5.2.2. Failure Prognosis

The failure prognosis behavior is studied through the algorithm response to the 175 simulated degradation patterns previously described and analyzed to check their convergence to the simulated ground truth and its expected performances in terms of nondimensional Prognostic Horizon and mean accuracy metrics [48]. Figure 23 depicts the prediction trajectories associated with the most probable RUL estimate for each prediction step of each degradation pattern, comparing their behavior against the simulated ground truth. It can be observed that all the considered failure modes converge toward the groundtruth solution, although with different patterns and different performances.

**Figure 23.** Elapsed time breakdown—average execution time of a particle-filtering step.

In particular, the RUL associated with a turn-to-turn short is often underestimated with respect to the ground truth. Although suboptimal, such a result is still positive, since it would cause, at worst, a slight anticipation of the maintenance action. On the other hand, the remaining investigated failure modes all fare well, quickly converging within an uncertainty cone equal to ±20% of the ground-truth RUL value.

The first prediction step, that is the one performed right after the fault detection, is affected by significant uncertainty and provides the less accurate results. Such behavior is expected, since the initial parameters of the degradation models employed within the particle-filtering routines are first-trial values for the first prediction step, with the tuning process requiring more data to converge to the ongoing degradation process. Results are also analyzed according to two traditional metrics, the Prognostic Horizon and the average accuracy [48], and reported in Table 2. The Prognostic Horizon is defined as the remaining useful life for which the most probable RUL estimate falls, and remains, within a certain accuracy threshold. Since the results pertain forcefully to accelerated degradation and not to a naturally evolving one, such a metric is provided as a nondimensional value over the simulated lifetime of the equipment for each considered failure mode. All the results are the average obtained for the considered degradation patterns.


**Table 2.** Expected performance metrics.

Overall, results are encouraging for long-lasting degradations, where high values of PH and good accuracy levels are observed. The low scores associated with the turn-to-turn failure mode denounce a lower level of accuracy associated with the prediction, but as already underlined, such a result is due to an underestimation of the RUL, which is less critical than an overestimation. Similarly, results for the efficiency loss are suboptimal in terms of the Prognostic Horizon. Such degradation is, however, a slowly evolving process requiring hundreds of flight hours; thus, the results still provide sufficient time to issue an early warning and plan the due maintenance accordingly.
