112,857 research outputs found
Shape optimization for quadratic functionals and states with random right-hand sides
In this work, we investigate a particular class of shape optimization
problems under uncertainties on the input parameters. More precisely, we are
interested in the minimization of the expectation of a quadratic objective in a
situation where the state function depends linearly on a random input
parameter. This framework covers important objectives such as tracking-type
functionals for elliptic second order partial differential equations and the
compliance in linear elasticity. We show that the robust objective and its
gradient are completely and explicitly determined by low-order moments of the
random input. We then derive a cheap, deterministic algorithm to minimize this
objective and present model cases in structural optimization
Optimal design and optimal control of structures undergoing finite rotations and elastic deformations
In this work we deal with the optimal design and optimal control of
structures undergoing large rotations. In other words, we show how to find the
corresponding initial configuration and the corresponding set of multiple load
parameters in order to recover a desired deformed configuration or some
desirable features of the deformed configuration as specified more precisely by
the objective or cost function. The model problem chosen to illustrate the
proposed optimal design and optimal control methodologies is the one of
geometrically exact beam. First, we present a non-standard formulation of the
optimal design and optimal control problems, relying on the method of Lagrange
multipliers in order to make the mechanics state variables independent from
either design or control variables and thus provide the most general basis for
developing the best possible solution procedure. Two different solution
procedures are then explored, one based on the diffuse approximation of
response function and gradient method and the other one based on genetic
algorithm. A number of numerical examples are given in order to illustrate both
the advantages and potential drawbacks of each of the presented procedures.Comment: 35 pages, 11 figure
Progressive construction of a parametric reduced-order model for PDE-constrained optimization
An adaptive approach to using reduced-order models as surrogates in
PDE-constrained optimization is introduced that breaks the traditional
offline-online framework of model order reduction. A sequence of optimization
problems constrained by a given Reduced-Order Model (ROM) is defined with the
goal of converging to the solution of a given PDE-constrained optimization
problem. For each reduced optimization problem, the constraining ROM is trained
from sampling the High-Dimensional Model (HDM) at the solution of some of the
previous problems in the sequence. The reduced optimization problems are
equipped with a nonlinear trust-region based on a residual error indicator to
keep the optimization trajectory in a region of the parameter space where the
ROM is accurate. A technique for incorporating sensitivities into a
Reduced-Order Basis (ROB) is also presented, along with a methodology for
computing sensitivities of the reduced-order model that minimizes the distance
to the corresponding HDM sensitivity, in a suitable norm. The proposed reduced
optimization framework is applied to subsonic aerodynamic shape optimization
and shown to reduce the number of queries to the HDM by a factor of 4-5,
compared to the optimization problem solved using only the HDM, with errors in
the optimal solution far less than 0.1%
Multidisciplinary design of a micro-USV for re-entry operations
Unmanned Space Vehicles (USV) are seen as a test-bed for enabling technologies and as a carrier to deliver and return experiments to and from low-Earth orbit. USV's are a potentially interesting solution also for the exploration of other planets or as long-range recognisance vehicles. As test bed, USV's are seen as a stepping stone for the development of future generation re-usable launchers but also as way to test key technologies for re-entry operations. Examples of recent developments are the PRORA-USV, designed by the Italian Aerospace Research Center (CIRA) in collaboration with Gavazzi Space, or the Boeing X-37B Orbital Test Vehicle (OTV), that is foreseen as an alternative to the space shuttle to deliver experiments into Earth orbit. Among the technologies to be demonstrated with the X-37 are improved thermal protection systems, avionics, the autonomous guidance system, and an advanced airfram
TVL<sub>1</sub> Planarity Regularization for 3D Shape Approximation
The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within.
This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy
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