Unsupervised complex semi-binary matrix factorization for activation sequence recovery of quasi-stationary sources

Industry 5.0 advocates for a sustainable industry, particularly in terms of energy. 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. This paper considers different industrial settings in which the identification of binary sub-system activation sequences is sought. In this context, source signals are assumed to be quasi-stationary and they may be correlated. Existing methods either restrict these assumptions, e.g., by imposing orthogonality or noise characteristics, or lift them using additional assumptions, typically using nonlinear transforms. This paper addresses these limitations, and introduces the unsupervised complex semi-binary matrix factorization (ℂSBMF) as its main contribution. In particular, we show that the exact recovery of source activation sequences from non-intrusive sensor data is intrinsically tied to the presence of problematic phase shifts, the causes of which are detailed. A greedy algorithm is proposed, iteratively resynchronizing sources to converge towards the maximum decomposition of each operation despite these phase shifts. The ℂSBMF is verified and compared to existing techniques on synthetic use cases, then validated on experimental data with signals of different nature. To that occasion, the CAFFEINE dataset for unsupervised time series multi-label classification is introduced.