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.

网络物理生产系统（CPPS）是由离散和连续部分组成的混合系统。但是，大多数应用的机器学习算法分别以不同的方式处理这两个部分的动态：对于离散部分，离散事件（及其定时）的概念至关重要（例如，在学习自动机或规则时），而连续零件的动力学通常由微分方程或时间序列模型定义。调和两者的不同性质是机器学习的主要挑战。一种解决方案是用离散术语表示连续行为，即提取显式事件。然后，以离散化导致的信息丢失为代价，可以共同分析整体行为。

本文提出了一种新的机器学习离散化方法，称为DENTA（深层网络定时自动机），该方法通过根据原始混合数据构造（总体）确定性定时自动机来解决上述挑战。首先，它使用堆叠式受限Boltzmann机器（RBM）的深度网络从连续数据中分层提取新特征。我们表明高级RBM抽象可以进一步用于自动检测连续系统行为中有意义的离散事件。最后，以定时自动机的形式创建了整体系统行为的离散表示形式，从而可以对整个系统进行联合时序分析。该模型通过在合成数据集和真实数据集上的异常检测进行验证，结果表明该方法对于特定类别的系统具有明显的优势。