Unsupervised Complex Semi-Binary Matrix Factorization for Activation Sequence Recovery of Quasi-Stationary Sources

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.