4,112 research outputs found
Robust and Efficient Uncertainty Quantification and Validation of RFIC Isolation
Modern communication and identification products impose demanding constraints on reliability of components. Due to this statistical constraints more and more enter optimization formulations of electronic products. Yield constraints often require efficient sampling techniques to obtain uncertainty quantification also at the tails of the distributions. These sampling techniques should outperform standard Monte Carlo techniques, since these latter ones are normally not efficient enough to deal with tail probabilities. One such a technique, Importance Sampling, has successfully been applied to optimize Static Random Access Memories (SRAMs) while guaranteeing very small failure probabilities, even going beyond 6-sigma variations of parameters involved. Apart from this, emerging uncertainty quantifications techniques offer expansions of the solution that serve as a response surface facility when doing statistics and optimization. To efficiently derive the coefficients in the expansions one either has to solve a large number of problems or a huge combined problem. Here parameterized Model Order Reduction (MOR) techniques can be used to reduce the work load. To also reduce the amount of parameters we identify those that only affect the variance in a minor way. These parameters can simply be set to a fixed value. The remaining parameters can be viewed as dominant. Preservation of the variation also allows to make statements about the approximation accuracy obtained by the parameter-reduced problem. This is illustrated on an RLC circuit. Additionally, the MOR technique used should not affect the variance significantly. Finally we consider a methodology for reliable RFIC isolation using floor-plan modeling and isolation grounding. Simulations show good comparison with measurements
Meta-models for structural reliability and uncertainty quantification
A meta-model (or a surrogate model) is the modern name for what was
traditionally called a response surface. It is intended to mimic the behaviour
of a computational model M (e.g. a finite element model in mechanics) while
being inexpensive to evaluate, in contrast to the original model which may take
hours or even days of computer processing time. In this paper various types of
meta-models that have been used in the last decade in the context of structural
reliability are reviewed. More specifically classical polynomial response
surfaces, polynomial chaos expansions and kriging are addressed. It is shown
how the need for error estimates and adaptivity in their construction has
brought this type of approaches to a high level of efficiency. A new technique
that solves the problem of the potential biasedness in the estimation of a
probability of failure through the use of meta-models is finally presented.Comment: Keynote lecture Fifth Asian-Pacific Symposium on Structural
Reliability and its Applications (5th APSSRA) May 2012, Singapor
Measure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems
Coupled problems with various combinations of multiple physics, scales, and
domains are found in numerous areas of science and engineering. A key challenge
in the formulation and implementation of corresponding coupled numerical models
is to facilitate the communication of information across physics, scale, and
domain interfaces, as well as between the iterations of solvers used for
response computations. In a probabilistic context, any information that is to
be communicated between subproblems or iterations should be characterized by an
appropriate probabilistic representation. Although the number of sources of
uncertainty can be expected to be large in most coupled problems, our
contention is that exchanged probabilistic information often resides in a
considerably lower dimensional space than the sources themselves. In this work,
we thus use a dimension-reduction technique for obtaining the representation of
the exchanged information. The main subject of this work is the investigation
of a measure-transformation technique that allows implementations to exploit
this dimension reduction to achieve computational gains. The effectiveness of
the proposed dimension-reduction and measure-transformation methodology is
demonstrated through a multiphysics problem relevant to nuclear engineering
Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations
Stochastic Galerkin methods for non-affine coefficient representations are
known to cause major difficulties from theoretical and numerical points of
view. In this work, an adaptive Galerkin FE method for linear parametric PDEs
with lognormal coefficients discretized in Hermite chaos polynomials is
derived. It employs problem-adapted function spaces to ensure solvability of
the variational formulation. The inherently high computational complexity of
the parametric operator is made tractable by using hierarchical tensor
representations. For this, a new tensor train format of the lognormal
coefficient is derived and verified numerically. The central novelty is the
derivation of a reliable residual-based a posteriori error estimator. This can
be regarded as a unique feature of stochastic Galerkin methods. It allows for
an adaptive algorithm to steer the refinements of the physical mesh and the
anisotropic Wiener chaos polynomial degrees. For the evaluation of the error
estimator to become feasible, a numerically efficient tensor format
discretization is developed. Benchmark examples with unbounded lognormal
coefficient fields illustrate the performance of the proposed Galerkin
discretization and the fully adaptive algorithm
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
Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints
This paper presents a stochastic model predictive control approach for
nonlinear systems subject to time-invariant probabilistic uncertainties in
model parameters and initial conditions. The stochastic optimal control problem
entails a cost function in terms of expected values and higher moments of the
states, and chance constraints that ensure probabilistic constraint
satisfaction. The generalized polynomial chaos framework is used to propagate
the time-invariant stochastic uncertainties through the nonlinear system
dynamics, and to efficiently sample from the probability densities of the
states to approximate the satisfaction probability of the chance constraints.
To increase computational efficiency by avoiding excessive sampling, a
statistical analysis is proposed to systematically determine a-priori the least
conservative constraint tightening required at a given sample size to guarantee
a desired feasibility probability of the sample-approximated chance constraint
optimization problem. In addition, a method is presented for sample-based
approximation of the analytic gradients of the chance constraints, which
increases the optimization efficiency significantly. The proposed stochastic
nonlinear model predictive control approach is applicable to a broad class of
nonlinear systems with the sufficient condition that each term is analytic with
respect to the states, and separable with respect to the inputs, states and
parameters. The closed-loop performance of the proposed approach is evaluated
using the Williams-Otto reactor with seven states, and ten uncertain parameters
and initial conditions. The results demonstrate the efficiency of the approach
for real-time stochastic model predictive control and its capability to
systematically account for probabilistic uncertainties in contrast to a
nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro
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