2,299 research outputs found
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
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
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
Polynomial Chaos Expansion of random coefficients and the solution of stochastic partial differential equations in the Tensor Train format
We apply the Tensor Train (TT) decomposition to construct the tensor product
Polynomial Chaos Expansion (PCE) of a random field, to solve the stochastic
elliptic diffusion PDE with the stochastic Galerkin discretization, and to
compute some quantities of interest (mean, variance, exceedance probabilities).
We assume that the random diffusion coefficient is given as a smooth
transformation of a Gaussian random field. In this case, the PCE is delivered
by a complicated formula, which lacks an analytic TT representation. To
construct its TT approximation numerically, we develop the new block TT cross
algorithm, a method that computes the whole TT decomposition from a few
evaluations of the PCE formula. The new method is conceptually similar to the
adaptive cross approximation in the TT format, but is more efficient when
several tensors must be stored in the same TT representation, which is the case
for the PCE. Besides, we demonstrate how to assemble the stochastic Galerkin
matrix and to compute the solution of the elliptic equation and its
post-processing, staying in the TT format.
We compare our technique with the traditional sparse polynomial chaos and the
Monte Carlo approaches. In the tensor product polynomial chaos, the polynomial
degree is bounded for each random variable independently. This provides higher
accuracy than the sparse polynomial set or the Monte Carlo method, but the
cardinality of the tensor product set grows exponentially with the number of
random variables. However, when the PCE coefficients are implicitly
approximated in the TT format, the computations with the full tensor product
polynomial set become possible. In the numerical experiments, we confirm that
the new methodology is competitive in a wide range of parameters, especially
where high accuracy and high polynomial degrees are required.Comment: This is a major revision of the manuscript arXiv:1406.2816 with
significantly extended numerical experiments. Some unused material is remove
Stochastic collocation on unstructured multivariate meshes
Collocation has become a standard tool for approximation of parameterized
systems in the uncertainty quantification (UQ) community. Techniques for
least-squares regularization, compressive sampling recovery, and interpolatory
reconstruction are becoming standard tools used in a variety of applications.
Selection of a collocation mesh is frequently a challenge, but methods that
construct geometrically "unstructured" collocation meshes have shown great
potential due to attractive theoretical properties and direct, simple
generation and implementation. We investigate properties of these meshes,
presenting stability and accuracy results that can be used as guides for
generating stochastic collocation grids in multiple dimensions.Comment: 29 pages, 6 figure
- …