  In the machine learning domain, active learning is an iterative data
selection algorithm for maximizing information acquisition and improving model
performance with limited training samples. It is very useful, especially for
the industrial applications where training samples are expensive,
time-consuming, or difficult to obtain. Existing methods mainly focus on active
learning for classification, and a few methods are designed for regression such
as linear regression or Gaussian process. Uncertainties from measurement errors
and intrinsic input noise inevitably exist in the experimental data, which
further affects the modeling performance. The existing active learning methods
do not incorporate these uncertainties for Gaussian process. In this paper, we
propose two new active learning algorithms for the Gaussian process with
uncertainties, which are variance-based weighted active learning algorithm and
D-optimal weighted active learning algorithm. Through numerical study, we show
that the proposed approach can incorporate the impact from uncertainties, and
realize better prediction performance. This approach has been applied to
improving the predictive modeling for automatic shape control of composite
fuselage.
