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Piecewise Linear (piecewise + linear)

Distribution by Scientific Domains
Engineering42%

Terms modified by Piecewise Linear

  • piecewise linear approximation
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  • piecewise linear function
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    Selected Abstracts

    A rational approach to mass matrix diagonalization in two-dimensional elastodynamics

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004
    E. A. Paraskevopoulos
    Abstract A variationally consistent methodology is presented, which yields diagonal mass matrices in two-dimensional elastodynamic problems. The proposed approach avoids ad hoc procedures and applies to arbitrary quadrilateral and triangular finite elements. As a starting point, a modified variational principle in elastodynamics is used. The time derivatives of displacements, the velocities, and the momentum type variables are assumed as independent variables and are approximated using piecewise linear or constant functions and combinations of piecewise constant polynomials and Dirac distributions. It is proved that the proposed methodology ensures consistency and stability. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    A Petrov,Galerkin finite element model for one-dimensional fully non-linear and weakly dispersive wave propagation

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2001
    Seung-Buhm Woo
    Abstract A new finite element method is presented to solve one-dimensional depth-integrated equations for fully non-linear and weakly dispersive waves. For spatial integration, the Petrov,Galerkin weighted residual method is used. The weak forms of the governing equations are arranged in such a way that the shape functions can be piecewise linear, while the weighting functions are piecewise cubic with C2 -continuity. For the time integration an implicit predictor,corrector iterative scheme is employed. Within the framework of linear theory, the accuracy of the scheme is discussed by considering the truncation error at a node. The leading truncation error is fourth-order in terms of element size. Numerical stability of the scheme is also investigated. If the Courant number is less than 0.5, the scheme is unconditionally stable. By increasing the number of iterations and/or decreasing the element size, the stability characteristics are improved significantly. Both Dirichlet boundary condition (for incident waves) and Neumann boundary condition (for a reflecting wall) are implemented. Several examples are presented to demonstrate the range of applicabilities and the accuracy of the model. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Improved bolus arrival time and arterial input function estimation for tracer kinetic analysis in DCE-MRI

    JOURNAL OF MAGNETIC RESONANCE IMAGING, Issue 1 2009
    Anup Singh PhD
    Abstract Purpose To develop a methodology for improved estimation of bolus arrival time (BAT) and arterial input function (AIF) which are prerequisites for tracer kinetic analysis of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data and to verify the applicability of the same in the case of intracranial lesions (brain tumor and tuberculoma). Materials and Methods A continuous piecewise linear (PL) model (with BAT as one of the free parameters) is proposed for concentration time curve C(t) in T1 -weighted DCE-MRI. The resulting improved procedure suggested for automatic extraction of AIF is compared with earlier methods. The accuracy of BAT and other estimated parameters is tested over simulated as well as experimental data. Results The proposed PL model provides a good approximation of C(t) trends of interest and fit parameters show their significance in a better understanding and classification of different tissues. BAT was correctly estimated. The automatic and robust estimation of AIF obtained using the proposed methodology also corrects for partial volume effects. The accuracy of tracer kinetic analysis is improved and the proposed methodology also reduces the time complexity of the computations. Conclusion The PL model parameters along with AIF measured by the proposed procedure can be used for an improved tracer kinetic analysis of DCE-MRI data. J. Magn. Reson. Imaging 2009;29:166,176. © 2008 Wiley-Liss, Inc. [source]

    A simple monotone process with application to radiocarbon-dated depth chronologies

    JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 4 2008
    John Haslett
    Summary., We propose a new and simple continuous Markov monotone stochastic process and use it to make inference on a partially observed monotone stochastic process. The process is piecewise linear, based on additive independent gamma increments arriving in a Poisson fashion. An independent increments variation allows very simple conditional simulation of sample paths given known values of the process. We take advantage of a reparameterization involving the Tweedie distribution to provide efficient computation. The motivating problem is the establishment of a chronology for samples taken from lake sediment cores, i.e. the attribution of a set of dates to samples of the core given their depths, knowing that the age,depth relationship is monotone. The chronological information arises from radiocarbon (14C) dating at a subset of depths. We use the process to model the stochastically varying rate of sedimentation. [source]

    Bayesian optimal reconstruction of the primordial power spectrum

    MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2009
    M. Bridges
    ABSTRACT The form of the primordial power spectrum has the potential to differentiate strongly between competing models of perturbation generation in the early universe and so is of considerable importance. The recent release of five years of Wilkinson Microwave Anisotropy Probe observations have confirmed the general picture of the primordial power spectrum as deviating slightly from scale invariance with a spectral tilt parameter of ns, 0.96. None the less, many attempts have been made to isolate further features such as breaks and cut-offs using a variety of methods, some employing more than ,10 varying parameters. In this paper, we apply the robust technique of the Bayesian model selection to reconstruct the optimal degree of structure in the spectrum. We model the spectrum simply and generically as piecewise linear in ln k between ,nodes' in k space whose amplitudes are allowed to vary. The number of nodes and their k -space positions are chosen by the Bayesian evidence so that we can identify both the complexity and location of any detected features. Our optimal reconstruction contains, perhaps, surprisingly few features, the data preferring just three nodes. This reconstruction allows for a degree of scale dependence of the tilt with the ,turn-over' scale occurring around k, 0.016 Mpc,1. More structure is penalized by the evidence as overfitting the data, so there is currently little point in attempting reconstructions that are more complex. [source]

    Robust modelling of DTARCH models

    THE ECONOMETRICS JOURNAL, Issue 2 2005
    Yer Van Hui
    Summary, Autoregressive conditional heteroscedastic (ARCH) models and its extensions are widely used in modelling volatility in financial time series. One of the variants, the double-threshold autoregressive conditional heteroscedastic (DTARCH) model, has been proposed to model the conditional mean and the conditional variance that are piecewise linear. The DTARCH model is also useful for modelling conditional heteroscedasticity with nonlinear structures such as asymmetric cycles, jump resonance and amplitude-frequence dependence. Since asset returns often display heavy tails and outliers, it is worth studying robust DTARCH modelling without specific distribution assumption. This paper studies DTARCH structures for conditional scale instead of conditional variance. We examine L1 -estimation of the DTARCH model and derive limiting distributions for the proposed estimators. A robust portmanteau statistic based on the L1 -norm fit is constructed to test the model adequacy. This approach captures various nonlinear phenomena and stylized facts with desirable robustness. Simulations show that the L1 -estimators are robust against innovation distributions and accurate for a moderate sample size, and the proposed test is not only robust against innovation distributions but also powerful in discriminating the delay parameters and ARCH models. It is noted that the quasi-likelihood modelling approach used in ARCH models is inappropriate to DTARCH models in the presence of outliers and heavy tail innovations. [source]

    Observer-based controller design of discrete-time piecewise affine systems

    ASIAN JOURNAL OF CONTROL, Issue 4 2010
    Ya-Hui Gao
    Abstract This paper presents a novel observer-based controller design method for discrete-time piecewise affine (PWA) systems. The basic idea is as follows: at first, a piecewise linear (without affine terms) state feedback controller and a PWA observer are designed separately, and then it is proved that the output feedback controller constructed by the resulting observer and state feedback controller gains can guarantee the stability of the closed-loop system. During the controller design, the piecewise-quadratic Lyapunov function technique is used. Moreover, the region information is taken into account to treat the affine terms, so the controller gains can be obtained by solving a set of linear matrix inequalities, which are numerically feasible with commercially available software. Three simulation examples are given finally to verify the proposed theoretical results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]