Fractional-order system identification for health monitoring

Abstract

Fractional-order differential equations can describe the dynamics of robot formations and other high-order systems. These equations are useful models for such systems because of the flexibility afforded by including noninteger derivatives. A system’s fractional order may change in response to mechanical or operational damage, but the possibility of an order change is not typically considered in structural health monitoring or other system monitoring tools. Typically, the order is assumed to be an integer from the physics of the system, while behaviors are captured by parameters within the chosen model. In contrast, this work presents a procedure to identify the fractional order of a system’s dynamics across a variety of parameter changes; the inclusion of fractional orders allows order itself to measure dynamical shifts. This work presents the identification procedure, its mathematical foundations, and results from example systems representing two mobile robot formations. The fractional order changes in a manner consistent with the physical changes modeled by damage, suggesting that this procedure is widely applicable in health monitoring.