180 research outputs found
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
Determination of Bond Wire Failure Probabilities in Microelectronic Packages
This work deals with the computation of industry-relevant bond wire failure
probabilities in microelectronic packages. Under operating conditions, a
package is subject to Joule heating that can lead to electrothermally induced
failures. Manufacturing tolerances result, e.g., in uncertain bond wire
geometries that often induce very small failure probabilities requiring a high
number of Monte Carlo (MC) samples to be computed. Therefore, a hybrid MC
sampling scheme that combines the use of an expensive computer model with a
cheap surrogate is used. The fraction of surrogate evaluations is maximized
using an iterative procedure, yielding accurate results at reduced cost.
Moreover, the scheme is non-intrusive, i.e., existing code can be reused. The
algorithm is used to compute the failure probability for an example package and
the computational savings are assessed by performing a surrogate efficiency
study.Comment: submitted to Therminic 2016, available at
http://ieeexplore.ieee.org/document/7748645
Modeling of Spatial Uncertainties in the Magnetic Reluctivity
In this paper a computationally efficient approach is suggested for the
stochastic modeling of an inhomogeneous reluctivity of magnetic materials.
These materials can be part of electrical machines, such as a single phase
transformer (a benchmark example that is considered in this paper). The
approach is based on the Karhunen-Lo\`{e}ve expansion. The stochastic model is
further used to study the statistics of the self inductance of the primary coil
as a quantity of interest.Comment: submitted to COMPE
Collision detection for rigid superellipsoids using the normal parameterization
The normal parameterization as an approach to describe geometries is introduced. The advantages of this description – as compared to other parameterizations or implicit functions – in the context of collision detection are: the possibility to explicitly calculate axis aligned bounding boxes for any convex geometry, an efficient iterative algorithm for collision detection between objects with arbitrary geometry that does not require any (analytical) derivatives. A system of several rigid superellipsoids is used to demonstrate the application and performance of the proposed approach in a multibody simulation
Coupled Simulation of Transient Heat Flow and Electric Currents in Thin Wires: Application to Bond Wires in Microelectronic Chip Packaging
This work addresses the simulation of heat flow and electric currents in thin
wires. An important application is the use of bond wires in microelectronic
chip packaging. The heat distribution is modeled by an electrothermal coupled
problem, which poses numerical challenges due to the presence of different
geometric scales. The necessity of very fine grids is relaxed by solving and
embedding a 1D sub-problem along the wire into the surrounding 3D geometry. The
arising singularities are described using de Rham currents. It is shown that
the problem is related to fluid flow in porous 3D media with 1D fractures [C.
D'Angelo, SIAM Journal on Numerical Analysis 50.1, pp. 194-215, 2012]. A
careful formulation of the 1D-3D coupling condition is essential to obtain a
stable scheme that yields a physical solution. Elliptic model problems are used
to investigate the numerical errors and the corresponding convergence rates.
Additionally, the transient electrothermal simulation of a simplified
microelectronic chip package as used in industrial applications is presented.Comment: all numerical results can be reproduced by the Matlab code openly
available at https://github.com/tc88/ETwireSi
Low-Dimensional Stochastic Modeling of the Electrical Properties of Biological Tissues
Uncertainty quantification plays an important role in biomedical engineering
as measurement data is often unavailable and literature data shows a wide
variability. Using state-of-the-art methods one encounters difficulties when
the number of random inputs is large. This is the case, e.g., when using
composite Cole-Cole equations to model random electrical properties. It is
shown how the number of parameters can be significantly reduced by the
Karhunen-Loeve expansion. The low-dimensional random model is used to quantify
uncertainties in the axon activation during deep brain stimulation. Numerical
results for a Medtronic 3387 electrode design are given.Comment: 4 pages, 5 figure
Energy-optimized bipedal running of a simple humanoid robot
A method to optimize energy efficiency for bipedal running robots is presented. A running model of a simple bipedal robot consisting of five rigid bodies connected by actuated revolute joints is introduced. The actuators’ torques are generated by a trajectory tracking controller to produce periodic running gaits. The controller’s reference trajectories are parameterized by Bézier polynomials. A numerical optimization is used to employ reference trajectories with optimal energy efficiency for average velocities in the range of 1.5 to 5.5 m/s
A Brief Survey on Non-standard Constraints: Simulation and Optimal Control
In terms of simulation and control holonomic constraints are well documented and thus termed standard. As non-standard constraints, we understand non-holonomic and unilateral constraints. We limit this survey to mechanical systems with a finite number of degrees of freedom. The long-term behavior of non-
holonomic integrators as compared to structure-preserving integrators for holonomically constrained systems is briefly discussed. Some recent research regarding the treatment of unilaterally constrained systems by event-driven or time-stepping schemes for time integration and in the context of optimal control problems is outlined
Investigation of optimal bipedal walking gaits subject to different energy-based objective functions
Optimal bipedal walking gaits subject to different energy-based objective functions are investigated using a simple planar rigid body model of a bipedal robot with upper body, thighs and shanks. The robot’s segments are connected by revolute joints actuated by electric motors. The actuators’ torques are generated by a trajectory tracking controller to produce periodic walking gaits. A numerical optimization routine is used to find optimal reference trajectories for average speeds in the range of 0.3 – 2.3 m/s to investigate the influence of different objective functions
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