Unsupervised mode detection in cyber-physical systems using variable order Markov models

Sequential data generated from various sources in a multi-mode industrial production system provides valuable information on the current mode of the system and enables one to build a model for each individual operating mode. Using these models in a multi-mode system, one may distinguish modes of the system and, furthermore, detect whether the current mode is a (normal or faulty) mode known from historical data, or a new mode. In this work, we model each individual mode by a probabilistic suffix tree (PST) used to implement variable order Markov models (VOMMs) and propose a novel unsupervised PST matching algorithm that compares the tree models by a matching cost once they are constructed. The matching cost we define comprises of a subsequence dissimilarity cost and a probability cost. Our tree matching method enables to compare two PSTs in linear time by one concurrent top-down pass. We use this matching cost as a similarity measure for k-medoid clustering and cluster PSTs obtained from system modes according to their matching costs. The overall approach yields promising results for unsupervised identification of modes on data obtained from of a physical factory demonstrator. Notably we can distinguish modes on two levels of granularity, both corresponding to human expert labels, with a RAND score of up to 73 % compared to a baseline of at most 42 %.