Begell House Inc.
International Journal for Uncertainty Quantification
IJUQ
2152-5080
9
5
2019
ROBUST UNCERTAINTY QUANTIFICATION USING RESPONSE SURFACE APPROXIMATIONS OF DISCONTINUOUS FUNCTIONS
415-437
Timothy
Wildey
Optimization and Uncertainty Quantification Department, Center for Computing Research,
Sandia National Laboratories, Albuquerque, NM 87185
A. A.
Gorodetsky
University of Michigan, Department of Aerospace Engineering, Ann Arbor, MI 48109
A.
Belme
Sorbonne Universités, UPMC Univ Paris 06, UMR 7190, Institut Jean le Rond d'Alembert, F-75005, Paris, France;
CNRS, UMR 7190, Institut Jean le Rond d'Alembert, F-75005, Paris, France
John N.
Shadid
Computational Mathematics Department, Center for Computing Research, Sandia National
Laboratories, Albuquerque, NM 87185, and Department of Mathematics and Statistics,
University of New Mexico
This paper considers response surface approximations for discontinuous quantities of interest. Our objective is not
to adaptively characterize the interface defining the discontinuity. Instead, we utilize an epistemic description of the uncertainty in the location of a discontinuity to produce robust bounds on sample-based estimates of probabilistic quantities of interest. We demonstrate that two common machine learning strategies for classification, one based on nearest neighbors (Voronoi cells) and one based on support vector machines, provide reasonable descriptions of the region where the discontinuity may reside. In higher dimensional spaces, we demonstrate that support vector machines are more accurate for discontinuities defined by smooth interfaces. We also show how gradient information, often available via adjoint-based approaches, can be used to define indicators to effectively detect a discontinuity and to decompose the samples into clusters using an unsupervised learning technique. Numerical results demonstrate the
epistemic bounds on probabilistic quantities of interest for simplistic models and for a compressible fluid model with a
shock-induced discontinuity.
BAYESIAN OPTIMAL EXPERIMENTAL DESIGN INVOLVING MULTIPLE SETUPS FOR DYNAMIC STRUCTURAL TESTING
439-452
Sahil
Bansal
Civil Engineering Department, Indian Institute of Technology Delhi, Delhi-110016, India
In an experimental design for dynamic structural testing, it is a common practice to obtain data from a structure using multiple setups, with each setup covering a different part of the structure. This is generally due to availability of limited number of sensors with synchronous data acquisition. This paper considers the problem of optimal placement of actuators and sensors with the aim of maximizing the data information in an experimental design with multiple setups so that the structural dynamic behavior can be fully characterized. The uncertainty in the model parameters is computed by a Bayesian statistical framework and expected utility is used to quantify the uncertainty of the set of identified model parameters. The problem of optimal experimental design with multiple setups is formulated as an optimization problem in which the actuators' and sensors' configuration, which maximizes the expected utility, is selected as the optimal one. The proposed approach can be used to compare and evaluate the quality of the parameter estimates that can be achieved with different numbers of setups in an experimental design and a different number of actuators and sensors in each setup. The effectiveness of the proposed approach is illustrated by optimal experimental design for a simple 12-degree-of-freedom (dof) chainlike spring-mass model of a structure and a 37-dof truss structure.
ROBUSTNESS OF THE SOBOL' INDICES TO DISTRIBUTIONAL UNCERTAINTY
453-469
Joseph
Hart
Department of Mathematics, North Carolina State University, Raleigh, NC
Pierre A.
Gremaud
Department of Mathematics, North Carolina State University, Raleigh, North Carolina
27695-8205
Global sensitivity analysis (GSA) is used to quantify the influence of uncertain variables in a mathematical model. Prior to performing GSA, the user must specify (or implicitly assume) a probability distribution to model the uncertainty, and possibly statistical dependencies, of the variables. Determining this distribution is challenging in practice as the user has limited and imprecise knowledge of the uncertain variables. This paper analyzes the robustness of the Sobol' indices, a commonly used tool in GSA, to changes in the distribution of the uncertain variables. A method for assessing such robustness is developed that requires minimal user specification and no additional evaluations of the model. Theoretical and computational aspects of the method are considered and illustrated through examples.