  Data driven soft sensor design has recently gained immense popularity, due to
advances in sensory devices, and a growing interest in data mining. While
partial least squares (PLS) is traditionally used in the process literature for
designing soft sensors, the statistical literature has focused on sparse
learners, such as Lasso and relevance vector machine (RVM), to solve the high
dimensional data problem. In the current study, predictive performances of
three regression techniques, PLS, Lasso and RVM were assessed and compared
under various offline and online soft sensing scenarios applied on datasets
from five real industrial plants, and a simulated process. In offline learning,
predictions of RVM and Lasso were found to be superior to those of PLS when a
large number of time-lagged predictors were used. Online prediction results
gave a slightly more complicated picture. It was found that the minimum
prediction error achieved by PLS under moving window (MW), or just-in-time
learning scheme was decreased up to ~5-10% using Lasso, or RVM. However, when a
small MW size was used, or the optimum number of PLS components was as low as
~1, prediction performance of PLS surpassed RVM, which was found to yield
occasional unstable predictions. PLS and Lasso models constructed via online
parameter tuning generally did not yield better predictions compared to those
constructed via offline tuning. We present evidence to suggest that retaining a
large portion of the available process measurement data in the predictor
matrix, instead of preselecting variables, would be more advantageous for
sparse learners in increasing prediction accuracy. As a result, Lasso is
recommended as a better substitute for PLS in soft sensors; while performance
of RVM should be validated before online application.
