9,189 research outputs found
Resampling Strategies to Improve Surrogate Model-based Uncertainty Quantification - Application to LES of LS89
Uncertainty Quantification (UQ) is receiving more and more attention for
engineering applications in particular from robust optimization. Indeed,
running a computer experiment only provides a limited knowledge in terms of
uncertainty and variability of the input parameters. These experiments are
often computationally expensive and surrogate models can be constructed to
address this issue. The outcome of a UQ study is in this case directly
correlated to the surrogate's quality. Thus, attention must be devoted to the
Design of Experiments (DoE) to retrieve as much information as possible. This
work presents two new strategies for parameter space resampling to improve a
Gaussian Process (GP) surrogate model. These techniques indeed show an
improvement of the predictive quality of the model with high dimensional
analytical input functions. Finally, the methods are successfully applied to a
turbine blade Large Eddy Simulation application: the aerothermal flow around
the LS89 blade cascade.Comment: Accepted in International Journal for Numerical Methods in Fluid
Efficient Construction of Local Parametric Reduced Order Models Using Machine Learning Techniques
Reduced order models are computationally inexpensive approximations that
capture the important dynamical characteristics of large, high-fidelity
computer models of physical systems. This paper applies machine learning
techniques to improve the design of parametric reduced order models.
Specifically, machine learning is used to develop feasible regions in the
parameter space where the admissible target accuracy is achieved with a
predefined reduced order basis, to construct parametric maps, to chose the best
two already existing bases for a new parameter configuration from accuracy
point of view and to pre-select the optimal dimension of the reduced basis such
as to meet the desired accuracy. By combining available information using bases
concatenation and interpolation as well as high-fidelity solutions
interpolation we are able to build accurate reduced order models associated
with new parameter settings. Promising numerical results with a viscous Burgers
model illustrate the potential of machine learning approaches to help design
better reduced order models.Comment: 28 pages, 15 figures, 6 table
Inferring causal impact using Bayesian structural time-series models
An important problem in econometrics and marketing is to infer the causal
impact that a designed market intervention has exerted on an outcome metric
over time. This paper proposes to infer causal impact on the basis of a
diffusion-regression state-space model that predicts the counterfactual market
response in a synthetic control that would have occurred had no intervention
taken place. In contrast to classical difference-in-differences schemes,
state-space models make it possible to (i) infer the temporal evolution of
attributable impact, (ii) incorporate empirical priors on the parameters in a
fully Bayesian treatment, and (iii) flexibly accommodate multiple sources of
variation, including local trends, seasonality and the time-varying influence
of contemporaneous covariates. Using a Markov chain Monte Carlo algorithm for
posterior inference, we illustrate the statistical properties of our approach
on simulated data. We then demonstrate its practical utility by estimating the
causal effect of an online advertising campaign on search-related site visits.
We discuss the strengths and limitations of state-space models in enabling
causal attribution in those settings where a randomised experiment is
unavailable. The CausalImpact R package provides an implementation of our
approach.Comment: Published at http://dx.doi.org/10.1214/14-AOAS788 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Data-Driven Framework for Assessing Cold Load Pick-up Demand in Service Restoration
Cold load pick-up (CLPU) has been a critical concern to utilities.
Researchers and industry practitioners have underlined the impact of CLPU on
distribution system design and service restoration. The recent large-scale
deployment of smart meters has provided the industry with a huge amount of data
that is highly granular, both temporally and spatially. In this paper, a
data-driven framework is proposed for assessing CLPU demand of residential
customers using smart meter data. The proposed framework consists of two
interconnected layers: 1) At the feeder level, a nonlinear auto-regression
model is applied to estimate the diversified demand during the system
restoration and calculate the CLPU demand ratio. 2) At the customer level,
Gaussian Mixture Models (GMM) and probabilistic reasoning are used to quantify
the CLPU demand increase. The proposed methodology has been verified using real
smart meter data and outage cases
Plasticity models of material variability based on uncertainty quantification techniques
The advent of fabrication techniques like additive manufacturing has focused
attention on the considerable variability of material response due to defects
and other micro-structural aspects. This variability motivates the development
of an enhanced design methodology that incorporates inherent material
variability to provide robust predictions of performance. In this work, we
develop plasticity models capable of representing the distribution of
mechanical responses observed in experiments using traditional plasticity
models of the mean response and recently developed uncertainty quantification
(UQ) techniques. We demonstrate that the new method provides predictive
realizations that are superior to more traditional ones, and how these UQ
techniques can be used in model selection and assessing the quality of
calibrated physical parameters
Quantifying Uncertainties in Fault Slip Distribution during the T\=ohoku Tsunami using Polynomial Chaos
An efficient method for inferring Manning's coefficients using water
surface elevation data was presented in Sraj et al. (2014) focusing on a test
case based on data collected during the earthquake and tsunami.
Polynomial chaos expansions were used to build an inexpensive surrogate for the
numerical model Geoclaw, which were then used to perform a sensitivity analysis
in addition to the inversion. In this paper, a new analysis is performed with
the goal of inferring the fault slip distribution of the earthquake
using a similar problem setup. The same approach to constructing the PC
surrogate did not lead to a converging expansion, however an alternative
approach based on Basis-Pursuit DeNoising was found to be suitable. Our result
shows that the fault slip distribution can be inferred using water surface
elevation data whereas the inferred values minimizes the error between
observations and the numerical model. The numerical approach and the resulting
inversion are presented in this work
Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations
The development of scramjet engines is an important research area for
advancing hypersonic and orbital flights. Progress toward optimal engine
designs requires accurate flow simulations together with uncertainty
quantification. However, performing uncertainty quantification for scramjet
simulations is challenging due to the large number of uncertain parameters
involved and the high computational cost of flow simulations. These
difficulties are addressed in this paper by developing practical uncertainty
quantification algorithms and computational methods, and deploying them in the
current study to large-eddy simulations of a jet in crossflow inside a
simplified HIFiRE Direct Connect Rig scramjet combustor. First, global
sensitivity analysis is conducted to identify influential uncertain input
parameters, which can help reduce the systems stochastic dimension. Second,
because models of different fidelity are used in the overall uncertainty
quantification assessment, a framework for quantifying and propagating the
uncertainty due to model error is presented. These methods are demonstrated on
a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry,
with parameter space up to 24 dimensions, using static and dynamic treatments
of the turbulence subgrid model, and with two-dimensional and three-dimensional
geometries.Comment: Preprint 29 pages, 10 figures (26 small figures); v1 submitted to the
AIAA Journal on May 3, 2017; v2 submitted on September 17, 2017. v2 changes:
(a) addition of flowcharts in Figures 4 and 5 to summarize the tools used;
(b) edits to clarify and reorganize certain parts; v3 submitted on February
7, 2018. v3 changes: (a) title; (b) minor edit
Surrogate-based global sensitivity analysis for turbulence and fire-spotting effects in regional-scale wildland fire modeling
In presence of strong winds, wildfires feature nonlinear behavior, possibly
inducing fire-spotting. We present a global sensitivity analysis of a new
sub-model for turbulence and fire-spotting included in a wildfire spread model
based on a stochastic representation of the fireline. To limit the number of
model evaluations, fast surrogate models based on generalized Polynomial Chaos
(gPC) and Gaussian Process are used to identify the key parameters affecting
topology and size of burnt area. This study investigates the application of
these surrogates to compute Sobol' sensitivity indices in an idealized test
case. The wind is known to drive the fire propagation. The results show that it
is a more general leading factor that governs the generation of secondary
fires. This study also compares the performance of the surrogates for varying
size and type of training sets as well as for varying parameterization and
choice of algorithms. The best performance was achieved using a gPC strategy
based on a sparse least-angle regression (LAR) and a low-discrepancy Halton's
sequence. Still, the LAR-based gPC surrogate tends to filter out the
information coming from parameters with large length-scale, which is not the
case of the cleaning-based gPC surrogate. For both algorithms, sparsity ensures
a surrogate can be built using an affordable number of forward model
evaluations, while the model response is highly multi-scale and nonlinear.
Using a sparse surrogate is thus a promising strategy to analyze new models and
its dependency on input parameters in wildfire applications
Bayesian inference and non-linear extensions of the CIRCE method for quantifying the uncertainty of closure relationships integrated into thermal-hydraulic system codes
Uncertainty Quantification of closure relationships integrated into
thermal-hydraulic system codes is a critical prerequisite in applying the
Best-Estimate Plus Uncertainty (BEPU) methodology for nuclear safety and
licensing processes.The purpose of the CIRCE method is to estimate the
(log)-Gaussian probability distribution of a multiplicative factor applied to a
reference closure relationship in order to assess its uncertainty. Even though
this method has been implemented with success in numerous physical scenarios,
it can still suffer from substantial limitations such as the linearity
assumption and the difficulty of properly taking into account the inherent
statistical uncertainty. In the paper, we will extend the CIRCE method in two
aspects. On the one hand, we adopt the Bayesian setting putting prior
probability distributions on the parameters of the (log)-Gaussian distribution.
The posterior distribution of the parameters is then computed with respect to
an experimental database by means of Markov Chain Monte Carlo (MCMC)
algorithms. On the other hand, we tackle the more general setting where the
simulations do not move linearly against the multiplicative factor(s). MCMC
algorithms then become time-prohibitive when the thermal-hydraulic simulations
exceed a few minutes. This handicap is overcome by using Gaussian process (GP)
emulators which can yield both reliable and fast predictions of the
simulations. The GP-based MCMC algorithms will be applied to quantify the
uncertainty of two condensation closure relationships at a safety injection
with respect to a database of experimental tests. The thermal-hydraulic
simulations will be run with the CATHARE 2 computer code.Comment: 37 pages, 5 figure
Software quality and reliability prediction using Dempster -Shafer theory
As software systems are increasingly deployed in mission critical applications, accurate quality and reliability predictions are becoming a necessity. Most accurate prediction models require extensive testing effort, implying increased cost and slowing down the development life cycle. We developed two novel statistical models based on Dempster-Shafer theory, which provide accurate predictions from relatively small data sets of direct and indirect software reliability and quality predictors. The models are flexible enough to incorporate information generated throughout the development life-cycle to improve the prediction accuracy.;Our first contribution is an original algorithm for building Dempster-Shafer Belief Networks using prediction logic. This model has been applied to software quality prediction. We demonstrated that the prediction accuracy of Dempster-Shafer Belief Networks is higher than that achieved by logistic regression, discriminant analysis, random forests, as well as the algorithms in two machine learning software packages, See5 and WEKA. The difference in the performance of the Dempster-Shafer Belief Networks over the other methods is statistically significant.;Our second contribution is also based on a practical extension of Dempster-Shafer theory. The major limitation of the Dempsters rule and other known rules of evidence combination is the inability to handle information coming from correlated sources. Motivated by inherently high correlations between early life-cycle predictors of software reliability, we extended Murphy\u27s rule of combination to account for these correlations. When used as a part of the methodology that fuses various software reliability prediction systems, this rule provided more accurate predictions than previously reported methods. In addition, we proposed an algorithm, which defines the upper and lower bounds of the belief function of the combination results. To demonstrate its generality, we successfully applied it in the design of the Online Safety Monitor, which fuses multiple correlated time varying estimations of convergence of neural network learning in an intelligent flight control system
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