Markov chains are simple yet powerful mathematical structures to model temporally dependent processes. They generally assume stationary data, i.e., fixed transition probabilities between observations/states. However, live, real-world processes, like in the context of activity tracking, biological time series, or industrial monitoring, often switch behavior over time. Such behavior switches can be modeled as transitions between higher-level modes (e.g., running, walking, etc.). Yet all modes are usually not previously known, often exhibit vastly differing transition probabilities, and can switch unpredictably. Thus, to track behavior changes of live, real-world processes, this study proposes an online and efficient method to construct Evolving Markov chains (EMCs). EMCs adaptively track transition probabilities, automatically discover modes, and detect mode switches in an online manner. In contrast to previous work, EMCs are of arbitrary order, the proposed update scheme does not rely on tracking windows, only updates the relevant region of the probability tensor, and enjoys geometric convergence of the expected estimates. Our evaluation of synthetic data and real-world applications on human activity recognition, electric motor condition monitoring, and eye-state recognition from electroencephalography (EEG) measurements illustrates the versatility of the approach and points to the potential of EMCs to efficiently track, model, and understand live, real-world processes.

End-of-line (EOL) tests are an important step to detect and respond to reliability issues that electric motors face. In addition to conventional signal processing methods to establish automated test systems, Artificial Intelligence (AI) and Machine Learning (ML) based methods in recent years, managed to become a major enabler for smart manufacturing thanks to advancements in hardware and software components. Inevitably, the importance of quality data made its way into considerations and requirements of automated fault detection and condition monitoring systems. In this regard, this study proposes an AI-based testing framework for electric motors. We provide information on the reasons of faults observed and a test procedure to detect them. We also give detailed specifications on hardware (sensors and data collection equipment), and provide a data architecture and analysis on properties of ML models that make sense to be used in such scenarios.

Multivariate Time Series (MTS) data obtained from large scale systems carry resourceful information about the internal system status. Multivariate Time Series Clustering is one of the exploratory methods that can enable one to discover the different types of behavior that is manifested in different working periods of a system. This knowledge can then be used for tasks such as anomaly detection or system maintenance. In this study, we make use of the statistical method, Variable Order Markov Models (VOMMs) to model each individual MTS and employ a new metric to calculate the distances between those VOMMs. The pairwise distances are then used to accomplish the MTS Clustering task. Two other MTS Clustering methods are presented and the superiority of the proposed method is confirmed with the experiments on two data sets from Cyber-Physical Systems. The computational complexity of the presented methods is also discussed.

In general, dynamic systems are systems with time-dependent behavior. Dynamic systems are characterized by the non-stationary data sequences they emit. One particular way to model these non-stationary sequences is to consider them as a sequence of stationary segments, regimes, where each regime is separated by regime switching points from both the preceding and subsequent regimes. In system identification and monitoring applications, it is crucial to correctly and timely detect these regime switching points. One promising estimation method that may be used for detecting regime switching points is the stochastic learning based weak estimation (SLWE) method by Oommen and Rueda. We use SLWE for estimating First Order Markov (FOM) probabilities between symbols emitted by a system and for predicting regime switching points. A switching point is detected when the SLWE estimator unlearns, i.e., adapts estimates of FOM probabilities to new observations, such that the estimate re-converges to a new value that reflects, for the new regime, the FOM dependency of system output tokens. In experiments with a real Dataset for Human Activity Recognition, we see that our method has attractive efficiency (time and space) and similar accuracy compared with the state-of the-art. Experiments with synthetic data, where we controlled noise and Hamming distance between regimes, show promising accuracy for noise rates up to 25%, a rate at which accuracy of state-of-the-art methods deteriorates. Our method is flexible and can be configured to use not only FOM but also second-order and prior symbol probabilities, and combinations thereof.

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 %.

In this paper, we present a methodology for automatic diagnosis of systems characterized by continuous signals. For each condition considered, the methodology requires the development of an alphabet of signal primitives, and a set of hierarchical fuzzy automatons (HFAs). Each alphabet is adaptively obtained by training an adaptive resonance theory (ART2) architecture with signal segments from a particular condition. Then, the original signal is transformed into a string of vectors of primitives, where each vector of primitives replaces a signal segment in the original signal. The string, in turn, is presented to the HFA characterizing that particular condition. Each set of HFA consists of a main automaton identifying the entire signal, and several sub-automata each identifying a particular significant structure in the signal. A transition in the main automaton occurs (i.e., the main automaton moves from one state to another) if the corresponding subautomaton recognizes a token where a token is a portion of the string of vectors of signal primitives with a significant structure. The fuzziness in automaton operation adds flexibility to the operation of the automaton, enabling the processing of imperfect input, allowing for toleration measurement noise and other ambiguities. The methodology is applied to the problem of automatic electrocardiogram diagnosis.

A methodology for automated diagnosis of systems characterized by continuous signals is presented. The methodology requires the definition and construction of several fuzzy automatons each capable of identifying a particular condition. When the diagnostic system is in operation, the time sampled system measurements are presented to all automatons simultaneously. The fuzziness in automaton operation enables input processing from several perspectives, consistent with the operation of the automatons, allowing for toleration of measurement noise and other ambiguities. The methodology is applied to the problem of automatic electrocardiogram diagnosis.