**4. PHM Framework Design**

Once the simulation environment, both in its high-fidelity and real-time declination, is defined, it is possible to use the data generated through repeated simulation cycles to inform the definition of the PHM system, study the expected behavior of the actuators under degraded health conditions, and assess which signals to use for health monitoring. This section details the approach followed in the definition of the PHM system, starting from the definition of the operational scenario.

#### *4.1. PHM Framework Design-Preliminary Operations*

The design of the PHM framework followed the procedures suggested by [1], where the high-fidelity model is first used to study the effects of the injected failure modes on the system performances, inform the feature selection process, and then lead to the choice of the fault diagnosis and failure prognosis routines.

The feature selection process was performed through the analysis of the simulation results, leading to the definition of a pool of possible feature candidates. Such feature candidates were then ranked according to metrics such as correlation with the failure mode behavior, signal-to-noise ratio, and precision. During this first stage of the design process, it was paramount to properly characterize the uncertainty surrounding the simulation results, including the effects that external disturbances, such as the external temperature, load, and command patterns, have on the system performance and on the possible feature candidates to obtain a statistically representative database of the possible operating conditions.

For the case study under analysis, this translates into the definition of a complete operative scenario, following the scheme provided in Figure 13. A sequence of position commands and aerodynamic load, representative of the expected operating cycle of the flight-control actuators under analysis, was provided by the industrial partners of the project. The operating cycle can be represented as a pair of (*t*, *xset*) and (*t*, *Fext*) time series where *t* is the time vector, *xset* is the position command, and *Fext* is the external force. Before each simulation, the sequence was warped and modified through the following equation

$$\begin{cases} \text{ } t = t \,\sigma\_t\\ \text{ } \chi\_{\text{set}} = \chi\_{\text{set}} \sigma\_x + \sigma\_{x0} \\ F\_{\text{ext}} = F\_{\text{set}} \sigma\_F + \sigma\_{F0} \end{cases} \tag{1}$$

where *σ<sup>t</sup>* is a random number drawn from a normal distribution with mean 1 and a standard deviation equal to 0.1. *σ<sup>x</sup>* and *σ<sup>F</sup>* are again drawn from a normal distribution with mean 1 and a standard deviation of 0.3, while *σx*<sup>0</sup> and *σF*<sup>0</sup> are chosen from a normal distribution with a 0 mean and standard deviation equal to 10% of the actuator stroke and of the nominal aerodynamic load, respectively.

**Figure 13.** Data generation process to support PHM design.

Ten possible aircraft were then selected by imposing small perturbations, compatible with the expected production tolerances, on the actuator parameters. Of these aircraft, 4 are supposed to operate in temperate climate conditions, 3 in cold conditions, and 3 in hot conditions. Three reference location were then chosen: Turin for temperate conditions, Abu Dhabi for hot conditions, and Vancouver for cold conditions, and historical temperature distribution for each were saved. For each simulated flight, the temperature varied between the ground value, randomly drawn from the reference location datasets, and −40 ◦C, which is the expected temperature during cruise for the considered aircraft type. A total of 100 flights for each aircraft were simulated under nominal health conditions. Degradations were then injected and their progression was simulated through accelerated fault-to-failure model. Results were then analyzed to search for the most significant effects of each failure mode and provide the basis for the feature selection process. Among a pool of more than 50 candidates, 1 preferential feature for failure mode was chosen according to correlation

and signal-to-noise ratio scores. A brief overview of the considered failure modes, along the signals required to compute the associated feature, is reported in Table 1. Between these failure modes, due to their interplay, 4 were analyzed in more detail: the occurrence of turn-to-turn short, magnet degradation efficiency loss, and wear-induced backlash in the mechanical transmission. This choice was justified by looking at the other failure modes. The occurrence of MOSFET Base Drive Open Circuit was expected to be a fastevolving failure mode, thus, was treated only for fault detection and isolation. Similarly, the occurrence of a static eccentricity within the motor was traced to misalignments or mounting errors persistent in time and not to slowly evolving degradation. The wear in the spherical joint was finally tracked through a feature that was not affected by the occurrence of the other failure modes. Figure 14 depicts the correlation of the chosen features for the 4, possibly interplaying, failure modes against the progression of each considered degradation. As anticipated in Section 3, the main symptom of the occurrence of a turn-to-turn short in the electric motor windings was the formation of a growing asymmetric behavior between the 3-phase currents. The feature *FTTS* exhibited high correlation marks as expected, while the other 3 selected features were less affected. A very loose correlation occurred with the feature *FMTEL* due to the reduction of the motor efficiency due to the ongoing short circuit.

**Table 1.** Selected features.


**Figure 14.** Feature correlation against several failure modes propagation.

The occurrence of a distributed magnet degradation is associated with good correlation indexes for the associated feature *FDMD* only. The occurrence of efficiency loss in the mechanical transmission can instead affect more features, showing the highest correlation value with *FMTEL*, while also exhibiting a high correlation with *FDMD* due to an increase in the absorbed current. This result is, of course, suboptimal but does not represent a critical issue: *FMTEL* shows good correlation only for the efficiency-loss case and is not significantly correlated with the occurrence of magnet degradation. The opening of an increasing backlash in the mechanical transmission is also highly correlated with its own associated feature (*FMTWEAR*). The feature *FDMD* is also affected due to the current spikes caused by the impacts which originate whenever the freeplay is recovered. Its correlation is, however, lower than that associated with *FMTWEAR*, while the correlation of *FMTWEAR* with the occurrence of magnet degradation is negligible. As such, the selected feature set is expected to be suitable for fault diagnosis and failure prognosis.
