Topology-driven identification of repetitions in multi-variate time series

Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from such a multi-variate time series is of a fundamental importance for many monitoring and control tasks. For a periodic time series this is equivalent to determining its period length. In this work we present a persistent homology framework to estimate recurrence times in multi-variate time series with different generalizations of cyclic behavior (periodic, repetitive, and recurring). To this end, we provide three specialized methods within our framework that are provably stable and validate them using real-world data, including a new benchmark dataset from an injection molding machine.

An OPC UA-based industrial Big Data architecture

Industry 4.0 factories are complex and data-driven. Data is yielded from many sources, including sensors, PLCs, and other devices, but also from IT, like ERP or CRM systems. We ask how to collect and process this data in a way, such that it includes metadata and can be used for industrial analytics or to derive intelligent support systems. This paper describes a new, query model based approach, which uses a big data architecture to capture data from various sources using OPC UA as a foundation. It buffers and preprocesses the information for the purpose of harmonizing and providing a holistic state space of a factory, as well as mappings to the current state of a production site. That information can be made available to multiple processing sinks, decoupled from the data sources, which enables them to work with the information without interfering with devices of the production, disturbing the network devices they are working in, or influencing the production process negatively. Metadata and connected semantic information is kept throughout the process, allowing to feed algorithms with meaningful data, so that it can be accessed in its entirety to perform time series analysis, machine learning or similar evaluations as well as replaying the data from the buffer for repeatable simulations.