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Sensitivity Calculations (sensitivity + calculation)

Distribution by Scientific Domains

Engineering	71%

Selected Abstracts

Forcing singular vectors and other sensitive model structures

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 592 2003
J. Barkmeijer
Abstract Model tendency perturbations can, like analysis perturbations, be an effective way to influence forecasts. In this paper, optimal model tendency perturbations, or forcing singular vectors, are computed with diabatic linear and adjoint T42L40 versions of the European Centre for Medium-Range Weather Forecasts' forecast model. During the forecast time, the spatial pattern of the tendency perturbation does not vary and the response at optimization time (48 hours) is measured in terms of total energy. Their properties are compared with those of initial singular vectors, and differences, such as larger horizontal scale and location, are discussed. Sensitivity calculations are also performed, whereby a cost function measuring the 2-day forecast error is minimized by only allowing tendency perturbations. For a given number of minimization steps, this approach yields larger cost-function reductions than the sensitivity calculation using only analysis perturbations. Nonlinear forecasts using only one type of perturbation confirm an improved performance in the case of tendency perturbations. For a summer experiment a substantial reduction of the systematic error is shown in the case of forcing sensitivity. Copyright © 2003 Royal Meteorological Society. [source]

Sensitivity analyses of FORM-based and DRM-based performance measure approach (PMA) for reliability-based design optimization (RBDO)

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2010
Ikjin Lee
Abstract In gradient-based design optimization, the sensitivities of the constraint with respect to the design variables are required. In reliability-based design optimization (RBDO), the probabilistic constraint is evaluated at the most probable point (MPP), and thus the sensitivities of the probabilistic constraints at MPP are required. This paper presents the rigorous analytic derivation of the sensitivities of the probabilistic constraint at MPP for both first-order reliability method (FORM)-based performance measure approach (PMA) and dimension reduction method (DRM)-based PMA. Numerical examples are used to demonstrate that the analytic sensitivities agree very well with the sensitivities obtained from the finite difference method (FDM). However, as the sensitivity calculation at the true DRM-based MPP requires the second-order derivatives and additional MPP search, the sensitivity derivation at the approximated DRM-based MPP, which does not require the second-order derivatives and additional MPP search to find the DRM-based MPP, is proposed in this paper. A convergence study illustrates that the sensitivity at the approximated DRM-based MPP converges to the sensitivity at the true DRM-based MPP as the design approaches the optimum design. Hence, the sensitivity at the approximated DRM-based MPP is proposed to be used for the DRM-based RBDO to enhance the efficiency of the optimization. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Forcing singular vectors and other sensitive model structures

Shape optimization of piezoelectric devices using an enriched meshfree method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2009
C. W. Liu
Abstract We present an enriched reproducing kernel particle method for shape sensitivity analysis and shape optimization of two-dimensional electromechanical domains. This meshfree method incorporates enrichment functions for better representation of discontinuous electromechanical fields across internal boundaries. We use cubic splines for delineating the geometry of internal/external domain boundaries; and the nodal coordinates and slopes of these splines at their control points become the design parameters. This approach enables smooth manipulations of bi-material interfaces and external boundaries during the optimization process. It also enables the calculation of displacement and electric-potential field sensitivities with respect to the design parameters through direct differentiation, for which we adopt the classical material derivative approach. We verify this implementation of sensitivity calculations against an exact solution to a variant of Lamé's problem, and also, finite-difference approximations. We follow a sequential quadratic programming approach to minimize the cost function; and demonstrate the utility of the overall technique through a model problem that involves the shape optimization of a piezoelectric fan. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Topology optimization by a neighbourhood search method based on efficient sensitivity calculations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2006
K. Svanberg
Abstract This paper deals with topology optimization of discretized load-carrying continuum structures, where the design of the structure is represented by binary design variables indicating material or void in the various finite elements. Efficient exact methods for discrete sensitivity calculations are developed. They utilize the fact that if just one or two binary variables are changed to their opposite binary values then the new stiffness matrix is essentially just a low-rank modification of the old stiffness matrix, even if some nodes in the structure may disappear or re-enter. As an application of these efficient sensitivity calculations, a new neighbourhood search method is presented, implemented, and applied on some test problems, one of them with 6912 nine-node finite elements where the von Mises stress in each non-void element is considered. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Fast implementations and rigorous models: Can both be accommodated in NMPC?

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2008
Victor M. Zavala
Abstract In less than two decades, nonlinear model predictive control has evolved from a conceptual framework to an attractive, general approach for the control of constrained nonlinear processes. These advances were realized both through better understanding of stability and robustness properties as well as improved algorithms for dynamic optimization. This study focuses on recent advances in optimization formulations and algorithms, particularly for the simultaneous collocation-based approach. Here, we contrast this approach with competing approaches for online application and discuss further advances to deal with applications of increasing size and complexity. To address these challenges, we adapt the real-time iteration concept, developed in the context of multiple shooting (Real-Time PDE-Constrained Optimization. SIAM: Philadelphia, PA, 2007; 25,52, 3,24), to a collocation-based approach with a full-space nonlinear programming solver. We show that straightforward sensitivity calculations from the Karush,Kuhn,Tucker system also lead to a real-time iteration strategy, with both direct and shifted variants. This approach is demonstrated on a large-scale polymer process, where online calculation effort is reduced by over two orders of magnitude. Copyright © 2007 John Wiley & Sons, Ltd. [source]