Discretization of hybrid CPPS data into timed automaton using restricted Boltzmann machines

Cyber-Physical Production Systems (CPPSs) are hybrid systems composed of a discrete and continuous part. However, most of the applied machine learning algorithms handle the dynamics of the two parts separately and in different fashions: for the discrete part, the notion of discrete events (and their timings) is essential (e.g. when learning automata or rules), while the dynamics of the continuous part is often defined by differential equations or time-series models. Reconciling the different nature of the two is a major challenge for machine learning. One solution is to express continuous behavior in discrete terms, i.e. the explicit events are extracted. Then, at the cost of information loss caused by discretization, the overall behavior can be jointly analyzed. This paper proposes a novel machine learning discretization approach called DENTA (Deep Network Timed Automaton) which solves the aforementioned challenges through the construction of an (overall) deterministic timed automaton from the original hybrid data. First, it hierarchically extracts new features from the continuous data using a deep network of stacked restricted Boltzmann machines (RBMs). We show that high-level RBM abstractions can further be used to automatically detect meaningful discrete events in continuous system behavior. Finally, a discrete representation of overall system behavior in the form of a timed automaton is created, which allows a joint timing analysis of the whole system. The model is verified by the anomaly detection on a synthetic and a real-world dataset and the results show clear advantages of the approach for a specific class of systems.