The Use of High-Performance Fatigue Mechanics and theExtended Kalman / Particle Filters, for Diagnostics andPrognostics of Aircraft Structures

In this paper, we propose an approach for diagnostics and prognostics of damaged aircraft structures, by combing high-performance fatigue mechanics with filtering theories. Fast & accurate deterministic analyses of fatigue crack prop- agations are carried out, by using the Finite Element Alternating Method (FEAM) for computing SIFs, and by using the newly developed Moving Least Squares (MLS) law for computing fatigue crack growth rates. Such algorithms for sim- ulating fatigue crack propagations are embedded in the computer program Safe- Flaw, which is called upon as a subroutine within the probabilistic framework of filter theories. Both the extended Kalman as well as particle filters are applied in this study, to obtain the statistically optimal and semi-optimal estimates of crack lengths, from a series of noisy measurements of crack-lengths over time. For the specific problem, a simple modification to the particle filter, which can drastically reduce the computational burden, is also proposed. Based on the results of such di- agnostic analyses, the prognostics of aerospace structures are thereafter achieved, to estimate the probabilistic distribution of the remaining useful life. By using a simple example of a single-crack near a fastener hole, we demonstrate the concept and effectiveness of the proposed framework. This paper thus forms the scientific foundation for the recently proposed concepts of VRAMS (Virtual Risk-Informed Agile Maneuver Sustainment) and Digital Twins of aerospace vehicles.