Begell House Inc.
International Journal for Uncertainty Quantification
IJUQ
2152-5080
9
6
2019
MULTILEVEL MONTE CARLO ON A HIGH-DIMENSIONAL PARAMETER SPACE FOR TRANSMISSION PROBLEMS WITH GEOMETRIC UNCERTAINTIES
515-541
10.1615/Int.J.UncertaintyQuantification.2019025335
Laura
Scarabosio
Technical University of Munich, Germany, Department of Mathematics, Boltzmannstrasse 3,
85748 Garching b. München
multilevel Monte Carlo
shape uncertainty
interface problem
L∞-estimates
discontinuities
In the framework of uncertainty quantification, we consider a quantity of interest which depends non-smoothly on the high-dimensional parameter representing the uncertainty. We show that, in this situation, the multilevel Monte Carlo algorithm is a valid option to compute moments of the quantity of interest (here we focus on the expectation), as it allows to bypass the precise location of discontinuities in the parameter space. We illustrate how such lack of smoothness occurs for the point evaluation of the solution to a (Helmholtz) transmission problem with uncertain interface, if the point can be crossed by the interface for some realizations. For this case, we provide a space regularity analysis for the solution, in order to state converge results in the L∞-norm for the finite element discretization. The latter are then used to determine the optimal distribution of samples among the Monte Carlo levels. Particular emphasis is given on the robustness of our estimates with respect to the dimension of the parameter space.
PROPAGATION OF HYBRID UNCERTAINTIES IN TRANSIENT HEAT CONDUCTION PROBLEMS
543-568
10.1615/Int.J.UncertaintyQuantification.2019030736
Lisha
Tan
School of Astronautics, Beihang University, Beijing, 100191, China
Zhongmin
Deng
School of Astronautics, Beihang University, Beijing, 100191, China
Benke
Shi
School of Astronautics, Beihang University, Beijing, 100191, China
uncertainty quantification
stochastic modeling
interval analysis
heat transfer
random parameters
uncertain-but-bounded parameters
In this paper, the propagation of hybrid uncertainties is studied in transient heat conduction problems. Based on the layer-by-layer analysis strategy, a novel mixed method using the stochastic theory and the convex model is presented. Two types of models for the uncertainties are considered: random parameters and uncertain-but-bounded parameters. Firstly, the matrix perturbation theory is utilized to deal with random parameters, obtaining the temperature response expectation and variance. Then using the Taylor series expansion and the Lagrange multiplier method to analyze the convex model, we derive the intervals of the temperature response probabilistic characters. Four numerical examples are presented to address transient heat conduction problems with random and uncertain-but-bounded parameters or pure uncertainties. The results are compared with those of the Monte Carlo method to verify the feasibility and practicality of the proposed method. In addition, the proposed method is also applicable to the steady-state problems.
MULTIVARIATE ANALYSIS OF EXTRAPOLATING TIME-INVARIANT DATA WITH UNCERTAINTY
569-587
10.1615/Int.J.UncertaintyQuantification.2019028125
Die Joseph Hassan
Millogo
Department of Mechanical Engineering, National Taiwan University, Taiwan
Kuei-Yuan
Chan
Department of Mechanical Engineering, National Taiwan University, Taiwan
data analysis
uncertainty identification
curve fitting
principal component analysis
extrapolation
Data analysis deciphers phenomena and system behaviors within a large number of experimental realizations. Transforming these massive quantities of raw data into knowledge about the data is made possible thanks to continuously improved computing techniques. In science and engineering, a particular interest lies within surrogate models for system behaviour prediction and data extrapolation. These models could, however, be under- or over- fitted when confronted to a complex dataset or one embedded with uncertainty. In this paper, we suggest a treatment approach of experimental data under uncertainty prior to its surrogate model creation. We specially focus on extrapolation an attempt to estimate the true underlying phenomena. We quantify the uncertainty quantity through eigenvalues, copy the behavior of the data through its covariance matrix, and reproduce an almost identical dataset whose particularity is a perfectly correlated inputs and output. This new dataset is then used as the basis for the creation of a surrogate model. Our approach shows consistency and a clear opportunity to obtain better predictions under uncertainty as it focuses on the overall dataset's behavior and stays faithful to each data.
EFFECT OF DEM UNCERTAINTY ON GEOPHYSICAL MASS FLOW VIA IDENTIFICATION OF STRONGLY COUPLED SUBSYSTEM
589-605
10.1615/Int.J.UncertaintyQuantification.2019029044
Arpan
Mukherjee
Materials Design and Innovation Department of University at Buffalo-SUNY, Buffalo, NY
Rahul
Rai
Mechanical and Aerospace Engineering Department of University at Buffalo-SUNY, Buffalo,
New York, 14260, USA
Puneet
Singla
Mechanical and Aerospace Engineering Department of University at Buffalo-SUNY, Buffalo,
New York, 14260, USA; Aerospace Engineering Dept. of Pennsylvania State University, State College, PA
Tarunraj
Singh
Mechanical and Aerospace Engineering Department of University at Buffalo-SUNY, Buffalo,
New York, 14260, USA
Abani
Patra
geophysical mass flow
digital elevation model
uncertainty quantification
strongly coupled subsystems
With the recent advent of aerial photography, capturing high-resolution terrain information has provided new opportunities to simulate geophysical mass flow on high-resolution digital elevation models (DEMs). This gives a better understanding of the flow of debris that has a wide range of size. However, performing uncertainty quantification (UQ) of debris flow on an uncertain terrain profile, especially creating a hazard map, still poses a challenge. Even though there exist advanced statistical methods to model the DEM, UQ on the DEM requires the generation of a huge number of realizations that make the problem intractable. The current paper focuses on the usefulness of a recently developed UQ methodology that identifies Strongly Coupled Subsystems (SCS) in a large-scale uncertain dynamical system using suitable graph-clustering techniques. The method is used to create a parallel sampling scheme for a high-resolution DEM to enable faster UQ by integrating with traditional sampling methods, such as Monte Carlo or Latin hypercube sampling. The realizations are used to propagate the uncertainty in DEMs via a geophysical mass flow model simulated in TITAN2D. The accuracy of the UQ framework in estimating hazard maps is demonstrated by applying it to the block-and-ash flows resulting from the 1991 Colima Volcano, Mexico.
INDEX, VOLUME 9, 2019
606-611
10.1615/Int.J.UncertaintyQuantification.v9.i6.50