Complexity signatures for system health monitoring

The ability to assess risk in complex systems is one of the fundamental challenges facing the aerospace industry in general, and NASA in particular. First, such an ability allows for quantifiable trade-offs during the design stage of a mission. Second, it allows the monitoring of die health of the system while in operation. Because many of the difficulties in complex systems arise from the interactions among the subsystems, system health monitoring cannot solely focus on the health of those subsystems. Instead system level signatures that encapsulate the complex system interactions are needed. In this work, we present the entropy-scale (ES) and entropy-resolution (ER) system-level signatures that are both computationally tractable and encapsulate many of the salient characteristics of a system. These signatures are based on the change of entropy as a system is observed across different resolutions and scales. We demonstrate the use of the ES and ER signatures on artificial data streams and simple dynamical systems and show that they allow the unambiguous clustering of many types of systems, and therefore are good indicators of system health. We then show how these signatures can be applied to graphical data as well as data strings by using a simple "graph-walking" method. This method extracts a data stream from a graphical system representation (e.g., fault tree, software call graph) that conserves the properties of the graph. Finally we apply these signatures to analysis of software packages, and show that they provide significantly better correlation with risk markers than many standard metrics. These results indicate that proper system level signatures, coupled with detailed component-level analysis enable the automatic detection of potentially hazardous subsystem interactions in complex systems before they lead to system deterioration or failures