Begell House Inc.
International Journal for Uncertainty Quantification
IJUQ
2152-5080
9
1
2019
PROPAGATION OF MODELING UNCERTAINTY IN STOCHASTIC HEAT-TRANSFER SIMULATION USING A CHAIN OF DETERMINISTIC MODELS
1-14
10.1615/Int.J.UncertaintyQuantification.2018027275
Deepak
Paudel
Department of Civil Engineering, Aalto University, Espoo, Finland
Simo
Hostikka
Department of Civil Engineering, Aalto University, Espoo, Finland
stochastic analysis
uncertainty propagation
modelling uncertainty
When using a chain of numerical models in a stochastic simulation, the distribution of the observed output depends on both the input parameter uncertainty and the errors of the individual models in the chain. In this work, the propagation of model uncertainty is studied in a simple one-dimensional heat-transfer system. The errors in temperature are found to depend on the heat flux coupling scenario and on the type of the input parameter distributions. The radiation heat flow boundary condition limits the error propagation by compensating the gas temperature errors through enhanced heat losses. Model biases were found to be detrimental to the accuracy of the predicted probabilities of exceeding safety criteria. Finally, corrections to the predicted distribution moments are proposed and tested, showing that the error contributions can be effectively eliminated from the observed distributions if the properties of the individual models are well known.
ENSEMBLE KALMAN FILTERS FOR RELIABILITY ESTIMATION IN PERFUSION INFERENCE
15-32
10.1615/Int.J.UncertaintyQuantification.2018024865
Peter
Zaspel
Department of Mathematics and Computer Science, University of Basel, Spiegelgasse 1, 4051
Basel, Switzerland
medical imaging
stochastic modeling
inverse problems
ensemble Kalman filter
dynamic contrast-enhanced imaging
perfusion
inference
We consider the solution of inverse problems in dynamic contrast–enhanced imaging by means of ensemble Kalman
filters. Our quantity of interest is blood perfusion, i.e., blood flow rates in tissue. While existing approaches to compute blood perfusion parameters for given time series of radiological measurements mainly rely on deterministic,
deconvolution–based methods, we aim at recovering probabilistic solution information for given noisy measurements. To this end, we model radiological image capturing as a sequential data assimilation process and solve it by an ensemble Kalman filter. Thereby, we recover deterministic results as an ensemble–based mean and are able to compute reliability information such as probabilities for the perfusion to be in a given range. Our target application is the inference of blood perfusion parameters in the human brain. A numerical study shows promising results for artificial measurements generated by a digital perfusion phantom.
ASSESSING THE PERFORMANCE OF LEJA AND CLENSHAW-CURTIS COLLOCATION FOR COMPUTATIONAL ELECTROMAGNETICS WITH RANDOM INPUT DATA
33-57
10.1615/Int.J.UncertaintyQuantification.2018025234
Dimitrios
Loukrezis
Centre for Computational Engineering, Technische Universität Darmstadt, Darmstadt,
Germany; Institut für Teilchenbeschleunigung und Elektromagnetische Felder (TEMF), Technische
Universität Darmstadt, Darmstadt, Germany
Ulrich
Römer
Institut für Dynamik und Schwingungen, Technische Universität Braunschweig, Schleinitzstraße
20, 38106 Braunschweig, Germany
Herbert
De Gersem
Institute for Accelerator Science and Electromagnetic Fields (TEMF), Technische Universität Darmstadt, Schlossgartenstraße 8, 64289 Darmstadt, Germany; Centre for Computational Engineering, Technische Universität Darmstadt, Dolivostraße 15,
64293 Darmstadt, Germany
dimension adaptivity
Clenshaw-Curtis
computational electromagnetics
Leja
sparse grids
stochastic collocation
uncertainty quantification
We consider the problem of quantifying uncertainty regarding the output of an electromagnetic field problem, in the
presence of a large number of uncertain input parameters. In order to reduce the growth in complexity with the number
of dimensions, we employ a dimension-adaptive stochastic collocation method based on nested univariate nodes.
We examine the accuracy and performance of collocation schemes based on Clenshaw-Curtis and Leja rules, for the
cases of uniform and bounded, nonuniform random inputs, respectively. Based on numerical experiments with an
academic electromagnetic field model, we compare the two rules in both the univariate and multivariate cases and
for both quadrature and interpolation purposes. Results for a real-world electromagnetic field application featuring
high-dimensional input uncertainty are also presented.
MODEL STRUCTURAL INFERENCE USING LOCAL DYNAMIC OPERATORS
59-83
10.1615/Int.J.UncertaintyQuantification.2019025828
Anthony M.
DeGennaro
Computational Science Initiative, Brookhaven National Laboratory, Upton, NY, 11973
Nathan M.
Urban
Computer, Computational, and Statistical Sciences, Los Alamos National Laboratory, Los
Alamos, NM, 87544
Balasubramanya T.
Nadiga
Computer, Computational, and Statistical Sciences, Los Alamos National Laboratory, Los
Alamos, NM, 87544
Terry
Haut
Computational Physics Group, Lawrence Livermore Laboratory, Livermore, CA, 94550
structural uncertainty quantification
model form uncertainty quantification
low-dimensional modeling
local dynamic operator
equation learning
model inference
This paper focuses on the problem of quantifying the effects of model-structure uncertainty in the context of time-evolving dynamical systems. This is motivated by multi-model uncertainty in computer physics simulations: developers often make different modeling choices in numerical approximations and process simplifications, leading to different numerical codes that ostensibly represent the same underlying dynamics. We consider model-structure inference as a two-step methodology: the first step is to perform system identification on numerical codes for which it is possible to observe the full state; the second step is structural uncertainty quantification, in which the goal is to search candidate models "close" to the numerical code surrogates for those that best match a quantity of interest (QOI) from some empirical data sets. Specifically, we (1) define a discrete, local representation of the structure of a partial differential equation,
which we refer to as the "local dynamical operator" (LDO); (2) identify model structure nonintrusively from numerical
code output; (3) nonintrusively construct a reduced-order model (ROM) of the numerical model through POD-DEIM-Galerkin
projection; (4) perturb the ROM dynamics to approximate the behavior of alternate model structures; and (5) apply Bayesian inference and energy conservation laws to calibrate a LDO to a given QOI. We demonstrate these techniques using the two-dimensional rotating shallow water equations as an example system.
STOCHASTIC MODELING OF MAGNETIC HYSTERETIC PROPERTIES BY USING MULTIVARIATE RANDOM FIELDS
85-102
10.1615/Int.J.UncertaintyQuantification.2019025638
Radoslav
Jankoski
Graduate School for Computational Engineering, Technische Universität Darmstadt,
Dolivostraße 15, 64293 Darmstadt, Germany
Ulrich
Römer
Institut für Dynamik und Schwingungen, Technische Universität Braunschweig, Schleinitzstraße
20, 38106 Braunschweig, Germany
Sebastian
Schöps
Centre for Computational Engineering, Technische Universität Darmstadt, Darmstadt,
Germany; Institut für Teilchenbeschleunigung und Elektromagnetische Felder (TEMF), Technische
Universität Darmstadt, Darmstadt, Germany
Duhem hysteresis model
cross-correlated random field
Karhunen-Loève expansion
In this paper a methodology is presented to model uncertainties in the hysteresis law of ferromagnetic materials. The uncertainties may arise, for example, from manufacturing imperfections. A phenomenological type of model, known as the Duhem model, is introduced to model the hysteretic properties. The Duhem model is described via two material functions and one scalar parameter. Random fields are used to incorporate uncertainties into the material law. The random field is discretized with a minimal number of random variables by the truncated Karhunen-Loève expansion.
Subsequently, the presented stochastic Duhem model is used to compute the statistics of the hysteresis loss in a simple
toroidal single-phase transformer for illustration purposes.