2 research outputs found
Sparse Polynomial Chaos Expansions via Compressed Sensing and D-optimal Design
In the field of uncertainty quantification, sparse polynomial chaos (PC)
expansions are commonly used by researchers for a variety of purposes, such as
surrogate modeling. Ideas from compressed sensing may be employed to exploit
this sparsity in order to reduce computational costs. A class of greedy
compressed sensing algorithms use least squares minimization to approximate PC
coefficients. This least squares problem lends itself to the theory of optimal
design of experiments (ODE). Our work focuses on selecting an experimental
design that improves the accuracy of sparse PC approximations for a fixed
computational budget. We propose DSP, a novel sequential design, greedy
algorithm for sparse PC approximation. The algorithm sequentially augments an
experimental design according to a set of the basis polynomials deemed
important by the magnitude of their coefficients, at each iteration. Our
algorithm incorporates topics from ODE to estimate the PC coefficients. A
variety of numerical simulations are performed on three physical models and
manufactured sparse PC expansions to provide a comparative study between our
proposed algorithm and other non-adaptive methods. Further, we examine the
importance of sampling by comparing different strategies in terms of their
ability to generate a candidate pool from which an optimal experimental design
is chosen. It is demonstrated that the most accurate PC coefficient
approximations, with the least variability, are produced with our
design-adaptive greedy algorithm and the use of a studied importance sampling
strategy. We provide theoretical and numerical results which show that using an
optimal sampling strategy for the candidate pool is key, both in terms of
accuracy in the approximation, but also in terms of constructing an optimal
design
Distributed Active State Estimation with User-Specified Accuracy
In this paper, we address the problem of controlling a network of mobile
sensors so that a set of hidden states are estimated up to a user-specified
accuracy. The sensors take measurements and fuse them online using an
Information Consensus Filter (ICF). At the same time, the local estimates guide
the sensors to their next best configuration. This leads to an LMI-constrained
optimization problem that we solve by means of a new distributed random
approximate projections method. The new method is robust to the state
disagreement errors that exist among the robots as the ICF fuses the collected
measurements. Assuming that the noise corrupting the measurements is zero-mean
and Gaussian and that the robots are self localized in the environment, the
integrated system converges to the next best positions from where new
observations will be taken. This process is repeated with the robots taking a
sequence of observations until the hidden states are estimated up to the
desired user-specified accuracy. We present simulations of sparse landmark
localization, where the robotic team achieves the desired estimation tolerances
while exhibiting interesting emergent behavior.Comment: IEEE Transactions on Automatic Control, June 201