Unsupervised Complex Semi-Binary Matrix Factorization for Activation
  Sequence Recovery of Quasi-Stationary Sources
Romain Delabeye Martin Ghienne Olivia Penas Jean-Luc Dion
Advocating for a sustainable, resilient and human-centric industry, the three
pillars of Industry 5.0 call for an increased understanding of industrial
processes and manufacturing systems, as well as their energy sustainability.
One of the most fundamental elements of comprehension is knowing when the
systems are operated, as this is key to locating energy intensive subsystems
and operations. Such knowledge is often lacking in practice. Activation
statuses can be recovered from sensor data though. Some non-intrusive sensors
(accelerometers, current sensors, etc.) acquire mixed signals containing
information about multiple actuators at once. Despite their low cost as regards
the fleet of systems they monitor, additional signal processing is required to
extract the individual activation sequences. To that end, sparse regression
techniques can extract leading dynamics in sequential data. Notorious
dictionary learning algorithms have proven effective in this regard. This paper
considers different industrial settings in which the identification of binary
subsystem activation sequences is sought. In this context, it is assumed that
each sensor measures an extensive physical property, source signals are
periodic, quasi-stationary and independent, albeit these signals may be
correlated and their noise distribution is arbitrary. Existing methods either
restrict these assumptions, e.g., by imposing orthogonality or noise
characteristics, or lift them using additional assumptions, typically using
nonlinear transforms.