Damage prediction for interconnected, degrading systems

Complex aerospace systems are highly integrated to achieve specific mission requirements, involving numerous coupled subsystems. In the case of mechanical systems undergoing progressive failures such as fatigue, the dynamic range of phenomena is vast (e.g. from 10^-3s to 10⁶s). Therefore, the connectivity manifests itself in the dynamics of the degradation process. Our analysis of this process distinguishes two distinct forms of coupling: cascade coupling, in which one part triggers the failure of another, and feedback coupling, in which two parts mutually affect the degradation of each other. We present a simple model which captures these effects on the failure prognosis for coupled systems, which is appropriate for on-line use in PHM systems. The model governs the evolution of the stochastic, hybrid "damage" state of each subsystem (i.e. a combination continuous and discrete state). The discrete states are represent the dynamic regimes of the well-known "bathtub curve" for failure. The continuous state represents a overall damage metric for the device. Within a regime, the degradation dynamics are linear system with stochastic inputs, and coupling dynamics which switch with the discrete states of other subsystems. The coupling sensitivity parameters must be obtained via experimentation or modeling. The model possesses a number of useful features including failure time statistics remarkably similar to those in real systems as typically fit with a Weibull distribution. Further, the hybrid model structure separates the effect of coupling from the effects of the part in isolation, making it possible to use unit tests to tune many of the model parameters. An example of using this model to represent the coupled failures within a gearbox is outlined.