1,913 research outputs found
Probability density adjoint for sensitivity analysis of the Mean of Chaos
Sensitivity analysis, especially adjoint based sensitivity analysis, is a
powerful tool for engineering design which allows for the efficient computation
of sensitivities with respect to many parameters. However, these methods break
down when used to compute sensitivities of long-time averaged quantities in
chaotic dynamical systems.
The following paper presents a new method for sensitivity analysis of {\em
ergodic} chaotic dynamical systems, the density adjoint method. The method
involves solving the governing equations for the system's invariant measure and
its adjoint on the system's attractor manifold rather than in phase-space. This
new approach is derived for and demonstrated on one-dimensional chaotic maps
and the three-dimensional Lorenz system. It is found that the density adjoint
computes very finely detailed adjoint distributions and accurate sensitivities,
but suffers from large computational costs.Comment: 29 pages, 27 figure
Quantification of airfoil geometry-induced aerodynamic uncertainties - comparison of approaches
Uncertainty quantification in aerodynamic simulations calls for efficient
numerical methods since it is computationally expensive, especially for the
uncertainties caused by random geometry variations which involve a large number
of variables. This paper compares five methods, including quasi-Monte Carlo
quadrature, polynomial chaos with coefficients determined by sparse quadrature
and gradient-enhanced version of Kriging, radial basis functions and point
collocation polynomial chaos, in their efficiency in estimating statistics of
aerodynamic performance upon random perturbation to the airfoil geometry which
is parameterized by 9 independent Gaussian variables. The results show that
gradient-enhanced surrogate methods achieve better accuracy than direct
integration methods with the same computational cost
Conformally Mapped Polynomial Chaos Expansions for Maxwell's Source Problem with Random Input Data
Generalized Polynomial Chaos (gPC) expansions are well established for
forward uncertainty propagation in many application areas. Although the
associated computational effort may be reduced in comparison to Monte Carlo
techniques, for instance, further convergence acceleration may be important to
tackle problems with high parametric sensitivities. In this work, we propose
the use of conformal maps to construct a transformed gPC basis, in order to
enhance the convergence order. The proposed basis still features orthogonality
properties and hence, facilitates the computation of many statistical
properties such as sensitivities and moments. The corresponding surrogate
models are computed by pseudo-spectral projection using mapped quadrature
rules, which leads to an improved cost accuracy ratio. We apply the methodology
to Maxwell's source problem with random input data. In particular, numerical
results for a parametric finite element model of an optical grating coupler are
given
Derivative based global sensitivity measures
The method of derivative based global sensitivity measures (DGSM) has
recently become popular among practitioners. It has a strong link with the
Morris screening method and Sobol' sensitivity indices and has several
advantages over them. DGSM are very easy to implement and evaluate numerically.
The computational time required for numerical evaluation of DGSM is generally
much lower than that for estimation of Sobol' sensitivity indices. This paper
presents a survey of recent advances in DGSM concerning lower and upper bounds
on the values of Sobol' total sensitivity indices . Using these
bounds it is possible in most cases to get a good practical estimation of the
values of . Several examples are used to illustrate an
application of DGSM
A variational approach to probing extreme events in turbulent dynamical systems
Extreme events are ubiquitous in a wide range of dynamical systems, including
turbulent fluid flows, nonlinear waves, large scale networks and biological
systems. Here, we propose a variational framework for probing conditions that
trigger intermittent extreme events in high-dimensional nonlinear dynamical
systems. We seek the triggers as the probabilistically feasible solutions of an
appropriately constrained optimization problem, where the function to be
maximized is a system observable exhibiting intermittent extreme bursts. The
constraints are imposed to ensure the physical admissibility of the optimal
solutions, i.e., significant probability for their occurrence under the natural
flow of the dynamical system. We apply the method to a body-forced
incompressible Navier--Stokes equation, known as the Kolmogorov flow. We find
that the intermittent bursts of the energy dissipation are independent of the
external forcing and are instead caused by the spontaneous transfer of energy
from large scales to the mean flow via nonlinear triad interactions. The global
maximizer of the corresponding variational problem identifies the responsible
triad, hence providing a precursor for the occurrence of extreme dissipation
events. Specifically, monitoring the energy transfers within this triad, allows
us to develop a data-driven short-term predictor for the intermittent bursts of
energy dissipation. We assess the performance of this predictor through direct
numerical simulations.Comment: Minor revisions, generalized the constraints in Eq. (2
Trim Flight Conditions for a Low-Boom Aircraft Design Under Uncertainty
The purpose of this paper is to investigate the noise generation of a low-boom aircraft design in flight trim conditions under uncertainty. The deflection of control surfaces to maintain a trimmed flight state has the potential to change the perceived loudness at the ground. Furthermore, the uncertainties associated with the control surface deflections can complicate the overall uncertainty quantification. Incorporation of the uncertainties in the prediction of perceived sound levels during the design phase can lead to improved robustness. In this paper, a brief review of low-boom flight trim research is presented. Realistic flight trim conditions requiring control surface deflection are integrated into the current research efforts for uncertainty quantification and vehicle design. In addition, a generalized set of procedures for the characterization of uncertainties in flight trim conditions are introduced. In a case study of the application of these procedures, a 5 decibel average difference in the perceived level of loudness was found between clean (no deflections) and trimmed configurations. Also, uncertainties attributable to control surface deflection were found to account for, on average, over 50% of the total near field uncertainty. Uncertainty discretization methods implemented were able to give more insight into the overall global variances
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