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Accuracy Problems (accuracy + problem)
Selected AbstractsSpeed Estimation from Single Loop Data Using an Unscented Particle FilterCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 7 2010Zhirui Ye The Kalman filters used in past speed estimation studies employ a Gaussian assumption that is hardly satisfied. The hybrid method that combines a parametric filter (Unscented Kalman Filter) and a nonparametric filter (Particle Filter) is thus proposed to overcome the limitations of the existing methods. To illustrate the advantage of the proposed approach, two data sets collected from field detectors along with a simulated data set are utilized for performance evaluation and comparison with the Extended Kalman Filter and the Unscented Kalman Filter. It is found that the proposed method outperforms the evaluated Kalman filter methods. The UPF method produces accurate speed estimation even for congested flow conditions in which many other methods have significant accuracy problems. [source] A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2010G. R. Liu Abstract In part I of this paper, we have established the G space theory and fundamentals for W2 formulation. Part II focuses on the applications of the G space theory to formulate W2 models for solid mechanics problems. We first define a bilinear form, prove some of the important properties, and prove that the W2 formulation will be spatially stable, and convergent to exact solutions. We then present examples of some of the possible W2 models including the SFEM, NS-FEM, ES-FEM, NS-PIM, ES-PIM, and CS-PIM. We show the major properties of these models: (1) they are variationally consistent in a conventional sense, if the solution is sought in a proper H space (compatible cases); (2) They pass the standard patch test when the solution is sought in a proper G space with discontinuous functions (incompatible cases); (3) the stiffness of the discretized model is reduced compared with the finite element method (FEM) model and possibly to the exact model, allowing us to obtain upper bound solutions with respect to both the FEM and the exact solutions and (4) the W2 models are less sensitive to the quality of the mesh, and triangular meshes can be used without any accuracy problems. These properties and theories have been confirmed numerically via examples solved using a number of W2 models including compatible and incompatible cases. We shall see that the G space theory and the W2 forms can formulate a variety of stable and convergent numerical methods with the FEM as one special case. Copyright © 2009 John Wiley & Sons, Ltd. [source] On evaluation of shape sensitivities of non-linear critical loadsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2003E. Parente Jr. Abstract The present paper focuses on the evaluation of the shape sensitivities of the limit and bifurcation loads of geometrically non-linear structures. The analytical approach is applied for isoparametric elements, leading to exact results for a given mesh. Since this approach is difficult to apply to other element types, the semi-analytical method has been widely used for shape sensitivity computation. This method combines ease of implementation with computational efficiency, but presents severe accuracy problems. Thus, a general procedure to improve the semi-analytical sensitivities of the non-linear critical loads is presented. The numerical examples show that this procedure leads to sensitivities with sufficient accuracy for shape optimization applications. Copyright © 2002 John Wiley & Sons, Ltd. [source] Refined second order semi-analytical design sensitivitiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2002H. de Boer Abstract Accurate and efficient calculation of second order design sensitivities in a finite element context is often difficult. The semi-analytical (SA) method is efficient and easy to implement but has accuracy problems even for first order shape design sensitivities. To overcome accuracy problems a refined semi-analytical (RSA) method has been developed for first order sensitivities. The present paper investigates the application of the RSA method to second order design sensitivities. It is found that second order RSA sensitivities are significantly more accurate than their SA counterparts. Copyright © 2002 John Wiley & Sons, Ltd. [source] | ||||||||||