a way that their prime subassemblies would be assembled using SLS fasteners. This would permit machines and robots to disconnect and replace these modules/parts with ease, greatly reducing life cycle costs of the products and greatly enhancing the quality, timeliness, and consistency of repairs, upgrades, and remanufacturing. The operation of the basic SLS fastener is detailed, including hardware and test results. Its extension into a comprehensive fastening strategy for NASA use in space is also outlined. Following this, the discussion turns toward potential commercial and government applications and the potential market significance of same.
The spline probability hypothesis density filter
NASA Astrophysics Data System (ADS)
Sithiravel, Rajiv; Tharmarasa, Ratnasingham; McDonald, Mike; Pelletier, Michel; Kirubarajan, Thiagalingam
2012-06-01
The Probability Hypothesis Density Filter (PHD) is a multitarget tracker for recursively estimating the number of targets and their state vectors from a set of observations. The PHD filter is capable of working well in scenarios with false alarms and missed detections. Two distinct PHD filter implementations are available in the literature: the Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) and the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filters. The SMC-PHD filter uses particles to provide target state estimates, which can lead to a high computational load, whereas the GM-PHD filter does not use particles, but restricts to linear Gaussian mixture models. The SMC-PHD filter technique provides only weighted samples at discrete points in the state space instead of a continuous estimate of the probability density function of the system state and thus suffers from the well-known degeneracy problem. This paper proposes a B-Spline based Probability Hypothesis Density (S-PHD) filter, which has the capability to model any arbitrary probability density function. The resulting algorithm can handle linear, non-linear, Gaussian, and non-Gaussian models and the S-PHD filter can also provide continuous estimates of the probability density function of the system state. In addition, by moving the knots dynamically, the S-PHD filter ensures that the splines cover only the region where the probability of the system state is significant, hence the high efficiency of the S-PHD filter is maintained at all times. Also, unlike the SMC-PHD filter, the S-PHD filter is immune to the degeneracy problem due to its continuous nature. The S-PHD filter derivations and simulations are provided in this paper.
NASA Technical Reports Server (NTRS)
Jarosch, H. S.
1982-01-01
A method based on the use of constrained spline fits is used to overcome the difficulties arising when body-wave data in the form of T-delta are reduced to the tau-p form in the presence of cusps. In comparison with unconstrained spline fits, the method proposed here tends to produce much smoother models which lie approximately in the middle of the bounds produced by the extremal method. The method is noniterative and, therefore, computationally efficient. The method is applied to the lunar seismic data, where at least one triplication is presumed to occur in the P-wave travel-time curve. It is shown, however, that because of an insufficient number of data points for events close to the antipode of the center of the lunar network, the present analysis is not accurate enough to resolve the problem of a possible lunar core.
Statistical modelling of collocation uncertainty in atmospheric thermodynamic profiles
NASA Astrophysics Data System (ADS)
Fassò, A.; Ignaccolo, R.; Madonna, F.; Demoz, B. B.; Franco-Villoria, M.
2014-06-01
The quantification of measurement uncertainty of atmospheric parameters is a key factor in assessing the uncertainty of global change estimates given by numerical prediction models. One of the critical contributions to the uncertainty budget is related to the collocation mismatch in space and time among observations made at different locations. This is particularly important for vertical atmospheric profiles obtained by radiosondes or lidar. In this paper we propose a statistical modelling approach capable of explaining the relationship between collocation uncertainty and a set of environmental factors, height and distance between imperfectly collocated trajectories. The new statistical approach is based on the heteroskedastic functional regression (HFR) model which extends the standard functional regression approach and allows a natural definition of uncertainty profiles. Along this line, a five-fold decomposition of the total collocation uncertainty is proposed, giving both a profile budget and an integrated column budget. HFR is a data-driven approach valid for any atmospheric parameter, which can be assumed smooth. It is illustrated here by means of the collocation uncertainty analysis of relative humidity from two stations involved in the GCOS reference upper-air network (GRUAN). In this case, 85% of the total collocation uncertainty is ascribed to reducible environmental error, 11% to irreducible environmental error, 3.4% to adjustable bias, 0.1% to sampling error and 0.2% to measurement error.
Subcell resolution in simplex stochastic collocation for spatial discontinuities
NASA Astrophysics Data System (ADS)
Witteveen, Jeroen A. S.; Iaccarino, Gianluca
2013-10-01
Subcell resolution has been used in the Finite Volume Method (FVM) to obtain accurate approximations of discontinuities in the physical space. Stochastic methods are usually based on local adaptivity for resolving discontinuities in the stochastic dimensions. However, the adaptive refinement in the probability space is ineffective in the non-intrusive uncertainty quantification framework, if the stochastic discontinuity is caused by a discontinuity in the physical space with a random location. The dependence of the discontinuity location in the probability space on the spatial coordinates then results in a staircase approximation of the statistics, which leads to first-order error convergence and an underprediction of the maximum standard deviation. To avoid these problems, we introduce subcell resolution into the Simplex Stochastic Collocation (SSC) method for obtaining a truly discontinuous representation of random spatial discontinuities in the interior of the cells discretizing the probability space. The presented SSC-SR method is based on resolving the discontinuity location in the probability space explicitly as function of the spatial coordinates and extending the stochastic response surface approximations up to the predicted discontinuity location. The applications to a linear advection problem, the inviscid Burgers' equation, a shock tube problem, and the transonic flow over the RAE 2822 airfoil show that SSC-SR resolves random spatial discontinuities with multiple stochastic and spatial dimensions accurately using a minimal number of samples.
Subcell resolution in simplex stochastic collocation for spatial discontinuities
Witteveen, Jeroen A.S.; Iaccarino, Gianluca
2013-10-15
Subcell resolution has been used in the Finite Volume Method (FVM) to obtain accurate approximations of discontinuities in the physical space. Stochastic methods are usually based on local adaptivity for resolving discontinuities in the stochastic dimensions. However, the adaptive refinement in the probability space is ineffective in the non-intrusive uncertainty quantification framework, if the stochastic discontinuity is caused by a discontinuity in the physical space with a random location. The dependence of the discontinuity location in the probability space on the spatial coordinates then results in a staircase approximation of the statistics, which leads to first-order error convergence and an underprediction of the maximum standard deviation. To avoid these problems, we introduce subcell resolution into the Simplex Stochastic Collocation (SSC) method for obtaining a truly discontinuous representation of random spatial discontinuities in the interior of the cells discretizing the probability space. The presented SSC–SR method is based on resolving the discontinuity location in the probability space explicitly as function of the spatial coordinates and extending the stochastic response surface approximations up to the predicted discontinuity location. The applications to a linear advection problem, the inviscid Burgers’ equation, a shock tube problem, and the transonic flow over the RAE 2822 airfoil show that SSC–SR resolves random spatial discontinuities with multiple stochastic and spatial dimensions accurately using a minimal number of samples.
Single-grid spectral collocation for the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Bernardi, Christine; Canuto, Claudio; Maday, Yvon; Metivet, Brigitte
1988-01-01
The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results.
A Simple and Fast Spline Filtering Algorithm for Surface Metrology
Zhang, Hao; Ott, Daniel; Song, John; Tong, Mingsi; Chu, Wei
2015-01-01
Spline filters and their corresponding robust filters are commonly used filters recommended in ISO (the International Organization for Standardization) standards for surface evaluation. Generally, these linear and non-linear spline filters, composed of symmetric, positive-definite matrices, are solved in an iterative fashion based on a Cholesky decomposition. They have been demonstrated to be relatively efficient, but complicated and inconvenient to implement. A new spline-filter algorithm is proposed by means of the discrete cosine transform or the discrete Fourier transform. The algorithm is conceptually simple and very convenient to implement. PMID:26958443
An Examination of New Paradigms for Spline Approximations.
Witzgall, Christoph; Gilsinn, David E; McClain, Marjorie A
2006-01-01
Lavery splines are examined in the univariate and bivariate cases. In both instances relaxation based algorithms for approximate calculation of Lavery splines are proposed. Following previous work Gilsinn, et al. [7] addressing the bivariate case, a rotationally invariant functional is assumed. The version of bivariate splines proposed in this paper also aims at irregularly spaced data and uses Hseih-Clough-Tocher elements based on the triangulated irregular network (TIN) concept. In this paper, the univariate case, however, is investigated in greater detail so as to further the understanding of the bivariate case. PMID:27274917
The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions
NASA Technical Reports Server (NTRS)
Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan
1995-01-01
The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.
Recent advances in (soil moisture) triple collocation analysis
NASA Astrophysics Data System (ADS)
Gruber, A.; Su, C.-H.; Zwieback, S.; Crow, W.; Dorigo, W.; Wagner, W.
2016-03-01
To date, triple collocation (TC) analysis is one of the most important methods for the global-scale evaluation of remotely sensed soil moisture data sets. In this study we review existing implementations of soil moisture TC analysis as well as investigations of the assumptions underlying the method. Different notations that are used to formulate the TC problem are shown to be mathematically identical. While many studies have investigated issues related to possible violations of the underlying assumptions, only few TC modifications have been proposed to mitigate the impact of these violations. Moreover, assumptions, which are often understood as a limitation that is unique to TC analysis are shown to be common also to other conventional performance metrics. Noteworthy advances in TC analysis have been made in the way error estimates are being presented by moving from the investigation of absolute error variance estimates to the investigation of signal-to-noise ratio (SNR) metrics. Here we review existing error presentations and propose the combined investigation of the SNR (expressed in logarithmic units), the unscaled error variances, and the soil moisture sensitivities of the data sets as an optimal strategy for the evaluation of remotely-sensed soil moisture data sets.
Detail view of redwood spline joinery of woodframe section against ...
Detail view of redwood spline joinery of wood-frame section against adobe addition (measuring tape denotes plumb line from center of top board) - First Theatre in California, Southwest corner of Pacific & Scott Streets, Monterey, Monterey County, CA
Modeling terminal ballistics using blending-type spline surfaces
NASA Astrophysics Data System (ADS)
Pedersen, Aleksander; Bratlie, Jostein; Dalmo, Rune
2014-12-01
We explore using GERBS, a blending-type spline construction, to represent deform able thin-plates and model terminal ballistics. Strategies to construct geometry for different scenarios of terminal ballistics are proposed.
Construction of spline functions in spreadsheets to smooth experimental data
Technology Transfer Automated Retrieval System (TEKTRAN)
A previous manuscript detailed how spreadsheet software can be programmed to smooth experimental data via cubic splines. This addendum corrects a few errors in the previous manuscript and provides additional necessary programming steps. ...
Positivity preserving using GC1 rational quartic spline
NASA Astrophysics Data System (ADS)
Abdul Karim, Samsul Ariffin; Pang, Kong Voon; Hashim, Ishak
2013-04-01
In this paper, we study the shape preserving interpolation for positive data using a rational quartic spline which has a quartic numerator and linear denominator. The rational quartic splines have GC1 continuity at join knots. Simple data dependent constraints are derived on the shape parameters in the description of the rational interpolant. Numerical comparison between the proposed scheme and the existing scheme is discussed. The results indicate that the proposed scheme works well for all tested data sets.
Collocation and Pattern Recognition Effects on System Failure Remediation
NASA Technical Reports Server (NTRS)
Trujillo, Anna C.; Press, Hayes N.
2007-01-01
Previous research found that operators prefer to have status, alerts, and controls located on the same screen. Unfortunately, that research was done with displays that were not designed specifically for collocation. In this experiment, twelve subjects evaluated two displays specifically designed for collocating system information against a baseline that consisted of dial status displays, a separate alert area, and a controls panel. These displays differed in the amount of collocation, pattern matching, and parameter movement compared to display size. During the data runs, subjects kept a randomly moving target centered on a display using a left-handed joystick and they scanned system displays to find a problem in order to correct it using the provided checklist. Results indicate that large parameter movement aided detection and then pattern recognition is needed for diagnosis but the collocated displays centralized all the information subjects needed, which reduced workload. Therefore, the collocated display with large parameter movement may be an acceptable display after familiarization because of the possible pattern recognition developed with training and its use.
Stable Local Volatility Calibration Using Kernel Splines
NASA Astrophysics Data System (ADS)
Coleman, Thomas F.; Li, Yuying; Wang, Cheng
2010-09-01
We propose an optimization formulation using L1 norm to ensure accuracy and stability in calibrating a local volatility function for option pricing. Using a regularization parameter, the proposed objective function balances the calibration accuracy with the model complexity. Motivated by the support vector machine learning, the unknown local volatility function is represented by a kernel function generating splines and the model complexity is controlled by minimizing the 1-norm of the kernel coefficient vector. In the context of the support vector regression for function estimation based on a finite set of observations, this corresponds to minimizing the number of support vectors for predictability. We illustrate the ability of the proposed approach to reconstruct the local volatility function in a synthetic market. In addition, based on S&P 500 market index option data, we demonstrate that the calibrated local volatility surface is simple and resembles the observed implied volatility surface in shape. Stability is illustrated by calibrating local volatility functions using market option data from different dates.
Statistical modelling of collocation uncertainty in atmospheric thermodynamic profiles
NASA Astrophysics Data System (ADS)
Fassò, A.; Ignaccolo, R.; Madonna, F.; Demoz, B. B.
2013-08-01
The uncertainty of important atmospheric parameters is a key factor for assessing the uncertainty of global change estimates given by numerical prediction models. One of the critical points of the uncertainty budget is related to the collocation mismatch in space and time among different observations. This is particularly important for vertical atmospheric profiles obtained by radiosondes or LIDAR. In this paper we consider a statistical modelling approach to understand at which extent collocation uncertainty is related to environmental factors, height and distance between the trajectories. To do this we introduce a new statistical approach, based on the heteroskedastic functional regression (HFR) model which extends the standard functional regression approach and allows us a natural definition of uncertainty profiles. Moreover, using this modelling approach, a five-folded uncertainty decomposition is proposed. Eventually, the HFR approach is illustrated by the collocation uncertainty analysis of relative humidity from two stations involved in GCOS reference upper-air network (GRUAN).
NASA Astrophysics Data System (ADS)
Gu, Renliang; Dogandžić, Aleksandar
2015-03-01
We develop a sparse image reconstruction method for polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. To obtain a parsimonious measurement model parameterization, we first rewrite the measurement equation using our mass-attenuation parameterization, which has the Laplace integral form. The unknown mass-attenuation spectrum is expanded into basis functions using a B-spline basis of order one. We develop a block coordinate-descent algorithm for constrained minimization of a penalized negative log-likelihood function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and sparsity of the density map image in the wavelet domain. This algorithm alternates between a Nesterov's proximal-gradient step for estimating the density map image and an active-set step for estimating the incident spectrum parameters. Numerical simulations demonstrate the performance of the proposed scheme.
Gu, Renliang E-mail: ald@iastate.edu; Dogandžić, Aleksandar E-mail: ald@iastate.edu
2015-03-31
We develop a sparse image reconstruction method for polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. To obtain a parsimonious measurement model parameterization, we first rewrite the measurement equation using our mass-attenuation parameterization, which has the Laplace integral form. The unknown mass-attenuation spectrum is expanded into basis functions using a B-spline basis of order one. We develop a block coordinate-descent algorithm for constrained minimization of a penalized negative log-likelihood function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and sparsity of the density map image in the wavelet domain. This algorithm alternates between a Nesterov’s proximal-gradient step for estimating the density map image and an active-set step for estimating the incident spectrum parameters. Numerical simulations demonstrate the performance of the proposed scheme.
Noise correction on LANDSAT images using a spline-like algorithm
NASA Technical Reports Server (NTRS)
Vijaykumar, N. L. (Principal Investigator); Dias, L. A. V.
1985-01-01
Many applications using LANDSAT images face a dilemma: the user needs a certain scene (for example, a flooded region), but that particular image may present interference or noise in form of horizontal stripes. During automatic analysis, this interference or noise may cause false readings of the region of interest. In order to minimize this interference or noise, many solutions are used, for instane, that of using the average (simple or weighted) values of the neighboring vertical points. In the case of high interference (more than one adjacent line lost) the method of averages may not suit the desired purpose. The solution proposed is to use a spline-like algorithm (weighted splines). This type of interpolation is simple to be computer implemented, fast, uses only four points in each interval, and eliminates the necessity of solving a linear equation system. In the normal mode of operation, the first and second derivatives of the solution function are continuous and determined by data points, as in cubic splines. It is possible, however, to impose the values of the first derivatives, in order to account for shapr boundaries, without increasing the computational effort. Some examples using the proposed method are also shown.
A mixed basis density functional approach for one-dimensional systems with B-splines
NASA Astrophysics Data System (ADS)
Ren, Chung-Yuan; Chang, Yia-Chung; Hsue, Chen-Shiung
2016-05-01
A mixed basis approach based on density functional theory is extended to one-dimensional (1D) systems. The basis functions here are taken to be the localized B-splines for the two finite non-periodic dimensions and the plane waves for the third periodic direction. This approach will significantly reduce the number of the basis and therefore is computationally efficient for the diagonalization of the Kohn-Sham Hamiltonian. For 1D systems, B-spline polynomials are particularly useful and efficient in two-dimensional spatial integrations involved in the calculations because of their absolute localization. Moreover, B-splines are not associated with atomic positions when the geometry structure is optimized, making the geometry optimization easy to implement. With such a basis set we can directly calculate the total energy of the isolated system instead of using the conventional supercell model with artificial vacuum regions among the replicas along the two non-periodic directions. The spurious Coulomb interaction between the charged defect and its repeated images by the supercell approach for charged systems can also be avoided. A rigorous formalism for the long-range Coulomb potential of both neutral and charged 1D systems under the mixed basis scheme will be derived. To test the present method, we apply it to study the infinite carbon-dimer chain, graphene nanoribbon, carbon nanotube and positively-charged carbon-dimer chain. The resulting electronic structures are presented and discussed in detail.
Generalized b-spline subdivision-surface wavelets and lossless compression
Bertram, M; Duchaineau, M A; Hamann, B; Joy, K I
1999-11-24
We present a new construction of wavelets on arbitrary two-manifold topology for geometry compression. The constructed wavelets generalize symmetric tensor product wavelets with associated B-spline scaling functions to irregular polygonal base mesh domains. The wavelets and scaling functions are tensor products almost everywhere, except in the neighborhoods of some extraordinary points (points of valence unequal four) in the base mesh that defines the topology. The compression of arbitrary polygonal meshes representing isosurfaces of scalar-valued trivariate functions is a primary application. The main contribution of this paper is the generalization of lifted symmetric tensor product B-spline wavelets to two-manifold geometries. Surfaces composed of B-spline patches can easily be converted to this scheme. We present a lossless compression method for geometries with or without associated functions like color, texture, or normals. The new wavelet transform is highly efficient and can represent surfaces at any level of resolution with high degrees of continuity, except at a finite number of extraordinary points in the base mesh. In the neighborhoods of these points detail can be added to the surface to approximate any degree of continuity.
Algebraic grid generation using tensor product B-splines. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Saunders, B. V.
1985-01-01
Finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. The development of an algorithm which produces such a grid when given the boundary description. Topological considerations in structuring the grid generation mapping are discussed. The concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid is examined. The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the splines produce Schoenberg's variation diminishing spline approximation to the boundary. Interior coefficients are initially chosen to give a variation diminishing approximation to the transfinite bilinear interpolant of the function mapping the boundary of the unit square onto the boundary grid. The practicality of optimizing the grid by minimizing a functional involving the Jacobian of the grid generation mapping at each interior grid point and the dot product of vectors tangent to the grid lines is investigated. Grids generated by using the algorithm are presented.
User's guide for Wilson-Fowler spline software: SPLPKG, WFCMPR, WFAPPX - CADCAM-010
Fletcher, S.K.
1985-02-01
The Wilson-Fowler spline is widely used in computer aided manufacturing, but is not available in all commercial CAD/CAM systems. These three programs provide a capability for generating, comparing, and approximating Wilson-Fowler splines. SPLPKG generates a spline passing through given nodes, and computes a piecewise linear approximation to the spline. WFCMPR computes the difference between two splines with common nodes. WFAPPX computes the difference between a spline and a piecewise linear curve. The programs are in Fortran 77 and are machine independent.
Growth curve analysis for plasma profiles using smoothing splines
Imre, K.
1993-05-01
We are developing a profile analysis code for the statistical estimation of the parametric dependencies of the temperature and density profiles in tokamaks. Our code uses advanced statistical techniques to determine the optimal fit, i.e. the fit which minimized the predictive error. For a forty TFTR Ohmic profile dataset, our preliminary results indicate that the profile shape depends almost exclusively on q[sub a][prime] but that the shape dependencies are not Gaussian. We are now comparing various shape models on the TFTR data. In the first six months, we have completed the core modules of the code, including a B-spline package for variable knot locations, a data-based method to determine the optimal smoothing parameters, self-consistent estimation of the bias errors, and adaptive fitting near the plasma edge. Visualization graphics already include three dimensional surface plots, and discharge by discharge plots of the predicted curves with error bars together with the actual measurements values, and plots of the basis functions with errors.
Collocational Strategies of Arab Learners of English: A Study in Lexical Semantics.
ERIC Educational Resources Information Center
Muhammad, Raji Zughoul; Abdul-Fattah, Hussein S.
Arab learners of English encounter a serious problem with collocational sequences. The present study purports to determine the extent to which university English language majors can use English collocations properly. A two-form translation test of 16 Arabic collocations was administered to both graduate and undergraduate students of English. The…
L2 Learner Production and Processing of Collocation: A Multi-Study Perspective
ERIC Educational Resources Information Center
Siyanova, Anna; Schmitt, Norbert
2008-01-01
This article presents a series of studies focusing on L2 production and processing of adjective-noun collocations (e.g., "social services"). In Study 1, 810 adjective-noun collocations were extracted from 31 essays written by Russian learners of English. About half of these collocations appeared frequently in the British National Corpus (BNC);…
An Exploratory Study of Collocational Use by ESL Students--A Task Based Approach
ERIC Educational Resources Information Center
Fan, May
2009-01-01
Collocation is an aspect of language generally considered arbitrary by nature and problematic to L2 learners who need collocational competence for effective communication. This study attempts, from the perspective of L2 learners, to have a deeper understanding of collocational use and some of the problems involved, by adopting a task based…
Redefining Creativity--Analyzing Definitions, Collocations, and Consequences
ERIC Educational Resources Information Center
Kampylis, Panagiotis G.; Valtanen, Juri
2010-01-01
How holistically is human creativity defined, investigated, and understood? Until recently, most scientific research on creativity has focused on its positive side. However, creativity might not only be a desirable resource but also be a potential threat. In order to redefine creativity we need to analyze and understand definitions, collocations,…
Beyond triple collocation: Applications to satellite soil moisture
Technology Transfer Automated Retrieval System (TEKTRAN)
Triple collocation is now routinely used to resolve the exact (linear) relationships between multiple measurements and/or representations of a geophysical variable that are subject to errors. It has been utilized in the context of calibration, rescaling and error characterisation to allow comparison...
The Effects of Vocabulary Learning on Collocation and Meaning
ERIC Educational Resources Information Center
Webb, Stuart; Kagimoto, Eve
2009-01-01
This study investigates the effects of receptive and productive vocabulary tasks on learning collocation and meaning. Japanese English as a foreign language students learned target words in three glossed sentences and in a cloze task. To determine the effects of the treatments, four tests were used to measure receptive and productive knowledge of…
Beyond Single Words: The Most Frequent Collocations in Spoken English
ERIC Educational Resources Information Center
Shin, Dongkwang; Nation, Paul
2008-01-01
This study presents a list of the highest frequency collocations of spoken English based on carefully applied criteria. In the literature, more than forty terms have been used for designating multi-word units, which are generally not well defined. To avoid this confusion, six criteria are strictly applied. The ten million word BNC spoken section…
Acoustic ranging of small arms fire using a single sensor node collocated with the target.
Lo, Kam W; Ferguson, Brian G
2015-06-01
A ballistic model-based method, which builds upon previous work by Lo and Ferguson [J. Acoust. Soc. Am. 132, 2997-3017 (2012)], is described for ranging small arms fire using a single acoustic sensor node collocated with the target, without a priori knowledge of the muzzle speed and ballistic constant of the bullet except that they belong to a known two-dimensional parameter space. The method requires measurements of the differential time of arrival and differential angle of arrival of the muzzle blast and ballistic shock wave at the sensor node. Its performance is evaluated using both simulated and real data. PMID:26093450
Collocation with nonlinear programming for two-sided flight path optimization
NASA Astrophysics Data System (ADS)
Horie, Kazuhiro
This research successfully develops a new numerical method for the problem of two-sided flight path optimization, that is, a method capable of finding trajectories satisfying the necessary condition of an open-loop representation of a saddle-point trajectory. The method of direct collocation with nonlinear programming is extended to find the solution of a zerosum two-person differential game by incorporating the analytical optimality condition for one player into the system equations. The new method is named semi-direct collocation with nonlinear programming (semi-DCNLP). We apply the new method to a variety of problems of increasing complexity; the dolichobrachistochrone, a problem of ballistic interception, the homicidal chauffeur problem and minimum-time spacecraft interception for optimally evasive target, and thus verify that the method is capable of identifying saddle-point trajectories. While the method is quite robust, ambitious problems require a reasonable initial guess of the discretized solution from which the optimizer may converge. A method for generating a good initial guess, requiring no a priori information about the solution, is developed using genetic algorithms. The semi-DCNLP, in combination with the genetic algorithm-based preprocessor, is then used to solve a very complicated pursuit-evasion problem; optimal air combat for realistic fighter aircraft models in three dimensions. Characteristics of the optimal air combat maneuvers for both aircraft are identified for many different initial conditions.
AnL1 smoothing spline algorithm with cross validation
NASA Astrophysics Data System (ADS)
Bosworth, Ken W.; Lall, Upmanu
1993-08-01
We propose an algorithm for the computation ofL1 (LAD) smoothing splines in the spacesWM(D), with . We assume one is given data of the formyiD(f(ti) +ɛi, iD1,...,N with {itti}iD1N ⊂D, theɛi are errors withE(ɛi)D0, andf is assumed to be inWM. The LAD smoothing spline, for fixed smoothing parameterλ?;0, is defined as the solution,sλ, of the optimization problem (1/N)∑iD1N yi-g(ti +λJM(g), whereJM(g) is the seminorm consisting of the sum of the squaredL2 norms of theMth partial derivatives ofg. Such an LAD smoothing spline,sλ, would be expected to give robust smoothed estimates off in situations where theɛi are from a distribution with heavy tails. The solution to such a problem is a "thin plate spline" of known form. An algorithm for computingsλ is given which is based on considering a sequence of quadratic programming problems whose structure is guided by the optimality conditions for the above convex minimization problem, and which are solved readily, if a good initial point is available. The "data driven" selection of the smoothing parameter is achieved by minimizing aCV(λ) score of the form .The combined LAD-CV smoothing spline algorithm is a continuation scheme in λ↘0 taken on the above SQPs parametrized inλ, with the optimal smoothing parameter taken to be that value ofλ at which theCV(λ) score first begins to increase. The feasibility of constructing the LAD-CV smoothing spline is illustrated by an application to a problem in environment data interpretation.
ERIC Educational Resources Information Center
Yamashita, Junko; Jiang, Nan
2010-01-01
This study investigated first language (L1) influence on the acquisition of second language (L2) collocations using a framework based on Kroll and Stewart (1994) and Jiang (2000), by comparing the performance on a phrase-acceptability judgment task among native speakers of English, Japanese English as a second language (ESL) users, and Japanese…
How to fly an aircraft with control theory and splines
NASA Technical Reports Server (NTRS)
Karlsson, Anders
1994-01-01
When trying to fly an aircraft as smoothly as possible it is a good idea to use the derivatives of the pilot command instead of using the actual control. This idea was implemented with splines and control theory, in a system that tries to model an aircraft. Computer calculations in Matlab show that it is impossible to receive enough smooth control signals by this way. This is due to the fact that the splines not only try to approximate the test function, but also its derivatives. A perfect traction is received but we have to pay in very peaky control signals and accelerations.
Numerical solution of the controlled Duffing oscillator by semi-orthogonal spline wavelets
NASA Astrophysics Data System (ADS)
Lakestani, M.; Razzaghi, M.; Dehghan, M.
2006-09-01
This paper presents a numerical method for solving the controlled Duffing oscillator. The method can be extended to nonlinear calculus of variations and optimal control problems. The method is based upon compactly supported linear semi-orthogonal B-spline wavelets. The differential and integral expressions which arise in the system dynamics, the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients. Illustrative examples are included to demonstrate the validity and applicability of the technique.
B-spline active rays segmentation of microcalcifications in mammography
Arikidis, Nikolaos S.; Skiadopoulos, Spyros; Karahaliou, Anna; Likaki, Eleni; Panayiotakis, George; Costaridou, Lena
2008-11-15
Accurate segmentation of microcalcifications in mammography is crucial for the quantification of morphologic properties by features incorporated in computer-aided diagnosis schemes. A novel segmentation method is proposed implementing active rays (polar-transformed active contours) on B-spline wavelet representation to identify microcalcification contour point estimates in a coarse-to-fine strategy at two levels of analysis. An iterative region growing method is used to delineate the final microcalcification contour curve, with pixel aggregation constrained by the microcalcification contour point estimates. A radial gradient-based method was also implemented for comparative purposes. The methods were tested on a dataset consisting of 149 mainly pleomorphic microcalcification clusters originating from 130 mammograms of the DDSM database. Segmentation accuracy of both methods was evaluated by three radiologists, based on a five-point rating scale. The radiologists' average accuracy ratings were 3.96{+-}0.77, 3.97{+-}0.80, and 3.83{+-}0.89 for the proposed method, and 2.91{+-}0.86, 2.10{+-}0.94, and 2.56{+-}0.76 for the radial gradient-based method, respectively, while the differences in accuracy ratings between the two segmentation methods were statistically significant (Wilcoxon signed-ranks test, p<0.05). The effect of the two segmentation methods in the classification of benign from malignant microcalcification clusters was also investigated. A least square minimum distance classifier was employed based on cluster features reflecting three morphological properties of individual microcalcifications (area, length, and relative contrast). Classification performance was evaluated by means of the area under ROC curve (A{sub z}). The area and length morphologic features demonstrated a statistically significant (Mann-Whitney U-test, p<0.05) higher patient-based classification performance when extracted from microcalcifications segmented by the proposed method (0
Higher-order numerical methods derived from three-point polynomial interpolation
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1976-01-01
Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.
Radial Splines Would Prevent Rotation Of Bearing Race
NASA Technical Reports Server (NTRS)
Kaplan, Ronald M.; Chokshi, Jaisukhlal V.
1993-01-01
Interlocking fine-pitch ribs and grooves formed on otherwise flat mating end faces of housing and outer race of rolling-element bearing to be mounted in housing, according to proposal. Splines bear large torque loads and impose minimal distortion on raceway.
NASA Astrophysics Data System (ADS)
Kevlahan, N. N.; Vasilyev, O. V.; Yuen, D. A.
2003-12-01
An adaptive multilevel wavelet collocation method for solving multi-dimensional elliptic problems with localized structures is developed. The method is based on the general class of multi-dimensional second generation wavelets and is an extension of the dynamically adaptive second generation wavelet collocation method for evolution problems. Wavelet decomposition is used for grid adaptation and interpolation, while O(N) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The multilevel structure of the wavelet approximation provides a natural way to obtain the solution on a near optimal grid. In order to accelerate the convergence of the iterative solver, an iterative procedure analogous to the multigrid algorithm is developed. For the problems with slowly varying viscosity simple diagonal preconditioning works. For problems with large laterally varying viscosity contrasts either direct solver on shared-memory machines or multilevel iterative solver with incomplete LU preconditioner may be used. The method is demonstrated for the solution of a number of two-dimensional elliptic test problems with both constant and spatially varying viscosity with multiscale character.
Radiation energy budget studies using collocated AVHRR and ERBE observations
Ackerman, S.A.; Inoue, Toshiro
1994-03-01
Changes in the energy balance at the top of the atmosphere are specified as a function of atmospheric and surface properties using observations from the Advanced Very High Resolution Radiometer (AVHRR) and the Earth Radiation Budget Experiment (ERBE) scanner. By collocating the observations from the two instruments, flown on NOAA-9, the authors take advantage of the remote-sensing capabilities of each instrument. The AVHRR spectral channels were selected based on regions that are strongly transparent to clear sky conditions and are therefore useful for characterizing both surface and cloud-top conditions. The ERBE instruments make broadband observations that are important for climate studies. The approach of collocating these observations in time and space is used to study the radiative energy budget of three geographic regions: oceanic, savanna, and desert. 25 refs., 8 figs.
ERIC Educational Resources Information Center
Walker, Crayton Phillip
2011-01-01
In this article I examine the collocational behaviour of groups of semantically related verbs (e.g., "head, run, manage") and nouns (e.g., "issue, factor, aspect") from the domain of business English. The results of this corpus-based study show that much of the collocational behaviour exhibited by these lexical items can be explained by examining…
A new kind of splines and their use for fast ray-tracing in reflective cavities
NASA Astrophysics Data System (ADS)
Pantelic, Dejan V.; Janevski, Zoran D.
1989-08-01
In this paper we are presenting a new kind of splines that are very effective in ray-tracing applications. They are designed in such a way to enable the fast and efficient computation of line-spline intersections (line representing the light ray, and spline representing the reflective cavity). These splines are piecewise parabolic polynomials, but with additional degrees of freedom. Polynomial sections of the spline can be rotated to a certain angle (each section has its own angle of rotation), enabling thus the continuity of the first derivative.
Evaluation of the spline reconstruction technique for PET
Kastis, George A. Kyriakopoulou, Dimitra; Gaitanis, Anastasios; Fernández, Yolanda; Hutton, Brian F.; Fokas, Athanasios S.
2014-04-15
Purpose: The spline reconstruction technique (SRT), based on the analytic formula for the inverse Radon transform, has been presented earlier in the literature. In this study, the authors present an improved formulation and numerical implementation of this algorithm and evaluate it in comparison to filtered backprojection (FBP). Methods: The SRT is based on the numerical evaluation of the Hilbert transform of the sinogram via an approximation in terms of “custom made” cubic splines. By restricting reconstruction only within object pixels and by utilizing certain mathematical symmetries, the authors achieve a reconstruction time comparable to that of FBP. The authors have implemented SRT in STIR and have evaluated this technique using simulated data from a clinical positron emission tomography (PET) system, as well as real data obtained from clinical and preclinical PET scanners. For the simulation studies, the authors have simulated sinograms of a point-source and three digital phantoms. Using these sinograms, the authors have created realizations of Poisson noise at five noise levels. In addition to visual comparisons of the reconstructed images, the authors have determined contrast and bias for different regions of the phantoms as a function of noise level. For the real-data studies, sinograms of an{sup 18}F-FDG injected mouse, a NEMA NU 4-2008 image quality phantom, and a Derenzo phantom have been acquired from a commercial PET system. The authors have determined: (a) coefficient of variations (COV) and contrast from the NEMA phantom, (b) contrast for the various sections of the Derenzo phantom, and (c) line profiles for the Derenzo phantom. Furthermore, the authors have acquired sinograms from a whole-body PET scan of an {sup 18}F-FDG injected cancer patient, using the GE Discovery ST PET/CT system. SRT and FBP reconstructions of the thorax have been visually evaluated. Results: The results indicate an improvement in FWHM and FWTM in both simulated and real
A counterexample concerning the L_2 -projector onto linear spline spaces
NASA Astrophysics Data System (ADS)
Oswald, Peter
2008-03-01
For the L_2 -orthogonal projection P_V onto spaces of linear splines over simplicial partitions in polyhedral domains in mathbb{R}^d , d>1 , we show that in contrast to the one-dimensional case, where Vert P_VVert _{L_inftyto L_infty} le 3 independently of the nature of the partition, in higher dimensions the L_infty -norm of P_V cannot be bounded uniformly with respect to the partition. This fact is folklore among specialists in finite element methods and approximation theory but seemingly has never been formally proved.
B-Spline Filtering for Automatic Detection of Calcification Lesions in Mammograms
NASA Astrophysics Data System (ADS)
Bueno, G.; Sánchez, S.; Ruiz, M.
2006-10-01
Breast cancer continues to be an important health problem between women population. Early detection is the only way to improve breast cancer prognosis and significantly reduce women mortality. It is by using CAD systems that radiologist can improve their ability to detect, and classify lesions in mammograms. In this study the usefulness of using B-spline based on a gradient scheme and compared to wavelet and adaptative filtering has been investigated for calcification lesion detection and as part of CAD systems. The technique has been applied to different density tissues. A qualitative validation shows the success of the method.
BSR: B-spline atomic R-matrix codes
NASA Astrophysics Data System (ADS)
Zatsarinny, Oleg
2006-02-01
BSR is a general program to calculate atomic continuum processes using the B-spline R-matrix method, including electron-atom and electron-ion scattering, and radiative processes such as bound-bound transitions, photoionization and polarizabilities. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme by including terms of the Breit-Pauli Hamiltonian. New version program summaryTitle of program: BSR Catalogue identifier: ADWY Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWY Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers on which the program has been tested: Microway Beowulf cluster; Compaq Beowulf cluster; DEC Alpha workstation; DELL PC Operating systems under which the new version has been tested: UNIX, Windows XP Programming language used: FORTRAN 95 Memory required to execute with typical data: Typically 256-512 Mwords. Since all the principal dimensions are allocatable, the available memory defines the maximum complexity of the problem No. of bits in a word: 8 No. of processors used: 1 Has the code been vectorized or parallelized?: no No. of lines in distributed program, including test data, etc.: 69 943 No. of bytes in distributed program, including test data, etc.: 746 450 Peripherals used: scratch disk store; permanent disk store Distribution format: tar.gz Nature of physical problem: This program uses the R-matrix method to calculate electron-atom and electron-ion collision processes, with options to calculate radiative data, photoionization, etc. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme, with options to include Breit-Pauli terms in the Hamiltonian. Method of solution: The R-matrix method is used [P.G. Burke, K.A. Berrington, Atomic and Molecular Processes: An R-Matrix Approach, IOP Publishing, Bristol, 1993; P.G. Burke, W.D. Robb, Adv. At. Mol. Phys. 11 (1975) 143; K.A. Berrington, W.B. Eissner, P.H. Norrington, Comput
Wang, Yuanjia
2011-01-01
Longitudinal data are routinely collected in biomedical research studies. A natural model describing longitudinal data decomposes an individual’s outcome as the sum of a population mean function and random subject-specific deviations. When parametric assumptions are too restrictive, methods modeling the population mean function and the random subject-specific functions nonparametrically are in demand. In some applications, it is desirable to estimate a covariance function of random subject-specific deviations. In this work, flexible yet computationally efficient methods are developed for a general class of semiparametric mixed effects models, where the functional forms of the population mean and the subject-specific curves are unspecified. We estimate nonparametric components of the model by penalized spline (P-spline, [1]), and reparametrize the random curve covariance function by a modified Cholesky decomposition [2] which allows for unconstrained estimation of a positive semidefinite matrix. To provide smooth estimates, we penalize roughness of fitted curves and derive closed form solutions in the maximization step of an EM algorithm. In addition, we present models and methods for longitudinal family data where subjects in a family are correlated and we decompose the covariance function into a subject-level source and observation-level source. We apply these methods to the multi-level Framingham Heart Study data to estimate age-specific heritability of systolic blood pressure (SBP) nonparametrically. PMID:21491474
NASA Technical Reports Server (NTRS)
Croom, D. R.; Dunham, R. E., Jr.
1975-01-01
The effectiveness of a forward-located spoiler, a spline, and span load alteration due to a flap configuration change as trailing-vortex-hazard alleviation methods was investigated. For the transport aircraft model in the normal approach configuration, the results indicate that either a forward-located spoiler or a spline is effective in reducing the trailing-vortex hazard. The results also indicate that large changes in span loading, due to retraction of the outboard flap, may be an effective method of reducing the trailing-vortex hazard.
NASA Astrophysics Data System (ADS)
Shi, Y.; Zhang, J.; Reid, J. S.; Liu, B.; Deshmukh, R.
2012-12-01
Unique in its ability of observing the atmospheric state in nine angles nearly simultaneously, the Multi-angle Imaging Spectroradiometer (MISR) instrument has been successfully used for various applications including remote sensing of aerosol properties. However, MISR has limited spectral channels compared with other multi-spectral sensors such as the Moderate Resolution Imaging Spectroradiometer (MODIS), which poses a challenge to cloud screening for applications using MISR. This is particularly important for aerosol property retrievals as cloud contamination and cloud artifacts are one of the larger error sources in satellite aerosol products. Using collocated MODIS and MISR data sets, the potential effects of cloud contamination on the MISR aerosol product are studied. Over global oceans, for non-glint regions, the cloud mask from the level 2 MODIS aerosol products (MOD04) is used. Over ocean glint regions as well as land, the level 2 MODIS cloud mask products (MOD35) are used. The relations between cloud coverage and the bias of MISR AOD are examined using collocated the MODIS cloud information and MISR AOD data. In particular, the suspicious high AOD loading band reported by the MISR aerosol product over high latitude southern oceans is investigated. Finally, a level 3 MISR aerosol product with a new cloud screening method is developed and the potential usage of such a product in satellite aerosol data assimilation is explored.
NASA Astrophysics Data System (ADS)
Man, Jun; Li, Weixuan; Zeng, Lingzao; Wu, Laosheng
2016-06-01
The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a sufficiently large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the polynomial chaos expansion (PCE) to represent and propagate the uncertainties in parameters and states. However, PCKF suffers from the so-called "curse of dimensionality". Its computational cost increases drastically with the increasing number of parameters and system nonlinearity. Furthermore, PCKF may fail to provide accurate estimations due to the joint updating scheme for strongly nonlinear models. Motivated by recent developments in uncertainty quantification and EnKF, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problems. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected at each assimilation step; the "restart" scheme is utilized to eliminate the inconsistency between updated model parameters and states variables. The performance of RAPCKF is systematically tested with numerical cases of unsaturated flow models. It is shown that the adaptive approach and restart scheme can significantly improve the performance of PCKF. Moreover, RAPCKF has been demonstrated to be more efficient than EnKF with the same computational cost.
Polynomial estimation of the smoothing splines for the new Finnish reference values for spirometry.
Kainu, Annette; Timonen, Kirsi
2016-07-01
Background Discontinuity of spirometry reference values from childhood into adulthood has been a problem with traditional reference values, thus modern modelling approaches using smoothing spline functions to better depict the transition during growth and ageing have been recently introduced. Following the publication of the new international Global Lung Initiative (GLI2012) reference values also new national Finnish reference values have been calculated using similar GAMLSS-modelling, with spline estimates for mean (Mspline) and standard deviation (Sspline) provided in tables. The aim of this study was to produce polynomial estimates for these spline functions to use in lieu of lookup tables and to assess their validity in the reference population of healthy non-smokers. Methods Linear regression modelling was used to approximate the estimated values for Mspline and Sspline using similar polynomial functions as in the international GLI2012 reference values. Estimated values were compared to original calculations in absolute values, the derived predicted mean and individually calculated z-scores using both values. Results Polynomial functions were estimated for all 10 spirometry variables. The agreement between original lookup table-produced values and polynomial estimates was very good, with no significant differences found. The variation slightly increased in larger predicted volumes, but a range of -0.018 to +0.022 litres of FEV1 representing ± 0.4% of maximum difference in predicted mean. Conclusions Polynomial approximations were very close to the original lookup tables and are recommended for use in clinical practice to facilitate the use of new reference values. PMID:27071737
On the role of exponential splines in image interpolation.
Kirshner, Hagai; Porat, Moshe
2009-10-01
A Sobolev reproducing-kernel Hilbert space approach to image interpolation is introduced. The underlying kernels are exponential functions and are related to stochastic autoregressive image modeling. The corresponding image interpolants can be implemented effectively using compactly-supported exponential B-splines. A tight l(2) upper-bound on the interpolation error is then derived, suggesting that the proposed exponential functions are optimal in this regard. Experimental results indicate that the proposed interpolation approach with properly-tuned, signal-dependent weights outperforms currently available polynomial B-spline models of comparable order. Furthermore, a unified approach to image interpolation by ideal and nonideal sampling procedures is derived, suggesting that the proposed exponential kernels may have a significant role in image modeling as well. Our conclusion is that the proposed Sobolev-based approach could be instrumental and a preferred alternative in many interpolation tasks. PMID:19520639
Monotonicity preserving splines using rational Ball cubic interpolation
NASA Astrophysics Data System (ADS)
Zakaria, Wan Zafira Ezza Wan; Jamal, Ena; Ali, Jamaludin Md.
2015-10-01
In scientific application and Computer Aided Design (CAD), users usually need to generate a spline passing through a given set of data which preserves certain shape properties of the data such as positivity, monotonicity or convexity [1]. The required curves have to be a smooth shape-preserving interpolation. In this paper a rational cubic spline in Ball representation is developed to generate an interpolant that preserves monotonicity. In this paper to control the shape of the interpolant three shape parameters are introduced. The shape parameters in the description of the rational cubic interpolation are subjected to monotonicity constrained. The necessary and sufficient conditions of the rational cubic interpolation are derived and visually the proposed rational cubic interpolant gives a very pleasing result.
Stiffness calculation and application of spline-ball bearing
NASA Astrophysics Data System (ADS)
Gu, Bo-Zhong; Zhou, Yu-Ming; Yang, De-Hua
2006-12-01
Spline-ball bearing is widely adopted in large precision instruments because of its distinctive performance. For the sake of carrying out detail investigation of a full instrument system, practical stiffness formulae of such bearing are introduced with elastic contact mechanics, which are successfully applied for calculating the stiffness of the bearing used in astronomical telescope. Appropriate treatment of the stiffness of such bearing in the finite element analysis is also discussed and illustrated.
Control theory and splines, applied to signature storage
NASA Technical Reports Server (NTRS)
Enqvist, Per
1994-01-01
In this report the problem we are going to study is the interpolation of a set of points in the plane with the use of control theory. We will discover how different systems generate different kinds of splines, cubic and exponential, and investigate the effect that the different systems have on the tracking problems. Actually we will see that the important parameters will be the two eigenvalues of the control matrix.
Application of integrodifferential splines to solving an interpolation problem
NASA Astrophysics Data System (ADS)
Burova, I. G.; Rodnikova, O. V.
2014-12-01
This paper deals with cases when the values of derivatives of a function are given at grid nodes or the values of integrals of a function over grid intervals are known. Polynomial and trigonometric integrodifferential splines for computing the value of a function from given values of its nodal derivatives and/or from its integrals over grid intervals are constructed. Error estimates are obtained, and numerical results are presented.
Defining window-boundaries for genomic analyses using smoothing spline techniques
Beissinger, Timothy M.; Rosa, Guilherme J.M.; Kaeppler, Shawn M.; Gianola, Daniel; de Leon, Natalia
2015-04-17
High-density genomic data is often analyzed by combining information over windows of adjacent markers. Interpretation of data grouped in windows versus at individual locations may increase statistical power, simplify computation, reduce sampling noise, and reduce the total number of tests performed. However, use of adjacent marker information can result in over- or under-smoothing, undesirable window boundary specifications, or highly correlated test statistics. We introduce a method for defining windows based on statistically guided breakpoints in the data, as a foundation for the analysis of multiple adjacent data points. This method involves first fitting a cubic smoothing spline to the data and then identifying the inflection points of the fitted spline, which serve as the boundaries of adjacent windows. This technique does not require prior knowledge of linkage disequilibrium, and therefore can be applied to data collected from individual or pooled sequencing experiments. Moreover, in contrast to existing methods, an arbitrary choice of window size is not necessary, since these are determined empirically and allowed to vary along the genome.
Defining window-boundaries for genomic analyses using smoothing spline techniques
Beissinger, Timothy M.; Rosa, Guilherme J.M.; Kaeppler, Shawn M.; Gianola, Daniel; de Leon, Natalia
2015-04-17
High-density genomic data is often analyzed by combining information over windows of adjacent markers. Interpretation of data grouped in windows versus at individual locations may increase statistical power, simplify computation, reduce sampling noise, and reduce the total number of tests performed. However, use of adjacent marker information can result in over- or under-smoothing, undesirable window boundary specifications, or highly correlated test statistics. We introduce a method for defining windows based on statistically guided breakpoints in the data, as a foundation for the analysis of multiple adjacent data points. This method involves first fitting a cubic smoothing spline to the datamore » and then identifying the inflection points of the fitted spline, which serve as the boundaries of adjacent windows. This technique does not require prior knowledge of linkage disequilibrium, and therefore can be applied to data collected from individual or pooled sequencing experiments. Moreover, in contrast to existing methods, an arbitrary choice of window size is not necessary, since these are determined empirically and allowed to vary along the genome.« less
Castillo, Edward; Castillo, Richard; Fuentes, David; Guerrero, Thomas
2014-01-01
Purpose: Block matching is a well-known strategy for estimating corresponding voxel locations between a pair of images according to an image similarity metric. Though robust to issues such as image noise and large magnitude voxel displacements, the estimated point matches are not guaranteed to be spatially accurate. However, the underlying optimization problem solved by the block matching procedure is similar in structure to the class of optimization problem associated with B-spline based registration methods. By exploiting this relationship, the authors derive a numerical method for computing a global minimizer to a constrained B-spline registration problem that incorporates the robustness of block matching with the global smoothness properties inherent to B-spline parameterization. Methods: The method reformulates the traditional B-spline registration problem as a basis pursuit problem describing the minimal l1-perturbation to block match pairs required to produce a B-spline fitting error within a given tolerance. The sparsity pattern of the optimal perturbation then defines a voxel point cloud subset on which the B-spline fit is a global minimizer to a constrained variant of the B-spline registration problem. As opposed to traditional B-spline algorithms, the optimization step involving the actual image data is addressed by block matching. Results: The performance of the method is measured in terms of spatial accuracy using ten inhale/exhale thoracic CT image pairs (available for download at www.dir-lab.com) obtained from the COPDgene dataset and corresponding sets of expert-determined landmark point pairs. The results of the validation procedure demonstrate that the method can achieve a high spatial accuracy on a significantly complex image set. Conclusions: The proposed methodology is demonstrated to achieve a high spatial accuracy and is generalizable in that in can employ any displacement field parameterization described as a least squares fit to block match
Jakeman, John D.; Narayan, Akil; Xiu, Dongbin
2013-06-01
We propose a multi-element stochastic collocation method that can be applied in high-dimensional parameter space for functions with discontinuities lying along manifolds of general geometries. The key feature of the method is that the parameter space is decomposed into multiple elements defined by the discontinuities and thus only the minimal number of elements are utilized. On each of the resulting elements the function is smooth and can be approximated using high-order methods with fast convergence properties. The decomposition strategy is in direct contrast to the traditional multi-element approaches which define the sub-domains by repeated splitting of the axes in the parameter space. Such methods are more prone to the curse-of-dimensionality because of the fast growth of the number of elements caused by the axis based splitting. The present method is a two-step approach. Firstly a discontinuity detector is used to partition parameter space into disjoint elements in each of which the function is smooth. The detector uses an efficient combination of the high-order polynomial annihilation technique along with adaptive sparse grids, and this allows resolution of general discontinuities with a smaller number of points when the discontinuity manifold is low-dimensional. After partitioning, an adaptive technique based on the least orthogonal interpolant is used to construct a generalized Polynomial Chaos surrogate on each element. The adaptive technique reuses all information from the partitioning and is variance-suppressing. We present numerous numerical examples that illustrate the accuracy, efficiency, and generality of the method. When compared against standard locally-adaptive sparse grid methods, the present method uses many fewer number of collocation samples and is more accurate.
Explicit B-spline regularization in diffeomorphic image registration
Tustison, Nicholas J.; Avants, Brian B.
2013-01-01
Diffeomorphic mappings are central to image registration due largely to their topological properties and success in providing biologically plausible solutions to deformation and morphological estimation problems. Popular diffeomorphic image registration algorithms include those characterized by time-varying and constant velocity fields, and symmetrical considerations. Prior information in the form of regularization is used to enforce transform plausibility taking the form of physics-based constraints or through some approximation thereof, e.g., Gaussian smoothing of the vector fields [a la Thirion's Demons (Thirion, 1998)]. In the context of the original Demons' framework, the so-called directly manipulated free-form deformation (DMFFD) (Tustison et al., 2009) can be viewed as a smoothing alternative in which explicit regularization is achieved through fast B-spline approximation. This characterization can be used to provide B-spline “flavored” diffeomorphic image registration solutions with several advantages. Implementation is open source and available through the Insight Toolkit and our Advanced Normalization Tools (ANTs) repository. A thorough comparative evaluation with the well-known SyN algorithm (Avants et al., 2008), implemented within the same framework, and its B-spline analog is performed using open labeled brain data and open source evaluation tools. PMID:24409140
Spline Driven: High Accuracy Projectors for Tomographic Reconstruction From Few Projections.
Momey, Fabien; Denis, Loïc; Burnier, Catherine; Thiébaut, Éric; Becker, Jean-Marie; Desbat, Laurent
2015-12-01
Tomographic iterative reconstruction methods need a very thorough modeling of data. This point becomes critical when the number of available projections is limited. At the core of this issue is the projector design, i.e., the numerical model relating the representation of the object of interest to the projections on the detector. Voxel driven and ray driven projection models are widely used for their short execution time in spite of their coarse approximations. Distance driven model has an improved accuracy but makes strong approximations to project voxel basis functions. Cubic voxel basis functions are anisotropic, accurately modeling their projection is, therefore, computationally expensive. Both smoother and more isotropic basis functions better represent the continuous functions and provide simpler projectors. These considerations have led to the development of spherically symmetric volume elements, called blobs. Set apart their isotropy, blobs are often considered too computationally expensive in practice. In this paper, we consider using separable B-splines as basis functions to represent the object, and we propose to approximate the projection of these basis functions by a 2D separable model. When the degree of the B-splines increases, their isotropy improves and projections can be computed regardless of their orientation. The degree and the sampling of the B-splines can be chosen according to a tradeoff between approximation quality and computational complexity. We quantitatively measure the good accuracy of our model and compare it with other projectors, such as the distance-driven and the model proposed by Long et al. From the numerical experiments, we demonstrate that our projector with an improved accuracy better preserves the quality of the reconstruction as the number of projections decreases. Our projector with cubic B-splines requires about twice as many operations as a model based on voxel basis functions. Higher accuracy projectors can be used to
Fourier analysis of finite element preconditioned collocation schemes
NASA Technical Reports Server (NTRS)
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
Change detection of lung cancer using image registration and thin-plate spline warping
NASA Astrophysics Data System (ADS)
Almasslawi, Dawood M. S.; Kabir, Ehsanollah
2011-06-01
Lung cancer has the lowest survival rate comparing to other types of cancer and determination of the patient's cancer stage is the most vital issue regarding the cancer treatment process. In most cases accurate estimation of the cancer stage is not easy to achieve. The changes in the size of the primary tumor can be detected using image registration techniques. The registration method proposed in this paper uses Normalized Mutual Information metric and Thin-Plate Spline transformation function for the accurate determination of the correspondence between series of the lung cancer Computed Tomography images. The Normalized Mutual Information is used as a metric for the rigid registration of the images to better estimate the global motion of the tissues and the Thin Plate Spline is used to deform the image in a locally supported manner. The Control Points needed for the transformation are extracted semiautomatically. This new approach in change detection of the lung cancer is implemented using the Insight Toolkit. The results from implementing this method on the CT images of 8 patients provided a satisfactory quality for change detection of the lung cancer.
Applications of B-spline Methodology to Three-Dimensional Simulations of Flow over a Cylinder
NASA Astrophysics Data System (ADS)
Kravchenko, Arthur; Moin, Parviz; Shariff, Karim
1997-11-01
A numerical method based on B-splines(A.G. Kravchenko, P. Moin, R. Moser, J. Comp. Phys.), 127, 412-423 (1996) is generalized for turbulence simulations on zonal grids in curvilinear coordinates. The performance of the method is assessed in three-dimensional simulations of a flow over a circular cylinder. Numerical simulations at Re=300 show good agreement with the corresponding spectral calculations. Coefficient of drag and Strouhal shedding frequency agree well with the experimental data for this flow. Large eddy simulations at the subcritical Reynolds number, Re=3900, are performed and compared with previous upwind-biased and central finite-difference computations. In the near-wake, all three simulations are in excellent agreement with each other and agree fairly well with the experimental data of Lourenco and Shih. In the far-wake, the results obtained from the B-spline computations are in better agreement with the experimental data of Ong and Wallace than those obtained in upwind and central finite-difference simulations. The influence of numerical resolution and the spanwise domain size on the three-dimensional simulations will be discussed.
Spline-Based Smoothing of Airfoil Curvatures
NASA Technical Reports Server (NTRS)
Li, W.; Krist, S.
2008-01-01
Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been
Alwan, Aravind; Aluru, N.R.
2013-12-15
This paper presents a data-driven framework for performing uncertainty quantification (UQ) by choosing a stochastic model that accurately describes the sources of uncertainty in a system. This model is propagated through an appropriate response surface function that approximates the behavior of this system using stochastic collocation. Given a sample of data describing the uncertainty in the inputs, our goal is to estimate a probability density function (PDF) using the kernel moment matching (KMM) method so that this PDF can be used to accurately reproduce statistics like mean and variance of the response surface function. Instead of constraining the PDF to be optimal for a particular response function, we show that we can use the properties of stochastic collocation to make the estimated PDF optimal for a wide variety of response functions. We contrast this method with other traditional procedures that rely on the Maximum Likelihood approach, like kernel density estimation (KDE) and its adaptive modification (AKDE). We argue that this modified KMM method tries to preserve what is known from the given data and is the better approach when the available data is limited in quantity. We test the performance of these methods for both univariate and multivariate density estimation by sampling random datasets from known PDFs and then measuring the accuracy of the estimated PDFs, using the known PDF as a reference. Comparing the output mean and variance estimated with the empirical moments using the raw data sample as well as the actual moments using the known PDF, we show that the KMM method performs better than KDE and AKDE in predicting these moments with greater accuracy. This improvement in accuracy is also demonstrated for the case of UQ in electrostatic and electrothermomechanical microactuators. We show how our framework results in the accurate computation of statistics in micromechanical systems.
Brown, C; Adcock, A; Azevedo, S; Liebman, J; Bond, E
2010-12-28
Some diagnostics at the National Ignition Facility (NIF), including the Gamma Reaction History (GRH) diagnostic, require multiple channels of data to achieve the required dynamic range. These channels need to be stitched together into a single time series, and they may have non-uniform and redundant time samples. We chose to apply the popular cubic smoothing spline technique to our stitching problem because we needed a general non-parametric method. We adapted one of the algorithms in the literature, by Hutchinson and deHoog, to our needs. The modified algorithm and the resulting code perform a cubic smoothing spline fit to multiple data channels with redundant time samples and missing data points. The data channels can have different, time-varying, zero-mean white noise characteristics. The method we employ automatically determines an optimal smoothing level by minimizing the Generalized Cross Validation (GCV) score. In order to automatically validate the smoothing level selection, the Weighted Sum-Squared Residual (WSSR) and zero-mean tests are performed on the residuals. Further, confidence intervals, both analytical and Monte Carlo, are also calculated. In this paper, we describe the derivation of our cubic smoothing spline algorithm. We outline the algorithm and test it with simulated and experimental data.
Non-Stationary Hydrologic Frequency Analysis using B-Splines Quantile Regression
NASA Astrophysics Data System (ADS)
Nasri, B.; St-Hilaire, A.; Bouezmarni, T.; Ouarda, T.
2015-12-01
Hydrologic frequency analysis is commonly used by engineers and hydrologists to provide the basic information on planning, design and management of hydraulic structures and water resources system under the assumption of stationarity. However, with increasing evidence of changing climate, it is possible that the assumption of stationarity would no longer be valid and the results of conventional analysis would become questionable. In this study, we consider a framework for frequency analysis of extreme flows based on B-Splines quantile regression, which allows to model non-stationary data that have a dependence on covariates. Such covariates may have linear or nonlinear dependence. A Markov Chain Monte Carlo (MCMC) algorithm is used to estimate quantiles and their posterior distributions. A coefficient of determination for quantiles regression is proposed to evaluate the estimation of the proposed model for each quantile level. The method is applied on annual maximum and minimum streamflow records in Ontario, Canada. Climate indices are considered to describe the non-stationarity in these variables and to estimate the quantiles in this case. The results show large differences between the non-stationary quantiles and their stationary equivalents for annual maximum and minimum discharge with high annual non-exceedance probabilities. Keywords: Quantile regression, B-Splines functions, MCMC, Streamflow, Climate indices, non-stationarity.
Railroad inspection based on ACFM employing a non-uniform B-spline approach
NASA Astrophysics Data System (ADS)
Chacón Muñoz, J. M.; García Márquez, F. P.; Papaelias, M.
2013-11-01
The stresses sustained by rails have increased in recent years due to the use of higher train speeds and heavier axle loads. For this reason surface and near-surface defects generate by Rolling Contact Fatigue (RCF) have become particularly significant as they can cause unexpected structural failure of the rail, resulting in severe derailments. The accident that took place in Hatfield, UK (2000), is an example of a derailment caused by the structural failure of a rail section due to RCF. Early detection of RCF rail defects is therefore of paramount importance to the rail industry. The performance of existing ultrasonic and magnetic flux leakage techniques in detecting rail surface-breaking defects, such as head checks and gauge corner cracking, is inadequate during high-speed inspection, while eddy current sensors suffer from lift-off effects. The results obtained through rail inspection experiments under simulated conditions using Alternating Current Field Measurement (ACFM) probes, suggest that this technique can be applied for the accurate and reliable detection of surface-breaking defects at high inspection speeds. This paper presents the B-Spline approach used for the accurate filtering the noise of the raw ACFM signal obtained during high speed tests to improve the reliability of the measurements. A non-uniform B-spline approximation is employed to calculate the exact positions and the dimensions of the defects. This method generates a smooth approximation similar to the ACFM dataset points related to the rail surface-breaking defect.
On the functional equivalence of fuzzy inference systems and spline-based networks.
Hunt, K J; Haas, R; Brown, M
1995-06-01
The conditions under which spline-based networks are functionally equivalent to the Takagi-Sugeno-model of fuzzy inference are formally established. We consider a generalized form of basis function network whose basis functions are splines. The result admits a wide range of fuzzy membership functions which are commonly encountered in fuzzy systems design. We use the theoretical background of functional equivalence to develop a hybrid fuzzy-spline net for inverse dynamic modeling of a hydraulically driven robot manipulator. PMID:7496588
On the Effect of Gender and Years of Instruction on Iranian EFL Learners' Collocational Competence
ERIC Educational Resources Information Center
Ganji, Mansoor
2012-01-01
This study investigates the Iranian EFL learners' Knowledge of Lexical Collocation at three academic levels: freshmen, sophomores, and juniors. The participants were forty three English majors doing their B.A. in English Translation studies in Chabahar Maritime University. They took a 50-item fill-in-the-blank test of lexical collocations. The…
Investigating the Viability of a Collocation List for Students of English for Academic Purposes
ERIC Educational Resources Information Center
Durrant, Philip
2009-01-01
A number of researchers are currently attempting to create listings of important collocations for students of EAP. However, so far these attempts have (1) failed to include positionally-variable collocations, and (2) not taken sufficient account of variation across disciplines. The present paper describes the creation of one listing of…
Symmetrical and Asymmetrical Scaffolding of L2 Collocations in the Context of Concordancing
ERIC Educational Resources Information Center
Rezaee, Abbas Ali; Marefat, Hamideh; Saeedakhtar, Afsaneh
2015-01-01
Collocational competence is recognized to be integral to native-like L2 performance, and concordancing can be of assistance in gaining this competence. This study reports on an investigation into the effect of symmetrical and asymmetrical scaffolding on the collocational competence of Iranian intermediate learners of English in the context of…
Going beyond Patterns: Involving Cognitive Analysis in the Learning of Collocations
ERIC Educational Resources Information Center
Liu, Dilin
2010-01-01
Since the late 1980s, collocations have received increasing attention in applied linguistics, especially language teaching, as is evidenced by the many publications on the topic. These works fall roughly into two lines of research (a) those focusing on the identification and use of collocations (Benson, 1989; Hunston, 2002; Hunston & Francis,…
Collocational Links in the L2 Mental Lexicon and the Influence of L1 Intralexical Knowledge
ERIC Educational Resources Information Center
Wolter, Brent; Gyllstad, Henrik
2011-01-01
This article assesses the influence of L1 intralexical knowledge on the formation of L2 intralexical collocations. Two tests, a primed lexical decision task (LDT) and a test of receptive collocational knowledge, were administered to a group of non-native speakers (NNSs) (L1 Swedish), with native speakers (NSs) of English serving as controls on the…
Corpora and Collocations in Chinese-English Dictionaries for Chinese Users
ERIC Educational Resources Information Center
Xia, Lixin
2015-01-01
The paper identifies the major problems of the Chinese-English dictionary in representing collocational information after an extensive survey of nine dictionaries popular among Chinese users. It is found that the Chinese-English dictionary only provides the collocation types of "v+n" and "v+n," but completely ignores those of…
Towards a Learner Need-Oriented Second Language Collocation Writing Assistant
ERIC Educational Resources Information Center
Ramos, Margarita Alonso; Carlini, Roberto; Codina-Filbà, Joan; Orol, Ana; Vincze, Orsolya; Wanner, Leo
2015-01-01
The importance of collocations, i.e. idiosyncratic binary word co-occurrences in the context of second language learning has been repeatedly emphasized by scholars working in the field. Some went even so far as to argue that "vocabulary learning is collocation learning" (Hausmann, 1984, p. 395). Empirical studies confirm this…
English Collocation Learning through Corpus Data: On-Line Concordance and Statistical Information
ERIC Educational Resources Information Center
Ohtake, Hiroshi; Fujita, Nobuyuki; Kawamoto, Takeshi; Morren, Brian; Ugawa, Yoshihiro; Kaneko, Shuji
2012-01-01
We developed an English Collocations On Demand system offering on-line corpus and concordance information to help Japanese researchers acquire a better command of English collocation patterns. The Life Science Dictionary Corpus consists of approximately 90,000,000 words collected from life science related research papers published in academic…
Cross-Linguistic Influence: Its Impact on L2 English Collocation Production
ERIC Educational Resources Information Center
Phoocharoensil, Supakorn
2013-01-01
This research study investigated the influence of learners' mother tongue on their acquisition of English collocations. Having drawn the linguistic data from two groups of Thai EFL learners differing in English proficiency level, the researcher found that the native language (L1) plays a significant role in the participants' collocation learning…
Study on the Causes and Countermeasures of the Lexical Collocation Mistakes in College English
ERIC Educational Resources Information Center
Yan, Hansheng
2010-01-01
The lexical collocation in English is an important content in the linguistics theory, and also a research topic which is more and more emphasized in English teaching practice of China. The collocation ability of English decides whether learners could masterly use real English in effective communication. In many years' English teaching practice,…
Collocation, Semantic Prosody, and Near Synonymy: A Cross-Linguistic Perspective
ERIC Educational Resources Information Center
Xiao, Richard; McEnery, Tony
2006-01-01
This paper explores the collocational behaviour and semantic prosody of near synonyms from a cross-linguistic perspective. The importance of these concepts to language learning is well recognized. Yet while collocation and semantic prosody have recently attracted much interest from researchers studying the English language, there has been little…
A comparison of boundary and global collocation solutions for K(I) and CMOD calibration functions
Sanford, R.J.; Kirk, M.T. U.S. Navy, David W. Taylor Naval Ship Research and Development Center, Annapolis, MD )
1991-03-01
Global and boundary collocation solutions for K(I), CMOD, and the full-field stress patterns of a single-edge notched tension specimen were compared to determine the accuracy of each technique and the utility of each for determining solutions for the short and the deep crack case. It was demonstrated that inclusion of internal stress conditions in the collocation, i.e., performing a global rather than a boundary collocation solution, expands the range of crack lengths over which accurate results can be obtained. In particular, the global collocation approach provided accurate results for crack lengths between 10 percent and 80 percent of the specimen width for a typical specimen geometry. Comparable accuracy for boundary collocation was found only for crack lengths between 20 percent and 60 percent of the specimen width. 27 refs.
A numerical solution of the linear Boltzmann equation using cubic B-splines
NASA Astrophysics Data System (ADS)
Khurana, Saheba; Thachuk, Mark
2012-03-01
A numerical method using cubic B-splines is presented for solving the linear Boltzmann equation. The collision kernel for the system is chosen as the Wigner-Wilkins kernel. A total of three different representations for the distribution function are presented. Eigenvalues and eigenfunctions of the collision matrix are obtained for various mass ratios and compared with known values. Distribution functions, along with first and second moments, are evaluated for different mass and temperature ratios. Overall it is shown that the method is accurate and well behaved. In particular, moments can be predicted with very few points if the representation is chosen well. This method produces sparse matrices, can be easily generalized to higher dimensions, and can be cast into efficient parallel algorithms.
Ahn, W.; Anderson, K.S.; De, S.
2013-01-01
An interpolating spline-based approach is presented for modeling multi-flexible-body systems in the divide-and-conquer (DCA) scheme. This algorithm uses the floating frame of reference formulation and piecewise spline functions to construct and solve the non-linear equations of motion of the multi-flexible-body system undergoing large rotations and translations. The new approach is compared with the flexible DCA (FDCA) that uses the assumed modes method [1]. The FDCA, in many cases, must resort to sub-structuring to accurately model the deformation of the system. We demonstrate, through numerical examples, that the interpolating spline-based approach is comparable in accuracy and superior in efficiency to the FDCA. The present approach is appropriate for modeling flexible mechanisms with thin 1D bodies undergoing large rotations and translations, including those with irregular shapes. As such, the present approach extends the current capability of the DCA to model deformable systems. The algorithm retains the theoretical logarithmic complexity inherent in the DCA when implemented in parallel. PMID:24124265
Barmpoutis, Angelos; Shepherd, Timothy M.; Forder, John R.
2009-01-01
In this paper, we present novel algorithms for statistically robust interpolation and approximation of diffusion tensors—which are symmetric positive definite (SPD) matrices—and use them in developing a significant extension to an existing probabilistic algorithm for scalar field segmentation, in order to segment diffusion tensor magnetic resonance imaging (DT-MRI) datasets. Using the Riemannian metric on the space of SPD matrices, we present a novel and robust higher order (cubic) continuous tensor product of B-splines algorithm to approximate the SPD diffusion tensor fields. The resulting approximations are appropriately dubbed tensor splines. Next, we segment the diffusion tensor field by jointly estimating the label (assigned to each voxel) field, which is modeled by a Gauss Markov measure field (GMMF) and the parameters of each smooth tensor spline model representing the labeled regions. Results of interpolation, approximation, and segmentation are presented for synthetic data and real diffusion tensor fields from an isolated rat hippocampus, along with validation. We also present comparisons of our algorithms with existing methods and show significantly improved results in the presence of noise as well as outliers. PMID:18041268
Use of tensor product splines in magnet optimization
Davey, K.R. )
1999-05-01
Variational Metrics and other direct search techniques have proved useful in magnetic optimization. At least one technique used in magnetic optimization is to first fit the data of the desired optimization parameter to the data. If this fit is smoothly differentiable, a number of powerful techniques become available for the optimization. The author shows the usefulness of tensor product splines in accomplishing this end. Proper choice of augmented knot placement not only makes the fit very accurate, but allows for differentiation. Thus the gradients required with direct optimization in divariate and trivariate applications are robustly generated.
Estimating error cross-correlations in soil moisture data sets using extended collocation analysis
NASA Astrophysics Data System (ADS)
Gruber, A.; Su, C.-H.; Crow, W. T.; Zwieback, S.; Dorigo, W. A.; Wagner, W.
2016-02-01
Global soil moisture records are essential for studying the role of hydrologic processes within the larger earth system. Various studies have shown the benefit of assimilating satellite-based soil moisture data into water balance models or merging multisource soil moisture retrievals into a unified data set. However, this requires an appropriate parameterization of the error structures of the underlying data sets. While triple collocation (TC) analysis has been widely recognized as a powerful tool for estimating random error variances of coarse-resolution soil moisture data sets, the estimation of error cross covariances remains an unresolved challenge. Here we propose a method—referred to as extended collocation (EC) analysis—for estimating error cross-correlations by generalizing the TC method to an arbitrary number of data sets and relaxing the therein made assumption of zero error cross-correlation for certain data set combinations. A synthetic experiment shows that EC analysis is able to reliably recover true error cross-correlation levels. Applied to real soil moisture retrievals from Advanced Microwave Scanning Radiometer-EOS (AMSR-E) C-band and X-band observations together with advanced scatterometer (ASCAT) retrievals, modeled data from Global Land Data Assimilation System (GLDAS)-Noah and in situ measurements drawn from the International Soil Moisture Network, EC yields reasonable and strong nonzero error cross-correlations between the two AMSR-E products. Against expectation, nonzero error cross-correlations are also found between ASCAT and AMSR-E. We conclude that the proposed EC method represents an important step toward a fully parameterized error covariance matrix for coarse-resolution soil moisture data sets, which is vital for any rigorous data assimilation framework or data merging scheme.
Local validation of EU-DEM using Least Squares Collocation
NASA Astrophysics Data System (ADS)
Ampatzidis, Dimitrios; Mouratidis, Antonios; Gruber, Christian; Kampouris, Vassilios
2016-04-01
In the present study we are dealing with the evaluation of the European Digital Elevation Model (EU-DEM) in a limited area, covering few kilometers. We compare EU-DEM derived vertical information against orthometric heights obtained by classical trigonometric leveling for an area located in Northern Greece. We apply several statistical tests and we initially fit a surface model, in order to quantify the existing biases and outliers. Finally, we implement a methodology for orthometric heights prognosis, using the Least Squares Collocation for the remaining residuals of the first step (after the fitted surface application). Our results, taking into account cross validation points, reveal a local consistency between EU-DEM and official heights, which is better than 1.4 meters.
Optimal spacecraft attitude control using collocation and nonlinear programming
NASA Astrophysics Data System (ADS)
Herman, A. L.; Conway, B. A.
1992-10-01
Direct collocation with nonlinear programming (DCNLP) is employed to find the optimal open-loop control histories for detumbling a disabled satellite. The controls are torques and forces applied to the docking arm and joint and torques applied about the body axes of the OMV. Solutions are obtained for cases in which various constraints are placed on the controls and in which the number of controls is reduced or increased from that considered in Conway and Widhalm (1986). DCLNP works well when applied to the optimal control problem of satellite attitude control. The formulation is straightforward and produces good results in a relatively small amount of time on a Cray X/MP with no a priori information about the optimal solution. The addition of joint acceleration to the controls significantly reduces the control magnitudes and optimal cost. In all cases, the torques and acclerations are modest and the optimal cost is very modest.
History matching by spline approximation and regularization in single-phase areal reservoirs
NASA Technical Reports Server (NTRS)
Lee, T. Y.; Kravaris, C.; Seinfeld, J.
1986-01-01
An automatic history matching algorithm is developed based on bi-cubic spline approximations of permeability and porosity distributions and on the theory of regularization to estimate permeability or porosity in a single-phase, two-dimensional real reservoir from well pressure data. The regularization feature of the algorithm is used to convert the ill-posed history matching problem into a well-posed problem. The algorithm employs the conjugate gradient method as its core minimization method. A number of numerical experiments are carried out to evaluate the performance of the algorithm. Comparisons with conventional (non-regularized) automatic history matching algorithms indicate the superiority of the new algorithm with respect to the parameter estimates obtained. A quasioptimal regularization parameter is determined without requiring a priori information on the statistical properties of the observations.
Non-rigid registration of multiphoton microscopy images using B-splines
NASA Astrophysics Data System (ADS)
Lorenz, Kevin S.; Salama, Paul; Dunn, Kenneth W.; Delp, Edward J.
2011-03-01
Optical microscopy poses many challenges for digital image analysis. One particular challenge includes correction of image artifacts due to respiratory motion from specimens imaged in vivo. We describe a non-rigid registration method using B-splines to correct these motion artifacts. Current attempts at non-rigid medical image registration have typically involved only a single pair of images. Extending these techniques to an entire series of images, possibly comprising hundreds of images, is presented in this paper. Our method involves creating a uniform grid of control points across each image in a stack. Each control point is manipulated by optimizing a cost function consisting of two parts: a term to determine image similarity, and a term to evaluate deformation grid smoothness. This process is repeated for all images in the stack. Analysis is evaluated using block motion estimation and other visualization techniques.
Full-turn symplectic map from a generator in a Fourier-spline basis
Berg, J.S.; Warnock, R.L.; Ruth, R.D.; Forest, E.
1993-04-01
Given an arbitrary symplectic tracking code, one can construct a full-turn symplectic map that approximates the result of the code to high accuracy. The map is defined implicitly by a mixed-variable generating function. The implicit definition is no great drawback in practice, thanks to an efficient use of Newton`s method to solve for the explicit map at each iteration. The generator is represented by a Fourier series in angle variables, with coefficients given as B-spline functions of action variables. It is constructed by using results of single-turn tracking from many initial conditions. The method has been appliedto a realistic model of the SSC in three degrees of freedom. Orbits can be mapped symplectically for 10{sup 7} turns on an IBM RS6000 model 320 workstation, in a run of about one day.
Systolic algorithms for B-spline patch generation
Megson, G.M. )
1991-03-01
This paper describes a systolic array for constructing the blending functions of B-spline curves and surfaces to be 7k times faster than the equivalent sequential computation. The array requires just 5k inner product cell equivalents, where k - 1 is the maximum degree of the blending function polynomials. This array is then used as a basis for a composite systolic architecture for generating single or multiple points on a B-spline curve or surface. The total hardware requirement is bounded by 5 max (k, l) + 3 (max(m,n) + 1) inner product cells and O(mn) registers, where m and n are the numbers of control points in the two available directions. The hardware can be reduced to 5 max(k, l) + max(m,n) + 1 if each component of a point is generated by separate passes of data through the array. Equations for the array speed-up are given and likely speed-ups for different sized patches considered.
NASA Technical Reports Server (NTRS)
Rummel, R.; Sjoeberg, L.; Rapp, R. H.
1978-01-01
A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.
Webster, Clayton G; Gunzburger, Max D
2013-01-01
We present a scalable, parallel mechanism for stochastic identification/control for problems constrained by partial differential equations with random input data. Several identification objectives will be discussed that either minimize the expectation of a tracking cost functional or minimize the difference of desired statistical quantities in the appropriate $L^p$ norm, and the distributed parameters/control can both deterministic or stochastic. Given an objective we prove the existence of an optimal solution, establish the validity of the Lagrange multiplier rule and obtain a stochastic optimality system of equations. The modeling process may describe the solution in terms of high dimensional spaces, particularly in the case when the input data (coefficients, forcing terms, boundary conditions, geometry, etc) are affected by a large amount of uncertainty. For higher accuracy, the computer simulation must increase the number of random variables (dimensions), and expend more effort approximating the quantity of interest in each individual dimension. Hence, we introduce a novel stochastic parameter identification algorithm that integrates an adjoint-based deterministic algorithm with the sparse grid stochastic collocation FEM approach. This allows for decoupled, moderately high dimensional, parameterized computations of the stochastic optimality system, where at each collocation point, deterministic analysis and techniques can be utilized. The advantage of our approach is that it allows for the optimal identification of statistical moments (mean value, variance, covariance, etc.) or even the whole probability distribution of the input random fields, given the probability distribution of some responses of the system (quantities of physical interest). Our rigorously derived error estimates, for the fully discrete problems, will be described and used to compare the efficiency of the method with several other techniques. Numerical examples illustrate the theoretical
NASA Astrophysics Data System (ADS)
Erdogan, Eren; Dettmering, Denise; Limberger, Marco; Schmidt, Michael; Seitz, Florian; Börger, Klaus; Brandert, Sylvia; Görres, Barbara; Kersten, Wilhelm F.; Bothmer, Volker; Hinrichs, Johannes; Venzmer, Malte
2015-04-01
In May 2014 DGFI-TUM (the former DGFI) and the German Space Situational Awareness Centre (GSSAC) started to develop an OPerational Tool for Ionospheric Mapping And Prediction (OPTIMAP); since November 2014 the Institute of Astrophysics at the University of Göttingen (IAG) joined the group as the third partner. This project aims on the computation and prediction of maps of the vertical total electron content (VTEC) and the electron density distribution of the ionosphere on a global scale from both various space-geodetic observation techniques such as GNSS and satellite altimetry as well as Sun observations. In this contribution we present first results, i.e. a near-real time processing framework for generating VTEC maps by assimilating GNSS (GPS, GLONASS) based ionospheric data into a two-dimensional global B-spline approach. To be more specific, the spatial variations of VTEC are modelled by trigonometric B-spline functions in longitude and by endpoint-interpolating polynomial B-spline functions in latitude, respectively. Since B-spline functions are compactly supported and highly localizing our approach can handle large data gaps appropriately and, thus, provides a better approximation of data with heterogeneous density and quality compared to the commonly used spherical harmonics. The presented method models temporal variations of VTEC inside a Kalman filter. The unknown parameters of the filter state vector are composed of the B-spline coefficients as well as the satellite and receiver DCBs. To approximate the temporal variation of these state vector components as part of the filter the dynamical model has to be set up. The current implementation of the filter allows to select between a random walk process, a Gauss-Markov process and a dynamic process driven by an empirical ionosphere model, e.g. the International Reference Ionosphere (IRI). For running the model ionospheric input data is acquired from terrestrial GNSS networks through online archive systems
Local Convexity-Preserving C2 Rational Cubic Spline for Convex Data
Abd Majid, Ahmad; Ali, Jamaludin Md.
2014-01-01
We present the smooth and visually pleasant display of 2D data when it is convex, which is contribution towards the improvements over existing methods. This improvement can be used to get the more accurate results. An attempt has been made in order to develop the local convexity-preserving interpolant for convex data using C2 rational cubic spline. It involves three families of shape parameters in its representation. Data dependent sufficient constraints are imposed on single shape parameter to conserve the inherited shape feature of data. Remaining two of these shape parameters are used for the modification of convex curve to get a visually pleasing curve according to industrial demand. The scheme is tested through several numerical examples, showing that the scheme is local, computationally economical, and visually pleasing. PMID:24757421
Reich, Brian J.; Storlie, Curtis B.; Bondell, Howard D.
2009-01-01
With many predictors, choosing an appropriate subset of the covariates is a crucial, and difficult, step in nonparametric regression. We propose a Bayesian nonparametric regression model for curve-fitting and variable selection. We use the smoothing spline ANOVA framework to decompose the regression function into interpretable main effect and interaction functions. Stochastic search variable selection via MCMC sampling is used to search for models that fit the data well. Also, we show that variable selection is highly-sensitive to hyperparameter choice and develop a technique to select hyperparameters that control the long-run false positive rate. The method is used to build an emulator for a complex computer model for two-phase fluid flow. PMID:19789732
Hierarchical Volume Representation with 3{radical}2 Subdivision and Trivariate B-Spline Wavelets
Linsen, L; Gray, JT; Pascucci, V; Duchaineau, M; Hamann, B
2002-01-11
Multiresolution methods provide a means for representing data at multiple levels of detail. They are typically based on a hierarchical data organization scheme and update rules needed for data value computation. We use a data organization that is based on what we call n{radical}2 subdivision. The main advantage of subdivision, compared to quadtree (n = 2) or octree (n = 3) organizations, is that the number of vertices is only doubled in each subdivision step instead of multiplied by a factor of four or eight, respectively. To update data values we use n-variate B-spline wavelets, which yields better approximations for each level of detail. We develop a lifting scheme for n = 2 and n = 3 based on the n{radical}2-subdivision scheme. We obtain narrow masks that could also provide a basis for view-dependent visualization and adaptive refinement.
Spline analysis of Holocene sediment magnetic records: Uncertainty estimates for field modeling
NASA Astrophysics Data System (ADS)
Panovska, S.; Finlay, C. C.; Donadini, F.; Hirt, A. M.
2012-02-01
Sediment and archeomagnetic data spanning the Holocene enable us to reconstruct the evolution of the geomagnetic field on time scales of centuries to millennia. In global field modeling the reliability of data is taken into account by weighting according to uncertainty estimates. Uncertainties in sediment magnetic records arise from (1) imperfections in the paleomagnetic recording processes, (2) coring and (sub) sampling methods, (3) adopted averaging procedures, and (4) uncertainties in the age-depth models. We take a step toward improved uncertainty estimates by performing a comprehensive statistical analysis of the available global database of Holocene magnetic records. Smoothing spline models that capture the robust aspects of individual records are derived. This involves a cross-validation approach, based on an absolute deviation measure of misfit, to determine the smoothing parameter for each spline model, together with the use of a minimum smoothing time derived from the sedimentation rate and assumed lock-in depth. Departures from the spline models provide information concerning the random variability in each record. Temporal resolution analysis reveals that 50% of the records have smoothing times between 80 and 250 years. We also perform comparisons among the sediment magnetic records and archeomagnetic data, as well as with predictions from the global historical and archeomagnetic field models. Combining these approaches, we arrive at individual uncertainty estimates for each sediment record. These range from 2.5° to 11.2° (median: 5.9°; interquartile range: 5.4° to 7.2°) for inclination, 4.1° to 46.9° (median: 13.4°; interquartile range: 11.4° to 18.9°) for relative declination, and 0.59 to 1.32 (median: 0.93; interquartile range: 0.86 to 1.01) for standardized relative paleointensity. These values suggest that uncertainties may have been underestimated in previous studies. No compelling evidence for systematic inclination shallowing is
Viola, Francesco; Coe, Ryan L.; Owen, Kevin; Guenther, Drake A.; Walker, William F.
2008-01-01
Image registration and motion estimation play central roles in many fields, including RADAR, SONAR, light microscopy, and medical imaging. Because of its central significance, estimator accuracy, precision, and computational cost are of critical importance. We have previously presented a highly accurate, spline-based time delay estimator that directly determines sub-sample time delay estimates from sampled data. The algorithm uses cubic splines to produce a continuous representation of a reference signal and then computes an analytical matching function between this reference and a delayed signal. The location of the minima of this function yields estimates of the time delay. In this paper we describe the MUlti-dimensional Spline-based Estimator (MUSE) that allows accurate and precise estimation of multidimensional displacements/strain components from multidimensional data sets. We describe the mathematical formulation for two- and three-dimensional motion/strain estimation and present simulation results to assess the intrinsic bias and standard deviation of this algorithm and compare it to currently available multi-dimensional estimators. In 1000 noise-free simulations of ultrasound data we found that 2D MUSE exhibits maximum bias of 2.6 × 10−4 samples in range and 2.2 × 10−3 samples in azimuth (corresponding to 4.8 and 297 nm, respectively). The maximum simulated standard deviation of estimates in both dimensions was comparable at roughly 2.8 × 10−3 samples (corresponding to 54 nm axially and 378 nm laterally). These results are between two and three orders of magnitude better than currently used 2D tracking methods. Simulation of performance in 3D yielded similar results to those observed in 2D. We also present experimental results obtained using 2D MUSE on data acquired by an Ultrasonix Sonix RP imaging system with an L14-5/38 linear array transducer operating at 6.6 MHz. While our validation of the algorithm was performed using ultrasound data, MUSE
TWO-LEVEL TIME MARCHING SCHEME USING SPLINES FOR SOLVING THE ADVECTION EQUATION. (R826371C004)
A new numerical algorithm using quintic splines is developed and analyzed: quintic spline Taylor-series expansion (QSTSE). QSTSE is an Eulerian flux-based scheme that uses quintic splines to compute space derivatives and Taylor series expansion to march in time. The new scheme...
Hsu, Yu-Mei; Wang, Xiaoliang; Chow, Judith C.; Watson, John G.; Percy, Kevin E.
2016-01-01
ABSTRACT Collocated comparisons for three PM2.5 monitors were conducted from June 2011 to May 2013 at an air monitoring station in the residential area of Fort McMurray, Alberta, Canada, a city located in the Athabasca Oil Sands Region. Extremely cold winters (down to approximately −40°C) coupled with low PM2.5 concentrations present a challenge for continuous measurements. Both the tapered element oscillating microbalance (TEOM), operated at 40°C (i.e., TEOM40), and Synchronized Hybrid Ambient Real-time Particulate (SHARP, a Federal Equivalent Method [FEM]), were compared with a Partisol PM2.5 U.S. Federal Reference Method (FRM) sampler. While hourly TEOM40 PM2.5 were consistently ~20–50% lower than that of SHARP, no statistically significant differences were found between the 24-hr averages for FRM and SHARP. Orthogonal regression (OR) equations derived from FRM and TEOM40 were used to adjust the TEOM40 (i.e., TEOMadj) and improve its agreement with FRM, particularly for the cold season. The 12-year-long hourly TEOMadj measurements from 1999 to 2011 based on the OR equations between SHARP and TEOM40 were derived from the 2-year (2011–2013) collocated measurements. The trend analysis combining both TEOMadj and SHARP measurements showed a statistically significant decrease in PM2.5 concentrations with a seasonal slope of −0.15 μg m−3 yr−1 from 1999 to 2014.Implications: Consistency in PM2.5 measurements are needed for trend analysis. Collocated comparison among the three PM2.5 monitors demonstrated the difference between FRM and TEOM, as well as between SHARP and TEOM. The orthogonal regressions equations can be applied to correct historical TEOM data to examine long-term trends within the network. PMID:26727574
Prediction of longitudinal dispersion coefficient using multivariate adaptive regression splines
NASA Astrophysics Data System (ADS)
Haghiabi, Amir Hamzeh
2016-07-01
In this paper, multivariate adaptive regression splines (MARS) was developed as a novel soft-computing technique for predicting longitudinal dispersion coefficient (D L ) in rivers. As mentioned in the literature, experimental dataset related to D L was collected and used for preparing MARS model. Results of MARS model were compared with multi-layer neural network model and empirical formulas. To define the most effective parameters on D L , the Gamma test was used. Performance of MARS model was assessed by calculation of standard error indices. Error indices showed that MARS model has suitable performance and is more accurate compared to multi-layer neural network model and empirical formulas. Results of the Gamma test and MARS model showed that flow depth (H) and ratio of the mean velocity to shear velocity (u/u ∗) were the most effective parameters on the D L .
Modeling human spine using dynamic spline approach for vibrational simulation
NASA Astrophysics Data System (ADS)
Valentini, Pier Paolo
2012-12-01
This paper deals with the description of an innovative numerical dynamic model of the human spine for vibrational behavior assessment. The modeling approach is based on the use of the dynamic spline formalism in order to achieve a condensed description requiring a smaller set of variables but maintaining the nonlinear characteristic and the accuracy of a fully multibody dynamic model. The methodology has been validated by comparing the modal behavior of the spine sub-assembly to other models available in literature. Moreover, the proposed dynamic sub-system has been integrated into a two dimensional multibody model of a seated vehicle occupant in order to compute the seat-to-head transmissibility. This characteristic has been compared to those obtained using other spine sub-models. Both modal behavior and acceleration transmissibility computed with the proposed approach show a very good accordance with others coming from more complex models.
Prediction of longitudinal dispersion coefficient using multivariate adaptive regression splines
NASA Astrophysics Data System (ADS)
Haghiabi, Amir Hamzeh
2016-07-01
In this paper, multivariate adaptive regression splines (MARS) was developed as a novel soft-computing technique for predicting longitudinal dispersion coefficient ( D L ) in rivers. As mentioned in the literature, experimental dataset related to D L was collected and used for preparing MARS model. Results of MARS model were compared with multi-layer neural network model and empirical formulas. To define the most effective parameters on D L , the Gamma test was used. Performance of MARS model was assessed by calculation of standard error indices. Error indices showed that MARS model has suitable performance and is more accurate compared to multi-layer neural network model and empirical formulas. Results of the Gamma test and MARS model showed that flow depth ( H) and ratio of the mean velocity to shear velocity ( u/ u ∗) were the most effective parameters on the D L .
Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan
2015-05-19
The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method.more » Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.« less
Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan
2015-05-19
The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method. Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.
COLLINARUS: collection of image-derived non-linear attributes for registration using splines
NASA Astrophysics Data System (ADS)
Chappelow, Jonathan; Bloch, B. Nicolas; Rofsky, Neil; Genega, Elizabeth; Lenkinski, Robert; DeWolf, William; Viswanath, Satish; Madabhushi, Anant
2009-02-01
We present a new method for fully automatic non-rigid registration of multimodal imagery, including structural and functional data, that utilizes multiple texutral feature images to drive an automated spline based non-linear image registration procedure. Multimodal image registration is significantly more complicated than registration of images from the same modality or protocol on account of difficulty in quantifying similarity between different structural and functional information, and also due to possible physical deformations resulting from the data acquisition process. The COFEMI technique for feature ensemble selection and combination has been previously demonstrated to improve rigid registration performance over intensity-based MI for images of dissimilar modalities with visible intensity artifacts. Hence, we present here the natural extension of feature ensembles for driving automated non-rigid image registration in our new technique termed Collection of Image-derived Non-linear Attributes for Registration Using Splines (COLLINARUS). Qualitative and quantitative evaluation of the COLLINARUS scheme is performed on several sets of real multimodal prostate images and synthetic multiprotocol brain images. Multimodal (histology and MRI) prostate image registration is performed for 6 clinical data sets comprising a total of 21 groups of in vivo structural (T2-w) MRI, functional dynamic contrast enhanced (DCE) MRI, and ex vivo WMH images with cancer present. Our method determines a non-linear transformation to align WMH with the high resolution in vivo T2-w MRI, followed by mapping of the histopathologic cancer extent onto the T2-w MRI. The cancer extent is then mapped from T2-w MRI onto DCE-MRI using the combined non-rigid and affine transformations determined by the registration. Evaluation of prostate registration is performed by comparison with the 3 time point (3TP) representation of functional DCE data, which provides an independent estimate of cancer
NASA Technical Reports Server (NTRS)
Eren, K.
1980-01-01
The mathematical background in spectral analysis as applied to geodetic applications is summarized. The resolution (cut-off frequency) of the GEOS 3 altimeter data is examined by determining the shortest wavelength (corresponding to the cut-off frequency) recoverable. The data from some 18 profiles are used. The total power (variance) in the sea surface topography with respect to the reference ellipsoid as well as with respect to the GEM-9 surface is computed. A fast inversion algorithm for matrices of simple and block Toeplitz matrices and its application to least squares collocation is explained. This algorithm yields a considerable gain in computer time and storage in comparison with conventional least squares collocation. Frequency domain least squares collocation techniques are also introduced and applied to estimating gravity anomalies from GEOS 3 altimeter data. These techniques substantially reduce the computer time and requirements in storage associated with the conventional least squares collocation. Numerical examples given demonstrate the efficiency and speed of these techniques.
NASA Astrophysics Data System (ADS)
Xing, Yufei; Spina, Domenico; Li, Ang; Dhaene, Tom; Bogaerts, Wim
2016-05-01
Abstract Integrated photonics, and especially silicon photonics, has been rapidly expanded its catalog of building blocks and functionalities. Now, it is maturing fast towards circuit-level integration to serve more complex applications in industry. However, performance variability due to the fabrication process and operational conditions can limit the yield of large-scale circuits. It is essential to assess this impact at the design level with an efficient variability analysis: how variations in geometrical, electrical and optical parameters propagate into components performance. In particular when implementing wavelength-selective filters, many primary functional parameters are affected by fabrication-induced variability. The key functional parameters that we assess in this paper are the waveguide propagation constant (the effective index, essential to define the exact length of a delay line) and the coupling coefficients in coupling structure (necessary to set the power distribution over different delay lines). The Monte Carlo (MC) method is the standard method for variability analysis, thanks to its accuracy and easy implementation. However, due to its slow convergence, it requires a large set of samples (simulations or measurements), making it computationally or experimentally expensive. More efficient methods to assess such variability can be used, such as generalized polynomial chaos (gPC) expansion or stochastic collocation. In this paper, we demonstrate stochastic collocation (SC) as an efficient alternative to MC or gPC to characterize photonic devices under the effect of uncertainty. The idea of SC is to interpolate stochastic solutions in the random space by interpolation polynomials. After sampling the deterministic problem at a pre-defined set of nodes in random space, the interpolation is constructed. SC drastically reduces computation and measurement cost. Also, like MC method, sampling-based SC is easy to implement. Its computation cost can be
NASA Astrophysics Data System (ADS)
Diwakar, S. V.; Das, Sarit K.; Sundararajan, T.
2009-12-01
A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor-corrector operations enforcing function ( C0) and derivative ( C1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.
Using Spline Functions for the Shape Description of the Surface of Shell Structures
NASA Astrophysics Data System (ADS)
Lenda, Grzegorz
2014-12-01
The assessment of the cover shape of shell structures makes an important issue both from the point of view of safety, as well as functionality of the construction. The most numerous group among this type of constructions are objects having the shape of a quadric (cooling towers, tanks with gas and liquids, radio-telescope dishes etc.). The material from observation of these objects (point sets), collected during periodic measurements is usually converted into a continuous form in the process of approximation, with the use of the quadric surface. The created models, are then applied in the assessment of the deformation of surface in the given period of time. Such a procedure has, however, some significant limitations. The approximation with the use of quadrics, allows the determination of basic dimensions and location of the construction, however it results in ideal objects, not providing any information on local surface deformations. They can only be defined by comparison of the model with the point set of observations. If the periodic measurements are carried out in independent, separate points, then it will be impossible to define the existing deformations directly. The second problem results from the one-equation character of the ideal approximation model. Real deformations of the object change its basic parameters, inter alia the lengths of half-axis of main quadrics. The third problem appears when the construction is not a quadric; no information on the equation describing its shape is available either. Accepting wrong kind of approximation function, causes the creation of a model of large deviations from the observed points. All the mentioned above inconveniences can be avoided by applying splines to the shape description of the surface of shell structures. The use of the function of this type, however, comes across other types of limitations. This study deals with the above subject, presenting several methods allowing the increase of accuracy and decrease of
An auroral scintillation observation using precise, collocated GPS receivers
NASA Astrophysics Data System (ADS)
Garner, T. W.; Harris, R. B.; York, J. A.; Herbster, C. S.; Minter, C. F., III; Hampton, D. L.
2011-02-01
On 10 January 2009, an unusual ionospheric scintillation event was observed by a Global Positioning System (GPS) receiver station in Fairbanks, Alaska. The receiver station is part of the National Geospatial-Intelligence Agency's (NGA) Monitoring Station Network (MSN). Each MSN station runs two identical geodetic-grade, dual-frequency, full-code tracking GPS receivers that share a common antenna. At the Fairbanks station, a third separate receiver with a separate antenna is located nearby. During the 10 January event, ionospheric conditions caused two of the receivers to loose lock on a single satellite. The third receiver tracked through the scintillation. The region of scintillation was collocated with an auroral arc and a slant total electron content (TEC) increase of 5.71 TECu (TECu = 1016/m2). The response of the full-code tracking receivers to the scintillation is intriguing. One of these receivers lost lock, but the other receiver did not. This fact argues that a receiver's internal state dictates its reaction to scintillation. Additionally, the scintillation only affected the L2 signal. While this causes the L1 signal to be lost on the semicodelessly receiver, the full-code tracking receiver only lost the L1 signal when the receiver attempted to reacquire the satellite link.
Collocated Dataglyphs for large-message storage and retrieval
NASA Astrophysics Data System (ADS)
Motwani, Rakhi C.; Breidenbach, Jeff A.; Black, John R.
2004-06-01
In contrast to the security and integrity of electronic files, printed documents are vulnerable to damage and forgery due to their physical nature. Researchers at Palo Alto Research Center utilize DataGlyph technology to render digital characteristics to printed documents, which provides them with the facility of tamper-proof authentication and damage resistance. This DataGlyph document is known as GlyphSeal. Limited DataGlyph carrying capacity per printed page restricted the application of this technology to a domain of graphically simple and small-sized single-paged documents. In this paper the authors design a protocol motivated by techniques from the networking domain and back-up strategies, which extends the GlyphSeal technology to larger-sized, graphically complex, multi-page documents. This protocol provides fragmentation, sequencing and data loss recovery. The Collocated DataGlyph Protocol renders large glyph messages onto multiple printed pages and recovers the glyph data from rescanned versions of the multi-page documents, even when pages are missing, reordered or damaged. The novelty of this protocol is the application of ideas from RAID to the domain of DataGlyphs. The current revision of this protocol is capable of generating at most 255 pages, if page recovery is desired and does not provide enough data density to store highly detailed images in a reasonable amount of page space.
NASA Astrophysics Data System (ADS)
Dai, Heng; Ye, Ming
2015-09-01
Sensitivity analysis is a vital tool in hydrological modeling to identify influential parameters for inverse modeling and uncertainty analysis, and variance-based global sensitivity analysis has gained popularity. However, the conventional global sensitivity indices are defined with consideration of only parametric uncertainty. Based on a hierarchical structure of parameter, model, and scenario uncertainties and on recently developed techniques of model- and scenario-averaging, this study derives new global sensitivity indices for multiple models and multiple scenarios. To reduce computational cost of variance-based global sensitivity analysis, sparse grid collocation method is used to evaluate the mean and variance terms involved in the variance-based global sensitivity analysis. In a simple synthetic case of groundwater flow and reactive transport, it is demonstrated that the global sensitivity indices vary substantially between the four models and three scenarios. Not considering the model and scenario uncertainties, might result in biased identification of important model parameters. This problem is resolved by using the new indices defined for multiple models and/or multiple scenarios. This is particularly true when the sensitivity indices and model/scenario probabilities vary substantially. The sparse grid collocation method dramatically reduces the computational cost, in comparison with the popular quasi-random sampling method. The new framework of global sensitivity analysis is mathematically general, and can be applied to a wide range of hydrologic and environmental problems.
NASA Astrophysics Data System (ADS)
Curà, Francesca; Mura, Andrea
2013-11-01
Tooth stiffness is a very important parameter in studying both static and dynamic behaviour of spline couplings and gears. Many works concerning tooth stiffness calculation are available in the literature, but experimental results are very rare, above all considering spline couplings. In this work experimental values of spline coupling tooth stiffness have been obtained by means of a special hexapod measuring device. Experimental results have been compared with the corresponding theoretical and numerical ones. Also the effect of angular misalignments between hub and shaft has been investigated in the experimental planning.
Determination of airplane model structure from flight data using splines and stepwise regression
NASA Technical Reports Server (NTRS)
Klein, V.; Batterson, J. G.
1983-01-01
A procedure for the determination of airplane model structure from flight data is presented. The model is based on a polynomial spline representation of the aerodynamic coefficients, and the procedure is implemented by use of a stepwise regression. First, a form of the aerodynamic force and moment coefficients amenable to the utilization of splines is developed. Next, expressions for the splines in one and two variables are introduced. Then the steps in the determination of an aerodynamic model structure and the estimation of parameters are discussed briefly. The focus is on the application to flight data of the techniques developed.
NASA Astrophysics Data System (ADS)
Plestenjak, Bor; Gheorghiu, Călin I.; Hochstenbach, Michiel E.
2015-10-01
In numerous science and engineering applications a partial differential equation has to be solved on some fairly regular domain that allows the use of the method of separation of variables. In several orthogonal coordinate systems separation of variables applied to the Helmholtz, Laplace, or Schrödinger equation leads to a multiparameter eigenvalue problem (MEP); important cases include Mathieu's system, Lamé's system, and a system of spheroidal wave functions. Although multiparameter approaches are exploited occasionally to solve such equations numerically, MEPs remain less well known, and the variety of available numerical methods is not wide. The classical approach of discretizing the equations using standard finite differences leads to algebraic MEPs with large matrices, which are difficult to solve efficiently. The aim of this paper is to change this perspective. We show that by combining spectral collocation methods and new efficient numerical methods for algebraic MEPs it is possible to solve such problems both very efficiently and accurately. We improve on several previous results available in the literature, and also present a MATLAB toolbox for solving a wide range of problems.
NASA Astrophysics Data System (ADS)
Calbet, X.
2016-01-01
A method is presented to assess whether a given reference ground-based point observation, typically a radiosonde measurement, is adequately collocated and sufficiently representative of space-borne hyperspectral infrared instrument measurements. Once this assessment is made, the ground-based data can be used to validate and potentially calibrate, with a high degree of accuracy, the hyperspectral retrievals of temperature and water vapour.
Hardy, David J; Wolff, Matthew A; Xia, Jianlin; Schulten, Klaus; Skeel, Robert D
2016-03-21
The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle-mesh Ewald method falls short. PMID:27004867
NASA Astrophysics Data System (ADS)
Hardy, David J.; Wolff, Matthew A.; Xia, Jianlin; Schulten, Klaus; Skeel, Robert D.
2016-03-01
The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle-mesh Ewald method falls short.
The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points
NASA Technical Reports Server (NTRS)
Don, Wai Sun; Gottlieb, David
1993-01-01
We present a new collocation method for the numerical solution of partial differential equations. This method uses the Chebyshev collocation points, but because of the way the boundary conditions are implemented, it has all the advantages of the Legendre methods. In particular, L2 estimates can be obtained easily for hyperbolic and parabolic problems.
Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming
NASA Technical Reports Server (NTRS)
Shi, Yun. Y.; Nelson, R. L.; Young, D. H.
1990-01-01
The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.
Quiet Clean Short-haul Experimental Engine (QCSEE). Ball spline pitch change mechanism design report
NASA Technical Reports Server (NTRS)
1978-01-01
Detailed design parameters are presented for a variable-pitch change mechanism. The mechanism is a mechanical system containing a ball screw/spline driving two counteracting master bevel gears meshing pinion gears attached to each of 18 fan blades.
A high-order conservative collocation scheme and its application to global shallow-water equations
NASA Astrophysics Data System (ADS)
Chen, C.; Li, X.; Shen, X.; Xiao, F.
2015-02-01
In this paper, an efficient and conservative collocation method is proposed and used to develop a global shallow-water model. Being a nodal type high-order scheme, the present method solves the pointwise values of dependent variables as the unknowns within each control volume. The solution points are arranged as Gauss-Legendre points to achieve high-order accuracy. The time evolution equations to update the unknowns are derived under the flux reconstruction (FR) framework (Huynh, 2007). Constraint conditions used to build the spatial reconstruction for the flux function include the pointwise values of flux function at the solution points, which are computed directly from the dependent variables, as well as the numerical fluxes at the boundaries of the computational element, which are obtained as Riemann solutions between the adjacent elements. Given the reconstructed flux function, the time tendencies of the unknowns can be obtained directly from the governing equations of differential form. The resulting schemes have super convergence and rigorous numerical conservativeness. A three-point scheme of fifth-order accuracy is presented and analyzed in this paper. The proposed scheme is adopted to develop the global shallow-water model on the cubed-sphere grid, where the local high-order reconstruction is very beneficial for the data communications between adjacent patches. We have used the standard benchmark tests to verify the numerical model, which reveals its great potential as a candidate formulation for developing high-performance general circulation models.
Parallel iterative solution of the Hermite Collocation equations on GPUs II
NASA Astrophysics Data System (ADS)
Vilanakis, N.; Mathioudakis, E.
2014-03-01
Hermite Collocation is a high order finite element method for Boundary Value Problems modelling applications in several fields of science and engineering. Application of this integration free numerical solver for the solution of linear BVPs results in a large and sparse general system of algebraic equations, suggesting the usage of an efficient iterative solver especially for realistic simulations. In part I of this work an efficient parallel algorithm of the Schur complement method coupled with Bi-Conjugate Gradient Stabilized (BiCGSTAB) iterative solver has been designed for multicore computing architectures with a Graphics Processing Unit (GPU). In the present work the proposed algorithm has been extended for high performance computing environments consisting of multiprocessor machines with multiple GPUs. Since this is a distributed GPU and shared CPU memory parallel architecture, a hybrid memory treatment is needed for the development of the parallel algorithm. The realization of the algorithm took place on a multiprocessor machine HP SL390 with Tesla M2070 GPUs using the OpenMP and OpenACC standards. Execution time measurements reveal the efficiency of the parallel implementation.
Visual Typo Correction by Collocative Optimization: A Case Study on Merchandize Images.
Wei, Xiao-Yong; Yang, Zhen-Qun; Ngo, Chong-Wah; Zhang, Wei
2014-02-01
Near-duplicate retrieval (NDR) in merchandize images is of great importance to a lot of online applications on e-Commerce websites. In those applications where the requirement of response time is critical, however, the conventional techniques developed for a general purpose NDR are limited, because expensive post-processing like spatial verification or hashing is usually employed to compromise the quantization errors among the visual words used for the images. In this paper, we argue that most of the errors are introduced because of the quantization process where the visual words are considered individually, which has ignored the contextual relations among words. We propose a "spelling or phrase correction" like process for NDR, which extends the concept of collocations to visual domain for modeling the contextual relations. Binary quadratic programming is used to enforce the contextual consistency of words selected for an image, so that the errors (typos) are eliminated and the quality of the quantization process is improved. The experimental results show that the proposed method can improve the efficiency of NDR by reducing vocabulary size by 1000% times, and under the scenario of merchandize image NDR, the expensive local interest point feature used in conventional approaches can be replaced by color-moment feature, which reduces the time cost by 9202% while maintaining comparable performance to the state-of-the-art methods. PMID:26270906
Xiao, Xun; Geyer, Veikko F; Bowne-Anderson, Hugo; Howard, Jonathon; Sbalzarini, Ivo F
2016-08-01
Biological filaments, such as actin filaments, microtubules, and cilia, are often imaged using different light-microscopy techniques. Reconstructing the filament curve from the acquired images constitutes the filament segmentation problem. Since filaments have lower dimensionality than the image itself, there is an inherent trade-off between tracing the filament with sub-pixel accuracy and avoiding noise artifacts. Here, we present a globally optimal filament segmentation method based on B-spline vector level-sets and a generalized linear model for the pixel intensity statistics. We show that the resulting optimization problem is convex and can hence be solved with global optimality. We introduce a simple and efficient algorithm to compute such optimal filament segmentations, and provide an open-source implementation as an ImageJ/Fiji plugin. We further derive an information-theoretic lower bound on the filament segmentation error, quantifying how well an algorithm could possibly do given the information in the image. We show that our algorithm asymptotically reaches this bound in the spline coefficients. We validate our method in comprehensive benchmarks, compare with other methods, and show applications from fluorescence, phase-contrast, and dark-field microscopy. PMID:27104582
A baseline correction algorithm for Raman spectroscopy by adaptive knots B-spline
NASA Astrophysics Data System (ADS)
Wang, Xin; Fan, Xian-guang; Xu, Ying-jie; Wang, Xiu-fen; He, Hao; Zuo, Yong
2015-11-01
The Raman spectroscopy technique is a powerful and non-invasive technique for molecular fingerprint detection which has been widely used in many areas, such as food safety, drug safety, and environmental testing. But Raman signals can be easily corrupted by a fluorescent background, therefore we presented a baseline correction algorithm to suppress the fluorescent background in this paper. In this algorithm, the background of the Raman signal was suppressed by fitting a curve called a baseline using a cyclic approximation method. Instead of the traditional polynomial fitting, we used the B-spline as the fitting algorithm due to its advantages of low-order and smoothness, which can avoid under-fitting and over-fitting effectively. In addition, we also presented an automatic adaptive knot generation method to replace traditional uniform knots. This algorithm can obtain the desired performance for most Raman spectra with varying baselines without any user input or preprocessing step. In the simulation, three kinds of fluorescent background lines were introduced to test the effectiveness of the proposed method. We showed that two real Raman spectra (parathion-methyl and colza oil) can be detected and their baselines were also corrected by the proposed method.
Miniaturized Multi-Band Antenna via Element Collocation
Martin, R P
2012-06-01
The resonant frequency of a microstrip patch antenna may be reduced through the addition of slots in the radiating element. Expanding upon this concept in favor of a significant reduction in the tuned width of the radiator, nearly 60% of the antenna metallization is removed, as seen in the top view of the antenna’s radiating element (shown in red, below, left). To facilitate an increase in the gain of the antenna, the radiator is suspended over the ground plane (green) by an air substrate at a height of 0.250" while being mechanically supported by 0.030" thick Rogers RO4003 laminate in the same profile as the element. Although the entire surface of the antenna (red) provides 2.45 GHz operation with insignificant negative effects on performance after material removal, the smaller square microstrip in the middle must be isolated from the additional aperture in order to afford higher frequency operation. A low insertion loss path centered at 2.45 GHz may simultaneously provide considerable attenuation at additional frequencies through the implementation of a series-parallel, resonant reactive path. However, an inductive reactance alone will not permit lower frequency energy to propagate across the intended discontinuity. To mitigate this, a capacitance is introduced in series with the inductor, generating a resonance at 2.45 GHz with minimum forward transmission loss. Four of these reactive pairs are placed between the coplanar elements as shown. Therefore, the aperture of the lower-frequency outer segment includes the smaller radiator while the higher frequency section is isolated from the additional material. In order to avoid cross-polarization losses due to the orientation of a transmitter or receiver in reference to the antenna, circular polarization is realized by a quadrature coupler for each collocated antenna as seen in the bottom view of the antenna (right). To generate electromagnetic radiation concentrically rotating about the direction of propagation
Calculation of laminar flows with second-order schemes and collocated variable arrangement
NASA Astrophysics Data System (ADS)
Biagioli, Fernando
1998-04-01
A numerical study of laminar flows is carried out to examine the performance of two second-order discretization schemes: a total variation diminishing scheme and a second-order upwind scheme. The former has the same form as the standard first-order hybrid central upwind scheme, but with a numerical diffusion reduced by the Van Leer limiter; the latter is based on the linear extrapolation of cell face values using the two upwind neighbors. A collocated grid arrangement is used; oscillations which could be generated by pressure-velocity decoupling are avoided via the Rhie-Chow interpolation. Two iterative solution methods are used: (i) the deferred correction procedure proposed by Khosla and Rubin and (ii) implicit treatment of the second-order upwind contribution. Three two-dimensional laminar test cases are considered for assessment: the plane lid-driven cavity, the plane backward facing step and the axisymmetric pipe with sudden contraction. Experimental data are available for the two last cases. Both the total variation diminishing and the second-order upwind schemes give wiggle-free results and can predict the flowfields more accurately than the standard first-order hybrid central upwind scheme.
Radecki, Peter P; Farinholt, Kevin M; Park, Gyuhae; Bement, Matthew T
2008-01-01
The machining process is very important in many engineering applications. In high precision machining, surface finish is strongly correlated with vibrations and the dynamic interactions between the part and the cutting tool. Parameters affecting these vibrations and dynamic interactions, such as spindle speed, cut depth, feed rate, and the part's material properties can vary in real-time, resulting in unexpected or undesirable effects on the surface finish of the machining product. The focus of this research is the development of an improved machining process through the use of active vibration damping. The tool holder employs a high bandwidth piezoelectric actuator with an adaptive positive position feedback control algorithm for vibration and chatter suppression. In addition, instead of using external sensors, the proposed approach investigates the use of a collocated piezoelectric sensor for measuring the dynamic responses from machining processes. The performance of this method is evaluated by comparing the surface finishes obtained with active vibration control versus baseline uncontrolled cuts. Considerable improvement in surface finish (up to 50%) was observed for applications in modern day machining.
Linsen, L; Pascucci, V; Duchaineau, M A; Hamann, B; Joy, K I
2002-11-19
Multiresolution methods for representing data at multiple levels of detail are widely used for large-scale two- and three-dimensional data sets. We present a four-dimensional multiresolution approach for time-varying volume data. This approach supports a hierarchy with spatial and temporal scalability. The hierarchical data organization is based on 4{radical}2 subdivision. The n{radical}2-subdivision scheme only doubles the overall number of grid points in each subdivision step. This fact leads to fine granularity and high adaptivity, which is especially desirable in the spatial dimensions. For high-quality data approximation on each level of detail, we use quadrilinear B-spline wavelets. We present a linear B-spline wavelet lighting scheme based on n{radical}2 subdivision to obtain narrow masks for the update rules. Narrow masks provide a basis for out-of-core data exploration techniques and view-dependent visualization of sequences of time steps.
NASA Technical Reports Server (NTRS)
Joshi, S. M.
1985-01-01
Robustness properties are investigated for two types of controllers for large flexible space structures, which use collocated sensors and actuators. The first type is an attitude controller which uses negative definite feedback of measured attitude and rate, while the second type is a damping enhancement controller which uses only velocity (rate) feedback. It is proved that collocated attitude controllers preserve closed loop global asymptotic stability when linear actuator/sensor dynamics satisfying certain phase conditions are present, or monotonic increasing nonlinearities are present. For velocity feedback controllers, the global asymptotic stability is proved under much weaker conditions. In particular, they have 90 phase margin and can tolerate nonlinearities belonging to the (0,infinity) sector in the actuator/sensor characteristics. The results significantly enhance the viability of both types of collocated controllers, especially when the available information about the large space structure (LSS) parameters is inadequate or inaccurate.
Mostafavi, Kamal; Tutunea-Fatan, O Remus; Bordatchev, Evgueni V; Johnson, James A
2014-12-01
The strong advent of computer-assisted technologies experienced by the modern orthopedic surgery prompts for the expansion of computationally efficient techniques to be built on the broad base of computer-aided engineering tools that are readily available. However, one of the common challenges faced during the current developmental phase continues to remain the lack of reliable frameworks to allow a fast and precise conversion of the anatomical information acquired through computer tomography to a format that is acceptable to computer-aided engineering software. To address this, this study proposes an integrated and automatic framework capable to extract and then postprocess the original imaging data to a common planar and closed B-Spline representation. The core of the developed platform relies on the approximation of the discrete computer tomography data by means of an original two-step B-Spline fitting technique based on successive deformations of the control polygon. In addition to its rapidity and robustness, the developed fitting technique was validated to produce accurate representations that do not deviate by more than 0.2 mm with respect to alternate representations of the bone geometry that were obtained through different-contact-based-data acquisition or data processing methods. PMID:25515225
Regression Splines in the Time-Dependent Coefficient Rates Model for Recurrent Event Data
Amorim, Leila D.; Cai, Jianwen; Zeng, Donglin; Barreto, Maurício L.
2009-01-01
SUMMARY Many epidemiologic studies involve the occurrence of recurrent events and much attention has been given for the development of modelling techniques that take into account the dependence structure of multiple event data. This paper presents a time-dependent coefficient rates model that incorporates regression splines in its estimation procedure. Such method would be appropriate in situations where the effect of an exposure or covariates changes over time in recurrent event data settings. The finite sample properties of the estimators are studied via simulation. Using data from a randomized community trial that was designed to evaluate the effect of vitamin A supplementation on recurrent diarrheal episodes in small children, we model the functional form of the treatment effect on the time to the occurrence of diarrhea. The results describe how this effect varies over time. In summary, we observed a major impact of the vitamin A supplementation on diarrhea after 2 months of the dosage, with the effect diminishing after the third dosage. The proposed method can be viewed as a flexible alternative to the marginal rates model with constant effect in situations where the effect of interest may vary over time. PMID:18696748
Merging quantum-chemistry with B-splines to describe molecular photoionization
NASA Astrophysics Data System (ADS)
Argenti, L.; Marante, C.; Klinker, M.; Corral, I.; Gonzalez, J.; Martin, F.
2016-05-01
Theoretical description of observables in attosecond pump-probe experiments requires a good representation of the system's ionization continuum. For polyelectronic atoms and molecules, however, this is still a challenge, due to the complicated short-range structure of correlated electronic wavefunctions. Whereas quantum chemistry packages (QCP) implementing sophisticated methods to compute bound electronic molecular states are well established, comparable tools for the continuum are not widely available yet. To tackle this problem, we have developed a new approach that, by means of a hybrid Gaussian-B-spline basis, interfaces existing QCPs with close-coupling scattering methods. To illustrate the viability of this approach, we report results for the multichannel ionization of the helium atom and of the hydrogen molecule that are in excellent agreement with existing accurate benchmarks. These findings, together with the flexibility of QCPs, make of this approach a good candidate for the theoretical study of the ionization of poly-electronic systems. FP7/ERC Grant XCHEM 290853.
Spline-based high-accuracy piecewise-polynomial phase-to-sinusoid amplitude converters.
Petrinović, Davor; Brezović, Marko
2011-04-01
We propose a method for direct digital frequency synthesis (DDS) using a cubic spline piecewise-polynomial model for a phase-to-sinusoid amplitude converter (PSAC). This method offers maximum smoothness of the output signal. Closed-form expressions for the cubic polynomial coefficients are derived in the spectral domain and the performance analysis of the model is given in the time and frequency domains. We derive the closed-form performance bounds of such DDS using conventional metrics: rms and maximum absolute errors (MAE) and maximum spurious free dynamic range (SFDR) measured in the discrete time domain. The main advantages of the proposed PSAC are its simplicity, analytical tractability, and inherent numerical stability for high table resolutions. Detailed guidelines for a fixed-point implementation are given, based on the algebraic analysis of all quantization effects. The results are verified on 81 PSAC configurations with the output resolutions from 5 to 41 bits by using a bit-exact simulation. The VHDL implementation of a high-accuracy DDS based on the proposed PSAC with 28-bit input phase word and 32-bit output value achieves SFDR of its digital output signal between 180 and 207 dB, with a signal-to-noise ratio of 192 dB. Its implementation requires only one 18 kB block RAM and three 18-bit embedded multipliers in a typical field-programmable gate array (FPGA) device. PMID:21507749
Evaluating techniques for multivariate classification of non-collocated spatial data.
McKenna, Sean Andrew
2004-09-01
Multivariate spatial classification schemes such as regionalized classification or principal components analysis combined with kriging rely on all variables being collocated at the sample locations. In these approaches, classification of the multivariate data into a finite number of groups is done prior to the spatial estimation. However, in some cases, the variables may be sampled at different locations with the extreme case being complete heterotopy of the data set. In these situations, it is necessary to adapt existing techniques to work with non-collocated data. Two approaches are considered: (1) kriging of existing data onto a series of 'collection points' where the classification into groups is completed and a measure of the degree of group membership is kriged to all other locations; and (2) independent kriging of all attributes to all locations after which the classification is done at each location. Calculations are conducted using an existing groundwater chemistry data set in the upper Dakota aquifer in Kansas (USA) and previously examined using regionalized classification (Bohling, 1997). This data set has all variables measured at all locations. To test the ability of the first approach for dealing with non-collocated data, each variable is reestimated at each sample location through a cross-validation process and the reestimated values are then used in the regionalized classification. The second approach for non-collocated data requires independent kriging of each attribute across the entire domain prior to classification. Hierarchical and non-hierarchical classification of all vectors is completed and a computationally less burdensome classification approach, 'sequential discrimination', is developed that constrains the classified vectors to be chosen from those with a minimal multivariate kriging variance. Resulting classification and uncertainty maps are compared between all non-collocated approaches as well as to the original collocated approach
Temporal gravity field modeling based on least square collocation with short-arc approach
NASA Astrophysics Data System (ADS)
ran, jiangjun; Zhong, Min; Xu, Houze; Liu, Chengshu; Tangdamrongsub, Natthachet
2014-05-01
After the launch of the Gravity Recovery And Climate Experiment (GRACE) in 2002, several research centers have attempted to produce the finest gravity model based on different approaches. In this study, we present an alternative approach to derive the Earth's gravity field, and two main objectives are discussed. Firstly, we seek the optimal method to estimate the accelerometer parameters, and secondly, we intend to recover the monthly gravity model based on least square collocation method. The method has been paid less attention compared to the least square adjustment method because of the massive computational resource's requirement. The positions of twin satellites are treated as pseudo-observations and unknown parameters at the same time. The variance covariance matrices of the pseudo-observations and the unknown parameters are valuable information to improve the accuracy of the estimated gravity solutions. Our analyses showed that introducing a drift parameter as an additional accelerometer parameter, compared to using only a bias parameter, leads to a significant improvement of our estimated monthly gravity field. The gravity errors outside the continents are significantly reduced based on the selected set of the accelerometer parameters. We introduced the improved gravity model namely the second version of Institute of Geodesy and Geophysics, Chinese Academy of Sciences (IGG-CAS 02). The accuracy of IGG-CAS 02 model is comparable to the gravity solutions computed from the Geoforschungszentrum (GFZ), the Center for Space Research (CSR) and the NASA Jet Propulsion Laboratory (JPL). In term of the equivalent water height, the correlation coefficients over the study regions (the Yangtze River valley, the Sahara desert, and the Amazon) among four gravity models are greater than 0.80.
Csébfalvi, Balázs
2010-01-01
In this paper, we demonstrate that quasi-interpolation of orders two and four can be efficiently implemented on the Body-Centered Cubic (BCC) lattice by using tensor-product B-splines combined with appropriate discrete prefilters. Unlike the nonseparable box-spline reconstruction previously proposed for the BCC lattice, the prefiltered B-spline reconstruction can utilize the fast trilinear texture-fetching capability of the recent graphics cards. Therefore, it can be applied for rendering BCC-sampled volumetric data interactively. Furthermore, we show that a separable B-spline filter can suppress the postaliasing effect much more isotropically than a nonseparable box-spline filter of the same approximation power. Although prefilters that make the B-splines interpolating on the BCC lattice do not exist, we demonstrate that quasi-interpolating prefiltered linear and cubic B-spline reconstructions can still provide similar or higher image quality than the interpolating linear box-spline and prefiltered quintic box-spline reconstructions, respectively. PMID:20224143
ERIC Educational Resources Information Center
Ying, Yang
2015-01-01
This study aimed to seek an in-depth understanding about English collocation learning and the development of learner autonomy through investigating a group of English as a Second Language (ESL) learners' perspectives and practices in their learning of English collocations using an AWARE approach. A group of 20 PRC students learning English in…
ERIC Educational Resources Information Center
Mohammadzadeh, Afsaneh
2012-01-01
This study was carried out to find out if there was any significant difference in learning English collocations by learning with different dominant experiential learning styles. Seventy-five participants took part in the study in which they were taught a series of English collocations. The entry knowledge of the participants with regard to…
ERIC Educational Resources Information Center
Krummes, Cedric; Ensslin, Astrid
2015-01-01
Whereas there exists a plethora of research on collocations and formulaic language in English, this article contributes towards a somewhat less developed area: the understanding and teaching of formulaic language in German as a foreign language. It analyses formulaic sequences and collocations in German writing (corpus-driven) and provides modern…
ERIC Educational Resources Information Center
Chang, Yu-Chia; Chang, Jason S.; Chen, Hao-Jan; Liou, Hsien-Chin
2008-01-01
Previous work in the literature reveals that EFL learners were deficient in collocations that are a hallmark of near native fluency in learner's writing. Among different types of collocations, the verb-noun (V-N) one was found to be particularly difficult to master, and learners' first language was also found to heavily influence their collocation…
NASA Astrophysics Data System (ADS)
Kovalerchuk, Boris
2013-12-01
Often multidimensional data are visualized by splitting n-D data to a set of low dimensional data. While it is useful it destroys integrity of n-D data, and leads to a shallow understanding complex n-D data. To mitigate this challenge a difficult perceptual task of assembling low-dimensional visualized pieces to the whole n-D vectors must be solved. Another way is a lossy dimension reduction by mapping n-D vectors to 2-D vectors (e.g., Principal Component Analysis). Such 2-D vectors carry only a part of information from n-D vectors, without a way to restore n-D vectors exactly from it. An alternative way for deeper understanding of n-D data is visual representations in 2-D that fully preserve n-D data. Methods of Parallel and Radial coordinates are such methods. Developing new methods that preserve dimensions is a long standing and challenging task that we address by proposing Paired Coordinates that is a new type of n-D data visual representation and by generalizing Parallel and Radial coordinates as a General Line coordinates. The important novelty of the concept of the Paired Coordinates is that it uses a single 2-D plot to represent n-D data as an oriented graph based on the idea of collocation of pairs of attributes. The advantage of the General Line Coordinates and Paired Coordinates is in providing a common framework that includes Parallel and Radial coordinates and generating a large number of new visual representations of multidimensional data without lossy dimension reduction.
Gearbox Reliability Collaborative Analytic Formulation for the Evaluation of Spline Couplings
Guo, Y.; Keller, J.; Errichello, R.; Halse, C.
2013-12-01
Gearboxes in wind turbines have not been achieving their expected design life; however, they commonly meet and exceed the design criteria specified in current standards in the gear, bearing, and wind turbine industry as well as third-party certification criteria. The cost of gearbox replacements and rebuilds, as well as the down time associated with these failures, has elevated the cost of wind energy. The National Renewable Energy Laboratory (NREL) Gearbox Reliability Collaborative (GRC) was established by the U.S. Department of Energy in 2006; its key goal is to understand the root causes of premature gearbox failures and improve their reliability using a combined approach of dynamometer testing, field testing, and modeling. As part of the GRC program, this paper investigates the design of the spline coupling often used in modern wind turbine gearboxes to connect the planetary and helical gear stages. Aside from transmitting the driving torque, another common function of the spline coupling is to allow the sun to float between the planets. The amount the sun can float is determined by the spline design and the sun shaft flexibility subject to the operational loads. Current standards address spline coupling design requirements in varying detail. This report provides additional insight beyond these current standards to quickly evaluate spline coupling designs.
Automatic lung lobe segmentation of COPD patients using iterative B-spline fitting
NASA Astrophysics Data System (ADS)
Shamonin, D. P.; Staring, M.; Bakker, M. E.; Xiao, C.; Stolk, J.; Reiber, J. H. C.; Stoel, B. C.
2012-02-01
We present an automatic lung lobe segmentation algorithm for COPD patients. The method enhances fissures, removes unlikely fissure candidates, after which a B-spline is fitted iteratively through the remaining candidate objects. The iterative fitting approach circumvents the need to classify each object as being part of the fissure or being noise, and allows the fissure to be detected in multiple disconnected parts. This property is beneficial for good performance in patient data, containing incomplete and disease-affected fissures. The proposed algorithm is tested on 22 COPD patients, resulting in accurate lobe-based densitometry, and a median overlap of the fissure (defined 3 voxels wide) with an expert ground truth of 0.65, 0.54 and 0.44 for the three main fissures. This compares to complete lobe overlaps of 0.99, 0.98, 0.98, 0.97 and 0.87 for the five main lobes, showing promise for lobe segmentation on data of patients with moderate to severe COPD.
Nonrigid Image Registration in Digital Subtraction Angiography Using Multilevel B-Spline
2013-01-01
We address the problem of motion artifact reduction in digital subtraction angiography (DSA) using image registration techniques. Most of registration algorithms proposed for application in DSA, have been designed for peripheral and cerebral angiography images in which we mainly deal with global rigid motions. These algorithms did not yield good results when applied to coronary angiography images because of complex nonrigid motions that exist in this type of angiography images. Multiresolution and iterative algorithms are proposed to cope with this problem, but these algorithms are associated with high computational cost which makes them not acceptable for real-time clinical applications. In this paper we propose a nonrigid image registration algorithm for coronary angiography images that is significantly faster than multiresolution and iterative blocking methods and outperforms competing algorithms evaluated on the same data sets. This algorithm is based on a sparse set of matched feature point pairs and the elastic registration is performed by means of multilevel B-spline image warping. Experimental results with several clinical data sets demonstrate the effectiveness of our approach. PMID:23971026
CT segmentation of dental shapes by anatomy-driven reformation imaging and B-spline modelling.
Barone, S; Paoli, A; Razionale, A V
2016-06-01
Dedicated imaging methods are among the most important tools of modern computer-aided medical applications. In the last few years, cone beam computed tomography (CBCT) has gained popularity in digital dentistry for 3D imaging of jawbones and teeth. However, the anatomy of a maxillofacial region complicates the assessment of tooth geometry and anatomical location when using standard orthogonal views of the CT data set. In particular, a tooth is defined by a sub-region, which cannot be easily separated from surrounding tissues by only considering pixel grey-intensity values. For this reason, an image enhancement is usually necessary in order to properly segment tooth geometries. In this paper, an anatomy-driven methodology to reconstruct individual 3D tooth anatomies by processing CBCT data is presented. The main concept is to generate a small set of multi-planar reformation images along significant views for each target tooth, driven by the individual anatomical geometry of a specific patient. The reformation images greatly enhance the clearness of the target tooth contours. A set of meaningful 2D tooth contours is extracted and used to automatically model the overall 3D tooth shape through a B-spline representation. The effectiveness of the methodology has been verified by comparing some anatomy-driven reconstructions of anterior and premolar teeth with those obtained by using standard tooth segmentation tools. Copyright © 2015 John Wiley & Sons, Ltd. PMID:26418417
Imre, K.
1993-05-01
We are developing a profile analysis code for the statistical estimation of the parametric dependencies of the temperature and density profiles in tokamaks. Our code uses advanced statistical techniques to determine the optimal fit, i.e. the fit which minimized the predictive error. For a forty TFTR Ohmic profile dataset, our preliminary results indicate that the profile shape depends almost exclusively on q{sub a}{prime} but that the shape dependencies are not Gaussian. We are now comparing various shape models on the TFTR data. In the first six months, we have completed the core modules of the code, including a B-spline package for variable knot locations, a data-based method to determine the optimal smoothing parameters, self-consistent estimation of the bias errors, and adaptive fitting near the plasma edge. Visualization graphics already include three dimensional surface plots, and discharge by discharge plots of the predicted curves with error bars together with the actual measurements values, and plots of the basis functions with errors.
Nonrigid image registration in digital subtraction angiography using multilevel B-spline.
Nejati, Mansour; Sadri, Saeid; Amirfattahi, Rassoul
2013-01-01
We address the problem of motion artifact reduction in digital subtraction angiography (DSA) using image registration techniques. Most of registration algorithms proposed for application in DSA, have been designed for peripheral and cerebral angiography images in which we mainly deal with global rigid motions. These algorithms did not yield good results when applied to coronary angiography images because of complex nonrigid motions that exist in this type of angiography images. Multiresolution and iterative algorithms are proposed to cope with this problem, but these algorithms are associated with high computational cost which makes them not acceptable for real-time clinical applications. In this paper we propose a nonrigid image registration algorithm for coronary angiography images that is significantly faster than multiresolution and iterative blocking methods and outperforms competing algorithms evaluated on the same data sets. This algorithm is based on a sparse set of matched feature point pairs and the elastic registration is performed by means of multilevel B-spline image warping. Experimental results with several clinical data sets demonstrate the effectiveness of our approach. PMID:23971026
Data-worth analysis through probabilistic collocation-based Ensemble Kalman Filter
NASA Astrophysics Data System (ADS)
Dai, Cheng; Xue, Liang; Zhang, Dongxiao; Guadagnini, Alberto
2016-09-01
We propose a new and computationally efficient data-worth analysis and quantification framework keyed to the characterization of target state variables in groundwater systems. We focus on dynamically evolving plumes of dissolved chemicals migrating in randomly heterogeneous aquifers. An accurate prediction of the detailed features of solute plumes requires collecting a substantial amount of data. Otherwise, constraints dictated by the availability of financial resources and ease of access to the aquifer system suggest the importance of assessing the expected value of data before these are actually collected. Data-worth analysis is targeted to the quantification of the impact of new potential measurements on the expected reduction of predictive uncertainty based on a given process model. Integration of the Ensemble Kalman Filter method within a data-worth analysis framework enables us to assess data worth sequentially, which is a key desirable feature for monitoring scheme design in a contaminant transport scenario. However, it is remarkably challenging because of the (typically) high computational cost involved, considering that repeated solutions of the inverse problem are required. As a computationally efficient scheme, we embed in the data-worth analysis framework a modified version of the Probabilistic Collocation Method-based Ensemble Kalman Filter proposed by Zeng et al. (2011) so that we take advantage of the ability to assimilate data sequentially in time through a surrogate model constructed via the polynomial chaos expansion. We illustrate our approach on a set of synthetic scenarios involving solute migrating in a two-dimensional random permeability field. Our results demonstrate the computational efficiency of our approach and its ability to quantify the impact of the design of the monitoring network on the reduction of uncertainty associated with the characterization of a migrating contaminant plume.
NASA Astrophysics Data System (ADS)
Bauer, K.; Muñoz, G.; Moeck, I.
2012-05-01
Joint interpretation of models from seismic tomography and inversion of magnetotelluric (MT) data is an efficient approach to determine the lithology of the subsurface. Statistical methods are well established but were developed for only two types of models so far (seismic P velocity and electrical resistivity). We apply self-organizing maps (SOMs), which have no limitations in the number of parameters considered in the joint interpretation. Our SOM method includes (1) generation of data vectors from the seismic and MT images, (2) unsupervised learning, (3) definition of classes by algorithmic segmentation of the SOM using image processing techniques and (4) application of learned knowledge to classify all data vectors and assign a lithological interpretation for each data vector. We apply the workflow to collocated P velocity, vertical P-velocity gradient and resistivity models derived along a 40 km profile around the geothermal site Groß Schönebeck in the Northeast German Basin. The resulting lithological model consists of eight classes covering Cenozoic, Mesozoic and Palaeozoic sediments down to 5 km depth. There is a remarkable agreement between the litho-type distribution from the SOM analysis and regional marker horizons interpolated from sparse 2-D industrial reflection seismic data. The most interesting features include (1) characteristic properties of the Jurassic (low P-velocity gradients, low resistivity values) interpreted as the signature of shales, and (2) a pattern within the Upper Permian Zechstein layer with low resistivity and increased P-velocity values within the salt depressions and increased resistivity and decreased P velocities in the salt pillows. The latter is explained in our interpretation by flow of less dense salt matrix components to form the pillows while denser and more brittle evaporites such as anhydrite remain in place during the salt mobilization.
Seismic porosity mapping in the Ekofisk Field using a new form of collocated cokriging
Doyen, P.M.; Boer, L.D. den; Pillet, W.R.
1996-12-31
An important practical problem in the geosciences is the integration of seismic attribute information in subsurface mapping applications. The aim is to utilize a more densely sampled secondary variable such as seismic impedance to guide the interpolation of a related primary variable such as porosity. The collocated cokriging technique was recently introduced to facilitate the integration process. Here we propose a simplified implementation of collocated cokriging based on a Bayesian updating rule. We demonstrate that the cokriging estimate at one point can be obtained by direct updating of the kriging estimate with the collocated secondary data. The linear update only requires knowledge of the kriging variance and the coefficient(s) of correlation between primary and secondary variables. No cokriging system need be solved and no reference to spatial cross-covariances is required. The new form of collocated cokriging is applied to predict the lateral variations of porosity in a reservoir layer of the Ekofisk Field, Norwegian North Sea. A cokriged porosity map is obtained by combining zone average porosity data at more than one hundred wells and acoustic impedance information extracted from a 3-D seismic survey. Utilization of the seismic information yields a more detailed and reliable image of the porosity distribution along the flanks of the producing structure.
Collocational Differences between L1 and L2: Implications for EFL Learners and Teachers
ERIC Educational Resources Information Center
Sadeghi, Karim
2009-01-01
Collocations are one of the areas that produce problems for learners of English as a foreign language. Iranian learners of English are by no means an exception. Teaching experience at schools, private language centers, and universities in Iran suggests that a significant part of EFL learners' problems with producing the language, especially at…
Your Participation Is "Greatly/Highly" Appreciated: Amplifier Collocations in L2 English
ERIC Educational Resources Information Center
Edmonds, Amanda; Gudmestad, Aarnes
2014-01-01
The current study sets out to investigate collocational knowledge for a set of 13 English amplifiers among native and nonnative speakers of English, by providing a partial replication of one of the projects reported on in Granger (1998). The project combines both phraseological and distributional approaches to research into formulaic language to…
The Role of Language for Thinking and Task Selection in EFL Learners' Oral Collocational Production
ERIC Educational Resources Information Center
Wang, Hung-Chun; Shih, Su-Chin
2011-01-01
This study investigated how English as a foreign language (EFL) learners' types of language for thinking and types of oral elicitation tasks influence their lexical collocational errors in speech. Data were collected from 42 English majors in Taiwan using two instruments: (1) 3 oral elicitation tasks and (2) an inner speech questionnaire. The…
Evaluating Remotely-Sensed Surface Soil Moisture Estimates Using Triple Collocation
Technology Transfer Automated Retrieval System (TEKTRAN)
Recent work has demonstrated the potential of enhancing remotely-sensed surface soil moisture validation activities through the application of triple collocation techniques which compare time series of three mutually independent geophysical variable estimates in order to acquire the root-mean-square...
Verb-Noun Collocations in Second Language Writing: A Corpus Analysis of Learners' English
ERIC Educational Resources Information Center
Laufer, Batia; Waldman, Tina
2011-01-01
The present study investigates the use of English verb-noun collocations in the writing of native speakers of Hebrew at three proficiency levels. For this purpose, we compiled a learner corpus that consists of about 300,000 words of argumentative and descriptive essays. For comparison purposes, we selected LOCNESS, a corpus of young adult native…
ERIC Educational Resources Information Center
Sonbul, Suhad; Schmitt, Norbert
2013-01-01
To date, there has been little empirical research exploring the relationship between implicit and explicit lexical knowledge (of collocations). As a first step in addressing this gap, two laboratory experiments were conducted that evaluate different conditions (enriched, enhanced, and decontextualized) under which both adult native speakers…
ERIC Educational Resources Information Center
Gyllstad, Henrik; Wolter, Brent
2016-01-01
The present study investigates whether two types of word combinations (free combinations and collocations) differ in terms of processing by testing Howarth's Continuum Model based on word combination typologies from a phraseological tradition. A visual semantic judgment task was administered to advanced Swedish learners of English (n = 27) and…
Strategies in Translating Collocations in Religious Texts from Arabic into English
ERIC Educational Resources Information Center
Dweik, Bader S.; Shakra, Mariam M. Abu
2010-01-01
The present study investigated the strategies adopted by students in translating specific lexical and semantic collocations in three religious texts namely, the Holy Quran, the Hadith and the Bible. For this purpose, the researchers selected a purposive sample of 35 MA translation students enrolled in three different public and private Jordanian…
Investigation of Native Speaker and Second Language Learner Intuition of Collocation Frequency
ERIC Educational Resources Information Center
Siyanova-Chanturia, Anna; Spina, Stefania
2015-01-01
Research into frequency intuition has focused primarily on native (L1) and, to a lesser degree, nonnative (L2) speaker intuitions about single word frequency. What remains a largely unexplored area is L1 and L2 intuitions about collocation (i.e., phrasal) frequency. To bridge this gap, the present study aimed to answer the following question: How…
Frequent Collocates and Major Senses of Two Prepositions in ESL and ENL Corpora
ERIC Educational Resources Information Center
Nkemleke, Daniel
2009-01-01
This contribution assesses in quantitative terms frequent collocates and major senses of "between" and "through" in the corpus of Cameroonian English (CCE), the corpus of East-African (Kenya and Tanzania) English which is part of the International Corpus of English (ICE) project (ICE-EA), and the London Oslo/Bergen (LOB) corpus of British English.…
Utilizing Lexical Data from a Web-Derived Corpus to Expand Productive Collocation Knowledge
ERIC Educational Resources Information Center
Wu, Shaoqun; Witten, Ian H.; Franken, Margaret
2010-01-01
Collocations are of great importance for second language learners, and a learner's knowledge of them plays a key role in producing language fluently (Nation, 2001: 323). In this article we describe and evaluate an innovative system that uses a Web-derived corpus and digital library software to produce a vast concordance and present it in a way…
The Effect of Corpus-Based Activities on Verb-Noun Collocations in EFL Classes
ERIC Educational Resources Information Center
Ucar, Serpil; Yükselir, Ceyhun
2015-01-01
This current study sought to reveal the impacts of corpus-based activities on verb-noun collocation learning in EFL classes. This study was carried out on two groups--experimental and control groups- each of which consists of 15 students. The students were preparatory class students at School of Foreign Languages, Osmaniye Korkut Ata University.…
Penalized splines for smooth representation of high-dimensional Monte Carlo datasets
NASA Astrophysics Data System (ADS)
Whitehorn, Nathan; van Santen, Jakob; Lafebre, Sven
2013-09-01
Detector response to a high-energy physics process is often estimated by Monte Carlo simulation. For purposes of data analysis, the results of this simulation are typically stored in large multi-dimensional histograms, which can quickly become both too large to easily store and manipulate and numerically problematic due to unfilled bins or interpolation artifacts. We describe here an application of the penalized spline technique (Marx and Eilers, 1996) [1] to efficiently compute B-spline representations of such tables and discuss aspects of the resulting B-spline fits that simplify many common tasks in handling tabulated Monte Carlo data in high-energy physics analysis, in particular their use in maximum-likelihood fitting.
Towards a More General Type of Univariate Constrained Interpolation with Fractal Splines
NASA Astrophysics Data System (ADS)
Chand, A. K. B.; Viswanathan, P.; Reddy, K. M.
2015-09-01
Recently, in [Electron. Trans. Numer. Anal. 41 (2014) 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional nonrecursive rational cubic splines and investigated their basic shape preserving properties. The main goal of the current paper is to embark on univariate constrained fractal interpolation that is more general than what was considered so far. To this end, we propose some strategies for selecting the parameters of the rational fractal spline so that the interpolating curves lie strictly above or below a prescribed linear or a quadratic spline function. Approximation property of the proposed rational cubic fractal spine is broached by using the Peano kernel theorem as an interlude. The paper also provides an illustration of background theory, veined by examples.
Reducing memory demands of splined orbitals in diffusion Monte Carlo calculations
NASA Astrophysics Data System (ADS)
Krogel, Jaron; Reboredo, Fernando
Quantum Monte Carlo calculations of defect properties of transition metal oxides have become feasible in recent years due to increases in computing power. As the system size has grown, availability of on-node memory has become a limiting factor. The main growth in memory demand stems from the B-spline representation of the single particle orbitals, especially for heavier elements such as transition metals where semi-core states are present. Despite the associated memory costs, splines are computationally efficient. In this work, we explore alternatives to reduce the memory usage of splined orbitals without significantly affecting numerical fidelity or computational efficiency. For the example case of bulk MnO we have currently achieved a memory savings of 50% while only increasing the overall computational cost of the simulation by 15%. This work is supported by the Materials Sciences & Engineering Division of the Office of Basic Energy Sciences, U.S. Department of Energy (DOE).
Modeling of complex-valued wiener systems using B-spline neural network.
Hong, Xia; Chen, Sheng
2011-05-01
In this brief, a new complex-valued B-spline neural network is introduced in order to model the complex-valued Wiener system using observational input/output data. The complex-valued nonlinear static function in the Wiener system is represented using the tensor product from two univariate B-spline neural networks, using the real and imaginary parts of the system input. Following the use of a simple least squares parameter initialization scheme, the Gauss-Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first-order derivatives recursion. Numerical examples, including a nonlinear high-power amplifier model in communication systems, are used to demonstrate the efficacy of the proposed approaches. PMID:21550875
Time Varying Compensator Design for Reconfigurable Structures Using Non-Collocated Feedback
NASA Technical Reports Server (NTRS)
Scott, Michael A.
1996-01-01
Analysis and synthesis tools are developed to improved the dynamic performance of reconfigurable nonminimum phase, nonstrictly positive real-time variant systems. A novel Spline Varying Optimal (SVO) controller is developed for the kinematic nonlinear system. There are several advantages to using the SVO controller, in which the spline function approximates the system model, observer, and controller gain. They are: The spline function approximation is simply connected, thus the SVO controller is more continuous than traditional gain scheduled controllers when implemented on a time varying plant; ft is easier for real-time implementations in storage and computational effort; where system identification is required, the spline function requires fewer experiments, namely four experiments; and initial startup estimator transients are eliminated. The SVO compensator was evaluated on a high fidelity simulation of the Shuttle Remote Manipulator System. The SVO controller demonstrated significant improvement over the present arm performance: (1) Damping level was improved by a factor of 3; and (2) Peak joint torque was reduced by a factor of 2 following Shuttle thruster firings.
NASA Astrophysics Data System (ADS)
Taylor, T. E.; O'Dell, C. W.; Frankenberg, C.; Partain, P.; Cronk, H. Q.; Savtchenko, A.; Nelson, R. R.; Rosenthal, E. J.; Chang, A. Y.; Fisher, B.; Osterman, G.; Pollock, R. H.; Crisp, D.; Eldering, A.; Gunson, M. R.
2015-12-01
The objective of the National Aeronautics and Space Administration's (NASA) Orbiting Carbon Observatory-2 (OCO-2) mission is to retrieve the column-averaged carbon dioxide (CO2) dry air mole fraction (XCO2) from satellite measurements of reflected sunlight in the near-infrared. These estimates can be biased by clouds and aerosols within the instrument's field of view (FOV). Screening of the most contaminated soundings minimizes unnecessary calls to the computationally expensive Level 2 (L2) XCO2 retrieval algorithm. Hence, robust cloud screening methods have been an important focus of the OCO-2 algorithm development team. Two distinct, computationally inexpensive cloud screening algorithms have been developed for this application. The A-Band Preprocessor (ABP) retrieves the surface pressure using measurements in the 0.76 μm O2 A-band, neglecting scattering by clouds and aerosols, which introduce photon path-length (PPL) differences that can cause large deviations between the expected and retrieved surface pressure. The Iterative Maximum A-Posteriori (IMAP) Differential Optical Absorption Spectroscopy (DOAS) Preprocessor (IDP) retrieves independent estimates of the CO2 and H2O column abundances using observations taken at 1.61 μm (weak CO2 band) and 2.06 μm (strong CO2 band), while neglecting atmospheric scattering. The CO2 and H2O column abundances retrieved in these two spectral regions differ significantly in the presence of cloud and scattering aerosols. The combination of these two algorithms, which key off of different features in the spectra, provides the basis for cloud screening of the OCO-2 data set. To validate the OCO-2 cloud screening approach, collocated measurements from NASA's Moderate Resolution Imaging Spectrometer (MODIS), aboard the Aqua platform, were compared to results from the two OCO-2 cloud screening algorithms. With tuning to allow throughputs of ≃ 30 %, agreement between the OCO-2 and MODIS cloud screening methods is found to be
NASA Astrophysics Data System (ADS)
Taylor, Thomas E.; O'Dell, Christopher W.; Frankenberg, Christian; Partain, Philip T.; Cronk, Heather Q.; Savtchenko, Andrey; Nelson, Robert R.; Rosenthal, Emily J.; Chang, Albert Y.; Fisher, Brenden; Osterman, Gregory B.; Pollock, Randy H.; Crisp, David; Eldering, Annmarie; Gunson, Michael R.
2016-03-01
The objective of the National Aeronautics and Space Administration's (NASA) Orbiting Carbon Observatory-2 (OCO-2) mission is to retrieve the column-averaged carbon dioxide (CO2) dry air mole fraction (XCO2) from satellite measurements of reflected sunlight in the near-infrared. These estimates can be biased by clouds and aerosols, i.e., contamination, within the instrument's field of view. Screening of the most contaminated soundings minimizes unnecessary calls to the computationally expensive Level 2 (L2) XCO2 retrieval algorithm. Hence, robust cloud screening methods have been an important focus of the OCO-2 algorithm development team. Two distinct, computationally inexpensive cloud screening algorithms have been developed for this application. The A-Band Preprocessor (ABP) retrieves the surface pressure using measurements in the 0.76 µm O2 A band, neglecting scattering by clouds and aerosols, which introduce photon path-length differences that can cause large deviations between the expected and retrieved surface pressure. The Iterative Maximum A Posteriori (IMAP) Differential Optical Absorption Spectroscopy (DOAS) Preprocessor (IDP) retrieves independent estimates of the CO2 and H2O column abundances using observations taken at 1.61 µm (weak CO2 band) and 2.06 µm (strong CO2 band), while neglecting atmospheric scattering. The CO2 and H2O column abundances retrieved in these two spectral regions differ significantly in the presence of cloud and scattering aerosols. The combination of these two algorithms, which are sensitive to different features in the spectra, provides the basis for cloud screening of the OCO-2 data set.To validate the OCO-2 cloud screening approach, collocated measurements from NASA's Moderate Resolution Imaging Spectrometer (MODIS), aboard the Aqua platform, were compared to results from the two OCO-2 cloud screening algorithms. With tuning of algorithmic threshold parameters that allows for processing of ≃ 20-25 % of all OCO-2 soundings
Inference in dynamic systems using B-splines and quasilinearized ODE penalties.
Frasso, Gianluca; Jaeger, Jonathan; Lambert, Philippe
2016-05-01
Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. We propose a smoothing approach regularized by a quasilinearized ODE-based penalty. Within the quasilinearized spline-based framework, the estimation reduces to a conditionally linear problem for the optimization of the spline coefficients. Furthermore, standard ODE compliance parameter(s) selection criteria are applicable. We evaluate the performances of the proposed strategy through simulated and real data examples. Simulation studies suggest that the proposed procedure ensures more accurate estimates than standard nonlinear least squares approaches when the state (initial and/or boundary) conditions are not known. PMID:26602190
Koch, M.
1995-12-31
A new mesh-adaptive 1D collocation technique has been developed to efficiently solve transient advection-dominated transport problems in porous media that are governed by a hyperbolic/parabolic (singularly perturbed) PDE. After spatial discretization a singularly perturbed ODE is obtained which is solved by a modification of the COLNEW ODE-collocation code. The latter also contains an adaptive mesh procedure that has been enhanced here to resolve linear and nonlinear transport flow problems with steep fronts where regular FD and FE methods often fail. An implicit first-order backward Euler and a third-order Taylor-Donea technique are employed for the time integration. Numerical simulations on a variety of high Peclet-number transport phenomena as they occur in realistic porous media flow situations are presented. Examples include classical linear advection-diffusion, nonlinear adsorption, two-phase Buckley-Leverett flow without and with capillary forces (Rapoport-Leas equation) and Burgers` equation for inviscid fluid flow. In most of these examples sharp fronts and/or shocks develop which are resolved in an oscillation-free manner by the present adaptive collocation method. The backward Euler method has some amount of numerical dissipation is observed when the time-steps are too large. The third-order Taylor-Donea technique is less dissipative but is more prone to numerical oscillations. The simulations show that for the efficient solution of nonlinear singularly perturbed PDE`s governing flow transport a careful balance must be struck between the optimal mesh adaptation, the nonlinear iteration method and the time-stepping procedure. More theoretical research is needed with this regard.
Multi-Processing Least Squares Collocation Applications to Gravity Field Analysis.
NASA Astrophysics Data System (ADS)
Kaas, Eigil; Sørensen, Brian; Tscherning, Carl Christian; Veicherts, Martin
2013-04-01
Least Squares Collocation (LSC) is used for the modeling of the gravity field, including predictions and error estimations of various quantities. The method requires that as many unknowns as number of data and parameters are solved for. Cholesky reduction must be used in a non-standard form due to missing positive-definiteness of the equation system. Furthermore the error estimation produces a rectangular or triangular matrix which must be Cholesky reduced in the non-standard manner. LSC have the possibility to add new sets of data without reprocessing earlier reduced parts of the equation system. Due to these factors standard Cholesky reduction programs using multi-processing cannot easily be applied. We have therefore implemented the use of Fortran Open Multi-Processing (OpenMP) and Message Passing Interface (MPI) to the non-standard Cholesky reduction. In the computation of matrix elements (covariances) as well as the evaluation spherical harmonic series used in the remove/restore setting we also take advantage of multi-processing. We describe the implementation using quadratic blocks, which aids in reducing the data transport overhead. Timing results for different block sizes and number of equations is presented. Both OpenMP and MPI scales favorably so that e.g. the prediction and error estimation of grids from GOCE TRF-data and ground gravity data can be done in the less than two hours for a 25deg by 25deg area with data selected close to 0.125 degree nodes. The results are obtained using a Dual Processor Intel(R) Xeon(R) CPU at 2.40GHz with a total of 24 threads.
Sokolova, L V; Cherkasova, A S
2015-01-01
Texts or words/pseudowords are often used as stimuli for human verbal activity research. Our study pays attention to decoding processes of grammatical constructions consisted of two-three words--collocations. Russian and English collocation sets without any narrative were presented to Russian-speaking students with different English language skill. Stimulus material had two types of collocations: paradigmatic and syntagmatic. 30 students (average age--20.4 ± 0.22) took part in the study, they were divided into two equal groups depending on their English language skill (linguists/nonlinguists). During reading brain bioelectrical activity of cortex has been registered from 12 electrodes in alfa-, beta-, theta-bands. Coherent function reflecting cooperation of different cortical areas during reading collocations has been analyzed. Increase of interhemispheric and diagonal connections while reading collocations in different languages in the group of students with low knowledge of foreign language testifies of importance of functional cooperation between the hemispheres. It has been found out that brain bioelectrical activity of students with good foreign language knowledge during reading of all collocation types in Russian and English is characterized by economization of nervous substrate resources compared to nonlinguists. Selective activation of certain cortical areas has also been observed (depending on the grammatical construction type) in nonlinguists group that is probably related to special decoding system which processes presented stimuli. Reading Russian paradigmatic constructions by nonlinguists entailed increase between left cortical areas, reading of English syntagmatic collocations--between right ones. PMID:26859985
Hub, Martina; Thieke, Christian; Kessler, Marc L.; Karger, Christian P.
2012-04-15
Purpose: In fractionated radiation therapy, image guidance with daily tomographic imaging becomes more and more clinical routine. In principle, this allows for daily computation of the delivered dose and for accumulation of these daily dose distributions to determine the actually delivered total dose to the patient. However, uncertainties in the mapping of the images can translate into errors of the accumulated total dose, depending on the dose gradient. In this work, an approach to estimate the uncertainty of mapping between medical images is proposed that identifies areas bearing a significant risk of inaccurate dose accumulation. Methods: This method accounts for the geometric uncertainty of image registration and the heterogeneity of the dose distribution, which is to be mapped. Its performance is demonstrated in context of dose mapping based on b-spline registration. It is based on evaluation of the sensitivity of dose mapping to variations of the b-spline coefficients combined with evaluation of the sensitivity of the registration metric with respect to the variations of the coefficients. It was evaluated based on patient data that was deformed based on a breathing model, where the ground truth of the deformation, and hence the actual true dose mapping error, is known. Results: The proposed approach has the potential to distinguish areas of the image where dose mapping is likely to be accurate from other areas of the same image, where a larger uncertainty must be expected. Conclusions: An approach to identify areas where dose mapping is likely to be inaccurate was developed and implemented. This method was tested for dose mapping, but it may be applied in context of other mapping tasks as well.
Explosion Source Location Study Using Collocated Acoustic and Seismic Networks in Israel
NASA Astrophysics Data System (ADS)
Pinsky, V.; Gitterman, Y.; Arrowsmith, S.; Ben-Horin, Y.
2013-12-01
We explore a joined analysis of seismic and infrasonic signals for improvement in automatic monitoring of small local/regional events, such as construction and quarry blasts, military chemical explosions, sonic booms, etc. using collocated seismic and infrasonic networks recently build in Israel (ISIN) in the frame of the project sponsored by the Bi-national USA-Israel Science Foundation (BSF). The general target is to create an automatic system, which will provide detection, location and identification of explosions in real-time or close-to-real time manner. At the moment the network comprises 15 stations hosting a microphone and seismometer (or accelerometer), operated by the Geophysical Institute of Israel (GII), plus two infrasonic arrays, operated by the National Data Center, Soreq: IOB in the South (Negev desert) and IMA in the North of Israel (Upper Galilee),collocated with the IMS seismic array MMAI. The study utilizes a ground-truth data-base of numerous Rotem phosphate quarry blasts, a number of controlled explosions for demolition of outdated ammunitions and experimental surface explosions for a structure protection research, at the Sayarim Military Range. A special event, comprising four military explosions in a neighboring country, that provided both strong seismic (up to 400 km) and infrasound waves (up to 300 km), is also analyzed. For all of these events the ground-truth coordinates and/or the results of seismic location by the Israel Seismic Network (ISN) have been provided. For automatic event detection and phase picking we tested the new recursive picker, based on Statistically optimal detector. The results were compared to the manual picks. Several location techniques have been tested using the ground-truth event recordings and the preliminary results obtained have been compared to the ground-truth locations: 1) a number of events have been located as intersection of azimuths estimated using the wide-band F-K analysis technique applied to the
NASA Astrophysics Data System (ADS)
Durmaz, Murat; Karslioglu, Mahmut Onur
2015-04-01
There are various global and regional methods that have been proposed for the modeling of ionospheric vertical total electron content (VTEC). Global distribution of VTEC is usually modeled by spherical harmonic expansions, while tensor products of compactly supported univariate B-splines can be used for regional modeling. In these empirical parametric models, the coefficients of the basis functions as well as differential code biases (DCBs) of satellites and receivers can be treated as unknown parameters which can be estimated from geometry-free linear combinations of global positioning system observables. In this work we propose a new semi-parametric multivariate adaptive regression B-splines (SP-BMARS) method for the regional modeling of VTEC together with satellite and receiver DCBs, where the parametric part of the model is related to the DCBs as fixed parameters and the non-parametric part adaptively models the spatio-temporal distribution of VTEC. The latter is based on multivariate adaptive regression B-splines which is a non-parametric modeling technique making use of compactly supported B-spline basis functions that are generated from the observations automatically. This algorithm takes advantage of an adaptive scale-by-scale model building strategy that searches for best-fitting B-splines to the data at each scale. The VTEC maps generated from the proposed method are compared numerically and visually with the global ionosphere maps (GIMs) which are provided by the Center for Orbit Determination in Europe (CODE). The VTEC values from SP-BMARS and CODE GIMs are also compared with VTEC values obtained through calibration using local ionospheric model. The estimated satellite and receiver DCBs from the SP-BMARS model are compared with the CODE distributed DCBs. The results show that the SP-BMARS algorithm can be used to estimate satellite and receiver DCBs while adaptively and flexibly modeling the daily regional VTEC.
NASA Astrophysics Data System (ADS)
Delogu, A.; Furini, F.
1991-09-01
Increasing interest in radar cross section (RCS) reduction is placing new demands on theoretical, computation, and graphic techniques for calculating scattering properties of complex targets. In particular, computer codes capable of predicting the RCS of an entire aircraft at high frequency and of achieving RCS control with modest structural changes, are becoming of paramount importance in stealth design. A computer code, evaluating the RCS of arbitrary shaped metallic objects that are computer aided design (CAD) generated, and its validation with measurements carried out using ALENIA RCS test facilities are presented. The code, based on the physical optics method, is characterized by an efficient integration algorithm with error control, in order to contain the computer time within acceptable limits, and by an accurate parametric representation of the target surface in terms of bicubic splines.
NASA Astrophysics Data System (ADS)
Xue, Juntao; Liu, Zhengguang; Zhang, Hongwei; Wang, Shucheng
2007-01-01
Snakes, or active contours, are used extensively in computer vision and image processing application, particularly to locate object boundaries. GVF (Gradient Vector Flow) model has resolved two key problems of the traditional deformable model. However, it still requires both the initial contour being close to the target and a large amount of computation. And it is difficult to process the cupped target edge. This paper analysis the characteristics of deformable model firstly, then proposed a new method based on B-spline lifting wavelet. Experimentations based on GVF model and MRI segmentation show that the proposed method is a good resolution to the initialization sensitivity and the large computation.
A Unified Representation Scheme for Solid Geometric Objects Using B-splines (extended Abstract)
NASA Technical Reports Server (NTRS)
Bahler, D.
1985-01-01
A geometric representation scheme called the B-spline cylinder, which consists of interpolation between pairs of uniform periodic cubic B-spline curves is discussed. This approach carries a number of interesting implications. For one, a single relatively simple database schema can be used to represent a reasonably large class of objects, since the spline representation is flexible enough to allow a large domain of representable objects at very little cost in data complexity. The model is thus very storage-efficient. A second feature of such a system is that it reduces to one the number of routines which the system must support to perform a given operation on objects. Third, the scheme enables easy conversion to and from other representations. The formal definition of the cylinder entity is given. In the geometric properties of the entity are explored and several operations on such objects are defined. Some general purpose criteria for evaluating any geometric representation scheme are introduced and the B-spline cylinder scheme according to these criteria is evaluated.
Technology Transfer Automated Retrieval System (TEKTRAN)
Cubic splines can be used to model fixed and random effects of lactation curves. A total of 64,138 test-day observations for first lactation Holstein cows recorded as treated with bovine somatotropin (bST) and 138,008 test-day observations for untreated cows were obtained from Dairy Records Manageme...
Processing of materials of laser scanning of roads on the basis of recursive cubic splines
NASA Astrophysics Data System (ADS)
Esharov, E. A.; Shumilov, B. M.
2015-01-01
The problem of approximation of discrete dependence (ti, yi) by means of continuous function f(t) arises in tasks of the analysis and data processing of measurements yi at successive time points of ti. The solution of the presented task becomes significantly complicated in cases when measurements form a continuous stream, and the results of processing are required to be used before full reception of measurements. The computational schemes based on recurrent spline of degree 3 depths 1 and 2 which provide accuracy for polynomials of the third degree were used in the work. The main results consist in elaboration of mathematical formulas and the proof of stability of the constructed computing schemes. Relevance of the work consists in possibility of application of the constructed splines, for example, for processing materials of laser scanning of roads. Advantages of the constructed splines are the piecewise cubic character of the recovering of the simulated smooth spatial curve and possibility of nonuniform sampling on the route when the quantity of spline knots are less than the number of samples of a function. Examples of calculation of parameters of computing schemes, and also results of numerical experiments are presented.
NASA Astrophysics Data System (ADS)
Li, H.; Zhang, Z.; Chen, X.
2012-12-01
It is widely accepted that they are oversampled in spatial grid spacing and temporal time step in the high speed medium if uniform grids are used for the numerical simulation. This oversampled grid spacing and time step will lower the efficiency of the calculation, especially high velocity contrast exists. Based on the collocated-grid finite-difference method (FDM), we present an algorithm of spatial discontinuous grid, with localized grid blocks and locally varying time steps, which will increase the efficiency of simulation of seismic wave propagation and earthquake strong ground motion. According to the velocity structure, we discretize the model into discontinuous grid blocks, and the time step of each block is determined according to the local stability. The key problem of the discontinuous grid method is the connection between grid blocks with different grid spacing. We use a transitional area overlapped by both of the finer and the coarser grids to deal with the problem. In the transitional area, the values of finer ghost points are obtained by interpolation from the coarser grid in space and time domain, while the values of coarser ghost points are obtained by downsampling from the finer grid. How to deal with coarser ghost points can influent the stability of long time simulation. After testing different downsampling methods and finally we choose the Gaussian filtering. Basically, 4th order Rung-Kutta scheme will be used for the time integral for our numerical method. For our discontinuous grid FDM, discontinuous time steps for the coarser and the finer grids will be used to increase the simulation efficiency. Numerical tests indicate that our method can provide a stable solution even for the long time simulation without any additional filtration for grid spacing ratio n=2. And for larger grid spacing ratio, Gaussian filtration could be used to preserve the stability. With the collocated-grid FDM, which is flexible and accurate in implementation of free
Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming
NASA Technical Reports Server (NTRS)
Shi, Yun Yuan; Young, D. H.
1991-01-01
The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem
Computational methods for estimation of parameters in hyperbolic systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Ito, K.; Murphy, K. A.
1983-01-01
Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized.
The convergence problem of collocation solutions in the framework of the stochastic interpretation
NASA Astrophysics Data System (ADS)
Sansò, F.; Venuti, G.
2011-01-01
The problem of the convergence of the collocation solution to the true gravity field was defined long ago (Tscherning in Boll Geod Sci Affini 39:221-252, 1978) and some results were derived, in particular by Krarup (Boll Geod Sci Affini 40:225-240, 1981). The problem is taken up again in the context of the stochastic interpretation of collocation theory and some new results are derived, showing that, when the potential T can be really continued down to a Bjerhammar sphere, we have a quite general convergence property in the noiseless case. When noise is present in data, still reasonable convergence results hold true. "Democrito che 'l mondo a caso pone" "Democritus who made the world stochastic" Dante Alighieri, La Divina Commedia, Inferno, IV - 136
NASA Technical Reports Server (NTRS)
Goldsmith, J. E. M.; Bisson, Scott E.; Ferrare, Richard A.; Evans, Keith D.; Whiteman, David N.; Melfi, S. H.
1994-01-01
Raman lidar is a leading candidate for providing the detailed space- and time-resolved measurements of water vapor needed by a variety of atmospheric studies. Simultaneous measurements of atmospheric water vapor are described using two collocated Raman lidar systems. These lidar systems, developed at the NASA/Goddard Space Flight Center and Sandia National Laboratories, acquired approximately 12 hours of simultaneous water vapor data during three nights in November 1992 while the systems were collocated at the Goddard Space Flight Center. Although these lidar systems differ substantially in their design, measured water vapor profiles agreeed within 0.15 g/kg between altitudes of 1 and 5 km. Comparisons with coincident radiosondes showed all instruments agreed within 0.2 g/kg in this same altitude range. Both lidars also clearly showed the advection of water vapor in the middle troposphere and the pronounced increase in water vapor in the nocturnal boundary layer that occurred during one night.
NASA Astrophysics Data System (ADS)
Zatsarinny, Oleg
2013-09-01
In recent years, the B-spline R-matrix (BSR) method has been applied to the treatment of a large number of atomic structure and electron-atom collision problems. Characteristic features of the BSR approach include the use of B-splines as a universal basis to describe the projectile electron inside the R-matrix box and the employment of term-dependent, and hence non-orthogonal, orbitals to construct the target states. The latter flexibility has proven to be of crucial importance for complex targets with several partially filled subshells. The published computer code has since been updated and extended to allow for a fully relativistic description at the level of the Dirac-Coulomb hamiltonian. Also, the systematic inclusion of a large number of pseudo-states in the close-coupling expansion has made it possible to extend the range of applicability from elastic and inelastic low-energy near-threshold phenomena to intermediate energies (up to several times the ionization threshold) and, in particular, to describe ionization processes as well. The basic ideas of the BSR approach will be reviewed, and its application will be illustrated for a variety of targets. Particular emphasis will be placed on systems of relevance for applications in gaseous electronics, such as the generation of complete datasets for electron collisions with the heavy noble gases Ne-Xe. Many of our data, which are needed for the description of transport processes in plasmas, are available through the LXCat database. This work was performed in collaboration with Klaus Bartschat. It is supported by the National Science Foundation under Grant No. PHY-1212450 and the XSEDE Allocation PHY-090031.
Design and Application of a Collocated Capacitance Sensor for Magnetic Bearing Spindle
NASA Technical Reports Server (NTRS)
Shin, Dongwon; Liu, Seon-Jung; Kim, Jongwon
1996-01-01
This paper presents a collocated capacitance sensor for magnetic bearings. The main feature of the sensor is that it is made of a specific compact printed circuit board (PCB). The signal processing unit has been also developed. The results of the experimental performance evaluation on the sensitivity, resolution and frequency response of the sensor are presented. Finally, an application example of the sensor to the active control of a magnetic bearing is described.
Forsberg, C.; Lewis, L.
2013-07-01
It is an accident of history that the current model of the fuel cycle is a separate set of facilities connected by transportation. The question is whether collocation and integration of reprocessing and fuel fabrication with the repository significantly reduce the costs of a closed fuel cycle while improving system performance in terms of safety and long-term repository performance. This paper examines the question in terms of higher-level functional requirements of reprocessing systems and geological repositories.
Active vibration control of a sandwich plate by non-collocated positive position feedback
NASA Astrophysics Data System (ADS)
Ferrari, Giovanni; Amabili, Marco
2015-04-01
The active vibration control of a free rectangular sandwich plate by using the Positive Position Feedback (PPF) algorithm was experimentally investigated in a previous study. Four normal modes were controlled by four nearly collocated couples of piezoelectric sensors and actuators. The experimental results of the control showed some limitation, especially in the Multi-Input Multi-Output (MIMO) configuration. This was attributed to the specific type of sensors and their conditioning, as well as to the phase shifts present in the vibration at different points of the structure. An alternative approach is here undertaken by abandoning the configuration of quasi-perfect collocation between sensor and actuator. The positioning of the piezoelectric patches is still led by the strain energy value distribution on the plate; each couple of sensor and actuator is now placed on the same face of the plate but in two distinct positions, opposed and symmetrical with respect to the geometric center of the plate. Single-Input Single-Output (SISO) PPF is tested and the transfer function parameters of the controller are tuned according to the measured values of modal damping. Then the participation matrices necessary for the MIMO control algorithm are determined by means of a completely experimental procedure. PPF is able to mitigate the vibration of the first four natural modes, in spite of the rigid body motions due to the free boundary conditions. The amplitude reduction achieved with the non-collocated configuration is much larger than the one obtained with the nearby collocated one. The phase lags were addressed in the MIMO algorithm by correction phase delays, further increasing the performance of the controller.
Ma, Chien-Ching; Chuang, Kuo-Chih; Pan, Shan-Ying
2011-12-01
Polyvinylidene fluoride (PVDF) films are light, flexible, and have high piezoelectricity. Because of these advantages, they have been widely used as sensors in applications such as underwater investigation, nondestructive damage detection, robotics, and active vibration suppression. PVDF sensors are especially preferred over conventional strain gauges in active vibration control because the PVDF sensors are easy to cut into different sizes or shapes as piezoelectric actuators and they can then be placed as collocated pairs. In this work, to focus on demonstrating the dynamic sensing performance of the PVDF film sensor, we revisit the active vibration control problem of a cantilever beam using a collocated lead zirconate titanate (PZT) actuator/PVDF film sensor pair. Before applying active vibration control, the measurement characteristics of the PVDF film sensor are studied by simultaneous comparison with a strain gauge. The loading effect of the piezoelectric actuator on the cantilever beam is also investigated in this paper. Finally, four simple, robust active vibration controllers are employed with the collocated PZT/PVDF pair to suppress vibration of the cantilever beam subjected to impact loadings. The four controllers are the velocity feedback controller, the integral resonant controller (IRC), the resonant controller, and the positive position feedback (PPF) controller. Suppression of impact disturbances is especially suitable for the purpose of demonstrating the dynamic sensing performance of the PVDF sensor. The experimental results also provide suggestions for choosing between the previously mentioned controllers, which have been proven to be effective in suppressing impact-induced vibrations. PMID:23443690
NASA Technical Reports Server (NTRS)
Robbins, J. W.
1985-01-01
An autonomous spaceborne gravity gradiometer mission is being considered as a post Geopotential Research Mission project. The introduction of satellite diometry data to geodesy is expected to improve solid earth gravity models. The possibility of utilizing gradiometer data for the determination of pertinent gravimetric quantities on a local basis is explored. The analytical technique of least squares collocation is investigated for its usefulness in local solutions of this type. It is assumed, in the error analysis, that the vertical gravity gradient component of the gradient tensor is used as the raw data signal from which the corresponding reference gradients are removed to create the centered observations required in the collocation solution. The reference gradients are computed from a high degree and order geopotential model. The solution can be made in terms of mean or point gravity anomalies, height anomalies, or other useful gravimetric quantities depending on the choice of covariance types. Selected for this study were 30 x 30 foot mean gravity and height anomalies. Existing software and new software are utilized to implement the collocation technique. It was determined that satellite gradiometry data at an altitude of 200 km can be used successfully for the determination of 30 x 30 foot mean gravity anomalies to an accuracy of 9.2 mgal from this algorithm. It is shown that the resulting accuracy estimates are sensitive to gravity model coefficient uncertainties, data reduction assumptions and satellite mission parameters.
Nilles, M.A.; Gordon, J.D.; Schroder, L.J.
1994-01-01
A collocated, wet-deposition sampler program has been operated since October 1988 by the U.S. Geological Survey to estimate the overall sampling precision of wet atmospheric deposition data collected at selected sites in the National Atmospheric Deposition Program and National Trends Network (NADP/NTN). A duplicate set of wet-deposition sampling instruments was installed adjacent to existing sampling instruments at four different NADP/NTN sites for each year of the study. Wet-deposition samples from collocated sites were collected and analysed using standard NADP/NTN procedures. Laboratory analyses included determinations of pH, specific conductance, and concentrations of major cations and anions. The estimates of precision included all variability in the data-collection system, from the point of sample collection through storage in the NADP/NTN database. Sampling precision was determined from the absolute value of differences in the analytical results for the paired samples in terms of median relative and absolute difference. The median relative difference for Mg2+, Na+, K+ and NH4+ concentration and deposition was quite variable between sites and exceeded 10% at most sites. Relative error for analytes whose concentrations typically approached laboratory method detection limits were greater than for analytes that did not typically approach detection limits. The median relative difference for SO42- and NO3- concentration, specific conductance, and sample volume at all sites was less than 7%. Precision for H+ concentration and deposition ranged from less than 10% at sites with typically high levels of H+ concentration to greater than 30% at sites with low H+ concentration. Median difference for analyte concentration and deposition was typically 1.5-2-times greater for samples collected during the winter than during other seasons at two northern sites. Likewise, the median relative difference in sample volume for winter samples was more than double the annual median
A spline-based parameter estimation technique for static models of elastic structures
NASA Technical Reports Server (NTRS)
Dutt, P.; Taasan, S.
1986-01-01
The problem of identifying the spatially varying coefficient of elasticity using an observed solution to the forward problem is considered. Under appropriate conditions this problem can be treated as a first order hyperbolic equation in the unknown coefficient. Some continuous dependence results are developed for this problem and a spline-based technique is proposed for approximating the unknown coefficient, based on these results. The convergence of the numerical scheme is established and error estimates obtained.
A spline-based parameter estimation technique for static models of elastic structures
NASA Technical Reports Server (NTRS)
Dutt, P.; Ta'asan, S.
1989-01-01
The problem of identifying the spatially varying coefficient of elasticity using an observed solution to the forward problem is considered. Under appropriate conditions this problem can be treated as a first order hyperbolic equation in the unknown coefficient. Some continuous dependence results are developed for this problem and a spline-based technique is proposed for approximating the unknown coefficient, based on these results. The convergence of the numerical scheme is established and error estimates obtained.
Estimation of Some Parameters from Morse-Morse-Spline-Van Der Waals Intermolecular Potential
Coroiu, I.
2007-04-23
Some parameters such as transport cross-sections and isotopic thermal diffusion factor have been calculated from an improved intermolecular potential, Morse-Morse-Spline-van der Waals (MMSV) potential proposed by R.A. Aziz et al. The treatment was completely classical and no corrections for quantum effects were made. The results would be employed for isotope separations of different spherical and quasi-spherical molecules.
Optimal Knot Selection for Least-squares Fitting of Noisy Data with Spline Functions
Jerome Blair
2008-05-15
An automatic data-smoothing algorithm for data from digital oscilloscopes is described. The algorithm adjusts the bandwidth of the filtering as a function of time to provide minimum mean squared error at each time. It produces an estimate of the root-mean-square error as a function of time and does so without any statistical assumptions about the unknown signal. The algorithm is based on least-squares fitting to the data of cubic spline functions.
A nonrational B-spline profiled horn with high displacement amplification for ultrasonic welding.
Nguyen, Huu-Tu; Nguyen, Hai-Dang; Uan, Jun-Yen; Wang, Dung-An
2014-12-01
A new horn with high displacement amplification for ultrasonic welding is developed. The profile of the horn is a nonrational B-spline curve with an open uniform knot vector. The ultrasonic actuation of the horn exploits the first longitudinal displacement mode of the horn. The horn is designed by an optimization scheme and finite element analyses. Performances of the proposed horn have been evaluated by experiments. The displacement amplification of the proposed horn is 41.4% and 8.6% higher than that of the traditional catenoidal horn and a Bézier-profile horn, respectively, with the same length and end surface diameters. The developed horn has a lower displacement amplification than the nonuniform rational B-spline profiled horn but a much smoother stress distribution. The developed horn, the catenoidal horn, and the Bézier horn are fabricated and used for ultrasonic welding of lap-shear specimens. The bonding strength of the joints welded by the open uniform nonrational B-spline (OUNBS) horn is the highest among the three horns for the various welding parameters considered. The locations of the failure mode and the distribution of the voids of the specimens are investigated to explain the reason of the high bonding strength achieved by the OUNBS horn. PMID:25081407
Drill string splined resilient tubular telescopic joint for balanced load drilling of deep holes
Garrett, W.R.
1981-08-04
A drill string splined resilient tubular telescopic joint for balanced load deep well drilling comprises a double acting damper having a very low spring rate upon both extension and contraction from the zero deflection condition. Preferably the spring means itself is a double acting compression spring means wherein the same spring means is compressed whether the joint is extended or contracted. The damper has a like low spring rate over a considerable range of deflection, both upon extension and contraction of the joint, but a gradually then rapidly increased spring rate upon approaching the travel limits in each direction. Stacks of spring rings are employed for the spring means, the rings being either shaped elastomer-metal sandwiches or, preferably, roller belleville springs. The spline and spring means are disposed in an annular chamber formed by mandrel and barrel members constituting the telescopic joint. The spring rings make only such line contact with one of the telescoping members as is required for guidance therefrom, and no contact with the other member. The chamber containing the spring means, and also containing the spline means, is filled with lubricant, the chamber being sealed with a pressure seal at its lower end and an inverted floating seal at its upper end. Magnetic and electrical means are provided to check for the presence and condition of the lubricant. To increase load capacity the spring means is made of a number of components acting in parallel.
Drill string splined resilient tubular telescopic joint for balanced load drilling of deep holes
Garrett, W.R.
1984-03-06
A drill string splined resilient tubular telescopic joint for balanced load deep well drilling comprises a double acting damper having a very low spring rate upon both extension and contraction from the zero deflection condition. Stacks of spring rings are employed for the spring means, the rings being either shaped elastomer-metal sandwiches or, preferably, roller Belleville springs. The spline and spring means are disposed in an annular chamber formed by mandrel and barrel members constituting the telescopic joint. The chamber containing the spring means, and also containing the spline means, is filled with lubricant, the chamber being sealed with a pressure seal at its lower end and an inverted floating seal at its upper end. A prototype includes of this a bellows seal instead of the floating seal at the upper end of the tool, and a bellows in the side of the lubricant chamber provides volume compensation. A second lubricant chamber is provided below the pressure seal, the lower end of the second chamber being closed by a bellows seal and a further bellows in the side of the second chamber providing volume compensation. Modifications provide hydraulic jars.
NASA Astrophysics Data System (ADS)
Shao, Chenxi; Xue, Yong; Fang, Fang; Bai, Fangzhou; Yin, Peifeng; Wang, Binghong
2015-07-01
The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedback control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily.
Shao, Chenxi; Xue, Yong; Fang, Fang; Bai, Fangzhou; Yin, Peifeng; Wang, Binghong
2015-07-01
The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedback control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily. PMID:26232956
Oguro, Sota; Tokuda, Junichi; Elhawary, Haytham; Haker, Steven; Kikinis, Ron; Tempany, Clare M.C.; Hata, Nobuhiko
2009-01-01
Purpose To apply an intensity-based nonrigid registration algorithm to MRI-guided prostate brachytherapy clinical data and to assess its accuracy. Materials and Methods A nonrigid registration of preoperative MRI to intraoperative MRI images was carried out in 16 cases using a Basis-Spline algorithm in a retrospective manner. The registration was assessed qualitatively by experts’ visual inspection and quantitatively by measuring the Dice similarity coefficient (DSC) for total gland (TG), central gland (CG), and peripheral zone (PZ), the mutual information (MI) metric, and the fiducial registration error (FRE) between corresponding anatomical landmarks for both the nonrigid and a rigid registration method. Results All 16 cases were successfully registered in less than 5 min. After the nonrigid registration, DSC values for TG, CG, PZ were 0.91, 0.89, 0.79, respectively, the MI metric was −0.19 ± 0.07 and FRE presented a value of 2.3 ± 1.8 mm. All the metrics were significantly better than in the case of rigid registration, as determined by one-sided t-tests. Conclusion The intensity-based nonrigid registration method using clinical data was demonstrated to be feasible and showed statistically improved metrics when compare to only rigid registration. The method is a valuable tool to integrate pre- and intraoperative images for brachytherapy. PMID:19856437
Shao, Chenxi Xue, Yong; Fang, Fang; Bai, Fangzhou; Yin, Peifeng; Wang, Binghong
2015-07-15
The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedback control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily.