A Hidden Markov Model for Condition Monitoring of Time Series Data in Complex Network Systems

Time series data are ubiquitous in complex network systems, where each component of the system is treated as a vertex and has sequentially collected autocorrelated observations for condition monitoring. In many cases, components transit between different states, such as "normal," "degrading," "failure," etc., and under different states their distributions vary, resulting in the mixture marginal distribution of each vertex's time series data. Moreover, states of different components influence each other through the system's network topology, i.e., the state of a component itself and its neighbors jointly affect its data distribution. For efficient condition monitoring, it is important to capture the state evolution of all vertices as a whole over time. However, the state-switching may be unobservable, which complicates the modeling. Hence, this article proposes a hidden Markov model for networked time series data with mixture marginal distributions. The Markov transition rule for latent states captures the state-switching behavior and the AR model reveals the temporal dependence of vertices. The states of different vertices further influence each other through the network topology structure. The Baum-Welch algorithm is used to estimate the parameters of the proposed model, allowing for state inference and data fitting. Extensive numerical studies as well as real case studies demonstrate the effectiveness and applicability of the proposed model.