Statistical mechanics of complex systems for pattern identification

This paper presents a statistical mechanics concept for identification of behavioral patterns in complex systems based on measurements (e.g., time series data) of macroscopically observable parameters and their operational characteristics. The tools of statistical mechanics, which provide a link between the microscopic (i.e., detailed) and macroscopic (i.e., aggregated) properties of a complex system are used to capture the emerging information and to identify the quasi-stationary evolution of behavioral patterns. The underlying theory is built upon thermodynamic formalism of symbol sequences in the setting of a generalized Ising model (GIM) of lattice-spin systems. In this context, transfer matrix analysis facilitates construction of pattern vectors from observed sequences. The proposed concept is experimentally validated on a richly instrumented laboratory apparatus that is operated under oscillating load for identification of evolving microstructural changes in polycrystalline alloys.